thewordsmiths/stem_mcqa · Datasets at Hugging Face

subject stringclasses 1 value	question stringlengths 3 1.14k	options listlengths 5 5	solution stringlengths 18 3.7k	answer stringclasses 5 values
mathematics	Martha has the unique talent of being able to guess other people’s height and weight. For every six people that Martha meets, she consistently guesses the people’s correct height five times, and for every eight people that she meets, she consistently guesses the people’s correct weight six times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?	[ "8/27", "2/5", "485/512", "98/125", "625/952" ]	Probability that she guesses the height correctly P(h)=5/6 Probability that she guesses the weight correctlyP(w)=6/8 Probability that she guesses both weight and height correctly(P(h)P(w))=5/6 6/8= 30/48 Now the Q asks about the probability of this happening atleast once. We calculate it by finding the probability of not being able to guess in any of the three occasions. Probability of not being able to guess any no. of times =1-30/48=18/48=3/8 For all three occasions P(A)=3/8 * 3/8 * 3/8=27/512 Probability of the event happening atleast once=1- P(A)=1-27/512=485/512 Ans should be C The answer is: C	C
mathematics	An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 21 as commission, the cloth sold through him on that day is worth	[ "333", "500", "840", "299", "132" ]	Explanation: Let the total sale be Rs. x. Then, 2.5%. of x = 21 <=> (25/10 * 1/100 * x) = 21 <=> x = 840. Answer: C The answer is: C	C
mathematics	Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Julie 's savings by the end of the year from these monthly savings were four times the amount she spent per month, what should be the fraction of her salary that she spent each month?	[ "5/3", "3/9", "3/2", "3/5", "3/4" ]	Let Julie 's monthly savings = S Julie 's monthly pay = P Julie 's monthly expenditure = P-S Julie 's savings by the end of the year from these monthly savings were Four times the amount she spent per month 12S = 4*(P-S) =>3S = P-S => P = 4S Julie's monthly expenditure = P-S = 4S-S = 3S fraction of her salary that Julie spent each month = 3S / 4S=P-S/P = 3/4. Answer is E The answer is: E	E
mathematics	Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?	[ "£ 300", "£ 330", "£ 360", "£ 420", "£ 460" ]	7week=300+holiday 1 week= (300+ holiday)/7 4 week =(300+ hliday)*4/7-- eqn1 bt 4 week = 30 + holiday(given)--eqn2 equate eqn 1 and eqn 2 to get th ecost of holiday=330 ANSWER:B The answer is: B	B
mathematics	A person buys an article at Rs.480. At what price should he sell the article so as to make a profit of 24%?	[ "595", "882", "772", "662", "521" ]	Cost price = Rs.480 profit = 24% of 480 = Rs.115 Selling price = Cost price + Profit = 480 + 115 = 595 Answer: A The answer is: A	A
mathematics	4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?	[ "4", "16", "8", "1", "2" ]	Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B The answer is: B	B
mathematics	In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together?	[ "6!/2!", "3!3!", "4!/2!", "4! (3!/2!)", "3!*3!/2" ]	In the word ABROAD , there are 3 vowels - 2 A's and O Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together = (4! * 3! )/2! We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! . The entire vowel group is considered as a single group . Answer D The answer is: D	D
mathematics	The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?	[ "43", "52", "12", "65", "13" ]	Explanation: x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 3*4 = 12 Answer: Option C The answer is: C	C
mathematics	Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?	[ "55/256", "255/256", "155/256", "5/256", "201/256" ]	Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads probability of flipping either a head or a tail = 1/2 probability of flipping 3 tails in a row (1/2)^5 probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256 Answer : B The answer is: B	B
mathematics	A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?	[ "13", "25", "17", "12", "11" ]	11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes The answer is: E	E
mathematics	The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?	[ "1500", "1600", "1750", "1900", "2000" ]	Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. The answer is: C	C
mathematics	A man can swim in still water at 4 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?	[ "1.3", "7.5", "2.25", "1.5", "4" ]	M = 4 S = x DS = 4 + x US = 4 - x 4 + x = (4 - x)2 4 + x = 8 -2x 3x = 4 x = 1.3 ANSWER:A The answer is: A	A
mathematics	Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen	[ "44/221", "55/221", "76/221", "45/221", "63/221" ]	WE HAVE N(S)=52C2=(5251)/(21)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(2625)/(21)=325, N(B)=4C2=(43)/(21)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B The answer is: B	B
mathematics	If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?	[ "-20", "0", "8", "12", "16" ]	s > r > q are consecutive even integers Testing for s2−r2−q2 I: For s = 0, r = -2, q = -4, s2−r2−q2=−20 II: For s = 2, r = 0, q = -2 s2−r2−q2=0 III: For s = 4, r = 2, q = 0 s2−r2−q2=12 Step II & Step III have consecutive representation of values of s, r, q. No other combination is possible. 8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12 Answer = C The answer is: C	C
mathematics	Bradley owns b video game cartridges. If Bradley’s total is one-fourth the total owned by James and six times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?	[ "(16/3)b", "(31/6)b", "(13/6)b", "(19/12)b", "(7/12)b" ]	b = Bradley’s total 4b = James’s total (1/6)b = Charlie’s total Add each total b + 4b+ (1/6)b = 5b + (1/6)b = = (31/6)b Answer : B The answer is: B	B
mathematics	A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?	[ "375", "400", "600", "800", "550" ]	C's 1 day's work =1/3-1/6 +1/7 =1/3 -7/24=1/24 . A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24= 4 : 3 : 1. C's share (for 3 days) = Rs. 3 x 1/24 x 3200 = Rs. 400. Option B The answer is: B	B
mathematics	A man sells a book at 5% profit. If he had bought it at 5% less and sold it for Re 1 less, he would have gained 10%. The cost price of the book is	[ "Rs 200", "Rs 150", "Rs 250", "Rs 240", "None of these" ]	Let the C.P of the article be Rs X Profit = 5% Therefore, S.P. = X + 5 % of X = 21X / 20 If C.P would have been (X - 5% of X), i.e., Rs 19 X / 20 and S.P would have been Rs [ (21 X / 20) - 1 ], Then, gain % = 10 % Therefore, [ { ( 21 X / 20) - 1 } - 19 X / 20 ] / (19 X /20 ) x 100 = 10 (2 X - 20 / 19 X) x 100 = 10 => X = 200 ANSWER:A The answer is: A	A
mathematics	Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.	[ "$204", "$231", "$156", "$165", "$200" ]	Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 165. So after completing the 1st week she will get $ (x+165). Similarly after completing the 2nd week she will get $ (x + 165) + $ 165. = $ (x + 165 + 165) = $ (x + 330) So in this way end of every week her salary will increase by $ 165. D The answer is: D	D
mathematics	The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?	[ "17", "16", "15", "14", "13" ]	I think brute force with some common sense should be used to solve this problem. Write down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64. Now, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd). We can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --> 3+5+6=14. Answer: D. The answer is: D	D
mathematics	A car traveled 75% of the way from town A to town B at an average speed of 90 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?	[ "15", "20", "25", "30", "37.5" ]	Total distance = 100 miles (easier to work with %) 75% of the distance = 75 miles 25% of the distance = 25 miles 1st part of the trip → 75/90 = 0.833 2nd part of the trip → 25/S = t Total trip → (75+25)/40 = 0.833+ t » 100/40 = 0.833 + t » 2.5 = 0.833+ t » t = 1.667 Back to 2nd part of the trip formula: 25/S = 1.667 » S = 15 Ans A The answer is: A	A
mathematics	The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?	[ "91.5", "91.4", "91.7", "91.3", "91.1" ]	Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A The answer is: A	A
mathematics	A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?	[ "3377", "2899", "2500", "2778", "1991" ]	A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 15000*1/6 = 2500 Answer: C The answer is: C	C
mathematics	If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer?	[ "3", "4", "5", "6", "7" ]	the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C The answer is: C	C
mathematics	In Orange County one tenth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?	[ "60.", "42.", "85.", "70.", "252." ]	The number must be an integer and multiple of both 10 and 7. Only option D fulfill this condition and hence is the answer. The answer is: D	D
mathematics	When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y? I. 15.19 II.18.16 III. 17.17	[ "I only", "II only", "III only", "I and II only", "I and III only" ]	Problem statement was difficult to parse. but some how I managed to understand what we can do. 1) x/y = 15 + 0.19 2) x/y = 18 + 0.16 3) x/y = 17 + 0.17 w.k.t x = yn (i.e Q) + yk=60 (i.e remainder) therefore : 1) y0.19=60 -- we can't get y an integer. 2) y0.16=60 -- we can get y an integer. 3) y*0.17=60 -- we can't get y an integer. Therefore 2 are possible answers. Ans B. The answer is: B	B
mathematics	Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?	[ "12", "14", "27", "53", "None of these" ]	Explanation: In this series, each number is repeated, then 13 is subtracted to arrive at the next number. Answer: Option B The answer is: B	B
mathematics	A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $45,000 in property taxes, but did not pay until October 15th?	[ "$1,400", "$1,800", "$2,400", "$21,400", "$12,150" ]	Original amount = 20,000 Fine for July = 20,000 * 1% = 450 Fine for August = lesser of the 2 , 450+600= 1050 or 4503=1350 . Pick 1350 Fine for September = 1350+600=1950 or 13503 = 4050. Pick 4050 Fine for October = 4050+600=4650 or 4050*3 = 12150. Pick 12150. The wording of the question should be have been clearer as total fines should be = 12150+4050+1350+450 = 18000 and NOT 12150. 12150 is the fine ONLY for the month of October! E The answer is: E	E
mathematics	10(150) ÷ 10(146) = ?	[ "10(6)", "100000", "1000", "10000", "None of these" ]	10(150) ÷ 10(146) = ? or ? = 10(150)/10(146)=10(150−146) i.e, [m(x)/m(y)=m(x−y)] = 10(4) = 10000 Answer D The answer is: D	D
mathematics	USC invited each South Carolina high school to send up to 39 students to watch a football game. A section which has 199 seats in each row is reserved for those students. What is the least number of rows needed to guarantee that if 2006 students show up, then all students from the same high school can be seated in the same row?	[ "11", "12", "13", "14", "15" ]	The answer is 12 rows. If 59 schools send 34 students each, then we can sit at most 5 groups of students in the same row, so we will need 12 rows. Next, 12 rows are sufficient. Assume that this is not the case. Suppose the groups of students are seated like this: first the largest group, then the second largest group, then the third largest group, etc. Suppose we run out of space - there are not enough seats in any row to seat together the next group. Suppose the first group that can not be seated together is the kth group and it consists of N students. Then k 61 since any row fits at least 5 groups. Also, N 2006/k 2006/61 < 33 (all groups already seated are no smaller than the kth group). So, N 32. Since there is not enough space in any of the 12 rows to seat the kth group, then there must be at least 168 students seated in each of the 12 rows. Now, 12 × 168 = 2016 > 2006 a contradiction. So, 12 rows are sufficient. correct answer B The answer is: B	B
mathematics	Find the circumference and area of radius 13 cm.	[ "124 cm²", "531 cm²", "354 cm²", "584 cm²", "594 cm²" ]	Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B The answer is: B	B
mathematics	Anna worked for h hours each day for d consecutive days. If she earns $3.50 per hour, what is the total amount she earned?	[ "3.50/d + h", "3.50 + d + h", "3.50 + dh", "3.50h + d", "3.50dh" ]	H hours for d days. Income each day = 3.5h Total income = 3.5h*d Correct option: E The answer is: E	E
mathematics	A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?	[ "67/90", "29/60", "17/30", "19/30", "11/15" ]	I think A - 67/90 is the correct answer. Here goes: Lets assume originally the number of beds = x After the new tower, the total combined no of beds = 7x So old = x, New = 6x Now 1/3 of x are occupied and 1/5 of 6x are occupied which simplifies to (6/5)x We are shifting 1/3 of x to the new ward so there will now be: 1/3 of x plus 6/5 of x occupied in the new ward. Add them up to get 23/15 of x There are 6x beds in New Tower so ratio is: (23/15)x / 6x = 23/90 of x Subtract that from 90/90 of x and you get the number of un-occupied beds to total capacity of New Tower = 67/90. A The answer is: A	A
mathematics	The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?	[ "28%", "25%", "24%", "23%", "27%" ]	explanation: 15 CP = 20 SP 20 --- 5 CP loss 100 --- ? => 25% loss Answer: B The answer is: B	B
mathematics	If r ≠ 1 and if sr/(s - r) = 1, what is the value of s in terms of r?	[ "(r+1)/r", "(r - 1)/r", "r/(r + 1)", "r/(1-r)", "(1 - r)/r" ]	This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: D The answer is: D	D
mathematics	if x/4-x-3/6=1,then find the value of x.	[ "2", "4", "6", "8", "5" ]	(x /4)-((x-3)/6)=1= (3x-2(x-3) )/12 = 1 = 3x-2x+6=12 = x=6 Answer is C. The answer is: C	C
mathematics	Which of the following fractions is greater than 3 /4 and less than 5 / 6 ?	[ "4/8", "4/5", "4/6", "4/1", "4/4" ]	Explanation: 3 /4 = 0.75, 5/6 = 0.833, 1/2 = .5, 2/3 = 0.66, 4/5 = 0.8, 9/10 = 0.9. clearly 0.8 lies between 0.75 and .833. 4/5 lies between 3/4 and 5/6.. Answer: B) 4 / 5 The answer is: B	B
mathematics	what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?	[ "1 or 7", "3 or 21", "4 or 28", "2 or 14", "5 or 14" ]	since the chord length=2sqrrt(r^2-d^2) chord length=32,r=20 then we get d=12 chord length=24,r=20 then we get d=16 then we add/subtract we get option c) 4 or 28 ANSWER:C The answer is: C	C
mathematics	The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?	[ "50min", "33min", "35min", "25min", "20min" ]	Clearly, the two will meet when they are 1000 m apart To be 20+13 = 33 km apart, they take 1 hour To be 1000 m apart, they take 33 * 1000/1000 = 33 min. Answer is B The answer is: B	B
mathematics	An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.	[ "6/13", "5/9", "1/24", "4/9", "2/5" ]	An empty wooden vessel weighs 14% of its total weight when filled with paint: Vessel = 0.14(Vessel + Paint); 14V = V + P (so the weight of completely filled vessel is 14V) P = 13V (so the weight of the paint when the vessels is completely filled is 13V). The weight of a partially filled vessel is one half that of a completely filled vessel: V + P' = 1/2*14V; P' = 6V (so the weight of the paint when the vessels is partially filled is 6V). What fraction of the vessel is filled? So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled: P'/P = 6V/13V = 6/13. Answer: A. The answer is: A	A
mathematics	The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 5 years ago ? (RBI Assistant 2015)	[ "24", "18", "12", "16", "13" ]	Let the present age of Viju be 7x years and that of Aju be 2x years. Then, 4 years from now 7x + 4 / 2x + 4 = 5 / 2 or 4x = 12 or x = 3 Viju present age = 7 * 3 = 21 years Viju age 5 years ago = 21 - 5 = 16 years answer :D The answer is: D	D
mathematics	The daily wage is increased by 50% and a person now gets Rs 25 per day. What was his daily wage before the increase ?	[ "Rs 20", "Rs 16.6", "Rs 18", "Rs 19", "none of these" ]	Let A be the daily wages before the increase, A ( 1 + x/100) = 25 (Given) Here, x = 50 Therefore, A( 1 + 50/100) = 25 A = (25 x 100) / (150) = Rs 16.6. ANSWER:B The answer is: B	B
mathematics	What is the remainder when the number R=14^2 * 15^8 is divided by 5?	[ "0", "1", "2", "4", "5" ]	14^2 has units digit 6 15^8 has units digit 5 Thus R=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero Answer: (A) The answer is: A	A
mathematics	A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?	[ "7 km/hr", "7.2 km/hr", "7.5 km/hr", "8 km/hr", "8.9 km/hr" ]	Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B The answer is: B	B
mathematics	A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?	[ "20 kmph", "24 kmph", "50 kmph", "35 kmph", "30 kmph" ]	Explanation: Distance from A and B be 'd' Average Speed = total distance/total time Average Speed = (2d)/[(d/20) + (d/30)] = (2d)/[5d/60) => 24 kmph. ANSWER IS B The answer is: B	B
mathematics	0.1+0.1^2+0.1^3 =	[ "0.1", "0.111", "0.1221", "0.2341", "0.3" ]	You have a mistake in your question. Choice B should be (.111) and not (.11). The equation in the solution can be simplified to (.1 + .01 + .001). Adding those together you get: .100 .010 .001 ------ .111 - Which is answer choice (B) The answer is: B	B
mathematics	A bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water?	[ "2/5", "3/5", "1/5", "1/7", "2/7" ]	Suppose the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water. Quantity of water in new mixture = 3 - 3x + x litres 8 Quantity of syrup in new mixture = 5 - 5x litres 8 3 - 3x + x = 5 - 5x 8 8 5x + 24 = 40 - 5x 10x = 16 x = 8 . 5 So, part of the mixture replaced = 8 x 1 = 1/5 5 8 5 C The answer is: C	C
mathematics	A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?	[ "230 m", "210 m", "260 m", "320 m", "330 m" ]	Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B The answer is: B	B
mathematics	There are 8 stations between Vijayawada and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?	[ "100", "90", "190", "110", "105" ]	The total number of stations = 10 From 10 stations we have to choose any two stations and the direction of travel (i.e.,Vijayawada to Chennai is different from Chennai to Vijayawada) in 10P2 ways. 10P2= 10 * 9 = 90 ANSWER: B The answer is: B	B
mathematics	The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?	[ "26", "17", "25", "33", "50" ]	Four consecutive odd numbers: k-2, k, k+2, k+4 Three consecutive even numbers: n-2, n, n+2 k-2+k+k+2+k+4=n-2+n+n+2 4k+4=3n 4(k+1)=3n k+1=(3/4)n k=(3/4)n-1 All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range: We know, 101<n<208 104<=n<=204 Count=(204-104)/4+1=100/4+1=25+1=26 Ans: 26. The answer is: A	A
mathematics	A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?	[ "12", "9", "8", "6", "5" ]	A's 1 hour's work = 1 ; 4 (B + C)'s 1 hour's work = 1 ; 3 (A + C)'s 1 hour's work = 1 . 2 (A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 . 4 3 12 B's 1 hour's work = ( 7 - 1 ) = 1 . 12 2 12 Therefore A alone will take 12 hours to do the work. The answer is: A	A
mathematics	A tree on first day grows 1/2 of its size second day 1/3 of its size on the previous day similarly than 1/4 and so on..U have calculate after how many days the tree will be 100 times of original size.	[ "188 days", "198 days", "178 days", "168 days", "158 days" ]	suppose 'x' is initial size and 'n' is no. of days. 1st day increment in size of tree = (1/2)x After 1st day , size of tree = x+(1/2)x= (3/2)x 2nd day increment in size of tree = (1/3)(3/2)x=(1/2)x After 2nd day , size of tree = (3/2)x+(1/2)x=2x 3rd day increment in size of tree =(1/4)2x=(1/2)x After 3rd day , size of tree = 2x+(1/2)=(5/2)x It is clear that every day tree grows (1/2)x in size. therefore , according to given condition x+ (1/2)x*n=100x n=198 days. ANSWER:B The answer is: B	B
mathematics	Three numbers are in the ratio 1:4:6 and their H.C.F is 9. The numbers are:	[ "1,4,6", "12,24,36", "10, 20, 30", "12, 24, 36", "9,36,54." ]	Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 9. The numbers are 9,36,54. ANSWER:E The answer is: E	E
mathematics	John and Jacob set out together on bicycle traveling at 18 and 15 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 18 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)	[ "3", "3 1/3", "3 1/2", "4", "4 1/3" ]	John's speed - 18 miles/hr Jacob's speed - 15 miles/hr After 40min (i.e 2/3hr), distance covered by John = 18x2/3 = 12 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 15x5/3 = 25 miles. Now, when John starts riding back, the distance between them is 13 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 18-15 = 3 miles/hr. Thus, to cover 13 miles at 3 miles/hr, John will take 13/3 = 4 1/3 hours Answer E The answer is: E	E
mathematics	The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 69, what is the least possible value of one of the other two integers?	[ "5", "8", "20", "21", "30" ]	When it comes to averages, we know thataverage value = (sum of n values)/n We can rewrite this into a useful formula:sum of n values = (average value)(n) The average of five integers is 63 So, the sum of ALL 5 integers = (63)(5) =315 The average of three of the integers is 65 So, the sum of the 3 integers = (69)(3) =207 So, the sum of the 2 REMAINING integers =315-207=108 If the sum of the 2 REMAINING integers =108, and we want to minimize one value, we must MAXIMIZE the other value. 100 is the maximum value so let 1 integer = 100, which means the other must equal 8 Answer: B The answer is: B	B
mathematics	One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in	[ "144 mins", "140 mins", "136 mins", "132 minw", "None of these" ]	Explanation: Let the slower pipe alone fill the tank in x minutes then faster will fill in x/3 minutes. Part filled by slower pipe in 1 minute = 1/x Part filled by faster pipe in 1 minute = 3/x Part filled by both in 1 minute = 1/x+3/x=1/35 =>4/x=1/35 x=35∗4=140 mins Option B The answer is: B	B
mathematics	What will come in place of the x in the following Number series? 5,28,57,88,125	[ "123", "143", "166", "190", "210" ]	28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C The answer is: C	C
mathematics	A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 49 hrs and a machine of type S does the same job in 14 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?	[ "49/9", "44/9", "46/9", "41/9", "43/9" ]	Rate of machine R =1/49 Rate of machine S =1/14 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/49 +x/14 =1/2 9x=49 x=49/9 So no of machine R is 49/9 Answer A The answer is: A	A
mathematics	Three liquids were mixed in 5:4:1 ratios. If cost per kg for ach of them is 4.50, 3.75& 5.10. Then in what price mixture should be sold to get 25% profit?	[ "52.25", "53.25", "54.25", "55.25", "56.25" ]	cp of the liquid=54.50+43.75+15.10=42.6 In order to gain 25%profit Sp=1.2542.6=53.25 ANSWER:B The answer is: B	B
mathematics	A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?	[ "9", "15", "18", "None of these", "Cannot be determined" ]	Explanation: Let the number be x. Therefore, 3(2x + 5) = 105 6x + 15 = 105 6x = 90 x = 15 ANSWER: B The answer is: B	B
mathematics	Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2376?	[ "2277", "2400", "2200", "2766", "2998" ]	Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2376. => (90%) of (110%) of x = Rs. 2376. => (90/100)(110/100)x = 2376 => x = (2376 * 100)/(9 * 11) => x = Rs. 2400 Answer: B The answer is: B	B
mathematics	At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?	[ "6", "5", "4", "78", "2" ]	150 = (7505R)/100 R = 4%.Answer: C The answer is: C	C
mathematics	If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?	[ "15", "60", "180", "90", "105" ]	This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one. Teena covers 55 miles in 60 mins. Joe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +37.5 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 37.5 miles in 150 mins So answer 30+150= 180 mins. (ANSWER C) The answer is: C	C
mathematics	If f is a function defined for all k by f(k) = k^(2/3)/16, what is f(64 k) in terms of f(k)?	[ "1/8 f(k)", "5/8 f(k)", "2 f(k)", "16 f(k)", "32 f(k)" ]	f(k) = k^(2/3)/16 f(64 k) = (64k)^(2/3)/16 = 16 * k^(2/3)/16 = 16 * (k^(2/3)/16) = 16 f(k). So answer is D. The answer is: D	D
mathematics	The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?	[ "388", "167", "195", "288", "261" ]	Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2 ==> 2(180 + X) = 750 ==> X = 195 m. Answer: C The answer is: C	C
mathematics	A man buys a cycle for Rs. 1200 and sells it at a loss of 15%. What is the selling price of the cycle?	[ "s. 1020", "s. 1160", "s. 1190", "s. 1202", "s. 1256" ]	S.P. = 85% of Rs. 1200 = Rs.85/100x 1200 = Rs. 1020 ANSWER :A The answer is: A	A
mathematics	The average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man. What is the weight of the new man?	[ "80 kg", "93 kg", "70 kg", "75 kg", "85 kg" ]	Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 68+10x2.5 68+25=93 Kg Ans: 'B' The answer is: B	B
mathematics	A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?	[ "40", "99", "88", "66", "21" ]	Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec.Answer: A The answer is: A	A
mathematics	The average (arithmetic mean) of y numbers is x. If 25 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?	[ "x/6 - 6", "x/6 - 5", "x/7 - 5", "x/5 - 7", "x/5 - 6" ]	(A1 + A2 + .. + Ay)/y = x (A1 + A2 + .. + Ay + 25)/(y+1) = x - 5 => (xy + 25)/(y+1) = x - 5 => xy + 25 = yx -5y + x - 5 => 30 = x - 5y => 5y = x - 30 => y = x/5 - 6 E The answer is: E	E
mathematics	Find the remainder when 2^31 is divided by 5.	[ "3", "7", "1", "9", "None of them" ]	2^10 = 1024. Unit digit of 2^10 x 2^10 x 2^10 is 4 [as 4 x 4 x 4 gives unit digit 4]. Unit digit of 231 is 8. Now, 8 when divided by 5, gives 3 as remainder. Hence, 231 when divided by 5, gives 3 as remainder. Answer is A. The answer is: A	A
mathematics	Given that a “16-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 16-inch pizza gives you approximately what percent increase in the total amount of pizza?	[ "33", "50", "67", "180", "300" ]	area of 8 inch pizza= 44pi=16 pi area of 16 inch pizza =88pi=64 pi 48/16*100=300% increase hence answer is E The answer is: E	E
mathematics	Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 64 hours respectively. The ratio of their speeds is?	[ "4:5", "8:3", "8:4", "4:8", "4:1" ]	Let us name the trains A and B. Then, (A's speed) : (B's speed) = √b : √a = √64 : √9 = 8:3 Answer: B The answer is: B	B
mathematics	If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?	[ "7 meters", "9 meters", "8 meters", "5 meters", "3 meters" ]	400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 168,000 m : C is the circumference C = 3 meters correct answer A The answer is: A	A
mathematics	Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent E of all the possible subcommittees that include Michael also include Anthony?	[ "20%", "30%", "40%", "50%", "60%" ]	The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability E= 1/5+4/5*1/4 = 2/5.C The answer is: C	C
mathematics	If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?	[ "27 grams", "30 grams", "29 grams", "31 grams", "35 grams" ]	Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 30 grams 28/7 = 4.285... C. 29 grams 29/7 = 4.142....... D. 31 grams 31/7 = 4.428..... E. 35 grams 35/7 = 5 Hence our answer will be (E) The answer is: E	E
mathematics	Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament. How many matches were played?	[ "99 matches.", "88 matches.", "77 matches.", "66 matches.", "119 matches." ]	Solution: 119 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played. Answer E The answer is: E	E
mathematics	A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?	[ "5litres, 7 litres", "7litres, 4 litres", "6litres, 6 litres", "4litres, 8 litres", "8litres, 10 litres" ]	Explanation: Solution 1 Let x and (12âˆ’x) litres of milk be mixed from the first and second container respectively. Amount of milk in x litres of the the first container =.75x Amount of water in x litres of the the first container =.25x Amount of milk in (12âˆ’xlitres of the the second container =5(12âˆ’x) Amount of water in (12âˆ’x)litres of the the second container =.5(12âˆ’x) Ratio of water to milk Since x=6,12âˆ’x=12âˆ’6=6 Hence 6 and 6 litres of milk should mixed from the first and second container respectively. Answer IS C The answer is: C	C
mathematics	7^6n -1^ 6n When n is an integer > 0 is divisible by	[ "119", "127", "134", "145", "154" ]	127 B The answer is: B	B
mathematics	If 1/(m – 2) = 1/(m + 2) + 1/(m – 1), which of the following is a possible value of m?	[ "0", "-1", "-2", "1", "2" ]	Multiply by (m-2)(m+2)(m-1) throughout to get: (m+2)(m-1) = (m-2)(m-1) + (m+2)(m-2) Of the given options, only m=0 satisfies this. Answer : A The answer is: A	A
mathematics	The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?	[ "65", "48", "37", "23", "12" ]	Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 276 - (A + D) = 276 - 132 = 144. B + B -28 = 144 B = (144 + 28)/2 = 86 Answer:B The answer is: B	B
mathematics	A train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?	[ "5 sec", "9 sec", "12 sec", "15 sec", "18 sec" ]	Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 300 m at 50/3 m / sec = 300 *3/ 50 sec = 18sec Answer : E The answer is: E	E
mathematics	In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?	[ "3990", "1540", "1995", "3672", "2314" ]	We must place all these books as under: XEXEX….XEX There are 21 books on English, 19 books on Hindi 19 places out of 22 can be chosen 22C19=22C3=1540 ways ANSWER B 1540 The answer is: B	B
mathematics	Which of the following CANNOT be a product of two distinct positive integers p and q?	[ "p", "q", "3q + 2p", "q - p", "qp" ]	In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take p = 1 and q = 2 and work with the options pq = 2 A) p take p =2, q = 1 B) q take p = 1 q = 2 C) 3q + 2p Seems tricky, lets see other options and then come back to it. D) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E)qp Always true You don't even have to worry what C is ! ans D The answer is: D	D
mathematics	If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B\|A)?	[ "2/3", "3/5", "2/7", "3/7", "4/9" ]	P(B\|A) = P(A ∪ B)/P(A) P(B\|A) = (4/17)/(6/17) = 4/6 = 2/3. A The answer is: A	A
mathematics	If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?	[ "2 days", "3 days", "4 days", "5 days", "6 days" ]	That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. B) The answer is: B	B
mathematics	The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 45 kmph, find the speed of the stream?	[ "12 kmph", "13 kmph", "14 kmph", "15 kmph", "16 kmph" ]	The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 45/3 = 15 kmph ANSWER:D The answer is: D	D
mathematics	If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be	[ "6x", "Q=4x", "Q=5x/3", "Q=3x/2", "3x/5" ]	OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B) But what about C,D,E? Any ideas why these could be wrong? Note that we have 5 positive temperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits. Answer: B. The answer is: B	B
mathematics	In a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument?	[ "2/125", "3/125", "C)2/25", "3/25", "1/25" ]	P(playing 2 or more instruments) = 128/800 = 4/25. Then, the probability of playing exactly one instrument is given by: P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 4/25 = 1/25. Answer E. The answer is: E	E
mathematics	In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 65% average total marks, it is necessary for him in third yearly examination to secure marks :	[ "300", "350", "400", "475", "500" ]	total marks:1500 for three exams 65% of 1500=975 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =975 X=475 ANSWER:D The answer is: D	D
mathematics	275, 132, 462, 396, 327, 891, 121	[ "327", "228", "2768", "028", "272" ]	Explanation: In each number except 327, the middle digit is the sum of the other two. ANSWER: A The answer is: A	A
mathematics	Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 60 white marbles. How many red marbles could be in bag A?	[ "1", "3", "4", "12", "8" ]	6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 60 = 6K+4k => k =6 Total Red's in bag A will be 2K = 12 D The answer is: D	D
mathematics	Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?	[ "20", "34", "38", "40", "46" ]	We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D The answer is: D	D
mathematics	An company has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?	[ "10", "12", "15", "24", "30" ]	An company has 6 employees;for male 1C1 = 1 ........ A foe female = 5C2 = 10.........B total = 10*1 = 10 - answer=A The answer is: A	A
mathematics	What is the units digit of 2222^(333)*3333^(222)?	[ "0", "2", "4", "6", "8" ]	(2222^333)(3333^222)=2222^111(2222^2223333^222) here please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 (2222^2223333^222). since 6 powered in any number more than 0 results in 6 as a units digit, as a result we have- 62222^111 2 has a cycle of 4 . 111=274+3 . 2^3=8 6*8=48 so the units digit is 8, and the answer is E The answer is: E	E
mathematics	X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.	[ "2", "4", "5", "6", "7" ]	Sol: The divisibility rule for 9 is sum of the digits is to be divisible by 9. So We calculate separately, sum of the digits in hundreds place, tenths place, and units place. Sum of the digits in hundreds place: 1 x 50 = 50 Sum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105 Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225 So total = 380 So remainder = 380 / 9 = 2 Answer:A The answer is: A	A
mathematics	A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface.	[ "69 m sqaure", "49 m sqaure", "52 m sqaure", "64 m sqaure", "None of these" ]	Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(51.40+71.40)]+7*5 = 69 m square Option A The answer is: A	A
mathematics	[( 3.241 x 14 ) / 100] = ?	[ "0.045374", "4.5388", "453.88", "473.88", "None of these" ]	Answer Multiplying 3.241 x 14=4.5374 Now divide 4.5374 by 100 So, 4.5374 ÷ 100= 0.045374 ∴ Shift the decimal two places to the left as 100 Correct Option: A The answer is: A	A
mathematics	Two taps A and B can fill a tank in 5 hours and 20hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?	[ "24 hr", "36 hr", "18 hr", "42 hr", "30 hr" ]	Part filled by A+B in 1 hour = 1/5 + 1/20 = 1/4 A and B together can fill the tank in 4 hour Work done by the leak in 1 hour = 1/4 - 2/9 = 1/36 leak will empty the tank in 36 hours. Answer is B The answer is: B	B
mathematics	The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?	[ "270", "280", "290", "300", "310" ]	Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. A) The answer is: A	A
mathematics	If 5x^2 has two different prime factors, at most how many different prime factors does x have?	[ "1", "2", "3", "4", "5" ]	x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors. Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors). Answer: B. The answer is: B	B
mathematics	What is the perimeter of a square with area 9p^2/25 ?	[ "3p/4", "3p^2/4", "12p/5", "3p^2", "4p/3" ]	Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4side = 4 (3p/5) = 12p/5 Answer is C. The answer is: C	C

mathematics

Martha has the unique talent of being able to guess other people’s height and weight. For every six people that Martha meets, she consistently guesses the people’s correct height five times, and for every eight people that she meets, she consistently guesses the people’s correct weight six times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?

[ "8/27", "2/5", "485/512", "98/125", "625/952" ]

Probability that she guesses the height correctly P(h)=5/6 Probability that she guesses the weight correctlyP(w)=6/8 Probability that she guesses both weight and height correctly(P(h)*P(w))=5/6 * 6/8= 30/48 Now the Q asks about the probability of this happening atleast once. We calculate it by finding the probability of not being able to guess in any of the three occasions. Probability of not being able to guess any no. of times =1-30/48=18/48=3/8 For all three occasions P(A)=3/8 * 3/8 * 3/8=27/512 Probability of the event happening atleast once=1- P(A)=1-27/512=485/512 Ans should be C The answer is: C

C

mathematics

An agent, gets a commission of 2.5% on the sales of cloth. If on a certain day, he gets Rs. 21 as commission, the cloth sold through him on that day is worth

[ "333", "500", "840", "299", "132" ]

Explanation: Let the total sale be Rs. x. Then, 2.5%. of x = 21 <=> (25/10 * 1/100 * x) = 21 <=> x = 840. Answer: C The answer is: C

C

mathematics

Julie decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Julie 's savings by the end of the year from these monthly savings were four times the amount she spent per month, what should be the fraction of her salary that she spent each month?

[ "5/3", "3/9", "3/2", "3/5", "3/4" ]

Let Julie 's monthly savings = S Julie 's monthly pay = P Julie 's monthly expenditure = P-S Julie 's savings by the end of the year from these monthly savings were Four times the amount she spent per month 12S = 4*(P-S) =>3S = P-S => P = 4S Julie's monthly expenditure = P-S = 4S-S = 3S fraction of her salary that Julie spent each month = 3S / 4S=P-S/P = 3/4. Answer is E The answer is: E

E

mathematics

Mr. Johnson was to earn £ 300 and a free holiday for seven weeks' work. He worked for only 4 weeks and earned £ 30 and a free holiday. What was the value of the holiday?

[ "£ 300", "£ 330", "£ 360", "£ 420", "£ 460" ]

7week=300+holiday 1 week= (300+ holiday)/7 4 week =(300+ hliday)*4/7-- eqn1 bt 4 week = 30 + holiday(given)--eqn2 equate eqn 1 and eqn 2 to get th ecost of holiday=330 ANSWER:B The answer is: B

B

mathematics

A person buys an article at Rs.480. At what price should he sell the article so as to make a profit of 24%?

[ "595", "882", "772", "662", "521" ]

Cost price = Rs.480 profit = 24% of 480 = Rs.115 Selling price = Cost price + Profit = 480 + 115 = 595 Answer: A The answer is: A

A

mathematics

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

[ "4", "16", "8", "1", "2" ]

Explanation: Let the required number of mats be x More mat-weavers, more mats (direct proportion) More days, more mats (direct proportion) Hence we can write as (mat-weavers) 4:8 (days) 4:8}::4:x ⇒4×4×x=8×8×4 ⇒x=2×2×4=16 Answer: Option B The answer is: B

B

mathematics

In how many ways can the letters of the word ABROAD be rearranged such that the vowels always appear together?

[ "6!/2!", "3!*3!", "4!/2!", "4! *(3!/2!)", "3!*3!/2" ]

In the word ABROAD , there are 3 vowels - 2 A's and O Number of ways the letters of word ABACUS be rearranged such that the vowels always appear together = (4! * 3! )/2! We can consider the the 3 vowels as a single unit and there are 3 ways to arrange them . But since 2 elements of vowel group are identical we divide by 2! . The entire vowel group is considered as a single group . Answer D The answer is: D

D

mathematics

The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?

[ "43", "52", "12", "65", "13" ]

Explanation: x, 2x (x-2):(2x-2) = 1:3 3x-6 = 2x-2 x = 4 x+2x = 3x => 3*4 = 12 Answer: Option C The answer is: C

C

mathematics

Suppose you flip a fair coin 8 times. What is the probability that, in 8 flips, you get at least one head?

[ "55/256", "255/256", "155/256", "5/256", "201/256" ]

Best way of solving an at least 1 type of question is to compute 1 - probability of flipping 0 heads probability of flipping either a head or a tail = 1/2 probability of flipping 3 tails in a row (1/2)^5 probability of flipping at least 1 head = 1 - (1/2)^8 = 255/256 Answer : B The answer is: B

B

mathematics

A merchant can place 8 large boxes or 10 small boxes into a carton for shipping. In one shipment, he sent a total of 96 boxes. If there are more large boxes than small boxes, how many cartons did he ship?

[ "13", "25", "17", "12", "11" ]

11 cartons total 7 large boxes (7 * 8 = 56 boxes) 4 small boxes (4 *10 = 40 boxes 11 total cartons and 96 boxes The answer is: E

E

mathematics

The total price of a basic computer and printer are $2,500. If the same printer had been purchased with an enhanced computer whose price was $500 more than the price of the basic computer, then the price of the printer would have been 1/4 of that total. What was the price of the basic computer?

[ "1500", "1600", "1750", "1900", "2000" ]

Let the price of basic computer be C and the price of the printer be P: C+P=$2,500. The price of the enhanced computer will be C+500 and total price for that computer and the printer will be 2,500+500=$3,000. Now, we are told that the price of the printer is 1/4 of that new total price: P=1/4*$3,000=$750. Plug this value in the first equation: C+750=$2,500 --> C=$1,750 Answer: C. The answer is: C

C

mathematics

A man can swim in still water at 4 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

[ "1.3", "7.5", "2.25", "1.5", "4" ]

M = 4 S = x DS = 4 + x US = 4 - x 4 + x = (4 - x)2 4 + x = 8 -2x 3x = 4 x = 1.3 ANSWER:A The answer is: A

A

mathematics

Two cards are drawn at random from a pack of 52 cards.what is the probability that either both are black or both are queen

[ "44/221", "55/221", "76/221", "45/221", "63/221" ]

WE HAVE N(S)=52C2=(52*51)/(2*1)=1326. LET A=EVENT OF GETTING BOTH BLACK CARDS B=EVENT OF GETTING BOTH QUEENS AB=EVENT OF GETTING QUEEN OF BLACK CARDS N(A)=26C2=(26*25)/(2*1)=325, N(B)=4C2=(4*3)/(2*1)=6 AND N(AB)=2C2=1 P(A)=N(A)/N(S)=325/1326; P(B)=N(B)/N(S)=6/1326 AND P(AB)=N(AB)/N(S)=1/1326 P(AB)=P(A)+P(B)-P(AB)=(325+6-1/1326)=330/1326=55/221 Option: B The answer is: B

B

mathematics

If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of s^2 – r^2 – q^2?

[ "-20", "0", "8", "12", "16" ]

s > r > q are consecutive even integers Testing for s2−r2−q2 I: For s = 0, r = -2, q = -4, s2−r2−q2=−20 II: For s = 2, r = 0, q = -2 s2−r2−q2=0 III: For s = 4, r = 2, q = 0 s2−r2−q2=12 Step II & Step III have consecutive representation of values of s, r, q. No other combination is possible. 8 cannot be the answer as for value of s = 6 & above, the resultant would be greater than 12 Answer = C The answer is: C

C

mathematics

Bradley owns b video game cartridges. If Bradley’s total is one-fourth the total owned by James and six times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?

[ "(16/3)b", "(31/6)b", "(13/6)b", "(19/12)b", "(7/12)b" ]

b = Bradley’s total 4b = James’s total (1/6)b = Charlie’s total Add each total b + 4b+ (1/6)b = 5b + (1/6)b = = (31/6)b Answer : B The answer is: B

B

mathematics

A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?

[ "375", "400", "600", "800", "550" ]

C's 1 day's work =1/3-1/6 +1/7 =1/3 -7/24=1/24 . A's wages : B's wages : C's wages = 1/6 : 1/8 : 1/24= 4 : 3 : 1. C's share (for 3 days) = Rs. 3 x 1/24 x 3200 = Rs. 400. Option B The answer is: B

B

mathematics

A man sells a book at 5% profit. If he had bought it at 5% less and sold it for Re 1 less, he would have gained 10%. The cost price of the book is

[ "Rs 200", "Rs 150", "Rs 250", "Rs 240", "None of these" ]

Let the C.P of the article be Rs X Profit = 5% Therefore, S.P. = X + 5 % of X = 21X / 20 If C.P would have been (X - 5% of X), i.e., Rs 19 X / 20 and S.P would have been Rs [ (21 X / 20) - 1 ], Then, gain % = 10 % Therefore, [ { ( 21 X / 20) - 1 } - 19 X / 20 ] / (19 X /20 ) x 100 = 10 (2 X - 20 / 19 X) x 100 = 10 => X = 200 ANSWER:A The answer is: A

A

mathematics

Mrs. Rodger got a weekly raise of $165. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

[ "$204", "$231", "$156", "$165", "$200" ]

Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 165. So after completing the 1st week she will get $ (x+165). Similarly after completing the 2nd week she will get $ (x + 165) + $ 165. = $ (x + 165 + 165) = $ (x + 330) So in this way end of every week her salary will increase by $ 165. D The answer is: D

D

mathematics

The number 70 can be written as the sum of the squares of 3 different positive integers. What is the sum of these 3 integers?

[ "17", "16", "15", "14", "13" ]

I think brute force with some common sense should be used to solve this problem. Write down all perfect squares less than 70: 1, 4, 9, 16, 25, 36, 49, 64. Now, 70 should be the sum of 3 of those 8 numbers. Also to simplify a little bit trial and error, we can notice that as 70 is an odd numbers then either all three numbers must be odd (odd+odd+odd=odd) OR two must be even and one odd (even+even+odd=odd). We can find that 60 equals to 9+25+36=3^2+5^2+6^2=70 --> 3+5+6=14. Answer: D. The answer is: D

D

mathematics

A car traveled 75% of the way from town A to town B at an average speed of 90 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?

[ "15", "20", "25", "30", "37.5" ]

Total distance = 100 miles (easier to work with %) 75% of the distance = 75 miles 25% of the distance = 25 miles 1st part of the trip → 75/90 = 0.833 2nd part of the trip → 25/S = t Total trip → (75+25)/40 = 0.833+ t » 100/40 = 0.833 + t » 2.5 = 0.833+ t » t = 1.667 Back to 2nd part of the trip formula: 25/S = 1.667 » S = 15 Ans A The answer is: A

A

mathematics

The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?

[ "91.5", "91.4", "91.7", "91.3", "91.1" ]

Perimeter of the sector = length of the arc + 2(radius) = (135/360 * 2 * 22/7 * 21) + 2(21) = 49.5 + 42 = 91.5 cm Answer:A The answer is: A

A

mathematics

A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?

[ "3377", "2899", "2500", "2778", "1991" ]

A:B:C = 2/3:1/6:1/6 = 4:1:1 x * 2/100 * 2/3 = 200 B capital = 15000*1/6 = 2500 Answer: C The answer is: C

C

mathematics

If we know that a positive integer is a multiple of 4, how many (distinct) possibilities are there for the last digit of the integer?

[ "3", "4", "5", "6", "7" ]

the last digit of the integer may be any of (0,2,4,6,8) so, 1/5 ANSWER:C The answer is: C

C

mathematics

In Orange County one tenth of the people are gathering mushrooms and one seventh of the people are collecting apples. What can be the number of people in Orange County?

[ "60.", "42.", "85.", "70.", "252." ]

The number must be an integer and multiple of both 10 and 7. Only option D fulfill this condition and hence is the answer. The answer is: D

D

mathematics

When the integer x is divided by the integer y, the remainder is 60. Which of the following is a possible value of the quotient x/y? I. 15.19 II.18.16 III. 17.17

[ "I only", "II only", "III only", "I and II only", "I and III only" ]

Problem statement was difficult to parse. but some how I managed to understand what we can do. 1) x/y = 15 + 0.19 2) x/y = 18 + 0.16 3) x/y = 17 + 0.17 w.k.t x = yn (i.e Q) + yk=60 (i.e remainder) therefore : 1) y*0.19=60 -- we can't get y an integer. 2) y*0.16=60 -- we can get y an integer. 3) y*0.17=60 -- we can't get y an integer. Therefore 2 are possible answers. Ans B. The answer is: B

B

mathematics

Look at this series: 53, 53, 40, 40, 27, 27, ... What number should come next?

[ "12", "14", "27", "53", "None of these" ]

Explanation: In this series, each number is repeated, then 13 is subtracted to arrive at the next number. Answer: Option B The answer is: B

B

mathematics

A town in California fines residents who do not pay their property taxes on time. All residents must pay their taxes before July 1st for that calendar year or face the following fine structure: For the first month the taxes are overdue (that would be any payment made on July 1st through July 31st), the total fine is 1% of the original tax bill; for each additional month that the taxes are overdue, the total fine is increased by $600 or tripled, whichever results in the lesser amount. What is the total fine for a resident of that town who originally owed $45,000 in property taxes, but did not pay until October 15th?

[ "$1,400", "$1,800", "$2,400", "$21,400", "$12,150" ]

Original amount = 20,000 Fine for July = 20,000 * 1% = 450 Fine for August = lesser of the 2 , 450+600= 1050 or 450*3=1350 . Pick 1350 Fine for September = 1350+600=1950 or 1350*3 = 4050. Pick 4050 Fine for October = 4050+600=4650 or 4050*3 = 12150. Pick 12150. The wording of the question should be have been clearer as total fines should be = 12150+4050+1350+450 = 18000 and NOT 12150. 12150 is the fine ONLY for the month of October! E The answer is: E

E

mathematics

10(150) ÷ 10(146) = ?

[ "10(6)", "100000", "1000", "10000", "None of these" ]

10(150) ÷ 10(146) = ? or ? = 10(150)/10(146)=10(150−146) i.e, [m(x)/m(y)=m(x−y)] = 10(4) = 10000 Answer D The answer is: D

D

mathematics

USC invited each South Carolina high school to send up to 39 students to watch a football game. A section which has 199 seats in each row is reserved for those students. What is the least number of rows needed to guarantee that if 2006 students show up, then all students from the same high school can be seated in the same row?

[ "11", "12", "13", "14", "15" ]

The answer is 12 rows. If 59 schools send 34 students each, then we can sit at most 5 groups of students in the same row, so we will need 12 rows. Next, 12 rows are sufficient. Assume that this is not the case. Suppose the groups of students are seated like this: first the largest group, then the second largest group, then the third largest group, etc. Suppose we run out of space - there are not enough seats in any row to seat together the next group. Suppose the first group that can not be seated together is the kth group and it consists of N students. Then k 61 since any row fits at least 5 groups. Also, N 2006/k 2006/61 < 33 (all groups already seated are no smaller than the kth group). So, N 32. Since there is not enough space in any of the 12 rows to seat the kth group, then there must be at least 168 students seated in each of the 12 rows. Now, 12 × 168 = 2016 > 2006 a contradiction. So, 12 rows are sufficient. correct answer B The answer is: B

B

mathematics

Find the circumference and area of radius 13 cm.

[ "124 cm²", "531 cm²", "354 cm²", "584 cm²", "594 cm²" ]

Area of circle = πr² = 22/7 × 13 × 13 cm² = 531 cm² ANSWER:B The answer is: B

B

mathematics

Anna worked for h hours each day for d consecutive days. If she earns $3.50 per hour, what is the total amount she earned?

[ "3.50/d + h", "3.50 + d + h", "3.50 + dh", "3.50h + d", "3.50dh" ]

H hours for d days. Income each day = 3.5*h Total income = 3.5*h*d Correct option: E The answer is: E

E

mathematics

A new tower has just been built at the Verbico military hospital; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built. Currently, 1/3 of the hospital's original beds, as well as 1/5 of the beds in the new tower, are occupied. For the purposes of renovating the hospital's original wing, all of the patients in the hospital's original beds must be transferred to beds in the new tower. If patients are neither admitted nor discharged during the transfer, what fraction of the beds in the new tower will be unoccupied once the transfer is complete?

[ "67/90", "29/60", "17/30", "19/30", "11/15" ]

I think A - 67/90 is the correct answer. Here goes: Lets assume originally the number of beds = x After the new tower, the total combined no of beds = 7x So old = x, New = 6x Now 1/3 of x are occupied and 1/5 of 6x are occupied which simplifies to (6/5)x We are shifting 1/3 of x to the new ward so there will now be: 1/3 of x plus 6/5 of x occupied in the new ward. Add them up to get 23/15 of x There are 6x beds in New Tower so ratio is: (23/15)x / 6x = 23/90 of x Subtract that from 90/90 of x and you get the number of un-occupied beds to total capacity of New Tower = 67/90. A The answer is: A

A

mathematics

The C.P of 15 books is equal to the S.P of 20 books. Find his gain% or loss%?

[ "28%", "25%", "24%", "23%", "27%" ]

explanation: 15 CP = 20 SP 20 --- 5 CP loss 100 --- ? => 25% loss Answer: B The answer is: B

B

mathematics

If r ≠ 1 and if sr/(s - r) = 1, what is the value of s in terms of r?

[ "(r+1)/r", "(r - 1)/r", "r/(r + 1)", "r/(1-r)", "(1 - r)/r" ]

This question comes with a particular 'quirk' (one that you probably won't see on Test Day). The GMAT won't test you on the concept of undefined numbers (re: numbers divided by 0), so any time that this concept is a possibility, the question writers have to add a restriction that removes the option that a 0 could occur in the denominator. Here, we're told that B CANNOT = 1, which is a bit strange because that restriction doesn't seem to impact the original equation much. In fact, it impacts JUST ONE of the answer choices - so you have to ask WHY that restriction is even there. It's actually because that one answer is the correct one. Final Answer: D The answer is: D

D

mathematics

if x/4-x-3/6=1,then find the value of x.

[ "2", "4", "6", "8", "5" ]

(x /4)-((x-3)/6)=1= (3x-2(x-3) )/12 = 1 = 3x-2x+6=12 = x=6 Answer is C. The answer is: C

C

mathematics

Which of the following fractions is greater than 3 /4 and less than 5 / 6 ?

[ "4/8", "4/5", "4/6", "4/1", "4/4" ]

Explanation: 3 /4 = 0.75, 5/6 = 0.833, 1/2 = .5, 2/3 = 0.66, 4/5 = 0.8, 9/10 = 0.9. clearly 0.8 lies between 0.75 and .833. 4/5 lies between 3/4 and 5/6.. Answer: B) 4 / 5 The answer is: B

B

mathematics

what is the distance between two parallel chords of length 32 cm and 24 cm in a circle of radius 20 cm ?

[ "1 or 7", "3 or 21", "4 or 28", "2 or 14", "5 or 14" ]

since the chord length=2sqrrt(r^2-d^2) chord length=32,r=20 then we get d=12 chord length=24,r=20 then we get d=16 then we add/subtract we get option c) 4 or 28 ANSWER:C The answer is: C

C

mathematics

The jogging track in a sports complex is 1000 meters in circumference. Deepak and his wife start from the same point and walk in opposite directions at 20 km/hr and 13 km/hr respectively. They will meet for the first time in?

[ "50min", "33min", "35min", "25min", "20min" ]

Clearly, the two will meet when they are 1000 m apart To be 20+13 = 33 km apart, they take 1 hour To be 1000 m apart, they take 33 * 1000/1000 = 33 min. Answer is B The answer is: B

B

mathematics

An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.

[ "6/13", "5/9", "1/24", "4/9", "2/5" ]

An empty wooden vessel weighs 14% of its total weight when filled with paint: Vessel = 0.14(Vessel + Paint); 14V = V + P (so the weight of completely filled vessel is 14V) P = 13V (so the weight of the paint when the vessels is completely filled is 13V). The weight of a partially filled vessel is one half that of a completely filled vessel: V + P' = 1/2*14V; P' = 6V (so the weight of the paint when the vessels is partially filled is 6V). What fraction of the vessel is filled? So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled: P'/P = 6V/13V = 6/13. Answer: A. The answer is: A

A

mathematics

The ratio of the present age of Viju to that of Aju is 7:2. Four years from now, the ratio of the ages of Viju to Aju will be 5:2. What was Viju age 5 years ago ? (RBI Assistant 2015)

[ "24", "18", "12", "16", "13" ]

Let the present age of Viju be 7x years and that of Aju be 2x years. Then, 4 years from now 7x + 4 / 2x + 4 = 5 / 2 or 4x = 12 or x = 3 Viju present age = 7 * 3 = 21 years Viju age 5 years ago = 21 - 5 = 16 years answer :D The answer is: D

D

mathematics

The daily wage is increased by 50% and a person now gets Rs 25 per day. What was his daily wage before the increase ?

[ "Rs 20", "Rs 16.6", "Rs 18", "Rs 19", "none of these" ]

Let A be the daily wages before the increase, A ( 1 + x/100) = 25 (Given) Here, x = 50 Therefore, A( 1 + 50/100) = 25 A = (25 x 100) / (150) = Rs 16.6. ANSWER:B The answer is: B

B

mathematics

What is the remainder when the number R=14^2 * 15^8 is divided by 5?

[ "0", "1", "2", "4", "5" ]

14^2 has units digit 6 15^8 has units digit 5 Thus R=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero Answer: (A) The answer is: A

A

mathematics

A car crosses a 600 m long bridge in 5 minutes. What is the speed of car in km per hr?

[ "7 km/hr", "7.2 km/hr", "7.5 km/hr", "8 km/hr", "8.9 km/hr" ]

Speed = 600 m/sec. 5 x 60 = 2 m/sec. Converting m/sec to km/hr (see important formulas section) = 2 x 18 km/hr 5 = 7.2 km/hr B The answer is: B

B

mathematics

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?

[ "20 kmph", "24 kmph", "50 kmph", "35 kmph", "30 kmph" ]

Explanation: Distance from A and B be 'd' Average Speed = total distance/total time Average Speed = (2d)/[(d/20) + (d/30)] = (2d)/[5d/60) => 24 kmph. ANSWER IS B The answer is: B

B

mathematics

0.1+0.1^2+0.1^3 =

[ "0.1", "0.111", "0.1221", "0.2341", "0.3" ]

You have a mistake in your question. Choice B should be (.111) and not (.11). The equation in the solution can be simplified to (.1 + .01 + .001). Adding those together you get: .100 .010 .001 ------ .111 - Which is answer choice (B) The answer is: B

B

mathematics

A bowl contains 3 parts of which are milk and 5 parts water. How much of the mixture must be drawn off and replaced with milk sothat the mixture may be half milk and half water?

[ "2/5", "3/5", "1/5", "1/7", "2/7" ]

Suppose the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water. Quantity of water in new mixture = 3 - 3x + x litres 8 Quantity of syrup in new mixture = 5 - 5x litres 8 3 - 3x + x = 5 - 5x 8 8 5x + 24 = 40 - 5x 10x = 16 x = 8 . 5 So, part of the mixture replaced = 8 x 1 = 1/5 5 8 5 C The answer is: C

C

mathematics

A 290 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?

[ "230 m", "210 m", "260 m", "320 m", "330 m" ]

Relative speed = (120 + 80) km/hr = (200 x(5/18))m/sec = (500/9)m/sec. Let the length of the other train be x metres. Then, (x + 290)/9 = 500/9 x + 290 = 500 x = 210. B The answer is: B

B

mathematics

There are 8 stations between Vijayawada and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?

[ "100", "90", "190", "110", "105" ]

The total number of stations = 10 From 10 stations we have to choose any two stations and the direction of travel (i.e.,Vijayawada to Chennai is different from Chennai to Vijayawada) in 10P2 ways. 10P2= 10 * 9 = 90 ANSWER: B The answer is: B

B

mathematics

The sum of four consecutive odd numbers is equal to the sum of 3 consecutive even numbers. Given that the middle term of the even numbers is greater than 101 and lesser than 208, how many such sequences can be formed?

[ "26", "17", "25", "33", "50" ]

Four consecutive odd numbers: k-2, k, k+2, k+4 Three consecutive even numbers: n-2, n, n+2 k-2+k+k+2+k+4=n-2+n+n+2 4k+4=3n 4(k+1)=3n k+1=(3/4)n k=(3/4)n-1 All n's that's divisible by 4 will have an integral k. So, we need to find out how many such n's are available within given range: We know, 101<n<208 104<=n<=204 Count=(204-104)/4+1=100/4+1=25+1=26 Ans: 26. The answer is: A

A

mathematics

A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?

[ "12", "9", "8", "6", "5" ]

A's 1 hour's work = 1 ; 4 (B + C)'s 1 hour's work = 1 ; 3 (A + C)'s 1 hour's work = 1 . 2 (A + B + C)'s 1 hour's work = ( 1 + 1 ) = 7 . 4 3 12 B's 1 hour's work = ( 7 - 1 ) = 1 . 12 2 12 Therefore A alone will take 12 hours to do the work. The answer is: A

A

mathematics

A tree on first day grows 1/2 of its size second day 1/3 of its size on the previous day similarly than 1/4 and so on..U have calculate after how many days the tree will be 100 times of original size.

[ "188 days", "198 days", "178 days", "168 days", "158 days" ]

suppose 'x' is initial size and 'n' is no. of days. 1st day increment in size of tree = (1/2)x After 1st day , size of tree = x+(1/2)x= (3/2)x 2nd day increment in size of tree = (1/3)*(3/2)x=(1/2)x After 2nd day , size of tree = (3/2)x+(1/2)x=2x 3rd day increment in size of tree =(1/4)*2x=(1/2)x After 3rd day , size of tree = 2x+(1/2)=(5/2)x It is clear that every day tree grows (1/2)x in size. therefore , according to given condition x+ (1/2)x*n=100x n=198 days. ANSWER:B The answer is: B

B

mathematics

Three numbers are in the ratio 1:4:6 and their H.C.F is 9. The numbers are:

[ "1,4,6", "12,24,36", "10, 20, 30", "12, 24, 36", "9,36,54." ]

Let the required numbers be x, 4x and 6x. Then, their H.C.F = x. So, x = 9. The numbers are 9,36,54. ANSWER:E The answer is: E

E

mathematics

John and Jacob set out together on bicycle traveling at 18 and 15 miles per hour, respectively. After 40 minutes, John stops to fix a flat tire. If it takes John one hour to fix the flat tire and Jacob continues to ride during this time, how many hours will it take John to catch up to Jacob assuming he resumes his ride at 18 miles per hour? (consider John's deceleration/acceleration before/after the flat to be negligible)

[ "3", "3 1/3", "3 1/2", "4", "4 1/3" ]

John's speed - 18 miles/hr Jacob's speed - 15 miles/hr After 40min (i.e 2/3hr), distance covered by John = 18x2/3 = 12 miles. Jacob continues to ride for a total of 1hour and 40min (until John's bike is repaired). Distance covered in 1 hour 40min (i.e 5/3hr) = 15x5/3 = 25 miles. Now, when John starts riding back, the distance between them is 13 miles. Jacob and John are moving in the same direction.For John to catch Jacob, the effective relative speed will be 18-15 = 3 miles/hr. Thus, to cover 13 miles at 3 miles/hr, John will take 13/3 = 4 1/3 hours Answer E The answer is: E

E

mathematics

The average of five integers is 63, and none of these integers is greater than 100. If the average of three of the integers is 69, what is the least possible value of one of the other two integers?

[ "5", "8", "20", "21", "30" ]

When it comes to averages, we know thataverage value = (sum of n values)/n We can rewrite this into a useful formula:sum of n values = (average value)(n) The average of five integers is 63 So, the sum of ALL 5 integers = (63)(5) =315 The average of three of the integers is 65 So, the sum of the 3 integers = (69)(3) =207 So, the sum of the 2 REMAINING integers =315-207=108 If the sum of the 2 REMAINING integers =108, and we want to minimize one value, we must MAXIMIZE the other value. 100 is the maximum value so let 1 integer = 100, which means the other must equal 8 Answer: B The answer is: B

B

mathematics

One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 35 minutes, then the slower pipe alone will be able to fill the tank in

[ "144 mins", "140 mins", "136 mins", "132 minw", "None of these" ]

Explanation: Let the slower pipe alone fill the tank in x minutes then faster will fill in x/3 minutes. Part filled by slower pipe in 1 minute = 1/x Part filled by faster pipe in 1 minute = 3/x Part filled by both in 1 minute = 1/x+3/x=1/35 =>4/x=1/35 x=35∗4=140 mins Option B The answer is: B

B

mathematics

What will come in place of the x in the following Number series? 5,28,57,88,125

[ "123", "143", "166", "190", "210" ]

28=23+5 57=29+28 88=31+57 125=37+88 166=41+125 =166 C The answer is: C

C

mathematics

A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 49 hrs and a machine of type S does the same job in 14 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

[ "49/9", "44/9", "46/9", "41/9", "43/9" ]

Rate of machine R =1/49 Rate of machine S =1/14 since same no of machines used for R and S to do the same work in 2 hrs So collective rate needed to finish the work in 2 hrs= 1/2 Let the no of machine be x So, x/49 +x/14 =1/2 9x=49 x=49/9 So no of machine R is 49/9 Answer A The answer is: A

A

mathematics

Three liquids were mixed in 5:4:1 ratios. If cost per kg for ach of them is 4.50, 3.75& 5.10. Then in what price mixture should be sold to get 25% profit?

[ "52.25", "53.25", "54.25", "55.25", "56.25" ]

cp of the liquid=5*4.50+4*3.75+1*5.10=42.6 In order to gain 25%profit Sp=1.25*42.6=53.25 ANSWER:B The answer is: B

B

mathematics

A number is doubled and 5 is added. If the resultant is trebled, it becomes 105. What is that number?

[ "9", "15", "18", "None of these", "Cannot be determined" ]

Explanation: Let the number be x. Therefore, 3(2x + 5) = 105 6x + 15 = 105 6x = 90 x = 15 ANSWER: B The answer is: B

B

mathematics

Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2376?

[ "2277", "2400", "2200", "2766", "2998" ]

Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2376. => (90%) of (110%) of x = Rs. 2376. => (90/100)(110/100)x = 2376 => x = (2376 * 100)/(9 * 11) => x = Rs. 2400 Answer: B The answer is: B

B

mathematics

At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?

[ "6", "5", "4", "78", "2" ]

150 = (750*5*R)/100 R = 4%.Answer: C The answer is: C

C

mathematics

If Teena is driving at 55 miles per hour and is currently 7.5 miles behind Joe, who is driving at 40 miles per hour in the same direction then in how many minutes will Teena be 37.5 miles ahead of Joe?

[ "15", "60", "180", "90", "105" ]

This type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30-40 seconds for a difficult one. Teena covers 55 miles in 60 mins. Joe covers 40 miles in 60 mins So teena gains 15 miles every 60 mins Teena need to cover 7.5 +37.5 miles. Teena can cover 7.5 miles in 30 mins Teena will cover 37.5 miles in 150 mins So answer 30+150= 180 mins. (ANSWER C) The answer is: C

C

mathematics

If f is a function defined for all k by f(k) = k^(2/3)/16, what is f(64 k) in terms of f(k)?

[ "1/8 f(k)", "5/8 f(k)", "2 f(k)", "16 f(k)", "32 f(k)" ]

f(k) = k^(2/3)/16 f(64 k) = (64k)^(2/3)/16 = 16 * k^(2/3)/16 = 16 * (k^(2/3)/16) = 16 f(k). So answer is D. The answer is: D

D

mathematics

The length of the bridge, which a train 180 meters long and travelling at 45 km/hr can cross in 30 seconds, is?

[ "388", "167", "195", "288", "261" ]

Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (180 + X)/30 = 25/2 ==> 2(180 + X) = 750 ==> X = 195 m. Answer: C The answer is: C

C

mathematics

A man buys a cycle for Rs. 1200 and sells it at a loss of 15%. What is the selling price of the cycle?

[ "s. 1020", "s. 1160", "s. 1190", "s. 1202", "s. 1256" ]

S.P. = 85% of Rs. 1200 = Rs.85/100x 1200 = Rs. 1020 ANSWER :A The answer is: A

A

mathematics

The average weight of 10 men is increased by 2 ½ kg when one of the men who weighs 68 kg is replaced by a new man. What is the weight of the new man?

[ "80 kg", "93 kg", "70 kg", "75 kg", "85 kg" ]

Since the average has increased by 1.5 kg, the weight of the man who stepped in must be equal to 68+10x2.5 68+25=93 Kg Ans: 'B' The answer is: B

B

mathematics

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

[ "40", "99", "88", "66", "21" ]

Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140 = 500 m Required time = 500 * 2/25 = 40 sec.Answer: A The answer is: A

A

mathematics

The average (arithmetic mean) of y numbers is x. If 25 is added to the set of numbers, then the average will be x - 5. What is the value of y in terms of x ?

[ "x/6 - 6", "x/6 - 5", "x/7 - 5", "x/5 - 7", "x/5 - 6" ]

(A1 + A2 + .. + Ay)/y = x (A1 + A2 + .. + Ay + 25)/(y+1) = x - 5 => (xy + 25)/(y+1) = x - 5 => xy + 25 = yx -5y + x - 5 => 30 = x - 5y => 5y = x - 30 => y = x/5 - 6 E The answer is: E

E

mathematics

Find the remainder when 2^31 is divided by 5.

[ "3", "7", "1", "9", "None of them" ]

2^10 = 1024. Unit digit of 2^10 x 2^10 x 2^10 is 4 [as 4 x 4 x 4 gives unit digit 4]. Unit digit of 231 is 8. Now, 8 when divided by 5, gives 3 as remainder. Hence, 231 when divided by 5, gives 3 as remainder. Answer is A. The answer is: A

A

mathematics

Given that a “16-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 8-inch pizza to a 16-inch pizza gives you approximately what percent increase in the total amount of pizza?

[ "33", "50", "67", "180", "300" ]

area of 8 inch pizza= 4*4*pi=16 pi area of 16 inch pizza =8*8*pi=64 pi 48/16*100=300% increase hence answer is E The answer is: E

E

mathematics

Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 64 hours respectively. The ratio of their speeds is?

[ "4:5", "8:3", "8:4", "4:8", "4:1" ]

Let us name the trains A and B. Then, (A's speed) : (B's speed) = √b : √a = √64 : √9 = 8:3 Answer: B The answer is: B

B

mathematics

If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?

[ "7 meters", "9 meters", "8 meters", "5 meters", "3 meters" ]

400 rev / minute = 400 * 60 rev / 60 minutes = 24,000 rev / hour 24,000 * C = 168,000 m : C is the circumference C = 3 meters correct answer A The answer is: A

A

mathematics

Anthony and Michael sit on the six member board of directors for company X. If the board is to be split up into 2 three-person subcommittees, what percent E of all the possible subcommittees that include Michael also include Anthony?

[ "20%", "30%", "40%", "50%", "60%" ]

The answer is C. Let's look at a committee where Mike belongs (he's person # 1) on that committee. When we choose person #2, there is a 1/5 probability that it's going to be Anthony (then it doesn't matter who the third person is), and 4/5 probability that it's going to be someone else (then person #3 is going to be Anthony with probability 1/4). Total probability E= 1/5+4/5*1/4 = 2/5.C The answer is: C

C

mathematics

If the original mass of an element, in grams, is a whole number and the element has decayed by exactly 93 percent in some time period, which of the following could be the final mass of that element?

[ "27 grams", "30 grams", "29 grams", "31 grams", "35 grams" ]

Let original mass be 100 The final mass of that element will be 7 So whatever option we have it will be divisible by 7 Check for the options the one that doesn't produce non terminating decimal is our answer A. 27 grams 27/7 = 3.857... B. 30 grams 28/7 = 4.285... C. 29 grams 29/7 = 4.142....... D. 31 grams 31/7 = 4.428..... E. 35 grams 35/7 = 5 Hence our answer will be (E) The answer is: E

E

mathematics

Let us say that a table tennis tournament was going on with knock out terms which means the one who loses the match is out of the tournament. 120 players took part in that tournament. How many matches were played?

[ "99 matches.", "88 matches.", "77 matches.", "66 matches.", "119 matches." ]

Solution: 119 matches. The number of matches will always sum up to one less than the number of players in a knock out tournament. You may calculate it in any manner. Thus 119 matches were played. Answer E The answer is: E

E

mathematics

A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?

[ "5litres, 7 litres", "7litres, 4 litres", "6litres, 6 litres", "4litres, 8 litres", "8litres, 10 litres" ]

Explanation: Solution 1 Let x and (12âˆ’x) litres of milk be mixed from the first and second container respectively. Amount of milk in x litres of the the first container =.75x Amount of water in x litres of the the first container =.25x Amount of milk in (12âˆ’xlitres of the the second container =5(12âˆ’x) Amount of water in (12âˆ’x)litres of the the second container =.5(12âˆ’x) Ratio of water to milk Since x=6,12âˆ’x=12âˆ’6=6 Hence 6 and 6 litres of milk should mixed from the first and second container respectively. Answer IS C The answer is: C

C

mathematics

7^6n -1^ 6n When n is an integer > 0 is divisible by

[ "119", "127", "134", "145", "154" ]

127 B The answer is: B

B

mathematics

If 1/(m – 2) = 1/(m + 2) + 1/(m – 1), which of the following is a possible value of m?

[ "0", "-1", "-2", "1", "2" ]

Multiply by (m-2)*(m+2)*(m-1) throughout to get: (m+2)*(m-1) = (m-2)*(m-1) + (m+2)(m-2) Of the given options, only m=0 satisfies this. Answer : A The answer is: A

A

mathematics

The average of four positive integers is 69. The highest integer is 93 and the least integer is 39. The difference between the remaining two integers is 28. Which of the following integers is the higher of the remaining two integers?

[ "65", "48", "37", "23", "12" ]

Let the four integers be A, B, C and D where A > B > C > D. (A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1) A = 93, D = 39 and B - C = 28 (1) => B + C = 276 - (A + D) = 276 - 132 = 144. B + B -28 = 144 B = (144 + 28)/2 = 86 Answer:B The answer is: B

B

mathematics

A train 300 m long is running at a speed of 68 kmph. How long does it take to pass a man who is running at 8 kmph in the same direction as the train?

[ "5 sec", "9 sec", "12 sec", "15 sec", "18 sec" ]

Speed of the train relative to man = (68 - 8) kmph = (60* 5/18) m/sec = (50/3)m/sec Time taken by the train to cross the man = Time taken by It to cover 300 m at 50/3 m / sec = 300 *3/ 50 sec = 18sec Answer : E The answer is: E

E

mathematics

In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together?

[ "3990", "1540", "1995", "3672", "2314" ]

We must place all these books as under: XEXEX….XEX There are 21 books on English, 19 books on Hindi 19 places out of 22 can be chosen 22C19=22C3=1540 ways ANSWER B 1540 The answer is: B

B

mathematics

Which of the following CANNOT be a product of two distinct positive integers p and q?

[ "p", "q", "3q + 2p", "q - p", "qp" ]

In these questions it is best to take an example as if something is true for all positive integers than it as to be true for the smallest and the easiest integers to work with take p = 1 and q = 2 and work with the options pq = 2 A) p take p =2, q = 1 B) q take p = 1 q = 2 C) 3q + 2p Seems tricky, lets see other options and then come back to it. D) q - p take q = 1 and p = 2 --> q - p = -1 .. How the hell can product of two positive integers be negative ?? or less than each of them? E)qp Always true You don't even have to worry what C is ! ans D The answer is: D

D

mathematics

If P(A) = 6/17, P(B) = 5/17, and P(A ∪ B) = 4/17 Find P(B|A)?

[ "2/3", "3/5", "2/7", "3/7", "4/9" ]

P(B|A) = P(A ∪ B)/P(A) P(B|A) = (4/17)/(6/17) = 4/6 = 2/3. A The answer is: A

A

mathematics

If 3 persons can do 3 times of a particular work in 3 days, then, 7 persons can do 7 times of that work in?

[ "2 days", "3 days", "4 days", "5 days", "6 days" ]

That is, 1 person can do one time of the work in 3 days. Therefore, 7 persons can do 7 times work in the same 3 days itself. B) The answer is: B

B

mathematics

The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 45 kmph, find the speed of the stream?

[ "12 kmph", "13 kmph", "14 kmph", "15 kmph", "16 kmph" ]

The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 45/3 = 15 kmph ANSWER:D The answer is: D

D

mathematics

If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum Q of the 3 greatest of these temperatures, in degrees Fahrenheit, could be

[ "6x", "Q=4x", "Q=5x/3", "Q=3x/2", "3x/5" ]

OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B) But what about C,D,E? Any ideas why these could be wrong? Note that we have 5 positive temperatures. Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits. Answer: B. The answer is: B

B

mathematics

In a group of 800 people, 1/5 play at least one instrument, 128 play two or more. What is the probability that one student play exactly one instrument?

[ "2/125", "3/125", "C)2/25", "3/25", "1/25" ]

P(playing 2 or more instruments) = 128/800 = 4/25. Then, the probability of playing exactly one instrument is given by: P(playing 1 or more instruments) - P(playing 2 or more instruments) = 1/5 - 4/25 = 1/25. Answer E. The answer is: E

E

mathematics

In three annual examinations, of which the aggregate marks of each was 500, a student secured average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 65% average total marks, it is necessary for him in third yearly examination to secure marks :

[ "300", "350", "400", "475", "500" ]

total marks:1500 for three exams 65% of 1500=975 first exam marks=45% of 500=225 second exam marks=55% of 500=275 let X be the third exam marks 225 + 275 + X =975 X=475 ANSWER:D The answer is: D

D

mathematics

275, 132, 462, 396, 327, 891, 121

[ "327", "228", "2768", "028", "272" ]

Explanation: In each number except 327, the middle digit is the sum of the other two. ANSWER: A The answer is: A

A

mathematics

Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 60 white marbles. How many red marbles could be in bag A?

[ "1", "3", "4", "12", "8" ]

6 is the answer. Bag A- R:W:B = 2:6:9 Let W in bag A be 6K Bab B - R:W = 1:4 Let W in bag B be 4k W = 60 = 6K+4k => k =6 Total Red's in bag A will be 2K = 12 D The answer is: D

D

mathematics

Shannon and Maxine work in the same building and leave work at the same time. Shannon lives due north of work and Maxine lives due south. The distance between Maxine's house and Shannon's house is 60 miles. If they both drive home at the rate 2R miles per hour, Maxine arrives home 40 minutes after Shannon. If Maxine rider her bike home at the rate of R per hour and Shannon still drives at a rate of 2R miles per hour, Shannon arrives home 2 hours before Maxine. How far does maxine live from work?

[ "20", "34", "38", "40", "46" ]

We have that X/24 - (60-X)/2R = 40 Also X/R - (60-X)/2R = 120 So we get that 2x - 60 = 80R 3x - 60 = 240R Get rid of R 120 = 3x x = 40 Hence answer is D The answer is: D

D

mathematics

An company has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?

[ "10", "12", "15", "24", "30" ]

An company has 6 employees;for male 1C1 = 1 ........ A foe female = 5C2 = 10.........B total = 10*1 = 10 - answer=A The answer is: A

A

mathematics

What is the units digit of 2222^(333)*3333^(222)?

[ "0", "2", "4", "6", "8" ]

(2222^333)*(3333^222)=2222^111*(2222^222*3333^222) here please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 (2222^222*3333^222). since 6 powered in any number more than 0 results in 6 as a units digit, as a result we have- 6*2222^111 2 has a cycle of 4 . 111=27*4+3 . 2^3=8 6*8=48 so the units digit is 8, and the answer is E The answer is: E

E

mathematics

X = 101102103104105106107......146147148149150 (From numbers 101-150). Find out the remainder when this number is divided by 9.

[ "2", "4", "5", "6", "7" ]

Sol: The divisibility rule for 9 is sum of the digits is to be divisible by 9. So We calculate separately, sum of the digits in hundreds place, tenths place, and units place. Sum of the digits in hundreds place: 1 x 50 = 50 Sum of the digits in tenths place : 0 x 9 + 1 x 10 + 2 x 10 + 3 x 10 + 4 x 10 + 5 x 1 = 105 Sum of the digits in units place : (1 + 2 + 3 + ...+ 9) x 5 = 225 So total = 380 So remainder = 380 / 9 = 2 Answer:A The answer is: A

A

mathematics

A cistern 7 m long and 5 m wide contains water up to a breadth of 1 m 40 cm. Find the total area of the wet surface.

[ "69 m sqaure", "49 m sqaure", "52 m sqaure", "64 m sqaure", "None of these" ]

Explanation: Area of the wet surface = 2[lb+bh+hl] - lb = 2 [bh+hl] + lb = 2[(5*1.40+7*1.40)]+7*5 = 69 m square Option A The answer is: A

A

mathematics

[( 3.241 x 14 ) / 100] = ?

[ "0.045374", "4.5388", "453.88", "473.88", "None of these" ]

Answer Multiplying 3.241 x 14=4.5374 Now divide 4.5374 by 100 So, 4.5374 ÷ 100= 0.045374 ∴ Shift the decimal two places to the left as 100 Correct Option: A The answer is: A

A

mathematics

Two taps A and B can fill a tank in 5 hours and 20hours respectively. If both the taps are open then due to a leakage, it took 30 minutes more to fill the tank. If the tank is full, how long will it take for the leakage alone to empty the tank?

[ "24 hr", "36 hr", "18 hr", "42 hr", "30 hr" ]

Part filled by A+B in 1 hour = 1/5 + 1/20 = 1/4 A and B together can fill the tank in 4 hour Work done by the leak in 1 hour = 1/4 - 2/9 = 1/36 leak will empty the tank in 36 hours. Answer is B The answer is: B

B

mathematics

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

[ "270", "280", "290", "300", "310" ]

Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. A) The answer is: A

A

mathematics

If 5x^2 has two different prime factors, at most how many different prime factors does x have?

[ "1", "2", "3", "4", "5" ]

x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors. Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors). Answer: B. The answer is: B

B

mathematics

What is the perimeter of a square with area 9p^2/25 ?

[ "3p/4", "3p^2/4", "12p/5", "3p^2", "4p/3" ]

Area of square, (side)^2 = (3p/5)^2 Therefore side of the square = 3p/5 Perimeter of square = 4*side = 4* (3p/5) = 12p/5 Answer is C. The answer is: C

C