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	The average age of 30 students of a class is 20 years. Out of these, the average age of 10 students is 16 years and that of the other 19 students is 22 years. The age of the 30th student is:	[ "22 years", "24 years", "15 years", "16 years", "None of these" ]	Explanation : Age of the 30th student = [30 x 20 - (10 x 16 + 19 x 22)] = (600 - 278) = 22 years. Answer : A The answer is: A	A
mathematics	If the complement of a certain angle is six times the measure of that certain angle, then what is the measure of that certain angle?	[ "45°", "30°", "12.9°", "18°", "15°" ]	Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example. The original angle is x, so the complement is 6x, and together, these add up to 90 degrees. x + 6x = 90 7x = 90 x = 12.9° Answer = (C) The answer is: C	C
mathematics	The difference of the squares of two consecutive even integers is divisible by which of the following integers ?	[ "5", "18", "7", "45", "4" ]	Explanation: Let the two consecutive even integers be 2n and (2n + 2). Then, (2n+2)^2 = (2n+2 2n)(2n 2-2n) = 2(4n + 2) =4(2n + 1), which is divisible by 4. ANSWER:E The answer is: E	E
mathematics	If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women?	[ "10 days", "11 days", "13 days", "15 days", "24 days" ]	8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*40= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E The answer is: E	E
mathematics	If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?	[ "3", "4", "5", "6", "7" ]	Given that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6. Answer: D. The answer is: D	D
mathematics	What number is that, to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second to the third?	[ "1", "2", "3", "4", "5" ]	Solution Let x= the number required. By the conditions, x+1:x+5 = a+5:x+13 Subtracting terms, (Art. 385,2.) x+1:4 = x+5:8 Therefore 8x+8 = 4x+20. And x = 3. Answer C The answer is: C	C
mathematics	The area of a square is 144 m². Find its perimeter.	[ "18 m", "28 m", "38 m", "42 m", "48 m" ]	Area of square = side × side Given; area of square = 144 m² Therefore, side² = 144 m² Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m ANSWER : E The answer is: E	E
mathematics	In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?	[ "1/2", "1", "2", "3", "5" ]	We can straightaway eliminate A & B, since the expression will always yields an integer for those values Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4. ANSWER:E The answer is: E	E
mathematics	A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?	[ "3.6sec", "18sec", "36sec", "72sec", "None" ]	Solution Speed of train relative to jogger =(45-9)km/hr =36km/hr (36*5/18)m/sec = 10 m/sec Distance to be covered = (240 +120)m= 360m ∴ Time taken =(360/10)sec= 36 sec Answer C The answer is: C	C
mathematics	1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?	[ "22", "77", "32", "27", "29" ]	1600 ---- 28 days 1600 ---- 24 1200 ---- ? 160024 = 1200x x = 32 days Answer: C The answer is: C	C
mathematics	If a+b=−9, and a=30/b, what is the value of a^2+b^2?	[ "31", "21", "41", "61", "51" ]	a^2 + b^2 should make you think of these formulas: (a+b)(a+b) = a^2+b^2+2ab We already know (a+b) = -9 and ab = 30 (a+b)(a+b) = (-9)(-9) = a^2+b^2+2(30) a^2+b^2 = 81 - 60 = 21 Answer : B The answer is: B	B
mathematics	A thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?	[ "6:34 p.m", "9:34 p.m", "3:34 p.m", "2:34 p.m", "3:41 p.m" ]	: Suppose the thief is overtaken x hrs after 2.30 p.m. Then, distance covered by the owner in (x - 1/2) hrs. 40x = 75(x - 1/2) => x = 15/14hrs. So, the thief is overtaken at 3:34 p.m.' Answer: C The answer is: C	C
mathematics	How many times are the hands of a clock at right angle in a day?	[ "44", "21", "22", "41", "40" ]	A 44 In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times. The answer is: A	A
mathematics	2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?	[ "39 and 31", "40 and 33", "42 and 33", "37 and 31", "35 and 32" ]	Let their marks be (x+9) and x. Then, x+9 = 56/100(x + 9 +x) => 25(x+9) => 14 (2x + 9) => 3x = 99 => x = 33. So, their marks are 42 and 33 C The answer is: C	C
mathematics	How many figures are required to number the pages the pages of a book containing 2200 pages?	[ "7593", "6693", "7693", "7793", "7893" ]	1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 to 2200 = 1201 * 4 = 4804 ----------- 7693 ANSWER:C The answer is: C	C
mathematics	In the biology lab of "Jefferson" High School there are 4.32*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?	[ "100", "200", "400", "1000", "5000" ]	4.3210^6/ 10800==> 43.210^3/108==> 43200/108= 400 ANSWER:C The answer is: C	C
mathematics	On a game show, a contestant spins two different wheels; each wheel is numbered 1 to 15. What is the probability that the contestant will spin all tens?	[ "25", "64", "8/7", "4/6", "1/225" ]	All 15s: 1st wheel = 15 = 1/15 2nd wheel = 15 = 1/15 (1/15)(1/15)= 1/225 Answer: E The answer is: E	E
mathematics	200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?	[ "14.29%", "15.29%", "16.29%", "17.29%", "18.29%" ]	--> Multiples of 7 are 7, 14, 21, 28, 35, 42.... Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd. So approx. 50 % of the 200 multiples are odd i.e 100 multiples. --> Similalrly, for 8 multiples are:8,16,24... All are even so 0 % are odd. Total odd= (100+0)/(200+500)= 100/700=1/7 = 14.29% Answer A The answer is: A	A
mathematics	If the first day of a year (other than leap year) was Sunday, then which was the last day of that year?	[ "Saturday", "Sunday", "Tuesday", "Monday", "None of these" ]	Explanation : Given that first day of a normal year was Sunday Odd days of the mentioned year = 1 (Since it is an ordinary year) Hence First day of the next year = (Sunday+ 1 Odd day) = Monday Therefore, last day of the mentioned year = Sunday. Answer : Option B The answer is: B	B
mathematics	If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:	[ "2.87", "2.965", "3.876", "3.9", "4.526" ]	log5 512 = log 512/ log 5 = log 2^9/log(10/2) =9 log 2 /log 10 - log 2 =(9*0.3010)/1-0.3010 =2.709/0.699 = 2709/699 = 3.876 ANSWER C The answer is: C	C
mathematics	Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?	[ "17/25", "17/24", "17/29", "17/20", "17/21" ]	n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20 Answer: D The answer is: D	D
mathematics	Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?	[ "6 days", "2 days", "7 days", "5 days", "1 days" ]	D 2M + 3W ----- 35 h 4M + 4W ------- 21 h 7M -------? d 70M + 105W = 84M +84M 21W = 14M => 2M = 3W 4 * 35 = 7 * x => x = 20 hours 20/4 = 5 days The answer is: D	D
mathematics	For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*?	[ "0.2", "1.2", "1.8", "2.2", "4.0" ]	Since s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4). Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2 Answer: B. The answer is: B	B
mathematics	Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is?	[ "54", "77", "36", "88", "21" ]	Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A The answer is: A	A
mathematics	In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?	[ "6.25", "6.22", "6.29", "6.39", "6.13" ]	Required run rate = [282 - (3.2 * 10)]/40 = 250/40 = 6.25 Answer: A The answer is: A	A
mathematics	How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336	[ "1", "4", "5", "7", "3" ]	B By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. The answer is: B	B
mathematics	If 2x = 3y = 10, then 6xy = ?	[ "100", "200", "120", "40", "20" ]	2x = 10;x=5 3y = 10;y=10/3 Multiply: 6xy=6510/3=100 Answer: A. The answer is: A	A
mathematics	If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many B such committees are possible?	[ "B=20", "40", "50", "B=80", "120" ]	Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10. But these 3 chosen couples can send two persons (either husband or wife): 222=2^3=8. Total # of ways: 5C3*2^3=80. Answer: D. The answer is: D	D
mathematics	Express 25 mps in kmph?	[ "22", "87", "90", "77", "22" ]	25 * 18/5 = 90 kmph Answer: C The answer is: C	C
mathematics	John and Peter are among the eight players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?	[ "7/15", "11/20", "14/25", "15/28", "16/35" ]	The total possible ways of selecting a 6-member team is 8C6 = 28 The possible ways which include John and Peter is 6C4 = 15 The probability of choosing both John and Peter is 15/28 The answer is D. The answer is: D	D
mathematics	The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?	[ "625", "286", "266", "191", "811" ]	Explanation: Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625. Answer: A The answer is: A	A
mathematics	By selling an article at Rs.120, a profit of 25% is made. Find its cost price?	[ "s.96", "s.45", "s.120", "s.180", "s.189" ]	SP = 120 CP = (SP)[100/(100+P)] = 120 [100/(100+25)] = 120* [100/125] = Rs.96 Answer: A The answer is: A	A
mathematics	If a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT	[ "a + c", "t + c", "ac", "(bc)/2", "(abc)/4" ]	I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian. The 3 numbers can be written as a, (a + 2)(a + 4). If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2. A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s. C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization. D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer. E - atc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C. B - b + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization. As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B The answer is: B	B
mathematics	If the side of a square is increased by 55%, its area is increased by?	[ "140%", "145%", "150%", "160%", "none of these" ]	Since Side x Side = Area Therefore, net% change in area = ( x + y + xy/100) % = [55 + 55 + (55 x 55)/100]% or 140.25% Therefore, area is increased by 140.25% ANSWER:A The answer is: A	A
mathematics	Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A’s area to rectangle B’s area?	[ "5/3", "9/5", "9/25", "3/5", "25/9" ]	The area of rectangle A is ab. c=5a/3 and d=5b/3. The area of rectangle B is cd=25ab/9. The ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25. The answer is C. The answer is: C	C
mathematics	Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?	[ "0", "3", "4", "5", "6" ]	Explanation : p + q = α –2 and pq = –α – 1 (p + q)2 = p2 + q2 + 2pq, Thus (α –2)2 = p2 + q2 + 2(–α – 1) p2 + q2 = α2 – 4α + 4 + 2α + 2 p2 + q2 = α2 – 2α + 6 p2 + q2 = α2 – 2α + 1 + 5 p2 + q2 = (α – 1)2 + 5 Thus, minimum value of p2 + q2 is 5. Answer : D The answer is: D	D
mathematics	I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?	[ "200", "600", "300", "800", "1000" ]	Let x be the number I chose, then x/5−154=6 x/5=160 x=800 correct answer D The answer is: D	D
mathematics	12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.	[ "360", "384", "432", "470", "None" ]	Solution: Given there are 12 numbered chairs, such that chairs numbered 1 to 8 should be occupied. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The various combinations of chairs that ensure that no two men are sitting together are listed. (1, 3, 5,__), The fourth chair can be 5,6,10,11 or 12, hence 5 ways. (1, 4, 8, __), The fourth chair can be 6,10,11 or 12 hence 4 ways. (1, 5, 8, __), the fourth chair can be 10,11 or 12 hence 3 ways. (1, 6, 8,__), the fourth chair can be 10,11 or 12 hence 3 ways. (1,8,10,12) is also one of the combinations. Hence, 16 such combinations exist. In case of each these combinations we can make the four men inter arrange in 4! ways. Hence, the required result =16*4!= 384. Answer: Option B The answer is: B	B
mathematics	Jake bought oranges at the supermarket for Y dollars an orange and sugar for M dollars per kilogram. Then, he made lemonade using P oranges and Q kgs of sugar per liter and he sold Z liters of lemonade for X dollars per liter. How much money has he made after selling all the lemonade?	[ "ZX(PY+QM)", "ZPM-ZQY", "XZ-PYZ-QMZ", "XZ-(MQ-YP)", "XQ-PY+ZM" ]	First, the cost of the lemonade per liter= PY+QM dollars Since Jake sold Z liters of lemonade, the cost price= Z(PY+QM) dollars The selling price=ZX dollars Profit=ZX-Z(PY+QM) =(X-PY-QM)Z The answer is C!! The answer is: C	C
mathematics	If S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer?	[ "3", "6", "7", "14", "26" ]	30! S must be divisible by (332)^k. As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18). Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly. 3 6 9* 12 15 18* 21 24 27** 30 The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively. 3=3 (occurs 10 times) +10 33=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3) 33*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted) Total: 14. For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result. Answer: 7 -> Answer choice: C. The answer is: C	C
mathematics	6x − 12 = 6y 4y + 4x = 12 Which of the following is the number of solutions to the system of equations shown above?	[ "More than three", "Exactly one", "Exactly two", "Exactly three", "None" ]	6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 4y + 4x = 12 =>x + y = 3 -- 2 From equation 1 and 2 , we get 2x = 5 => x=2.5 y=.5 Therefore , the given system will have Exactly one solution Answer : B The answer is: B	B
mathematics	The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 41 kg, then the weight of B is:	[ "27 kg", "20 kg", "26 kg", "31 kg", "35 kg" ]	let d sum of a, b, c is 345=135 and sum of a and b s 240=80 sum of b and c is 2*41=82 hence 80+82-135=27 ans=27 ANSWER:A The answer is: A	A
mathematics	If x > 1, which of the following decreases as x decreases? I. x + x^3 II. 2x^2 − x III. 1/(x + 1)	[ "I only", "II only", "III only", "I and III", "II and II" ]	let x= 4 and 3 b old and new values ST1: x= 4 -> 4+64 = 68 x=3-> 3+27= 30 ...decreased ST2:x= 4-> 216-4 = 28 x=3->29-3 = 15 decreased St3: x=4-> 1/4 = .25 x=3->1/3 = .33 Ans: E The answer is: E	E
mathematics	John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?	[ "50 ml", "60 ml", "70 ml", "80 ml", "90 ml" ]	concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =310 By rule of alligation, concentration of water in mixture1 (29) concentration of water in pure water (1) Mean concentration (310) 1−310=710 310−29=790 => Quantity of mixture1 : Quantity of water =710:790=110:190=1:19 Given that Quantity of mixture1 = 630 ml => 630 : Quantity of water =1:19 => Quantity of water =630×19=70 ml C The answer is: C	C
mathematics	A warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 8. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used. The manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?	[ "981", "1000", "1011", "1101", "200" ]	The number of codes possible if leading zero is allowed = 101010=10^3 The number of codes possible if leading zero is NOT allowed = 81010=910^2 The difference = 10^3 - 810^2 = 10^2(10-8) = 2*10^2. Answer: E. Similar questions to practice: Hope it helps. The answer is: E	E
mathematics	If the cost of A metres of wire is C rupees, then what is the cost of E metres of wire at the same rate?	[ "Rs. (EC/A)", "Rs. (EC)", "Rs. (C/A)", "Rs. (E/A)", "Rs. (AC/E)" ]	cost of A metres of wire = Rs.C cost of 1 metre of wire = Rs.(C/A) cost of E metre of wire = Rs.(E×C/A)=Rs. (EC/A) ANSWER:A The answer is: A	A
mathematics	If a copier makes 20 copies every 6 seconds, then continues at this rate, how many minutes will it take to make 2,000 copies?	[ "13", "15", "12", "11", "10" ]	20 copies 6 seconds 2000 copies = (2000*6)/20 seconds = 600/60 minutes = 10 minutes Answer : E The answer is: E	E
mathematics	In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 284. What is the sum of all the integers in the sequence?	[ "552", "568", "574", "586", "600" ]	let the first term of the sequence be x since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms) now, sum of first 4 terms =284 or, 4x+12=284 x=272/4=68 Thus the answer can now be calculated by either summing up 68+70+72+... 8th term or s=n/2(2a+(n-1)d =8/2(268+(72)) =4(136+14)=600 E The answer is: E	E
mathematics	A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?	[ "25%", "30%", "35%", "40%", "45%" ]	D for me. Let managers comminsion rate be M. m5000+ 20.055000=2500 5000m=2000 m=40/100=40% The answer is: D	D
mathematics	The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The present worth is	[ "Rs. 480", "Rs. 520", "Rs. 600", "Rs. 960", "None" ]	Solution T.D = (B.G x 100/Rate x Time) = Rs.(24x100 / 10x 2) = Rs.120. P.W = (100 x T.D/Rate x Time) = Rs.(100x120 / 10x 2) = Rs.600. Answer C The answer is: C	C
mathematics	A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.238 less than the sum lent. What was the sum lent?	[ "228", "350", "289", "500", "821" ]	P - 238 = (P48)/100 P = 350 Answer: B The answer is: B	B
mathematics	What is the greatest number of three digits which is divisible by 8, 16, 32 ?	[ "997", "992", "999", "998", "990" ]	Greatest number of 3 digits = 999 LCM of 8, 16, 32 = 32 999 ÷ 32 = 31, remainder = 7 Hence, greatest number of four digits which is divisible by 8,16,32 = 999 - 7 = 992 answer : B The answer is: B	B
mathematics	Alice can bake a pie in 5 minutes. Bob can bake a pie in 6 minutes. Compute how many more pies Alice can bake than Bob in 60 minutes.	[ "1", "2", "3", "4", "5" ]	Alice can bake 60/5 = 12 pies in 60 minutes. Bob can bake 60/6 = 10 pies in 60 minutes. Alice can therefore bake 12 - 10 = 2 more pies than Bob. correct answer B The answer is: B	B
mathematics	A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?	[ "8867", "299", "279", "600", "2612" ]	Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6 And also given that, profit share of B is Rs. 1500 => 5 parts out of 15 parts is Rs. 1500 Now, required difference is 6 - 4 = 2 parts Required difference = 2/5 (1500) = Rs. 600.Answer: D The answer is: D	D
mathematics	It has been raining at the rate of 5 centimeters per hour. If the rain filled a cylindrical drum with a depth of 15 centimeters, and area 300 square centimeters, how long did it take to fill the drum completely?	[ "3 hours", "4 hours 15 minutes", "6 hours", "2 hours 5 minutes", "8 hours" ]	Answer is : A, 3 hours The volume of the drum is irrelevant and only height matters since rain fell all over the city. Thus, it takes only 15 / 5 = 3 hours of rain to fill the drum The answer is: A	A
mathematics	Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?	[ "10%", "18%", "19%", "12%", "13%" ]	Let the rate of interest during the second year be R%. Given, 4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A The answer is: A	A
mathematics	12 times a positive integer is more than its square by 36, then the positive integer is	[ "6", "10", "11", "12", "14" ]	Explanation: Let the number be x. Then, 12x = x2 + 36 => x2 - 12x + 36 = 0 =>(x - 6)(x - 6) = 0 => x = 6 Answer: A The answer is: A	A
mathematics	A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 1 rounds per hour and 1 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?	[ "A)5", "B)6", "C)8", "D)3", "E)9" ]	Relative speed = 1 + 1 = 2 rounds per hour. So, they cross each other 2 times in an hour and 1 times in half an hour. Hence, they cross each other 3 times before 9.30 a.m. ANSWER:D The answer is: D	D
mathematics	It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?	[ "(2^90 - 1)", "(2^90 + 1)", "(2^96 - 1)", "(2^96 + 1)", "(2^95 + 1)" ]	Let 232 = x. Then, (232 + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N. D) The answer is: D	D
mathematics	A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?	[ "11.11 km/hr", "21.11 km/hr", "71.11 km/hr", "81.11 km/hr", "41.11 km/hr" ]	Explanation: Total time taken = (160/64 + 160/8)hrs = 9/2 hrs. Average speed = (320 x 2/9) km.hr = 71.11 km/hr. Answer: C The answer is: C	C
mathematics	Three partners A, B, C in a business invested money such that 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) then, The ratio of their capitals is	[ "63 : 45 : 34", "63 : 54 : 34", "5 : 2 : 1", "63 : 45 : 35", "None of these" ]	Explanation: Let 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) = Rs.x Then, Aâ€™s capital = Rs x/2, Bâ€™s capital = Rs. x/5 and Câ€™s capital = Rs. x/10 A : B : C = x/2 : x/5 : x/10 5 : 2 : 1 Answer: Option C The answer is: C	C
mathematics	If X and Y are both positive two-digit integers and share no digits, and X > Y, what is the smallest possible value of X - Y?	[ "0", "1", "2", "3", "9" ]	Answer = B = 1 20 - 19 = 30-29 = 40-39 = 50-49 = 1 The answer is: B	B
mathematics	If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?	[ "-42 < xy < 30", "-42 < xy < 24", "-28 < xy < 18", "-24 < xy < 21", "-24 < xy < 24" ]	The least value of xy is a bit more than 7(-6)=-42 and the largest value of xy is a bit less than (-5)(-6)=30. Therefore -42 < xy < 30. Answer: A. The answer is: A	A
mathematics	A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be	[ "8 days", "9 days", "10 days", "12 days", "13 days" ]	If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days Therefore, here, the required number of days = 12 × 24/ 36 = 8 days. A The answer is: A	A
mathematics	Bunny's brother Sunny is 562 days older to him while his sister Jenny is 75 weeks older to Sunny. If Jenny was born on Tuesday, on which day was Bunny born?	[ "Monday", "Tuesday", "Friday", "Saturday", "Thursday" ]	562-(757)=37 37--------75=35 remaing 2+tuesday ans:thursday ANSWER:E The answer is: E	E
mathematics	Sravan travelled for 15 hours. He covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph. Find the distance travelled by Sravan?	[ "520", "540", "550", "560", "440" ]	Let the distance travelled be x km. Total time = (x/2)/45 + (x/2)/30 = 15 => x/90+ x/60 = 15 => (2x + 3x)/180 = 15 => x = 540 km Answer:B The answer is: B	B
mathematics	In how many different number of ways 4 boys and 2 girls can sit on a bench?	[ "600", "640", "720", "740", "760" ]	npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) The answer is: C	C
mathematics	When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 38, what is the remainder when k is divided by 7?	[ "2", "4", "3", "5", "6" ]	Cant think of a straight approach but here is how I solved it: K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer) so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 38) Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5 so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 38) 17 is the only common number in both the sets. Hence k = 17 Answer : C The answer is: C	C
mathematics	As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, four orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?	[ "1/9", "1/6", "5/18", "4/45", "5/6" ]	Probability of not getting the same flavor -> Favorable -> Cherry - orange [ 2C1 * 4C1 [or simply 24 ] or Cherry - lemon [ 24] or orange - lemon [44] Prob = (24 + 24 + 44 ) / 9C2 = 32/360 = 4/45 Answer -> D The answer is: D	D
mathematics	If log 27 = 1.431, then the value of log 9 is :	[ "0.934", "0.945", "0.954", "0.958", "None of these" ]	Solution Log 27 = 1.431 ⇒ log (33) = 1.431 ⇒ 3 log 3 = 1.431 ⇒ log 3 = 0.477 ∴ log 9 = log (32) = 2 log 3 = (2 × 0.477) = 0.954. Answer C The answer is: C	C
mathematics	Davidson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another. Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?	[ "0.8", "0.7", "0.6", "0.5", "0.49" ]	probability of adams approval = 0.7 baker approval =0.5 corfu approval=0.4 proabability of approval is must adam approval and atleast one approval = adam approvalbaker approvalcorfu approval(approval of both remaining)+adam approvalbaker approvalcorfu not approval(atleast one remaining approval)+ adam approvalbaker not approvalcoffu approval( atleast one remaining approval = 0.70.50.4+0.70.50.6+0.70.50.4 =0.14+0.21+0.14 =0.49 E The answer is: E	E
mathematics	If 50 percent of X is 25 percent of Y, then what is the relation between X and Y?	[ "X=Y", "2X=Y", "X=2Y", "1", "NONE OF ABOVE" ]	50/100(X) = 25/100(Y) 2X=Y.. Option B. The answer is: B	B
mathematics	A mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?	[ "10 gallons", "8.5gallons", "8gallons", "8.33gallons", "9.33gallons" ]	In 125 gallons of the solution there are 0.2∗125=25 gallons of water. We want to add w gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution: 25+w=0.25(125+w) --> w=253≈8.33. ANSWER:D The answer is: D	D
mathematics	Robert walks from point A to point B at an average speed of 10 kilometers per hour. At what speed, in kilometers per hour, must Robert walk from point B to point A so that her average speed for the entire trip is 12 kilometers per hour?	[ "15km/hr", "21km/hr", "16km/hr", "20km/hr", "17km/hr" ]	Let's suppose that speed while returning was x km/h Since the distance is same, we can apply the formula of avg speed Avg speed= 2S1S2/S1+S2 12= 210x/10+x x= 15 km/hr answer is A The answer is: A	A
mathematics	If books bought at prices ranging from Rs. 250 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?	[ "23267", "1400", "1800", "2778", "76611" ]	Explanation: Least Cost Price = Rs. (250 * 8) = Rs. 2000. Greatest Selling Price = Rs. (425 * 8) = Rs. 3400. Required profit = Rs. (3400 - 2000) = Rs. 1400. Answer: B) 1400 The answer is: B	B
mathematics	If a 3 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?	[ "40%", "100%", "150%", "200%", "300%" ]	The area A of the large cube is 336 = 54 square cm. The area of the 27 small cubes is 276 = 543 = 3A, an increase of 200%. The answer is D. The answer is: D	D
mathematics	Cost of 16 mirror and 8 comb is Rs.352 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?	[ "10", "12", "20", "21", "22" ]	Let the cost of each pen and pencil be 'p' and 'q' respectively. 16m + 8c = 352 --- (1) 4m + 4c = 96 8m + 8c = 192 --- (2) (1) - (2) => 8p = 160 => m = 20 C The answer is: C	C
mathematics	How many integers between 1 and 1,800 are divisible by 20,30,40?	[ "14", "15", "16", "17", "18" ]	LCM of the given numbers=120 Therefore , number of integers = 1800/120 =15 Option B is answer The answer is: B	B
mathematics	Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?	[ "33", "98", "25", "29", "27" ]	Explanation: Let Varun's age today = x years. Then, Varun's age after 1 year = (x + 1) years. Therefore x + 1 = 2 (x - 12) x + 1 = 2x - 24 x = 25 Answer: C) 25 years The answer is: C	C
mathematics	Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?	[ "1245 m^2", "1345 m^2", "2520 m^2", "2560 m^2", "2678 m^2" ]	Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C The answer is: C	C
mathematics	If a certain sample of data has a mean of 25.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?	[ "(19.0; 26.5)", "(14.5; 28.0)", "(23.0; 28.5)", "(22.5; 26.0)", "(19.0; 30.5)" ]	The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5. The values between 20 and 30 are within 2.5 standard deviations from the mean. The answer is E. The answer is: E	E
mathematics	A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?	[ "1/7", "2/9", "1/12", "4/17", "2/3" ]	Total number of balls = 7+2 = 9 n(S) = 9C3 = 987 / 32 = 84 n(E) = 2C2 7C1 = 7 Probability = 7/84 = 1/12 Answer is C The answer is: C	C
mathematics	What approximate value should come in place of question mark (?) in the following equation 287.532 + 1894.029 – 657.48 = 543.095 + ?	[ "870", "790", "980", "770", "890" ]	? = 285 + 1895 – 655 – 545 or, ? = 980 Answer C The answer is: C	C
mathematics	Smitha bought 8 Kg of kiwi fruit at an average rate of 360.If she returned 3.5kg to the retailer,at an average rate of remaining fruit was 202.5, Then what is the average price, of the returned 3.5 Kgs ?	[ "41.5", "43", "42", "45", "47.3" ]	Total price of 8Kg kiwi fruit=845=360 Total price of 4.5Kg kiwi fruit=4.545=202.5 Total price of 3.5Kg kiwi fruit=360-202.5=157.5 Average price of 3.5 Kgs kiwi fruit= 157.5/3=45 Correct option Answer:D The answer is: D	D
mathematics	Aman started a business investing Rs. 60,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?	[ "12:15:18", "72:105:112", "52:105:112", "62:105:112", "12:105:112" ]	Explanation: Aman : Rakhi : Sagar = (60000 * 36) : (105000 * 30) : (140000 * 24) = 72:105:112 Answer: B The answer is: B	B
mathematics	Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?	[ "70", "90", "60", "80", "10" ]	D 80 We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule) (60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300 D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80. The answer is: D	D
mathematics	Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?	[ "7 3/8 km", "5 7/8 km", "17 7/8 km", "7 7/8 km", "2 7/8 km" ]	RS = 6 ¾ - 4 ½ = 2 ¼ T = 3 ½ h. D = 9/4 * 7/2 = 63/8 = 7 7/8 km ANSWER:D The answer is: D	D
mathematics	For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.267] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?	[ "0", "0", "27", "54", "Cannot be determined" ]	K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^24^25^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . B The answer is: B	B
mathematics	Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?	[ "5 km", "10 4/3 km", "4 3/8 km", "18 km", "6 km" ]	Explanation: RS = 5 ¾ - 4 ½ = 1 ¼ T = 3 ½ h. D = 5/4 * 7/2 = 35/8 = 4 3/8 km C) The answer is: C	C
mathematics	In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?	[ "6!/2!∗C57∗5!3!", "4!/2!∗C57∗5!3!", "6!/2!∗C57∗6!3!", "3!/2!∗C57∗5!3!", "12!/2!∗C57∗5!3!" ]	Step 1: Separate consonants with 7 empty slots CRPRTN*. Step 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's); Step 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57 Step 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's). Total = 6!/2!∗C57∗5!3! Answer: A The answer is: A	A
mathematics	A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?	[ "Rs.14000", "Rs.1000", "Rs.10500", "Rs.2050", "Rs.5500" ]	Explanation: 2512: 3012: 358 15:18:14 14/47 47000 = Rs.14000 ANSWER:A The answer is: A	A
mathematics	If in k+1 years from now John will be m years old, then how old was John t-1 years ago?	[ "m-k-t", "m+k-t+2", "m+k-t+1", "k-m-t+2", "k+t-m" ]	Age t-1 years ago is m - k - 1 - ( t - 1 ) Or, Age t-1 years ago is m - k - 1 - t + 1 Or, Age t-1 years ago is m - k - t Hence, Answer will definitely be (A) m - k - t The answer is: A	A
mathematics	The average earning of amechanic for the first 4days of a week is Rs.25 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?	[ "s. 10", "s. 24", "s. 30", "s. 40", "s. 50" ]	Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day = 4 x 25+ 4 x 22 -20 = Rs. 168 âˆ´ Average earning = 168/ 7 = Rs. 24 B The answer is: B	B
mathematics	x, y and z are consecutive positive integers such that x < y < z; which of the following must be true? 1. xyz is divisible by 6 2. (z-x)(y-x+1) = 4 3. xy is even	[ "I only", "II only", "III only", "I and II only", "I, II, and III" ]	Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1 Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6. Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))(y-(y-1)+1) = 22 = 4 So, always true Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true. So, I II and III are always true and hence answer is E. The answer is: E	E
mathematics	if 5xx+14x+k=0 having two reciprocal roots find the value of k.	[ "1", "2", "3", "4", "5" ]	Product of reciprocal roots =1 Product of roots of quadratic eqn ax^2+bx+c = 0 is c/a. Hence k/5 =1 k=5 ANSWER:E The answer is: E	E
mathematics	If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?	[ "100 men", "101 men", "102 men", "103 men", "104 men" ]	C 102 men From the above formula i.e (m1t1/w1) = (m2t2/w2) so, (3489/(2/5)) = (x69/(3/5)) so, x = 136 men number of men to be added to finish the work = 136-34 = 102 men The answer is: C	C
mathematics	If 3a = 4b and ab ≠0, what is the ratio of a/4 to b/3?	[ "64/27", "9/16", "1", "6/8", "8/6" ]	A nice fast approach is the first find a pair of numbers that satisfy the given equation: 3a = 4b Here's one pair: a =4 and b =3 What is the ratio of a/9 to b/8? In other words, what is the value of (a/4)/(b/3)? Plug in values to get: (a/4)/(b/3) = (4/4)/(3/3) = 1/1 = 1 C The answer is: C	C
mathematics	A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?	[ "Grandfather", "Daughter", "Grandmother", "Granddaughter", "SISTER" ]	A is the sister of B and B is the daughter of C. So, A is the daughter of C. Also, D is the father of C. So, A is the granddaughter of D. Answer: D The answer is: D	D
mathematics	The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?	[ "11%", "82%", "14%", "12%", "17%" ]	100 * 100 = 10000 80 * 110 = 8800 10000------- 1200 100 ------- ? = 12% Answer:D The answer is: D	D
mathematics	17200 x 223 + 17200 x 77 = ?	[ "2736900", "2738800", "2658560", "5160000", "None of them" ]	=17200 x (223+77) (by distributive law) =17200 x 300 =5160000 Answer is D The answer is: D	D

mathematics

The average age of 30 students of a class is 20 years. Out of these, the average age of 10 students is 16 years and that of the other 19 students is 22 years. The age of the 30th student is:

[ "22 years", "24 years", "15 years", "16 years", "None of these" ]

Explanation : Age of the 30th student = [30 x 20 - (10 x 16 + 19 x 22)] = (600 - 278) = 22 years. Answer : A The answer is: A

A

mathematics

If the complement of a certain angle is six times the measure of that certain angle, then what is the measure of that certain angle?

[ "45°", "30°", "12.9°", "18°", "15°" ]

Thecomplementof angle A is the angle which, when added to angle A, gives 90 degrees. The two acute angles of a right triangle are complements, for example. The original angle is x, so the complement is 6x, and together, these add up to 90 degrees. x + 6x = 90 7x = 90 x = 12.9° Answer = (C) The answer is: C

C

mathematics

The difference of the squares of two consecutive even integers is divisible by which of the following integers ?

[ "5", "18", "7", "45", "4" ]

Explanation: Let the two consecutive even integers be 2n and (2n + 2). Then, (2n+2)^2 = (2n+2 2n)(2n 2-2n) = 2(4n + 2) =4(2n + 1), which is divisible by 4. ANSWER:E The answer is: E

E

mathematics

If 8 men or 12 women can do a piece of work in 40 days, in how many days can the same work be done by 6 men and 11 women?

[ "10 days", "11 days", "13 days", "15 days", "24 days" ]

8men = 12women (i.e 2men = 3women) 12women 1 day work= 1/40 soln: 6men(9women)+ 11women=20women=? 1 women 1 day work =12*40= 1/480 so, 20 women work= 20/480=1/24 ans: 24 days ANSWER:E The answer is: E

E

mathematics

If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 54. By how much do the two digits differ?

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

Given that (10a + b) - (10b + a) = 54 --> 9a - 9b =54 --> a - b = 6. Answer: D. The answer is: D

D

mathematics

What number is that, to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second to the third?

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

Solution Let x= the number required. By the conditions, x+1:x+5 = a+5:x+13 Subtracting terms, (Art. 385,2.) x+1:4 = x+5:8 Therefore 8x+8 = 4x+20. And x = 3. Answer C The answer is: C

C

mathematics

The area of a square is 144 m². Find its perimeter.

[ "18 m", "28 m", "38 m", "42 m", "48 m" ]

Area of square = side × side Given; area of square = 144 m² Therefore, side² = 144 m² Therefore, side = √(144 m²) = √(2 × 2 × 2 × 2 × 3 × 3) m² = 2 × 2 × 3 m = 12 m Now, the perimeter of the square = 4 x side = 4 × 12 m = 48 m ANSWER : E The answer is: E

E

mathematics

In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?

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

We can straightaway eliminate A & B, since the expression will always yields an integer for those values Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4. ANSWER:E The answer is: E

E

mathematics

A jogger running at 9 kmph alongside a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the direction opposite to that in which the train is going ?

[ "3.6sec", "18sec", "36sec", "72sec", "None" ]

Solution Speed of train relative to jogger =(45-9)km/hr =36km/hr (36*5/18)m/sec = 10 m/sec Distance to be covered = (240 +120)m= 360m ∴ Time taken =(360/10)sec= 36 sec Answer C The answer is: C

C

mathematics

1600 men have provisions for 28 days in the temple. If after 4 days, 400 men leave the temple, how long will the food last now?

[ "22", "77", "32", "27", "29" ]

1600 ---- 28 days 1600 ---- 24 1200 ---- ? 1600*24 = 1200*x x = 32 days Answer: C The answer is: C

C

mathematics

If a+b=−9, and a=30/b, what is the value of a^2+b^2?

[ "31", "21", "41", "61", "51" ]

a^2 + b^2 should make you think of these formulas: (a+b)(a+b) = a^2+b^2+2ab We already know (a+b) = -9 and a*b = 30 (a+b)(a+b) = (-9)(-9) = a^2+b^2+2*(30) a^2+b^2 = 81 - 60 = 21 Answer : B The answer is: B

B

mathematics

A thief steals at a car at 2.30 p.m. and drives it at 40 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?

[ "6:34 p.m", "9:34 p.m", "3:34 p.m", "2:34 p.m", "3:41 p.m" ]

: Suppose the thief is overtaken x hrs after 2.30 p.m. Then, distance covered by the owner in (x - 1/2) hrs. 40x = 75(x - 1/2) => x = 15/14hrs. So, the thief is overtaken at 3:34 p.m.' Answer: C The answer is: C

C

mathematics

How many times are the hands of a clock at right angle in a day?

[ "44", "21", "22", "41", "40" ]

A 44 In 12 hours, they are at right angles 22 times. In 24 hours, they are at right angles 44 times. The answer is: A

A

mathematics

2 students appeared at an examination. 1 of them secured 9 marks more than the other one and hismarks was 56% of the sum of their marks. Find the marks obtained by them are?

[ "39 and 31", "40 and 33", "42 and 33", "37 and 31", "35 and 32" ]

Let their marks be (x+9) and x. Then, x+9 = 56/100(x + 9 +x) => 25(x+9) => 14 (2x + 9) => 3x = 99 => x = 33. So, their marks are 42 and 33 C The answer is: C

C

mathematics

How many figures are required to number the pages the pages of a book containing 2200 pages?

[ "7593", "6693", "7693", "7793", "7893" ]

1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 to 2200 = 1201 * 4 = 4804 ----------- 7693 ANSWER:C The answer is: C

C

mathematics

In the biology lab of "Jefferson" High School there are 4.32*10^6 germs, equally divided among 10,800 Petri dishes. How many germs live happily in a single dish?

[ "100", "200", "400", "1000", "5000" ]

4.32*10^6/ 10800==> 43.2*10^3/108==> 43200/108= 400 ANSWER:C The answer is: C

C

mathematics

On a game show, a contestant spins two different wheels; each wheel is numbered 1 to 15. What is the probability that the contestant will spin all tens?

[ "25", "64", "8/7", "4/6", "1/225" ]

All 15s: 1st wheel = 15 = 1/15 2nd wheel = 15 = 1/15 (1/15)(1/15)= 1/225 Answer: E The answer is: E

E

mathematics

200 hundred multiples of seven are chosen at random, and 500 multiples of eight are chosen at random. Approximately what percentage of the 700 selected numbers are odd?

[ "14.29%", "15.29%", "16.29%", "17.29%", "18.29%" ]

--> Multiples of 7 are 7, 14, 21, 28, 35, 42.... Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd. So approx. 50 % of the 200 multiples are odd i.e 100 multiples. --> Similalrly, for 8 multiples are:8,16,24... All are even so 0 % are odd. Total odd= (100+0)/(200+500)= 100/700=1/7 = 14.29% Answer A The answer is: A

A

mathematics

If the first day of a year (other than leap year) was Sunday, then which was the last day of that year?

[ "Saturday", "Sunday", "Tuesday", "Monday", "None of these" ]

Explanation : Given that first day of a normal year was Sunday Odd days of the mentioned year = 1 (Since it is an ordinary year) Hence First day of the next year = (Sunday+ 1 Odd day) = Monday Therefore, last day of the mentioned year = Sunday. Answer : Option B The answer is: B

B

mathematics

If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:

[ "2.87", "2.965", "3.876", "3.9", "4.526" ]

log5 512 = log 512/ log 5 = log 2^9/log(10/2) =9 log 2 /log 10 - log 2 =(9*0.3010)/1-0.3010 =2.709/0.699 = 2709/699 = 3.876 ANSWER C The answer is: C

C

mathematics

Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?

[ "17/25", "17/24", "17/29", "17/20", "17/21" ]

n(S) = 20 n(Even no) = 10 = n(E) n(Prime no) = 8 = n(P) P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20 Answer: D The answer is: D

D

mathematics

Two men and three women working 7 hours a day finish a work in 5 days. Four men and four women working 3 hours a day complete the work in 7 days. The number of days in which only 7 men working 4 hours a day will finish the work is?

[ "6 days", "2 days", "7 days", "5 days", "1 days" ]

D 2M + 3W ----- 35 h 4M + 4W ------- 21 h 7M -------? d 70M + 105W = 84M +84M 21W = 14M => 2M = 3W 4 * 35 = 7 * x => x = 20 hours 20/4 = 5 days The answer is: D

D

mathematics

For any number s, s* is defined as the greatest positive even integer less than or equal to s. What is the value of 5.2 – 5.2*?

[ "0.2", "1.2", "1.8", "2.2", "4.0" ]

Since s* is defined as the greatest positive even integer less than or equal to s, then 5.2* = 4 (the greatest positive even integer less than or equal to 5.2 is 4). Hence, 5.2 – 5.2* = 5.2 - 4 = 1.2 Answer: B. The answer is: B

B

mathematics

Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 8 sec, then the speed of each train is?

[ "54", "77", "36", "88", "21" ]

Let the speed of each train be x m/sec. Then, relative speed of the two trains = 2x m/sec. So, 2x = (120 + 120)/8 => x = 15 Speed of each train = 15 m/sec. = 15 * 18/5 =- 54 km/hr.Answer: A The answer is: A

A

mathematics

In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to reach the target of 282 runs?

[ "6.25", "6.22", "6.29", "6.39", "6.13" ]

Required run rate = [282 - (3.2 * 10)]/40 = 250/40 = 6.25 Answer: A The answer is: A

A

mathematics

How many of the following numbers are divisible by 132 ? 264, 396, 462, 792, 968, 2178, 5184, 6336

[ "1", "4", "5", "7", "3" ]

B By using your calculator you can calculate that the following numbers are divisible by 132 : 264, 396, 792 and 6336. Required number of number = 4. The answer is: B

B

mathematics

If 2x = 3y = 10, then 6xy = ?

[ "100", "200", "120", "40", "20" ]

2x = 10;x=5 3y = 10;y=10/3 Multiply: 6xy=6*5*10/3=100 Answer: A. The answer is: A

A

mathematics

If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many B such committees are possible?

[ "B=20", "40", "50", "B=80", "120" ]

Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10. But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8. Total # of ways: 5C3*2^3=80. Answer: D. The answer is: D

D

mathematics

Express 25 mps in kmph?

[ "22", "87", "90", "77", "22" ]

25 * 18/5 = 90 kmph Answer: C The answer is: C

C

mathematics

John and Peter are among the eight players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?

[ "7/15", "11/20", "14/25", "15/28", "16/35" ]

The total possible ways of selecting a 6-member team is 8C6 = 28 The possible ways which include John and Peter is 6C4 = 15 The probability of choosing both John and Peter is 15/28 The answer is D. The answer is: D

D

mathematics

The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Re. 1. The sum (in Rs. ) is?

[ "625", "286", "266", "191", "811" ]

Explanation: Let the sum be Rs. x. Then, [x (1 + 4/100)2 - x] = (676/625 x - x) = 51/625 x S.I. = (x * 4 * 2)/100 = 2x/25 51x/625 - 2x/25 = 1 or x = 625. Answer: A The answer is: A

A

mathematics

By selling an article at Rs.120, a profit of 25% is made. Find its cost price?

[ "s.96", "s.45", "s.120", "s.180", "s.189" ]

SP = 120 CP = (SP)*[100/(100+P)] = 120* [100/(100+25)] = 120* [100/125] = Rs.96 Answer: A The answer is: A

A

mathematics

If a, t, and c are consecutive even integers and a < t < c, all of the following must be divisible by 4 EXCEPT

[ "a + c", "t + c", "ac", "(bc)/2", "(abc)/4" ]

I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian. The 3 numbers can be written as a, (a + 2)(a + 4). If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2. A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s. C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization. D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer. E - atc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C. B - b + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization. As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B The answer is: B

B

mathematics

If the side of a square is increased by 55%, its area is increased by?

[ "140%", "145%", "150%", "160%", "none of these" ]

Since Side x Side = Area Therefore, net% change in area = ( x + y + xy/100) % = [55 + 55 + (55 x 55)/100]% or 140.25% Therefore, area is increased by 140.25% ANSWER:A The answer is: A

A

mathematics

Rectangle A has sides a and b, and rectangle B has sides c and d. If a/c=b/d=3/5, what is the ratio of rectangle A’s area to rectangle B’s area?

[ "5/3", "9/5", "9/25", "3/5", "25/9" ]

The area of rectangle A is ab. c=5a/3 and d=5b/3. The area of rectangle B is cd=25ab/9. The ratio of rectangle A's area to rectangle B's area is ab / (25ab/9) = 9/25. The answer is C. The answer is: C

C

mathematics

Let p and q be the root of the quadratic equation x2 - (∝ - 2)x - ∝ -1 =0. what is the minimum possible value of p2 + q2 ?

[ "0", "3", "4", "5", "6" ]

Explanation : p + q = α –2 and pq = –α – 1 (p + q)2 = p2 + q2 + 2pq, Thus (α –2)2 = p2 + q2 + 2(–α – 1) p2 + q2 = α2 – 4α + 4 + 2α + 2 p2 + q2 = α2 – 2α + 6 p2 + q2 = α2 – 2α + 1 + 5 p2 + q2 = (α – 1)2 + 5 Thus, minimum value of p2 + q2 is 5. Answer : D The answer is: D

D

mathematics

I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?

[ "200", "600", "300", "800", "1000" ]

Let x be the number I chose, then x/5−154=6 x/5=160 x=800 correct answer D The answer is: D

D

mathematics

12 chairs are arranged in a row and are numbered 1 to 12. 4 men have to be seated in these chairs so that the chairs numbered 1 to 8 should be occupied and no two men occupy adjacent chairs. Find the number of ways the task can be done.

[ "360", "384", "432", "470", "None" ]

Solution: Given there are 12 numbered chairs, such that chairs numbered 1 to 8 should be occupied. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. The various combinations of chairs that ensure that no two men are sitting together are listed. (1, 3, 5,__), The fourth chair can be 5,6,10,11 or 12, hence 5 ways. (1, 4, 8, __), The fourth chair can be 6,10,11 or 12 hence 4 ways. (1, 5, 8, __), the fourth chair can be 10,11 or 12 hence 3 ways. (1, 6, 8,__), the fourth chair can be 10,11 or 12 hence 3 ways. (1,8,10,12) is also one of the combinations. Hence, 16 such combinations exist. In case of each these combinations we can make the four men inter arrange in 4! ways. Hence, the required result =16*4!= 384. Answer: Option B The answer is: B

B

mathematics

Jake bought oranges at the supermarket for Y dollars an orange and sugar for M dollars per kilogram. Then, he made lemonade using P oranges and Q kgs of sugar per liter and he sold Z liters of lemonade for X dollars per liter. How much money has he made after selling all the lemonade?

[ "ZX(PY+QM)", "ZPM-ZQY", "XZ-PYZ-QMZ", "XZ-(MQ-YP)", "XQ-PY+ZM" ]

First, the cost of the lemonade per liter= PY+QM dollars Since Jake sold Z liters of lemonade, the cost price= Z(PY+QM) dollars The selling price=ZX dollars Profit=ZX-Z(PY+QM) =(X-PY-QM)Z The answer is C!! The answer is: C

C

mathematics

If S is the product of all positive integers less than 31, than what is the greatest integer k for which S/18^k is an integer?

[ "3", "6", "7", "14", "26" ]

30! S must be divisible by (3*3*2)^k. As I will find a lot of 2's among 30!'s factors I will focus on the 3's (that also occurs twice instead of only once as a factor in 18). Every multiple of 3 will provide me with atleast one factor of 3. There aren't that many so I list them quickly. 3 6 9* 12 15 18* 21 24 27** 30 The stars are marked as they are multiples of 9* or 27** and thus provides two or three 3's respectively. 3=3 (occurs 10 times) +10 3*3=9 (occurs 3 times) +3(adding just one additional three each as they were not counted for in the multiples of 3) 3*3*3=27 (occurs 1 time) +1 (again, adding just one as they were previously not counted) Total: 14. For every k we add two 3's. So we must divide 14 by 2 to get the highest integer K before we receive a non-integer result. Answer: 7 -> Answer choice: C. The answer is: C

C

mathematics

6x − 12 = 6y 4y + 4x = 12 Which of the following is the number of solutions to the system of equations shown above?

[ "More than three", "Exactly one", "Exactly two", "Exactly three", "None" ]

6x − 12 = 6y => 6x - 6y = 12 => x- y =2 -- 1 4y + 4x = 12 =>x + y = 3 -- 2 From equation 1 and 2 , we get 2x = 5 => x=2.5 y=.5 Therefore , the given system will have Exactly one solution Answer : B The answer is: B

B

mathematics

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 41 kg, then the weight of B is:

[ "27 kg", "20 kg", "26 kg", "31 kg", "35 kg" ]

let d sum of a, b, c is 3*45=135 and sum of a and b s 2*40=80 sum of b and c is 2*41=82 hence 80+82-135=27 ans=27 ANSWER:A The answer is: A

A

mathematics

If x > 1, which of the following decreases as x decreases? I. x + x^3 II. 2x^2 − x III. 1/(x + 1)

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

let x= 4 and 3 b old and new values ST1: x= 4 -> 4+64 = 68 x=3-> 3+27= 30 ...decreased ST2:x= 4-> 2*16-4 = 28 x=3->2*9-3 = 15 decreased St3: x=4-> 1/4 = .25 x=3->1/3 = .33 Ans: E The answer is: E

E

mathematics

John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?

[ "50 ml", "60 ml", "70 ml", "80 ml", "90 ml" ]

concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1) concentration of water in pure water= 1 ...(2) Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3 => concentration of water in mixture2 =310 By rule of alligation, concentration of water in mixture1 (29) concentration of water in pure water (1) Mean concentration (310) 1−310=710 310−29=790 => Quantity of mixture1 : Quantity of water =710:790=110:190=1:19 Given that Quantity of mixture1 = 630 ml => 630 : Quantity of water =1:19 => Quantity of water =630×19=70 ml C The answer is: C

C

mathematics

A warehouse is labeling computer inventory with 3-digit codes. Each code is to consist of four digits between the numbers 0 and 8. The manager is debating whether to allow any 3-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like0025cannot be used. The manager wants to measure the magnitude of the number of 3-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?

[ "981", "1000", "1011", "1101", "200" ]

The number of codes possible if leading zero is allowed = 10*10*10=10^3 The number of codes possible if leading zero is NOT allowed = 8*10*10=9*10^2 The difference = 10^3 - 8*10^2 = 10^2(10-8) = 2*10^2. Answer: E. Similar questions to practice: Hope it helps. The answer is: E

E

mathematics

If the cost of A metres of wire is C rupees, then what is the cost of E metres of wire at the same rate?

[ "Rs. (EC/A)", "Rs. (EC)", "Rs. (C/A)", "Rs. (E/A)", "Rs. (AC/E)" ]

cost of A metres of wire = Rs.C cost of 1 metre of wire = Rs.(C/A) cost of E metre of wire = Rs.(E×C/A)=Rs. (EC/A) ANSWER:A The answer is: A

A

mathematics

If a copier makes 20 copies every 6 seconds, then continues at this rate, how many minutes will it take to make 2,000 copies?

[ "13", "15", "12", "11", "10" ]

20 copies 6 seconds 2000 copies = (2000*6)/20 seconds = 600/60 minutes = 10 minutes Answer : E The answer is: E

E

mathematics

In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 284. What is the sum of all the integers in the sequence?

[ "552", "568", "574", "586", "600" ]

let the first term of the sequence be x since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms) now, sum of first 4 terms =284 or, 4x+12=284 x=272/4=68 Thus the answer can now be calculated by either summing up 68+70+72+... 8th term or s=n/2(2a+(n-1)d =8/2(2*68+(7*2)) =4(136+14)=600 E The answer is: E

E

mathematics

A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,500 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?

[ "25%", "30%", "35%", "40%", "45%" ]

D for me. Let managers comminsion rate be M. m*5000+ 2*0.05*5000=2500 5000*m=2000 m=40/100=40% The answer is: D

D

mathematics

The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs.24. The present worth is

[ "Rs. 480", "Rs. 520", "Rs. 600", "Rs. 960", "None" ]

Solution T.D = (B.G x 100/Rate x Time) = Rs.(24x100 / 10x 2) = Rs.120. P.W = (100 x T.D/Rate x Time) = Rs.(100x120 / 10x 2) = Rs.600. Answer C The answer is: C

C

mathematics

A person lent a certain sum of money at 4% per annum at simple interest and in 8 years the interest amounted to Rs.238 less than the sum lent. What was the sum lent?

[ "228", "350", "289", "500", "821" ]

P - 238 = (P*4*8)/100 P = 350 Answer: B The answer is: B

B

mathematics

What is the greatest number of three digits which is divisible by 8, 16, 32 ?

[ "997", "992", "999", "998", "990" ]

Greatest number of 3 digits = 999 LCM of 8, 16, 32 = 32 999 ÷ 32 = 31, remainder = 7 Hence, greatest number of four digits which is divisible by 8,16,32 = 999 - 7 = 992 answer : B The answer is: B

B

mathematics

Alice can bake a pie in 5 minutes. Bob can bake a pie in 6 minutes. Compute how many more pies Alice can bake than Bob in 60 minutes.

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

Alice can bake 60/5 = 12 pies in 60 minutes. Bob can bake 60/6 = 10 pies in 60 minutes. Alice can therefore bake 12 - 10 = 2 more pies than Bob. correct answer B The answer is: B

B

mathematics

A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1500. The difference between the profit shares of A and C is?

[ "8867", "299", "279", "600", "2612" ]

Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6 And also given that, profit share of B is Rs. 1500 => 5 parts out of 15 parts is Rs. 1500 Now, required difference is 6 - 4 = 2 parts Required difference = 2/5 (1500) = Rs. 600.Answer: D The answer is: D

D

mathematics

It has been raining at the rate of 5 centimeters per hour. If the rain filled a cylindrical drum with a depth of 15 centimeters, and area 300 square centimeters, how long did it take to fill the drum completely?

[ "3 hours", "4 hours 15 minutes", "6 hours", "2 hours 5 minutes", "8 hours" ]

Answer is : A, 3 hours The volume of the drum is irrelevant and only height matters since rain fell all over the city. Thus, it takes only 15 / 5 = 3 hours of rain to fill the drum The answer is: A

A

mathematics

Rs.4500 amounts to Rs.5544 in two years at compound interest, compounded annually. If the rate of the interest for the first year is 12%, find the rate of interest for the second year?

[ "10%", "18%", "19%", "12%", "13%" ]

Let the rate of interest during the second year be R%. Given, 4500 * {(100 + 12)/100} * {(100 + R)/100} = 5544 R = 10% Answer:A The answer is: A

A

mathematics

12 times a positive integer is more than its square by 36, then the positive integer is

[ "6", "10", "11", "12", "14" ]

Explanation: Let the number be x. Then, 12x = x2 + 36 => x2 - 12x + 36 = 0 =>(x - 6)(x - 6) = 0 => x = 6 Answer: A The answer is: A

A

mathematics

A and B walk around a circular track. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 1 rounds per hour and 1 rounds per hour respectively. How many times shall they cross each other before 9.30 a.m. ?

[ "A)5", "B)6", "C)8", "D)3", "E)9" ]

Relative speed = 1 + 1 = 2 rounds per hour. So, they cross each other 2 times in an hour and 1 times in half an hour. Hence, they cross each other 3 times before 9.30 a.m. ANSWER:D The answer is: D

D

mathematics

It is being given that (2^32 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

[ "(2^90 - 1)", "(2^90 + 1)", "(2^96 - 1)", "(2^96 + 1)", "(2^95 + 1)" ]

Let 232 = x. Then, (232 + 1) = (x + 1). Let (x + 1) be completely divisible by the natural number N. Then, (296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N. D) The answer is: D

D

mathematics

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?

[ "11.11 km/hr", "21.11 km/hr", "71.11 km/hr", "81.11 km/hr", "41.11 km/hr" ]

Explanation: Total time taken = (160/64 + 160/8)hrs = 9/2 hrs. Average speed = (320 x 2/9) km.hr = 71.11 km/hr. Answer: C The answer is: C

C

mathematics

Three partners A, B, C in a business invested money such that 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) then, The ratio of their capitals is

[ "63 : 45 : 34", "63 : 54 : 34", "5 : 2 : 1", "63 : 45 : 35", "None of these" ]

Explanation: Let 2(Aâ€™s capital) = 5(Bâ€™s capital) = 10(Câ€™s capital) = Rs.x Then, Aâ€™s capital = Rs x/2, Bâ€™s capital = Rs. x/5 and Câ€™s capital = Rs. x/10 A : B : C = x/2 : x/5 : x/10 5 : 2 : 1 Answer: Option C The answer is: C

C

mathematics

If X and Y are both positive two-digit integers and share no digits, and X > Y, what is the smallest possible value of X - Y?

[ "0", "1", "2", "3", "9" ]

Answer = B = 1 20 - 19 = 30-29 = 40-39 = 50-49 = 1 The answer is: B

B

mathematics

If -5 < x < 7 and -6 < y < 3, which of the following specifies all the possible values of xy?

[ "-42 < xy < 30", "-42 < xy < 24", "-28 < xy < 18", "-24 < xy < 21", "-24 < xy < 24" ]

The least value of xy is a bit more than 7*(-6)=-42 and the largest value of xy is a bit less than (-5)*(-6)=30. Therefore -42 < xy < 30. Answer: A. The answer is: A

A

mathematics

A completes a work in 12 days and B complete the same work in 24 days. If both of them work together, then the number of days required to complete the work will be

[ "8 days", "9 days", "10 days", "12 days", "13 days" ]

If A can complete a work in x days and B can complete the same work in y days, then, both of them together can complete the work in x y/ x+ y days Therefore, here, the required number of days = 12 × 24/ 36 = 8 days. A The answer is: A

A

mathematics

Bunny's brother Sunny is 562 days older to him while his sister Jenny is 75 weeks older to Sunny. If Jenny was born on Tuesday, on which day was Bunny born?

[ "Monday", "Tuesday", "Friday", "Saturday", "Thursday" ]

562-(75*7)=37 37--------7*5=35 remaing 2+tuesday ans:thursday ANSWER:E The answer is: E

E

mathematics

Sravan travelled for 15 hours. He covered the first half of the distance at 45 kmph and remaining half of the distance at 30 kmph. Find the distance travelled by Sravan?

[ "520", "540", "550", "560", "440" ]

Let the distance travelled be x km. Total time = (x/2)/45 + (x/2)/30 = 15 => x/90+ x/60 = 15 => (2x + 3x)/180 = 15 => x = 540 km Answer:B The answer is: B

B

mathematics

In how many different number of ways 4 boys and 2 girls can sit on a bench?

[ "600", "640", "720", "740", "760" ]

npn = n! 6p6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 C) The answer is: C

C

mathematics

When positive integer k is divided by 5, the remainder is 2. When k is divided by 6, the remainder is 5. If k is less than 38, what is the remainder when k is divided by 7?

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

Cant think of a straight approach but here is how I solved it: K is divided by 5 and remainder is 2. This means k = 5n + 2 (n is an integer) so the possible values of K = {2, 7, 12, 17, 22, 27, 32, 37} (less than 38) Secondly, if K is divided by 6, the remainder is 5 => k= 6m + 5 so the possible value set for k = {5, 11, 17, 23, 29,35} (less than 38) 17 is the only common number in both the sets. Hence k = 17 Answer : C The answer is: C

C

mathematics

As a treat for her two crying children, a mother runs to the freezer in which she has two cherry ice pops, four orange ice pops, and four lemon-lime ice pops. If she chooses two at random to bring outside to the children, but realizes as she runs out the door that she cannot bring them different flavors without one invariably being jealous of the other and getting even more upset, what is the probability that she has to return to the freezer to make sure that they each receive the same flavor?

[ "1/9", "1/6", "5/18", "4/45", "5/6" ]

Probability of not getting the same flavor -> Favorable -> Cherry - orange [ 2C1 * 4C1 [or simply 2*4 ] or Cherry - lemon [ 2*4] or orange - lemon [4*4] Prob = (2*4 + 2*4 + 4*4 ) / 9C2 = 32/360 = 4/45 Answer -> D The answer is: D

D

mathematics

If log 27 = 1.431, then the value of log 9 is :

[ "0.934", "0.945", "0.954", "0.958", "None of these" ]

Solution Log 27 = 1.431 ⇒ log (33) = 1.431 ⇒ 3 log 3 = 1.431 ⇒ log 3 = 0.477 ∴ log 9 = log (32) = 2 log 3 = (2 × 0.477) = 0.954. Answer C The answer is: C

C

mathematics

Davidson has a corporate proposal. The probability that vice-president Adams will approve the proposal is 0.7. The probability that vice-president Baker will approve the proposal is 0.5. The probability that vice-president Corfu will approve the proposal is 0.4. The approvals of the three VPs are entirely independent of one another. Suppose the Johnson must get VP Adam’s approval, as well as the approval of at least one of the other VPs, Baker or Corfu, to win funding. What is the probability that Johnson’s proposal is funded?

[ "0.8", "0.7", "0.6", "0.5", "0.49" ]

probability of adams approval = 0.7 baker approval =0.5 corfu approval=0.4 proabability of approval is must adam approval and atleast one approval = adam approval*baker approval*corfu approval(approval of both remaining)+adam approval*baker approval*corfu not approval(atleast one remaining approval)+ adam approval*baker not approval*coffu approval( atleast one remaining approval = 0.7*0.5*0.4+0.7*0.5*0.6+0.7*0.5*0.4 =0.14+0.21+0.14 =0.49 E The answer is: E

E

mathematics

If 50 percent of X is 25 percent of Y, then what is the relation between X and Y?

[ "X=Y", "2X=Y", "X=2Y", "1", "NONE OF ABOVE" ]

50/100(X) = 25/100(Y) 2X=Y.. Option B. The answer is: B

B

mathematics

A mixture of 125 gallons of wine and water contains 20% of water. How much water must be added to the mixture in order to increase the percentage of water to 25% of the new mixture?

[ "10 gallons", "8.5gallons", "8gallons", "8.33gallons", "9.33gallons" ]

In 125 gallons of the solution there are 0.2∗125=25 gallons of water. We want to add w gallons of water to 125 gallons of solution so that 25+w gallons of water to be 25% of new solution: 25+w=0.25(125+w) --> w=253≈8.33. ANSWER:D The answer is: D

D

mathematics

Robert walks from point A to point B at an average speed of 10 kilometers per hour. At what speed, in kilometers per hour, must Robert walk from point B to point A so that her average speed for the entire trip is 12 kilometers per hour?

[ "15km/hr", "21km/hr", "16km/hr", "20km/hr", "17km/hr" ]

Let's suppose that speed while returning was x km/h Since the distance is same, we can apply the formula of avg speed Avg speed= 2S1S2/S1+S2 12= 2*10*x/10+x x= 15 km/hr answer is A The answer is: A

A

mathematics

If books bought at prices ranging from Rs. 250 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?

[ "23267", "1400", "1800", "2778", "76611" ]

Explanation: Least Cost Price = Rs. (250 * 8) = Rs. 2000. Greatest Selling Price = Rs. (425 * 8) = Rs. 3400. Required profit = Rs. (3400 - 2000) = Rs. 1400. Answer: B) 1400 The answer is: B

B

mathematics

If a 3 cm cube is cut into 1 cm cubes, then what is the percentage increase in the surface area of the resulting cubes?

[ "40%", "100%", "150%", "200%", "300%" ]

The area A of the large cube is 3*3*6 = 54 square cm. The area of the 27 small cubes is 27*6 = 54*3 = 3A, an increase of 200%. The answer is D. The answer is: D

D

mathematics

Cost of 16 mirror and 8 comb is Rs.352 and the cost of 4 mirror and 4 comb is Rs.96. Find the cost of each mirror?

[ "10", "12", "20", "21", "22" ]

Let the cost of each pen and pencil be 'p' and 'q' respectively. 16m + 8c = 352 --- (1) 4m + 4c = 96 8m + 8c = 192 --- (2) (1) - (2) => 8p = 160 => m = 20 C The answer is: C

C

mathematics

How many integers between 1 and 1,800 are divisible by 20,30,40?

[ "14", "15", "16", "17", "18" ]

LCM of the given numbers=120 Therefore , number of integers = 1800/120 =15 Option B is answer The answer is: B

B

mathematics

Today is Varun's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?

[ "33", "98", "25", "29", "27" ]

Explanation: Let Varun's age today = x years. Then, Varun's age after 1 year = (x + 1) years. Therefore x + 1 = 2 (x - 12) x + 1 = 2x - 24 x = 25 Answer: C) 25 years The answer is: C

C

mathematics

Difference between the length &breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is?? We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103?

[ "1245 m^2", "1345 m^2", "2520 m^2", "2560 m^2", "2678 m^2" ]

Solving the two equations, we get: l = 63 and b = 40. Area = (l x b) = (63 x 40) m2 = 2520 m^2 C The answer is: C

C

mathematics

If a certain sample of data has a mean of 25.0 and a standard deviation of 2.0, which of the following pairs contain two values that are each at least 2.5 standard deviations from the mean?

[ "(19.0; 26.5)", "(14.5; 28.0)", "(23.0; 28.5)", "(22.5; 26.0)", "(19.0; 30.5)" ]

The standard deviation is 2, so 2.5 standard deviations would be (2.5)(2) = 5. The values between 20 and 30 are within 2.5 standard deviations from the mean. The answer is E. The answer is: E

E

mathematics

A bag contains 7 red, 2 green balls. 3 balls are drawn randomly. What is the probability that balls drawn contain exactly two green balls?

[ "1/7", "2/9", "1/12", "4/17", "2/3" ]

Total number of balls = 7+2 = 9 n(S) = 9C3 = 9*8*7 / 3*2 = 84 n(E) = 2C2* 7C1 = 7 Probability = 7/84 = 1/12 Answer is C The answer is: C

C

mathematics

What approximate value should come in place of question mark (?) in the following equation 287.532 + 1894.029 – 657.48 = 543.095 + ?

[ "870", "790", "980", "770", "890" ]

? = 285 + 1895 – 655 – 545 or, ? = 980 Answer C The answer is: C

C

mathematics

Smitha bought 8 Kg of kiwi fruit at an average rate of 360.If she returned 3.5kg to the retailer,at an average rate of remaining fruit was 202.5, Then what is the average price, of the returned 3.5 Kgs ?

[ "41.5", "43", "42", "45", "47.3" ]

Total price of 8Kg kiwi fruit=8*45=360 Total price of 4.5Kg kiwi fruit=4.5*45=202.5 Total price of 3.5Kg kiwi fruit=360-202.5=157.5 Average price of 3.5 Kgs kiwi fruit= 157.5/3=45 Correct option Answer:D The answer is: D

D

mathematics

Aman started a business investing Rs. 60,000. Rakhi joined him after six months with an amount of Rs. 1,05,000 and Sagar joined them with Rs. 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?

[ "12:15:18", "72:105:112", "52:105:112", "62:105:112", "12:105:112" ]

Explanation: Aman : Rakhi : Sagar = (60000 * 36) : (105000 * 30) : (140000 * 24) = 72:105:112 Answer: B The answer is: B

B

mathematics

Sixty men can stitch 200 shirts in 30 days working 8 hours a day. In how many days can 45 men stitch 300 shirts working 6 hours a day?

[ "70", "90", "60", "80", "10" ]

D 80 We have M1 D1 H1 / W1 = M2 D2 H2 / W2 (Variation rule) (60 * 30 * 8)/ 200 = (45 * D2 * 6) / 300 D2 = (60 * 30 * 8 * 300) / (200 * 45 * 6) => D2 = 80. The answer is: D

D

mathematics

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?

[ "7 3/8 km", "5 7/8 km", "17 7/8 km", "7 7/8 km", "2 7/8 km" ]

RS = 6 ¾ - 4 ½ = 2 ¼ T = 3 ½ h. D = 9/4 * 7/2 = 63/8 = 7 7/8 km ANSWER:D The answer is: D

D

mathematics

For any positive number x, the function [x] denotes the greatest integer less than or equal to x. For example, [1] = 1, [1.267] = 1 and [1.999] = 1. If k is a positive integer such that k^2 is divisible by 45 and 80, what is the units digit of k^3/4000 ?

[ "0", "0", "27", "54", "Cannot be determined" ]

K=[lCM of 80 and 45] * (any integer) however minimum value of k is sq.rt of 3^2*4^2*5^2 = 60 * any integer for value of k(60) * any integer unit value will be always zero . B The answer is: B

B

mathematics

Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?

[ "5 km", "10 4/3 km", "4 3/8 km", "18 km", "6 km" ]

Explanation: RS = 5 ¾ - 4 ½ = 1 ¼ T = 3 ½ h. D = 5/4 * 7/2 = 35/8 = 4 3/8 km C) The answer is: C

C

mathematics

In how many different ways can the letters of the word "CORPORATION" be arranged in such a way that no two vowels are together?

[ "6!/2!∗C57∗5!3!", "4!/2!∗C57∗5!3!", "6!/2!∗C57∗6!3!", "3!/2!∗C57∗5!3!", "12!/2!∗C57∗5!3!" ]

Step 1: Separate consonants with 7 empty slots *C*R*P*R*T*N*. Step 2: 6 consonants CRPRTN can be arranged in 6!/2! ways (6 letters with two R's); Step 3: we have 5 vowels OOAIO. Choose 5 slots out of 7 for them (this way no two vowels will be together): C57 Step 4: 5 vowels in their slots can be arranged in 5!/3! ways (5 letters with three O's). Total = 6!/2!∗C57∗5!3! Answer: A The answer is: A

A

mathematics

A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?

[ "Rs.14000", "Rs.1000", "Rs.10500", "Rs.2050", "Rs.5500" ]

Explanation: 25*12: 30*12: 35*8 15:18:14 14/47 * 47000 = Rs.14000 ANSWER:A The answer is: A

A

mathematics

If in k+1 years from now John will be m years old, then how old was John t-1 years ago?

[ "m-k-t", "m+k-t+2", "m+k-t+1", "k-m-t+2", "k+t-m" ]

Age t-1 years ago is m - k - 1 - ( t - 1 ) Or, Age t-1 years ago is m - k - 1 - t + 1 Or, Age t-1 years ago is m - k - t Hence, Answer will definitely be (A) m - k - t The answer is: A

A

mathematics

The average earning of amechanic for the first 4days of a week is Rs.25 and for the last four days is Rs.22. If heearns Rs.20 on the fourth day, his average earning forthe whole week is?

[ "s. 10", "s. 24", "s. 30", "s. 40", "s. 50" ]

Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day = 4 x 25+ 4 x 22 -20 = Rs. 168 âˆ´ Average earning = 168/ 7 = Rs. 24 B The answer is: B

B

mathematics

x, y and z are consecutive positive integers such that x < y < z; which of the following must be true? 1. xyz is divisible by 6 2. (z-x)(y-x+1) = 4 3. xy is even

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

Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1 Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 3 so xyz would be divisible by 6. Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence true. So, I II and III are always true and hence answer is E. The answer is: E

E

mathematics

if 5x*x+14*x+k=0 having two reciprocal roots find the value of k.

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

Product of reciprocal roots =1 Product of roots of quadratic eqn ax^2+bx+c = 0 is c/a. Hence k/5 =1 k=5 ANSWER:E The answer is: E

E

mathematics

If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?

[ "100 men", "101 men", "102 men", "103 men", "104 men" ]

C 102 men From the above formula i.e (m1*t1/w1) = (m2*t2/w2) so, (34*8*9/(2/5)) = (x*6*9/(3/5)) so, x = 136 men number of men to be added to finish the work = 136-34 = 102 men The answer is: C

C

mathematics

If 3a = 4b and ab ≠0, what is the ratio of a/4 to b/3?

[ "64/27", "9/16", "1", "6/8", "8/6" ]

A nice fast approach is the first find a pair of numbers that satisfy the given equation: 3a = 4b Here's one pair: a =4 and b =3 What is the ratio of a/9 to b/8? In other words, what is the value of (a/4)/(b/3)? Plug in values to get: (a/4)/(b/3) = (4/4)/(3/3) = 1/1 = 1 C The answer is: C

C

mathematics

A is B's sister. C is B's mother. D is C's father. E is D's mother. Then, how is A related to D?

[ "Grandfather", "Daughter", "Grandmother", "Granddaughter", "SISTER" ]

A is the sister of B and B is the daughter of C. So, A is the daughter of C. Also, D is the father of C. So, A is the granddaughter of D. Answer: D The answer is: D

D

mathematics

The tax on a commodity is diminished by 20% but its consumption is increased by 10%. Find the decrease percent in the revenue derived from it?

[ "11%", "82%", "14%", "12%", "17%" ]

100 * 100 = 10000 80 * 110 = 8800 10000------- 1200 100 ------- ? = 12% Answer:D The answer is: D

D

mathematics

17200 x 223 + 17200 x 77 = ?

[ "2736900", "2738800", "2658560", "5160000", "None of them" ]

=17200 x (223+77) (by distributive law) =17200 x 300 =5160000 Answer is D The answer is: D

D