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	Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together?	[ "1.5", "2", "2.4", "3", "3.6" ]	Answer is 3.6 hours. Tom does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6 answer is E The answer is: E	E
mathematics	In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 54, the dividend is:	[ "6324", "7344", "8336", "9356", "9400" ]	Divisor = (5 * 54) = 270 = 10 * Quotient = Divisor => Quotient = 270/10 = 27 Dividend = (Divisor * Quotient) + Remainder Dividend = (270 * 27) + 54 = 7344. B The answer is: B	B
mathematics	What is 0.05 percent of 12,356?	[ "0.6178", "61.78", "6.178", "0.06178", "0.006178" ]	Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.05(1/100)12,356. The answer is 6.178. Hence, the correct answer is C. The answer is: C	C
mathematics	When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 9 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?	[ "30", "34", "42", "46", "55" ]	Total # of students 26+28+18-(9+7+10)+9=55. Answer: E. The answer is: E	E
mathematics	Four people need to cross a dark river at night. * They have only one torch and the river is too risky to cross without the torch. * If all people cross simultaneously then torch light wont be sufficient. * Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes. What is the shortest time needed for all four of them to cross the river ?	[ "16 minutes", "17 minutes", "18 minutes", "19 minutes", "20 minutes" ]	Solution: 17 min The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question. Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together. 1 and 2 go cross 2 comes back 7 and 10 go across 1 comes back 1 and 2 go across (done) Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes Answer B The answer is: B	B
mathematics	A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?	[ "75%", "25%", "28%", "85%", "28%" ]	800 --- 200 100 --- ? => 25% Answer: B The answer is: B	B
mathematics	In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?	[ "16", "8", "1", "1/8", "1/64" ]	Say r=1 => V1 = 1/8 when r=1/2; V2 = 1 V2 = 1*V1. Answer : B The answer is: B	B
mathematics	At what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price?	[ "65.25", "62.6", "62.1", "62.7", "62.2" ]	CP = 47.50 SP = 47.50(125/100) = 59.375 MP(91/100) = 59.375 MP = 65.25 Answer: A The answer is: A	A
mathematics	Which of the following inequalities is equivalent to –2 < x < 4 ?	[ "\| x – 2 \| < 4", "\| x – 1 \| < 3", "\| x + 1 \| < 3", "\| x + 2 \| < 4", "None of the above" ]	First remove the mod then set the expression to 0 then get a value of X then add and subtract the value from the given number on the RHS Lets try with an example (B) --------------> \| x – 1 \| < 3 First remove the mod -------------------> x-1 then set the expression to 0--------------> x-1=0 then get a value of x---------------------> x=1 then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2 the range become -2 to 4 correct answer Now try its with an incorrect option (C) \| ----------> \|x + 1 \| < 3 First remove the mod --------------------------> x+1 then set the expression to 0----------------------> x+1=0 then get a value of x------------------------------> x=-1 then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4 the range become -4 to 2 Incorrect THE CORRECT ANSWER IS B The answer is: B	B
mathematics	How many of the positive divisors of 600 are also multiples of 4 not including 600?	[ "6", "8", "9", "11", "12" ]	600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2 Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2. There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4. We must subtract 1 because one of these multiples is 600. The answer is D. The answer is: D	D
mathematics	If the sides of a cube are in the ratio 5:4. What is the ratio of their diagonals?	[ "4:3", "5:4", "4:7", "3:4", "4:5" ]	Explanation: Diagonal of a Cube=a√3 where a is side a1:a2 = 5:4 d1:d2 = 5:4 where√3 cancelled both side ANSWER:B The answer is: B	B
mathematics	The L.C.M. of two numbers is 54. The numbers are in the ratio 2 : 3. Then sum of the number is:	[ "28", "32", "40", "45", "54" ]	Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 54 or x = 9. The numbers are 18 and 27. Hence, required sum = (18 + 27) = 45. Answer: Option D The answer is: D	D
mathematics	The list price of an article is Rs.70. A customer pays Rs.61.74 for it. He was given two successive discounts, one of them being 10%. The other discount is?	[ "8%", "7%", "10%", "2%", "4%" ]	Explanation: 70(90/100)((100-x)/100) = 61.74 x = 2% Option D The answer is: D	D
mathematics	A trader bought a car at 20% discount on its original price. He sold it at a 30% increase on the price he bought it. What percent of profit did he make on the original price?	[ "A)4%", "B)12%", "C)14%", "D)20%", "E)22%" ]	Original price = 100 CP = 80 S = 80*(130/100) = 104 100 - 104 = 4% A) The answer is: A	A
mathematics	In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount R in 1996 as they paid in 1995?	[ "33 1⁄3%", "40%", "50%", "66 2⁄3%", "100%" ]	water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount R in 1996 as they paid in 1995, water use should decrease in the same ratio 150-> 100 means 1/3 rd= 33(1/3) %.A The answer is: A	A
mathematics	If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2(x+ y) > 2z III. yz > xz IV. xy > y + z	[ "I only", "II only", "II and III only", "II and IV only", "III and IV only" ]	we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2(x+ y) > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B The answer is: B	B
mathematics	A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage	[ "10% Gain", "10% Loss", "20% Loss", "25% Loss", "30% Loss" ]	Formula = (Selling price ~ Cost price)/Cost price * 100 = (810 ~ 900)/900 = 10% Loss B The answer is: B	B
mathematics	Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 28,000. What was Simran's share in the profit?	[ "Rs. 9423", "Rs. 10,250", "Rs. 12,000", "Rs. 14,000", "None of these" ]	Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 28000 * 3/7 = Rs. 12000 ANSWER:C The answer is: C	C
mathematics	There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?	[ "5/4", "5/7", "5/3", "5/8", "5/1" ]	Let the two numbers be x and y. 20/100 * x + y = 5/4y => 1/5 x = 1/4 y => x/y = 5/4 Answer: A The answer is: A	A
mathematics	Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.	[ "2300", "3300", "4300", "1300", "None of them" ]	Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months. So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3) = 540000 : 540000 : 270000 = 2 : 2 : 1. Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600 Peter's share = Rs. (16500 x (2/5)) = Rs. 6600 Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300. Answer is B. The answer is: B	B
mathematics	A girl has 7 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?	[ "A)100", "B)102", "C)108", "D)110", "E)84" ]	The girl can select one jeans in 7 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 7 * 12 = 84 ways. E The answer is: E	E
mathematics	A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1620 are infected, how manyworkersinhabit the colony?	[ "1500", "2500", "2750", "3000", "3250" ]	From two question we get wo equations: (1) 0,3s + 0,14w = 1620 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1620 0,16s=640 64000:16= 4000 =s In (2) 4000 + w = 7000 w= 3000 D The answer is: D	D
mathematics	Lakshmi went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 20%. then what was the cost of the tax free items?	[ "Rs. 197", "Rs. 190", "Rs. 187", "Rs. 167", "Rs. 191" ]	Solution Let the amount of taxable purchases be Rs.x. Then, 20% of x = 50/100 x ‹=› (50/100×100/20) = 2.50 Cost of tax free items = Rs.[200 - (2.50 + 0.50)] = Rs. 197 Answer A The answer is: A	A
mathematics	A man can row with a speed of 12 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?	[ "22", "28", "20", "82", "23" ]	M = 12 S = 11 DS = 12 + 11 = 23. Answer:E The answer is: E	E
mathematics	If \|x + 10\| = 10 what is the sum of all the values of x.	[ "20", "40", "-20", "0", "-40" ]	There will be two cases x+10 = 10 and x+10 = -10 Solve for x => x=10-10=> x=0 or x= -10 - 10 => x= -20 The sum of both values will be 0 + -20 =-20 Answer is C The answer is: C	C
mathematics	Certain stocks in January were 40% less than they were in February and 15% greater than they were in March. What was the percentage decrease in the stocks from February to March?	[ "50.81%", "15.11%", "20.7%", "48.8%", "40%" ]	Let stocks value in Feb = 100 => In Jan = 60 and March = 60 * 100/115 = 51.2% Thus, percent decrease in stocks from Feb to March = 100 - 51.2 = 48.8% Hence Answer is D The answer is: D	D
mathematics	Which of the following is closer to √0.8+√0.1?	[ "0.5", "0.7", "0.9", "1.1", "1.2" ]	√0.8+√0.1=approximately √0.81+√0.09=0.9+0.3=1.2. Hence, the correct answer is E. The answer is: E	E
mathematics	The sum of the first 80 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?	[ "5,050", "7,500", "10,500", "15,000", "19,600" ]	101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 80 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 80 positive even integers = 2550 sum of 1st 100 odd numbers = 5050 - 2550 = 2500 so 101+103+.......199 = 80 * 100 + (1+3+5+7+......) = 8000 + 2500 =10500 C is the answer. The answer is: C	C
mathematics	Shreyas bought an article and sold it for 105% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42000/-?	[ "Rs.40000", "Rs.45640", "Rs.44250/-", "Rs.43200", "None of these" ]	Explanation: 105% of CP = Rs.42000 :. CP = Rs.42000x100/105 = Rs.40000. Answer: Option A The answer is: A	A
mathematics	A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?	[ "22", "27", "19", "37", "21" ]	16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D The answer is: D	D
mathematics	A gambler has won 40% of his 20 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?	[ "20", "25", "30", "35", "40" ]	Let x be the number of additional games the gambler needs to play. 0.4(20) + 0.8x = 0.6(x+20) 0.2x = 4 x = 20 The answer is A. The answer is: A	A
mathematics	If a, b, c are integers; a² + b² = 45 and b² + c² = 40, then the values of a, b and c respectively are :	[ "2, 6, 3", "3, 2, 6", "5, 4, 3", "4,5,3", "None of these" ]	a² + b² = 45 ….(1) and b² + c² = 40 Subtracting, we get: a² - c² = 5 => (a + c) (a – c) = 5. (a + c) = 5 and (a – c) = 1. Solving we get: a = 3, c = 2. Putting c = 2 in (ii), we get b = 6. ANSWER:B The answer is: B	B
mathematics	What is the diagonal of a square field whose perimeter is 24m?	[ "8 m", "2 m", "7 m", "10 m", "6√2 m" ]	Sol: Let the side of the square be x meters. Therefore, 4x=24 x=6 Diagonal of the square is= √2*(6)^2=6√2 Answer: E The answer is: E	E
mathematics	A garrison of 400 men had a provision for 31 days. After 28 days 300 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?	[ "65 days", "45 days", "10 days", "16 days", "12 days" ]	400 --- 31 400 --- 3 100 --- ? 4003 = 100x => x =12 days. Answer: E The answer is: E	E
mathematics	A, B, C, D, E, F are the only six families in Indira Nagar. A, B, C, D, E and F has 7, 8, 10, 13, 6, and 10 member in their families respectively. If 1 member from all the six families left their respective families to accommodate themselves in the hostel of IIM Lucknow, then the average number of member now in each family of Indira nagar is	[ "8", "9", "10", "13", "15" ]	Answer Required average = (( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + (6 - 1) +( 10 - 1 ) )/ 6 = ( 7 + 8 +10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 =9 - 1 = 8 Correct Option: A The answer is: A	A
mathematics	A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?	[ "9:8", "8:9", "4:9", "2:3", "1:2" ]	The ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4. The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9. Thus, L:S = 4:9. Answer: C. The answer is: C	C
mathematics	Using all the letters of the word "HEAD", how many words can be formed, which begin with H and end with D?	[ "8", "4", "2", "7", "9" ]	There are five letters in the given word. Consider 4 blanks .... The first blank and last blank must be filled with H and D all the remaining three blanks can be filled with the remaining 2 letters in 2! ways. The number of words = 2! = 2. Answer:C The answer is: C	C
mathematics	How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?	[ "6 ways", "7 ways", "9 ways", "11 ways", "13 ways" ]	E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways A) The answer is: A	A
mathematics	What percent of a day is nine hours?	[ "20.83%", "16x1/2%", "18x2/3%", "37.5%", "None of these" ]	Explanation : Required percentage = (9/24100)% = 37.5%. Answer : D The answer is: D	D
mathematics	The sum of five consecutive odd numbers of set p is 435. What is the sum of five consecutive numbers of another set q. Whose largest number is 45 more than the largest number of set p?	[ "530", "670", "730", "770", "None of these" ]	Let the five consecutive odd numbers of set p be 2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5. Sum of these five numbers = 2n - 3 + 2n - 1 + 2n + 1 + 2n + 3 + 2n + 5 = 10n + 5 = 435 => n = 43 Largest number of set p = 2(43) + 5 = 91 The largest number of set q = 91 + 45 = 136 => The five numbers of set q are 132, 133, 134, 135, 136. Sum of above numbers = 132 + 133 + 134 + 135 + 136 = 670. ANSWER:B The answer is: B	B
mathematics	In the line xy plane line m has the equation y = 3x - 9, then the line m passes through which of the following points?	[ "(3, 1)", "(3, 4)", "(4, 2)", "(6, 9)", "(6, 15)" ]	Yes it is y=3x-8....extremely sorry for mistake.... IF that's the case then answer is D y=3x-8 9=3X6-9 9=18-9 9=9 (satisfied) The answer is: D	D
mathematics	39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?	[ "11", "12", "13", "15", "14" ]	First codition=total hours to complete the work=39 persons * 12 days * 5 hr Second codition=total hours to complete the work=30 persons * x days * 6 hr since the work is still the same so 39125=30x6 x=13 answer :C The answer is: C	C
mathematics	A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?	[ "40 days", "20 days", "10 days", "60 days", "40 days" ]	C 10 days C = 1/5 – 1/10 = 1/10 => 10 days The answer is: C	C
mathematics	A man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are	[ "40dozens", "60dozens", "70dozens", "80dozens", "90dozens" ]	let total no of mangoes is 2x.. then we profit=sp-cp 160=13*2x-(12x+10x) 160=4x x=40 hence 2x=80 so total no are 80dozens ANSWER:D The answer is: D	D
mathematics	In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased?	[ "7", "9", "11", "13", "15" ]	We have S = the sum of all integer from 1 to N x = the missing integer So as sum = average * Nb of terms S-x= 27(4/13) * (N-1) (A) As S-x should be an integer N-1 should be a multiple of 13. So we have some possible scenario N-1= 13 => N=14 N-1= 26 => N=17 N-1= 39 => N=40 N-1= 52 => N=53 .... Back to our formula (A) x = S - 27(4/13)(N-1) x = (N(N+1))/2 - 27(4/13)(N-1) As x>0 (N(N+1))/2 > 27(4/13)(N-1) approx 27(4/13) by 27 (N(N+1))/2 > 27(N-1) N(N+1) > 54(N-1) So we see than N=53 is working (indeed 5354>5452) So if N=53: x = (53(54))/2 - 27(4/13)(52) x = (53(54))/2 - (27+4/13)(52) x = (53(54))/2 - 2752-(4/13)52 x = 5327 - 2752-(4/13)52 x = 5327 - 2752-44 x = 27(53-52) - 16 x = 27 - 16 x=11 ANSWER:C The answer is: C	C
mathematics	A series of boxes are placed on a conveyor belt at one end and unloaded at the other. The boxes are each 0.5 meters on each side and are placed immediately adjacent to one another as they are loaded. If the conveyor belt is 30 meters long and moves the boxes at a speed of 0.25 m/s, how long does it take for 100 boxes to be loaded and unloaded?	[ "4 min 30 sec", "4 min 50 sec", "5 min 20 sec", "5 min 40 sec", "6 min 10 sec" ]	C 5 min 20 sec d = 100 * 0.5 m +30 m = 80 m T = 80 m / 0.25 m/s = 320 s = 5 min 20 sec The answer is: C	C
mathematics	The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres?	[ "16 seconds", "76 seconds", "10.8 seconds", "12 seconds", "18 seconds" ]	Speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5/18 = 50/9 m/s Hence time taken to cover 60 m = 60*9/50 = 10.8 seconds. Answer: C The answer is: C	C
mathematics	A group of men decided to do a work in 50days, but 10 of them became absent. If the rest of the group did the work in 60days, Find the original number of men?	[ "60", "50", "40", "100", "25" ]	Original number of men = 10*60 / (60-50) = 60 Answer is A The answer is: A	A
mathematics	An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?	[ "5", "6", "3", "8", "9" ]	Going down = 20 m Going Up = 10 --> Total = 30 Going down = 10 --> Total = 40 Going Up = 5 --> Total = 45 Going down = 5 --> Total = 50 Going up = 2.5 --> Total = 52.5 Going down = 2.5 --> Total =55(Caught) No of bouncing = 3 Answer : C The answer is: C	C
mathematics	Sides of a rectangular park are in the ratio 4: 3 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?	[ "s.132.3", "s.129", "s.125", "s.120", "s.121" ]	4x * 3x = 3750 => x = 17.7 2(82.3 + 50) = 264.6 m 264.6 * 1/2 = Rs.132.3 Answer:A The answer is: A	A
mathematics	A chair is bought for Rs.1000/- and sold at a loss of 20% find its selling price	[ "Rs.800/-", "Rs.510/-", "Rs.515/-", "Rs.530/-", "Rs.540/-" ]	Loss = 1000*20/100 = 200 S.P = C.P - Loss = 1000- 200 =Rs.800/- Answer :A The answer is: A	A
mathematics	33 1/3% of 36?	[ "16", "21", "18", "12 number", "18" ]	Explanation: 33 1/3 % = 1/3 1/3 * 36 = 12 Answer: Option D The answer is: D	D
mathematics	There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point.	[ "(2,10)", "(5,10)", "(7,10)", "(3,10)", "(1,10)" ]	If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A The answer is: A	A
mathematics	There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?	[ "6", "5", "8", "6", "3" ]	Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C The answer is: C	C
mathematics	Marsha and Wenbao picked strawberries one afternoon. They combined all of their strawberries together and divided them evenly (50/50). If Marsha picked an odd number of strawberries which of the following is true?	[ "Wenbao picked 50 strawberries.", "Wenbao picked 49 strawberries.", "Wenbao picked 52 strawberries.", "Wenbao picked 40 strawberries.", "Wenbao picked 56 strawberries." ]	From Parity Mathematics Rule: The sum of two odd numbers is even. The sum of and odd number and an even number is odd. Marsha and Wenbao divided their strawberries evenly (50/50) after adding them together. Marsha picked an odd number of strawberries, so Wenbao had to have picked an odd number of strawberries. Answer: B The answer is: B	B
mathematics	Set Y consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set Y?	[ "767", "76", "7", "5", "1" ]	Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median). Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working.... Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values... Putting the 7 numbers in order, we have: -27, -3, -2, 2, 3, 15, 17 This means that the2will either be the 4th term or the 5th term (depending on the value of N). IF.... N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5 N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0 Neither of those answers is among the choices though, so N must be something relativelycloseto 2..... IF.... N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done. E The answer is: E	E
mathematics	Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?	[ "A)Rs.520", "B)Rs.594", "C)Rs.596", "D)Rs.595", "None of these" ]	Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A The answer is: A	A
mathematics	Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?	[ "565", "444", "676", "456", "663" ]	1h ----- 6 ? ------ 60 12 h RS = 16 + 22 = 38 T = 12 D = 38 * 12 =456 Answer: D The answer is: D	D
mathematics	In a bag there are a certain number of blue balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of blue balls to white balls in the bag	[ "1:1", "1:2", "1:5", "1:4", "1:6" ]	since the probability of drawing a white ball out of two picks is 1/2. the ratio of the white ball to blue balls should be 1:1 Answer : A The answer is: A	A
mathematics	The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?	[ "46", "83", "45", "53", "64" ]	Sum of all the 13 numbers = 13 * 60 = 780 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 780 = 46. Answer:A The answer is: A	A
mathematics	If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?	[ "90", "100", "110", "120", "130" ]	The projectiles travel a total of 999 km per hour. The time to meet is 1998/999=2 hours = 120 minutes The answer is D. The answer is: D	D
mathematics	A radio station has to choose one day of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?	[ "7", "15", "21", "35", "56" ]	Behind the story, we are really being asked to evaluate 7C1. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C1, the third entry of the seventh row, is 7. Answer = A. The answer is: A	A
mathematics	The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?	[ "50", "55", "60", "65", "70" ]	Look at the options available Value of x seems to 50 < = x < = 70 A. 50 B. 55 C. 60 D. 65 E. 70 So position of x is second 30 , x , 80 , 90 , 100 Median = 80 Median number of apples was 10 points higher than the average, so average = 70 30 + x + 80 + 90 + 100 = 350 x = 50 = Answer = A The answer is: A	A
mathematics	A and B are mixed together in the ratio 9 : 11. What is the weight of mixture, if 26.1 kg of A has been consumed in it?	[ "56", "45", "58.2", "58", "46" ]	Explanation : For 9 kg A, mixture = (9 + 11) kg. For 26.1 kg A, mixture = ((20/9) x 26.1)kg = 58 kg. Answer : D The answer is: D	D
mathematics	Which one the following fractions has the Lowest value?	[ "A)488/850", "B)499/850", "C)477/850", "D)511/850", "E)501/850" ]	All options have the same denominator 850. If denominator is same, the fraction with the lowest value will be the one with the Lowest numerator. Answer (C). The answer is: C	C
mathematics	Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?	[ "$600", "$1000", "$3800", "$5300", "$6200" ]	Pay out for plan A: Cost-$1,000 or Cost-0.5Cost=0.5Cost, when 0.5Cost<$1,000; Pay out for plan B: 0.8(Cost-$300); The question is: for which of the following costs the pay outs are the same. C-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer. Or you can use backsolving for this question: A. C=$600: pay out for plan A will be 0.5600=300 (as 0.5600<1,000) and pay out for plan B will be 0.8(600-300)=240; B. C=$1000: pay out for plan A will be 0.51,00=500 (as 0.51,000<1,000) and pay out for plan B will be 0.8(1,000-300)=560; C. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.53,800>1,000) and pay out for plan B will be 0.8(3,800-300)=2,800 --> 2,800=2,800; D. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.55,300>1,000) and pay out for plan B will be 0.8(5,300-300)=4,000; E. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.56,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720. Answer: C. The answer is: C	C
mathematics	Of the mutual funds on a “select list,” 2/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 100 funds on the list have 3-star ratings, how many funds are on the list?	[ "500", "750", "1,000", "1,200", "1,500" ]	A Fraction of 5- and 4-star funds: 2/3 + (2/5)(1/3) = 2/3 + 2/15 = 12/15=4/5 Fraction of 3-star funds = 1 - 4/5 = 1/5 (1/5)Total = 100 Total = 500 The answer is: A	A
mathematics	The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8. How many 3s are used in numbering these buildings?Express your answer in base 10	[ "192", "200", "196", "198", "None" ]	Explanation : Number 3 in 1-100 comes 20 times. 101-200-> 20 times 201-300-> 20 times 301-400->120 times 401-500-> 20 times 501-600-> 20 times 601-700-> 20 times 701-800-> 20 times 801-900-> 20 times 901-1000-> 20 times Total times: 300 times (any no. from 1 to 9 except 0 will occur 300 times) 8 based planet.. then 38(2) + 08(1) + 0*8(0) = 192 Answer : A The answer is: A	A
mathematics	Two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?	[ "11 sec", "12 sec", "17 sec", "21 sec", "23 sec" ]	Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/12 = 10 m/sec. Relative speed = 12 + 10 = 22 m/sec. Required time = (120 + 120)/22 = 11 sec. Answer: A The answer is: A	A
mathematics	8,27,64,125,216,???,512	[ "346", "343", "348", "339", "340" ]	it is a series of cubes of numbers.... 8=2^3 27=3^3 64=4^3 125=5^3 216=6^3 512=8^3 So, 7^3=343 is the missing number. ANSWER:B The answer is: B	B
mathematics	There are 50 doors marked with numbers 1 to 50. There are 50 individuals marked 1 to 50. An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. If every individual in the group gets one turn, then how many doors are open at the end?	[ "0", "2", "5", "7", "9" ]	If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors. The doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49 for a total of 7 doors. The answer is D. The answer is: D	D
mathematics	If the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?	[ "6:1", "12:1", "24:1", "36:1", "72:1" ]	Let x be the length of the small cube's side. The total surface area of the small cube is 6x^2. The total surface area of the large cube is 6(6x)^2=216x^2. The ratio of surface areas is 36:1. The answer is D. The answer is: D	D
mathematics	If the average marks of three batches of 62, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is	[ "54.48", "54.68", "54.6", "54.49", "None of these" ]	Explanation: (62Ã—50)+(60Ã—55)+(45Ã—60)/(62+60+45)=54.49 Answer: Option D The answer is: D	D
mathematics	How many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both?	[ "13", "19", "15", "16", "17" ]	for 13: 13...117=139 = 117 for 12: 12...120=1210 =120 but there is one integer 13*12. so N=(9)+(10)=19 B The answer is: B	B
mathematics	The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is	[ "48", "22", "80", "27", "35" ]	Explanation: Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 20. L.C.M. of 16 and 20 = 80. Answer: Option C The answer is: C	C
mathematics	The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?	[ "2000", "2160", "2299", "2778", "2771" ]	Let C.P. be Rs. x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 135 % of Rs. 1600 = 135/100 * 1600 = Rs. 2160. Answer:B The answer is: B	B
mathematics	An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?	[ "1/5", "3/7", "2/5", "5/14", "2/7" ]	Let E and F denote respectively the events that first and second ball drawn are black. We have to find P(E n F) or P (EF). Now P(E) = P (black ball in first draw) = 5/8 Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and three white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred. That is P(F\|E) = 4/7 By multiplication rule of probability, we have P (E n F) = P(E) P(F\|E) = 5/8 × 4/7 = 5/14 D The answer is: D	D
mathematics	A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs.900in the same period of 2 years, What must be the rate of interest?	[ "25%", "10%", "15%", "20%", "30%" ]	Explanation: Given: 800 = (P * R * 2) / 100 S.I. For 1 year = Rs. 400 Thus, (900 – 800) = S.I. on Rs. 400 for 1 year 100 = (400 * R * 1) / 100 R = 25% p.a. ANSWER: A The answer is: A	A
mathematics	Three dice are thrown together, Find the probability of getting a total of atmost 5?	[ "2/35", "1/8", "3/31", "2/9", "5/108" ]	Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216. Number of events of getting a total of atmost 5 = 10 i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2). Therefore, probability of getting a total of atmost 5 P(E) = Number of favorable outcomes/Total number of possible outcome = 10/216 = 5/108 The answer is: E	E
mathematics	A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?	[ "3", "6", "9", "10", "12" ]	221 + 43 = 264/17 = 9 (Remainder) C The answer is: C	C
mathematics	Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 20 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?	[ "a) x minutes", "b) x/2 minutes", "c) 2x/3 minutes", "d) 3x/2 minutes", "e) 2x minutes" ]	Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min. Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km. So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = x/2. hence answer should be B The answer is: B	B
mathematics	Six years hence,a fathers age will be three times his son's age and three years ago the fathers age is nine times as old as his son. the fathers present age is	[ "24 years", "28 years", "30 years", "40 years", "45 years" ]	Let "f" nd "s" be the father's nd son's present age respectively (f+6) = 3(s+6) f=3s+18-6 f=3s+12 f-3 = 9(s-3) f = 9s-27+3 f=9s-24 Equate "f" 9s-24 = 3s+12 6s = 36 s=6 f=3(6)+12 f=30 ANSWER:C The answer is: C	C
mathematics	If x and y are distinct prime numbers less than ten, what must be true about the product of x and y?	[ "xy is even", "xy is odd", "xy < 0", "xy < 36", "xy > 6" ]	Prime numbers less than 10 = 2, 3, 5, 7. x and y can take any oth the values On checking the options A. xy is even xy can be even or odd both B. xy is odd xy can be even or odd both C. xy < 0 Product of two prime numbers can never be < 0 Prime numbers are always positive D. xy < 36 The maximum value of multiplication can be 5*7 = 35. Hence this is true always E. xy > 6 x = 2, y = 3 In this case, xy = 6. FALSE Correct Option: D The answer is: D	D
mathematics	At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/3 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?	[ "12 greater", "17 fewer", "92 fewer", "36 fewer", "44 fewer" ]	Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/3* 480 =160 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 160-68 =92>>> therfore answer is 92 fewer C The answer is: C	C
mathematics	An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:	[ "300 kmph", "360 kmph", "600 kmph", "720 kmph", "750 kmph" ]	Explanation: Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. Required speed =(1200 X 3/5)km/hr = 720 km/hr. ANSWER IS D The answer is: D	D
mathematics	What is the remainder when 3^30 is divided by 5?	[ "0", "1", "2", "3", "4" ]	The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1} 30 has the form 4k+2, so the units digit of 3^30 is 9. The remainder when dividing by 5 is 4. The answer is E. The answer is: E	E
mathematics	Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a + b ?	[ "110", "100", "190", "200", "210" ]	Answer is 10 Yes! there is really a faster way to solve it. Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2 Here A = sum of even ints from 2 to 20, inclusive number of even ints = 10, first int + last int = 2+20 = 22 A = 1022 / 2 = 110 B = sum of odd ints from 1 to 19, inclusive number of odd ints = 10, first int + last int = 1+19 = 20 A = 1020 / 2 = 100 A+B = 110 + 100 = 210 Ans :E The answer is: E	E
mathematics	In a club there are no more than 20 persons. What is the smallest number of fruits that must be brought to the club so that each person receives the same number of fruits?	[ "26", "75", "80", "45", "33" ]	The number of persons is not specified. We are just given that there are no more than 20 persons. If we assume that number of persons is 15 then answer will be B. If we assume that number of persons is 20 then answer will be C because only 80 is divisible by 20. The answer is: C	C
mathematics	Which of the following is closest to (-2/3)^199？	[ "-1", "-1/2", "0", "1", "2" ]	(-2/3)^4 = 16/81 which is already less than 1/2. For larger exponents, the expression will get closer and closer to zero. The answer is C. The answer is: C	C
mathematics	X, Y, W and Z are intezers and the expressing X - Y - Z is even and Y - W - Z is odd. If X is even then which of	[ "W must be odd", "J must be odd", "Y must be odd", "Z must be odd", "F must be odd" ]	Ans. If X is even and X - Y - Z is even then Y and Z both should be odd or both should be even. If Y - W - Z is odd, and Y and Z are also odd W should be odd If Y - W - Z is even, and Y and Z are even then W should be odd. W must be ODD Answer:A The answer is: A	A
mathematics	On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 6) II. (3, 11) III. (5, 4)	[ "I only", "II only", "III only", "I and II", "I, II, and III" ]	Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive. When x = 1, y = 5 lies on the parabola, so (1, 6) will not be enclosed by the parabola and x axis. When x = 3, y = 9 lies on the parabola, so (3, 11) will not be enclosed by the parabola and x axis. When x = 5, y = 5 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis. The answer is C. The answer is: C	C
mathematics	The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.	[ "290 sq cm", "800 sq cm", "209 sq cm", "Cannot be determined", "200 sq cm" ]	Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer: Option D The answer is: D	D
mathematics	Five fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?	[ "6", "8", "12", "16", "20" ]	5*4 = 20 The answer is E. The answer is: E	E
mathematics	Abhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?	[ "9: 13: 26", "9 :12 :13", "8 :14: 24", "12:14:16", "8 :15: 12" ]	Ratio of their investments = 70 × 36 : 105 × 32: 140 × 26 = 9 : 12 : 13 Answer B The answer is: B	B
mathematics	If w,x,y and z are distinct odd positive integers,then the maximum value of the expression (w^2+x^2)*(y^2+z^2) can be divisible by?	[ "2", "3", "5", "8", "10" ]	ANY ODD NUMBER SQUARE WILL GIVE ODD NUMBER ONLY.. SIMILARLY WEN WE ADD 2 ODD NUMBERS WE WILL GET EVEN NUMBER.. WEN WE MULTIPLY 2 EVEN OWE WILL GET EVEN NUBER.. SO THE RESULT OF THE ABOVE EXPRESSION IS AN EVEN NUMBER ONLY.. HENCE IT IS DIVISIBLE BY 2... ANSWER:A The answer is: A	A
mathematics	The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :	[ "15", "16", "18", "20", "None of these" ]	Let the larger number be x. Then, x -12 = 20% of x<>x-(x/5)=12 4x/5=12<=> x=(12∗5)/5=15. Answer :A The answer is: A	A
mathematics	When 6 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?	[ "1", "3", "16", "31", "30" ]	Total outcome is 2^6 = 64 Favourable cases = H_ _ _ _ H The second, third, fourth and fifth places can be occupied by either H or T There are 2^4 =16 ways that can be done. Hence, the correct option is C The answer is: C	C
mathematics	Tough and Tricky questions: Word Problems. In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 5. Based on this information, how many gold coins would there be in this collection after the proposed trade?	[ "50", "60", "180", "200", "300" ]	The correct answer is D. The answer is: D	D
mathematics	If Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously?	[ "5", "8", "4", "7", "6" ]	If Total Work is X. Ram rate of working=X/10 per day. Gohul rate of working=X/15 per day. Rate of work=(x/10)+(x/15)=30X/5X =6 days Answer is option E The answer is: E	E
mathematics	A train 125 m long passes a man running at 5 km/hr in the same direction in which the train is going in 10 sec. The speed of the train is?	[ "33 km/hr", "50 km/hr", "77 km/hr", "65 km/hr", "99 km/hr" ]	Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer:B The answer is: B	B

mathematics

Working alone, Tom finishes cleaning half the house in a third of the time it takes Nick to clean the entire house alone. Tom alone cleans the entire house in 6 hours. How many hours will it take Nick and Tom to clean the entire house if they work together?

[ "1.5", "2", "2.4", "3", "3.6" ]

Answer is 3.6 hours. Tom does the complete house in 6 hours while Nick does it in 9 hours. 1/ (1/6+1/9)= 3.6 answer is E The answer is: E

E

mathematics

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 54, the dividend is:

[ "6324", "7344", "8336", "9356", "9400" ]

Divisor = (5 * 54) = 270 = 10 * Quotient = Divisor => Quotient = 270/10 = 27 Dividend = (Divisor * Quotient) + Remainder Dividend = (270 * 27) + 54 = 7344. B The answer is: B

B

mathematics

What is 0.05 percent of 12,356?

[ "0.6178", "61.78", "6.178", "0.06178", "0.006178" ]

Since, Percent=1/100, what=something(s), and is:=. We can write the question as s=0.05(1/100)12,356. The answer is 6.178. Hence, the correct answer is C. The answer is: C

C

mathematics

When Professor Wang looked at the rosters for this term's classes, she saw that the roster for her economics class (E) had 26 names, the roster for her marketing class (M) had 28, and the roster for her statistics class (S) had 18. When she compared the rosters, she saw that E and M had 9 names in common, E and S had 7, and M and S had 10. She also saw that 9 names were on all 3 rosters. If the rosters for Professor Wang's 3 classes are combined with no student's name listed more than once, how many names will be on the combined roster?

[ "30", "34", "42", "46", "55" ]

Total # of students 26+28+18-(9+7+10)+9=55. Answer: E. The answer is: E

E

mathematics

Four people need to cross a dark river at night. * They have only one torch and the river is too risky to cross without the torch. * If all people cross simultaneously then torch light wont be sufficient. * Speed of each person of crossing the river is different.cross time for each person is 1 min, 2 minutes, 7 minutes and 10 minutes. What is the shortest time needed for all four of them to cross the river ?

[ "16 minutes", "17 minutes", "18 minutes", "19 minutes", "20 minutes" ]

Solution: 17 min The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. How long would that take? 10 + 1 + 7 + 1 + 2 = 21 minutes. Is that it? No. That would make this question too simple even as a warm up question. Let's brainstorm a little further. To reduce the amount of time, we should find a way for 10 and 7 to go together. If they cross together, then we need one of them to come back to get the others. That would not be ideal. How do we get around that? Maybe we can have 1 waiting on the other side to bring the torch back. Ahaa, we are getting closer. The fastest way to get 1 across and be back is to use 2 to usher 1 across. So let's put all this together. 1 and 2 go cross 2 comes back 7 and 10 go across 1 comes back 1 and 2 go across (done) Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes Answer B The answer is: B

B

mathematics

A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?

[ "75%", "25%", "28%", "85%", "28%" ]

800 --- 200 100 --- ? => 25% Answer: B The answer is: B

B

mathematics

In the formula V = 1/(2r)^3, if r is halved, then V is multiplied by?

[ "16", "8", "1", "1/8", "1/64" ]

Say r=1 => V1 = 1/8 when r=1/2; V2 = 1 V2 = 1*V1. Answer : B The answer is: B

B

mathematics

At what price must an article costing Rs.47.50 be marked in order that after deducting 9% from the list price. It may be sold at a profit of 25% on the cost price?

[ "65.25", "62.6", "62.1", "62.7", "62.2" ]

CP = 47.50 SP = 47.50*(125/100) = 59.375 MP*(91/100) = 59.375 MP = 65.25 Answer: A The answer is: A

A

mathematics

Which of the following inequalities is equivalent to –2 < x < 4 ?

[ "| x – 2 | < 4", "| x – 1 | < 3", "| x + 1 | < 3", "| x + 2 | < 4", "None of the above" ]

First remove the mod then set the expression to 0 then get a value of X then add and subtract the value from the given number on the RHS Lets try with an example (B) --------------> | x – 1 | < 3 First remove the mod -------------------> x-1 then set the expression to 0--------------> x-1=0 then get a value of x---------------------> x=1 then add and subtract the value from the given number on the RHS 1+3=4 and 1-3= -2 the range become -2 to 4 correct answer Now try its with an incorrect option (C) | ----------> |x + 1 | < 3 First remove the mod --------------------------> x+1 then set the expression to 0----------------------> x+1=0 then get a value of x------------------------------> x=-1 then add and subtract the value from the given number on the RHS -1+3=2 and -1-3= -4 the range become -4 to 2 Incorrect THE CORRECT ANSWER IS B The answer is: B

B

mathematics

How many of the positive divisors of 600 are also multiples of 4 not including 600?

[ "6", "8", "9", "11", "12" ]

600 = 2^6 * 3 * 5 = (4) * 2 * 3 * 5^2 Besides (4), the exponents of 2, 3, and 5 are 1, 1, and 2. There are (1+1)(1+1)(2+1) = 12 ways to make multiples of 4. We must subtract 1 because one of these multiples is 600. The answer is D. The answer is: D

D

mathematics

If the sides of a cube are in the ratio 5:4. What is the ratio of their diagonals?

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

Explanation: Diagonal of a Cube=a√3 where a is side a1:a2 = 5:4 d1:d2 = 5:4 where√3 cancelled both side ANSWER:B The answer is: B

B

mathematics

The L.C.M. of two numbers is 54. The numbers are in the ratio 2 : 3. Then sum of the number is:

[ "28", "32", "40", "45", "54" ]

Let the numbers be 2x and 3x. Then, their L.C.M. = 6x. So, 6x = 54 or x = 9. The numbers are 18 and 27. Hence, required sum = (18 + 27) = 45. Answer: Option D The answer is: D

D

mathematics

The list price of an article is Rs.70. A customer pays Rs.61.74 for it. He was given two successive discounts, one of them being 10%. The other discount is?

[ "8%", "7%", "10%", "2%", "4%" ]

Explanation: 70*(90/100)*((100-x)/100) = 61.74 x = 2% Option D The answer is: D

D

mathematics

A trader bought a car at 20% discount on its original price. He sold it at a 30% increase on the price he bought it. What percent of profit did he make on the original price?

[ "A)4%", "B)12%", "C)14%", "D)20%", "E)22%" ]

Original price = 100 CP = 80 S = 80*(130/100) = 104 100 - 104 = 4% A) The answer is: A

A

mathematics

In 1995, the Johnsons spent $800 on the family’s water bills. Anticipating that water rates would increase in 1996 by 50%, the Johnsons cut back their water usage. By how much must the Johnsons have reduced their 1996 water usage to pay exactly the same amount R in 1996 as they paid in 1995?

[ "33 1⁄3%", "40%", "50%", "66 2⁄3%", "100%" ]

water rate increases by 50 % in 1996 means 150% of rate in 1995. to pay exactly the same amount R in 1996 as they paid in 1995, water use should decrease in the same ratio 150-> 100 means 1/3 rd= 33(1/3) %.A The answer is: A

A

mathematics

If x, y, and z are consecutive positive integers greater than 1, not necessarily in that order, then which of the following is (are) true? I. x > z II. 2(x+ y) > 2z III. yz > xz IV. xy > y + z

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

we do not know the values or the relative values but that the three are consecutive.. so the max difference in any two number is 2 and min 1.. lets see the choices.. I. x > z... we do not know the values or the relative values... need not be true.. II. 2(x+ y) > 2z or x+ y > z we take the worst case that z is teh largest and x and y are lowest possible..... so 2+3>4.. 5>4.. always true III. yz > xz we do not know the values or the relative values between x and y..need not be true IV. xy > y + z xy-y>z or y(x-1)>z... again lets take the worst scenario.. we take the worst case that z is the largest and x and y are lowest possible..... so (2-1)3>4.. 3>4.. not true only ii is true ans B The answer is: B

B

mathematics

A chair is bought for Rs.900/- and sold at Rs.810/- find the loss percentage

[ "10% Gain", "10% Loss", "20% Loss", "25% Loss", "30% Loss" ]

Formula = (Selling price ~ Cost price)/Cost price * 100 = (810 ~ 900)/900 = 10% Loss B The answer is: B

B

mathematics

Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 28,000. What was Simran's share in the profit?

[ "Rs. 9423", "Rs. 10,250", "Rs. 12,000", "Rs. 14,000", "None of these" ]

Simran : Nanda = (50000 * 36) : (80000 * 30) = 3:4 Simran's share = 28000 * 3/7 = Rs. 12000 ANSWER:C The answer is: C

C

mathematics

There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?

[ "5/4", "5/7", "5/3", "5/8", "5/1" ]

Let the two numbers be x and y. 20/100 * x + y = 5/4y => 1/5 x = 1/4 y => x/y = 5/4 Answer: A The answer is: A

A

mathematics

Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.

[ "2300", "3300", "4300", "1300", "None of them" ]

Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months. So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3) = 540000 : 540000 : 270000 = 2 : 2 : 1. Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600 Peter's share = Rs. (16500 x (2/5)) = Rs. 6600 Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300. Answer is B. The answer is: B

B

mathematics

A girl has 7 jeans and 12 shirts. In how many different ways can she select a jeans and a shirts?

[ "A)100", "B)102", "C)108", "D)110", "E)84" ]

The girl can select one jeans in 7 ways. The girl can select one shirt in 12 ways. The number of ways in which he can select one jeans and one shirt is 7 * 12 = 84 ways. E The answer is: E

E

mathematics

A disease has infected an ant colony that consists ofworkersandsoldiers: 30% of the soldiers and 14% of theworkerswere infected. If that colony is inhabited by 7000 ants, out of which 1620 are infected, how manyworkersinhabit the colony?

[ "1500", "2500", "2750", "3000", "3250" ]

From two question we get wo equations: (1) 0,3s + 0,14w = 1620 (2) s + w = 7000 From (2) we get w=7000-s In (1) 0,3s + 980-0,14s= 1620 0,16s=640 64000:16= 4000 =s In (2) 4000 + w = 7000 w= 3000 D The answer is: D

D

mathematics

Lakshmi went to the stationers and bought things worth Rs. 200, out of which 50 paise went on sales tax on taxable purchases. If the tax rate was 20%. then what was the cost of the tax free items?

[ "Rs. 197", "Rs. 190", "Rs. 187", "Rs. 167", "Rs. 191" ]

Solution Let the amount of taxable purchases be Rs.x. Then, 20% of x = 50/100 x ‹=› (50/100×100/20) = 2.50 Cost of tax free items = Rs.[200 - (2.50 + 0.50)] = Rs. 197 Answer A The answer is: A

A

mathematics

A man can row with a speed of 12 kmph in still water. If the stream flows at 11 kmph, then the speed in downstream is?

[ "22", "28", "20", "82", "23" ]

M = 12 S = 11 DS = 12 + 11 = 23. Answer:E The answer is: E

E

mathematics

If |x + 10| = 10 what is the sum of all the values of x.

[ "20", "40", "-20", "0", "-40" ]

There will be two cases x+10 = 10 and x+10 = -10 Solve for x => x=10-10=> x=0 or x= -10 - 10 => x= -20 The sum of both values will be 0 + -20 =-20 Answer is C The answer is: C

C

mathematics

Certain stocks in January were 40% less than they were in February and 15% greater than they were in March. What was the percentage decrease in the stocks from February to March?

[ "50.81%", "15.11%", "20.7%", "48.8%", "40%" ]

Let stocks value in Feb = 100 => In Jan = 60 and March = 60 * 100/115 = 51.2% Thus, percent decrease in stocks from Feb to March = 100 - 51.2 = 48.8% Hence Answer is D The answer is: D

D

mathematics

Which of the following is closer to √0.8+√0.1?

[ "0.5", "0.7", "0.9", "1.1", "1.2" ]

√0.8+√0.1=approximately √0.81+√0.09=0.9+0.3=1.2. Hence, the correct answer is E. The answer is: E

E

mathematics

The sum of the first 80 positive even integers is 2,550. What is the sum of the odd integers from 101 to 200, inclusive?

[ "5,050", "7,500", "10,500", "15,000", "19,600" ]

101+103+.......199 If we remove 100 from each of these it will be sum of 1st 100 odd numbers. so 101+103+.......199 = 80 * 100 + (1+3+5+7+......) sum of 1st 100 natural numbers = (100 * 101) / 2 = 5050 Sum of 1st 80 positive even integers = 2550 sum of 1st 100 odd numbers = 5050 - 2550 = 2500 so 101+103+.......199 = 80 * 100 + (1+3+5+7+......) = 8000 + 2500 =10500 C is the answer. The answer is: C

C

mathematics

Shreyas bought an article and sold it for 105% of its cost price. What was the cost price of the article, if Shreyas sold it for Rs.42000/-?

[ "Rs.40000", "Rs.45640", "Rs.44250/-", "Rs.43200", "None of these" ]

Explanation: 105% of CP = Rs.42000 :. CP = Rs.42000x100/105 = Rs.40000. Answer: Option A The answer is: A

A

mathematics

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?

[ "22", "27", "19", "37", "21" ]

16x + 85 = 17(x + 3) x = 34 + 3 = 37 Answer: D The answer is: D

D

mathematics

A gambler has won 40% of his 20 poker games for the week so far. If, all of a sudden, his luck changes and he begins winning 80% of the time, how many more games must he play to end up winning 60% of all his games for the week?

[ "20", "25", "30", "35", "40" ]

Let x be the number of additional games the gambler needs to play. 0.4(20) + 0.8x = 0.6(x+20) 0.2x = 4 x = 20 The answer is A. The answer is: A

A

mathematics

If a, b, c are integers; a² + b² = 45 and b² + c² = 40, then the values of a, b and c respectively are :

[ "2, 6, 3", "3, 2, 6", "5, 4, 3", "4,5,3", "None of these" ]

a² + b² = 45 ….(1) and b² + c² = 40 Subtracting, we get: a² - c² = 5 => (a + c) (a – c) = 5. (a + c) = 5 and (a – c) = 1. Solving we get: a = 3, c = 2. Putting c = 2 in (ii), we get b = 6. ANSWER:B The answer is: B

B

mathematics

What is the diagonal of a square field whose perimeter is 24m?

[ "8 m", "2 m", "7 m", "10 m", "6√2 m" ]

Sol: Let the side of the square be x meters. Therefore, 4x=24 x=6 Diagonal of the square is= √2*(6)^2=6√2 Answer: E The answer is: E

E

mathematics

A garrison of 400 men had a provision for 31 days. After 28 days 300 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient?

[ "65 days", "45 days", "10 days", "16 days", "12 days" ]

400 --- 31 400 --- 3 100 --- ? 400*3 = 100*x => x =12 days. Answer: E The answer is: E

E

mathematics

A, B, C, D, E, F are the only six families in Indira Nagar. A, B, C, D, E and F has 7, 8, 10, 13, 6, and 10 member in their families respectively. If 1 member from all the six families left their respective families to accommodate themselves in the hostel of IIM Lucknow, then the average number of member now in each family of Indira nagar is

[ "8", "9", "10", "13", "15" ]

Answer Required average = (( 7 - 1 ) + ( 8 - 1 ) + ( 10 - 1 ) + ( 13 - 1 ) + (6 - 1) +( 10 - 1 ) )/ 6 = ( 7 + 8 +10 + 13 + 6 + 10 ) / 6 - ( 6 x 1 ) / 6 =9 - 1 = 8 Correct Option: A The answer is: A

A

mathematics

A certain car dealership sells economy cars, luxury cars, and sport utility vehicles. The ratio of economy to luxury cars is 3:1. The ratio of economy cars to sport utility vehicles is 4:3. What is the ratio of luxury cars to sport utility vehicles?

[ "9:8", "8:9", "4:9", "2:3", "1:2" ]

The ratio of economy to luxury cars is 3:1 --> E:L = 3:1 = 12:4. The ratio of economy cars to sport utility vehicles is 4:3 --> E:S = 4:3 = 12:9. Thus, L:S = 4:9. Answer: C. The answer is: C

C

mathematics

Using all the letters of the word "HEAD", how many words can be formed, which begin with H and end with D?

[ "8", "4", "2", "7", "9" ]

There are five letters in the given word. Consider 4 blanks .... The first blank and last blank must be filled with H and D all the remaining three blanks can be filled with the remaining 2 letters in 2! ways. The number of words = 2! = 2. Answer:C The answer is: C

C

mathematics

How many arrangements of the letters of the word BEGIN can be made, without changing the place of the vowels in the word?

[ "6 ways", "7 ways", "9 ways", "11 ways", "13 ways" ]

E,I fixed. Consonants can be arrangements in 3P3 = 3! = 6 ways A) The answer is: A

A

mathematics

What percent of a day is nine hours?

[ "20.83%", "16x1/2%", "18x2/3%", "37.5%", "None of these" ]

Explanation : Required percentage = (9/24100)% = 37.5%. Answer : D The answer is: D

D

mathematics

The sum of five consecutive odd numbers of set p is 435. What is the sum of five consecutive numbers of another set q. Whose largest number is 45 more than the largest number of set p?

[ "530", "670", "730", "770", "None of these" ]

Let the five consecutive odd numbers of set p be 2n - 3, 2n - 1, 2n + 1, 2n + 3, 2n + 5. Sum of these five numbers = 2n - 3 + 2n - 1 + 2n + 1 + 2n + 3 + 2n + 5 = 10n + 5 = 435 => n = 43 Largest number of set p = 2(43) + 5 = 91 The largest number of set q = 91 + 45 = 136 => The five numbers of set q are 132, 133, 134, 135, 136. Sum of above numbers = 132 + 133 + 134 + 135 + 136 = 670. ANSWER:B The answer is: B

B

mathematics

In the line xy plane line m has the equation y = 3x - 9, then the line m passes through which of the following points?

[ "(3, 1)", "(3, 4)", "(4, 2)", "(6, 9)", "(6, 15)" ]

Yes it is y=3x-8....extremely sorry for mistake.... IF that's the case then answer is D y=3x-8 9=3X6-9 9=18-9 9=9 (satisfied) The answer is: D

D

mathematics

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work?

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

First codition=total hours to complete the work=39 persons * 12 days * 5 hr Second codition=total hours to complete the work=30 persons * x days * 6 hr since the work is still the same so 39*12*5=30*x*6 x=13 answer :C The answer is: C

C

mathematics

A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?

[ "40 days", "20 days", "10 days", "60 days", "40 days" ]

C 10 days C = 1/5 – 1/10 = 1/10 => 10 days The answer is: C

C

mathematics

A man bought some mangoes at Rs12 per dozen and bought the same number of at Rs 10 per kg. He sold these mangoes at Rs 13 per dozen and gained Rs 160.The total number of mangos bought by him are

[ "40dozens", "60dozens", "70dozens", "80dozens", "90dozens" ]

let total no of mangoes is 2x.. then we profit=sp-cp 160=13*2x-(12x+10x) 160=4x x=40 hence 2x=80 so total no are 80dozens ANSWER:D The answer is: D

D

mathematics

In a class, the teacher wrote a set of consecutive integers beginning with 1 on the blackboard. Little Johnny came and erased one number. The average of the remaining numbers was 2741327413. What was the number that Little Johnny erased?

[ "7", "9", "11", "13", "15" ]

We have S = the sum of all integer from 1 to N x = the missing integer So as sum = average * Nb of terms S-x= 27(4/13) * (N-1) (A) As S-x should be an integer N-1 should be a multiple of 13. So we have some possible scenario N-1= 13 => N=14 N-1= 26 => N=17 N-1= 39 => N=40 N-1= 52 => N=53 .... Back to our formula (A) x = S - 27(4/13)*(N-1) x = (N(N+1))/2 - 27(4/13)*(N-1) As x>0 (N(N+1))/2 > 27(4/13)*(N-1) approx 27(4/13) by 27 (N(N+1))/2 > 27*(N-1) N(N+1) > 54*(N-1) So we see than N=53 is working (indeed 53*54>54*52) So if N=53: x = (53(54))/2 - 27(4/13)*(52) x = (53(54))/2 - (27+4/13)*(52) x = (53(54))/2 - 27*52-(4/13)*52 x = 53*27 - 27*52-(4/13)*52 x = 53*27 - 27*52-4*4 x = 27*(53-52) - 16 x = 27 - 16 x=11 ANSWER:C The answer is: C

C

mathematics

A series of boxes are placed on a conveyor belt at one end and unloaded at the other. The boxes are each 0.5 meters on each side and are placed immediately adjacent to one another as they are loaded. If the conveyor belt is 30 meters long and moves the boxes at a speed of 0.25 m/s, how long does it take for 100 boxes to be loaded and unloaded?

[ "4 min 30 sec", "4 min 50 sec", "5 min 20 sec", "5 min 40 sec", "6 min 10 sec" ]

C 5 min 20 sec d = 100 * 0.5 m +30 m = 80 m T = 80 m / 0.25 m/s = 320 s = 5 min 20 sec The answer is: C

C

mathematics

The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 5 kmph, what time will he take to cover 60 metres?

[ "16 seconds", "76 seconds", "10.8 seconds", "12 seconds", "18 seconds" ]

Speed of the boat downstream = 15 + 5 = 20 kmph = 20 * 5/18 = 50/9 m/s Hence time taken to cover 60 m = 60*9/50 = 10.8 seconds. Answer: C The answer is: C

C

mathematics

A group of men decided to do a work in 50days, but 10 of them became absent. If the rest of the group did the work in 60days, Find the original number of men?

[ "60", "50", "40", "100", "25" ]

Original number of men = 10*60 / (60-50) = 60 Answer is A The answer is: A

A

mathematics

An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 20-meter platform and caught it after it had traveled 55 meters. How many times did the ball bounce?

[ "5", "6", "3", "8", "9" ]

Going down = 20 m Going Up = 10 --> Total = 30 Going down = 10 --> Total = 40 Going Up = 5 --> Total = 45 Going down = 5 --> Total = 50 Going up = 2.5 --> Total = 52.5 Going down = 2.5 --> Total =55(Caught) No of bouncing = 3 Answer : C The answer is: C

C

mathematics

Sides of a rectangular park are in the ratio 4: 3 and its area is 3750 sq m, the cost of fencing it at 50 ps per meter is?

[ "s.132.3", "s.129", "s.125", "s.120", "s.121" ]

4x * 3x = 3750 => x = 17.7 2(82.3 + 50) = 264.6 m 264.6 * 1/2 = Rs.132.3 Answer:A The answer is: A

A

mathematics

A chair is bought for Rs.1000/- and sold at a loss of 20% find its selling price

[ "Rs.800/-", "Rs.510/-", "Rs.515/-", "Rs.530/-", "Rs.540/-" ]

Loss = 1000*20/100 = 200 S.P = C.P - Loss = 1000- 200 =Rs.800/- Answer :A The answer is: A

A

mathematics

33 1/3% of 36?

[ "16", "21", "18", "12 number", "18" ]

Explanation: 33 1/3 % = 1/3 1/3 * 36 = 12 Answer: Option D The answer is: D

D

mathematics

There exists exactly one positive value of k such that the line y = kx intersects the parabola y = x2 + x + 4 at exactly one point. Compute the intersection point.

[ "(2,10)", "(5,10)", "(7,10)", "(3,10)", "(1,10)" ]

If the line is tangent, then we must have that x2 + x + 4 = kx has a unique solution in x, or x2 + (1 - k)x + 4 = 0 has a unique solution. Thus, (1 - k)2- 16 = 0, or (1- k) = 4. Therefore, k = -3 or k = 5. Taking k = 5, we have that y = 5x intersects y = x2 + x + 4 when x = 2, and the intersection point is (2, 10) . correct answer A The answer is: A

A

mathematics

There are two circles of different radii. The are of a square is 784 sq cm and its side is twice the radius of the larger circle. The radius of the larger circle is seven - third that of the smaller circle. Find the circumference of the smaller circle?

[ "6", "5", "8", "6", "3" ]

Let the radii of the larger and the smaller circles be l cm and s cm respectively. Let the side of the square be a cm. a2 = 784 = (4)(196) = (22).(142) a = (2)(14) = 28 a = 2l, l = a/2 = 14 l = (7/3)s Therefore s = (3/7)(l) = 6 Circumference of the smaller circle = 2∏s = 12∏ cm. Answer: C The answer is: C

C

mathematics

Marsha and Wenbao picked strawberries one afternoon. They combined all of their strawberries together and divided them evenly (50/50). If Marsha picked an odd number of strawberries which of the following is true?

[ "Wenbao picked 50 strawberries.", "Wenbao picked 49 strawberries.", "Wenbao picked 52 strawberries.", "Wenbao picked 40 strawberries.", "Wenbao picked 56 strawberries." ]

From Parity Mathematics Rule: The sum of two odd numbers is even. The sum of and odd number and an even number is odd. Marsha and Wenbao divided their strawberries evenly (50/50) after adding them together. Marsha picked an odd number of strawberries, so Wenbao had to have picked an odd number of strawberries. Answer: B The answer is: B

B

mathematics

Set Y consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set Y?

[ "767", "76", "7", "5", "1" ]

Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median). Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working.... Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values... Putting the 7 numbers in order, we have: -27, -3, -2, 2, 3, 15, 17 This means that the2will either be the 4th term or the 5th term (depending on the value of N). IF.... N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5 N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0 Neither of those answers is among the choices though, so N must be something relativelycloseto 2..... IF.... N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done. E The answer is: E

E

mathematics

Mohan purchased 10 kgs of rice at the rate of Rs.26 per kg and 10 kgs of pulses at the rate of Rs.26 per kg. Whaat is the total amount that he paid to the shopkeeper?

[ "A)Rs.520", "B)Rs.594", "C)Rs.596", "D)Rs.595", "None of these" ]

Explanation: Price of 10 kgs of rice at Rs.26/kg = 10x26 = Rs.260 Price of 8 kgs of pulses at Rs.26/kg = 10x26 = Rs.260 Therefore, Total amount = Rs.260+Rs.260 = Rs.520. Answer: Option A The answer is: A

A

mathematics

Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 22 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?

[ "565", "444", "676", "456", "663" ]

1h ----- 6 ? ------ 60 12 h RS = 16 + 22 = 38 T = 12 D = 38 * 12 =456 Answer: D The answer is: D

D

mathematics

In a bag there are a certain number of blue balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of blue balls to white balls in the bag

[ "1:1", "1:2", "1:5", "1:4", "1:6" ]

since the probability of drawing a white ball out of two picks is 1/2. the ratio of the white ball to blue balls should be 1:1 Answer : A The answer is: A

A

mathematics

The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?

[ "46", "83", "45", "53", "64" ]

Sum of all the 13 numbers = 13 * 60 = 780 Sum of the first 7 of them = 7 * 57 = 399 Sum of the last 7 of them = 7 * 61 = 427 So, the 8th number = 427 + 399 - 780 = 46. Answer:A The answer is: A

A

mathematics

If two projectiles are launched at the same moment from 1998 km apart and travel directly towards each other at 444 km per hour and 555 km per hour respectively, how many minutes will it take for them to meet?

[ "90", "100", "110", "120", "130" ]

The projectiles travel a total of 999 km per hour. The time to meet is 1998/999=2 hours = 120 minutes The answer is D. The answer is: D

D

mathematics

A radio station has to choose one day of the seven in a week to broadcast a certain program, and that set will repeat each week. The program can be broadcast equally on any of the seven weekdays —- weekdays vs. weekends don’t matter at all —- nor does it matter whether the days the program airs are adjacent or not. Absolutely any three of the seven weekdays can be chosen. How many different three-day combinations of the seven weekdays can be constructed?

[ "7", "15", "21", "35", "56" ]

Behind the story, we are really being asked to evaluate 7C1. We could use the factorial formula, but above we conveniently happen to have Pascal’s Triangle written out to the seventh row. We see that 7C1, the third entry of the seventh row, is 7. Answer = A. The answer is: A

A

mathematics

The grocer ordered deliveries of apples on each weekday. The numbers of apples he ordered per day were 80, 30, 100, 90 and x. If the median apple delivery was 10 apples larger than the average (arithmetic mean) number of apples delivered, which of the following could be x?

[ "50", "55", "60", "65", "70" ]

Look at the options available Value of x seems to 50 < = x < = 70 A. 50 B. 55 C. 60 D. 65 E. 70 So position of x is second 30 , x , 80 , 90 , 100 Median = 80 Median number of apples was 10 points higher than the average, so average = 70 30 + x + 80 + 90 + 100 = 350 x = 50 = Answer = A The answer is: A

A

mathematics

A and B are mixed together in the ratio 9 : 11. What is the weight of mixture, if 26.1 kg of A has been consumed in it?

[ "56", "45", "58.2", "58", "46" ]

Explanation : For 9 kg A, mixture = (9 + 11) kg. For 26.1 kg A, mixture = ((20/9) x 26.1)kg = 58 kg. Answer : D The answer is: D

D

mathematics

Which one the following fractions has the Lowest value?

[ "A)488/850", "B)499/850", "C)477/850", "D)511/850", "E)501/850" ]

All options have the same denominator 850. If denominator is same, the fraction with the lowest value will be the one with the Lowest numerator. Answer (C). The answer is: C

C

mathematics

Health insurance Plan A requires the insured to pay $1000 or 50% of total cost, whichever is lower. Plan B requires the insured to pay the initial $300, but then pays 80% of the cost over $300. Which of the following is a cost level for which both insurance plans pay out the same amount?

[ "$600", "$1000", "$3800", "$5300", "$6200" ]

Pay out for plan A: Cost-$1,000 or Cost-0.5*Cost=0.5*Cost, when 0.5*Cost<$1,000; Pay out for plan B: 0.8(Cost-$300); The question is: for which of the following costs the pay outs are the same. C-1,000=0.8(C-300) --> for C=3,800 and 0.5C=0.8(C-300) --> for C=800. As we have only $3,800 listed then it must be a correct answer. Or you can use backsolving for this question: A. C=$600: pay out for plan A will be 0.5*600=300 (as 0.5*600<1,000) and pay out for plan B will be 0.8*(600-300)=240; B. C=$1000: pay out for plan A will be 0.5*1,00=500 (as 0.5*1,000<1,000) and pay out for plan B will be 0.8*(1,000-300)=560; C. C=$3800: pay out for plan A will be 3,800-1,000=2,800 (as 0.5*3,800>1,000) and pay out for plan B will be 0.8*(3,800-300)=2,800 --> 2,800=2,800; D. C=$5300: pay out for plan A will be 5,300-1,000=4,300 (as 0.5*5,300>1,000) and pay out for plan B will be 0.8*(5,300-300)=4,000; E. C=$6200:pay out for plan A will be 6,200-1,000=5,200 (as 0.5*6,200>1,000) and pay out for plan B will be 0.8*(6,200-300)=4,720. Answer: C. The answer is: C

C

mathematics

Of the mutual funds on a “select list,” 2/3 have 5-star ratings, and 2/5 of the remaining funds have 4-star ratings. If the remaining 100 funds on the list have 3-star ratings, how many funds are on the list?

[ "500", "750", "1,000", "1,200", "1,500" ]

A Fraction of 5- and 4-star funds: 2/3 + (2/5)*(1/3) = 2/3 + 2/15 = 12/15=4/5 Fraction of 3-star funds = 1 - 4/5 = 1/5 (1/5)*Total = 100 Total = 500 The answer is: A

A

mathematics

The citizens of planet nigiet are 8 fingered and have thus developed their decimal system in base 8. A certain street in nigiet contains 1000 buildings numbered 1 to 1000 in base 8. How many 3s are used in numbering these buildings?Express your answer in base 10

[ "192", "200", "196", "198", "None" ]

Explanation : Number 3 in 1-100 comes 20 times. 101-200-> 20 times 201-300-> 20 times 301-400->120 times 401-500-> 20 times 501-600-> 20 times 601-700-> 20 times 701-800-> 20 times 801-900-> 20 times 901-1000-> 20 times Total times: 300 times (any no. from 1 to 9 except 0 will occur 300 times) 8 based planet.. then 3*8(2) + 0*8(1) + 0*8(0) = 192 Answer : A The answer is: A

A

mathematics

Two trains of equal lengths take 10 sec and 12 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?

[ "11 sec", "12 sec", "17 sec", "21 sec", "23 sec" ]

Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/12 = 10 m/sec. Relative speed = 12 + 10 = 22 m/sec. Required time = (120 + 120)/22 = 11 sec. Answer: A The answer is: A

A

mathematics

8,27,64,125,216,???,512

[ "346", "343", "348", "339", "340" ]

it is a series of cubes of numbers.... 8=2^3 27=3^3 64=4^3 125=5^3 216=6^3 512=8^3 So, 7^3=343 is the missing number. ANSWER:B The answer is: B

B

mathematics

There are 50 doors marked with numbers 1 to 50. There are 50 individuals marked 1 to 50. An operation on a door is defined as changing the status of the door from open to closed or vice versa. All the doors are closed to start with. One at a time, one randomly chosen individual goes and operates the doors. The individual however operates only those doors which are a multiple of the number he/she is carrying. For example, the individual marked with number 5 operates the doors marked with 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. If every individual in the group gets one turn, then how many doors are open at the end?

[ "0", "2", "5", "7", "9" ]

If a door is closed at the start, it requires an odd number of people to operate to be open at the end. Only the perfect squares have an odd number of factors. The doors which are open at the end are: 1, 4, 9, 16, 25, 36, 49 for a total of 7 doors. The answer is D. The answer is: D

D

mathematics

If the length of the sides of two cubes are in the ratio 6:1, what is the ratio of their total surface area?

[ "6:1", "12:1", "24:1", "36:1", "72:1" ]

Let x be the length of the small cube's side. The total surface area of the small cube is 6x^2. The total surface area of the large cube is 6(6x)^2=216x^2. The ratio of surface areas is 36:1. The answer is D. The answer is: D

D

mathematics

If the average marks of three batches of 62, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is

[ "54.48", "54.68", "54.6", "54.49", "None of these" ]

Explanation: (62Ã—50)+(60Ã—55)+(45Ã—60)/(62+60+45)=54.49 Answer: Option D The answer is: D

D

mathematics

How many positive integers less than 120 are there such that they are multiples of 13 or multiples of 12 but not both?

[ "13", "19", "15", "16", "17" ]

for 13: 13...117=13*9 = 117 for 12: 12...120=12*10 =120 but there is one integer 13*12. so N=(9)+(10)=19 B The answer is: B

B

mathematics

The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is

[ "48", "22", "80", "27", "35" ]

Explanation: Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4. So, the numbers 16 and 20. L.C.M. of 16 and 20 = 80. Answer: Option C The answer is: C

C

mathematics

The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 35% profit?

[ "2000", "2160", "2299", "2778", "2771" ]

Let C.P. be Rs. x. Then, (1920 - x)/x * 100 = (x - 1280)/x * 100 1920 - x = x - 1280 2x = 3200 => x = 1600 Required S.P. = 135 % of Rs. 1600 = 135/100 * 1600 = Rs. 2160. Answer:B The answer is: B

B

mathematics

An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?

[ "1/5", "3/7", "2/5", "5/14", "2/7" ]

Let E and F denote respectively the events that first and second ball drawn are black. We have to find P(E n F) or P (EF). Now P(E) = P (black ball in first draw) = 5/8 Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and three white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred. That is P(F|E) = 4/7 By multiplication rule of probability, we have P (E n F) = P(E) P(F|E) = 5/8 × 4/7 = 5/14 D The answer is: D

D

mathematics

A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs.900in the same period of 2 years, What must be the rate of interest?

[ "25%", "10%", "15%", "20%", "30%" ]

Explanation: Given: 800 = (P * R * 2) / 100 S.I. For 1 year = Rs. 400 Thus, (900 – 800) = S.I. on Rs. 400 for 1 year 100 = (400 * R * 1) / 100 R = 25% p.a. ANSWER: A The answer is: A

A

mathematics

Three dice are thrown together, Find the probability of getting a total of atmost 5?

[ "2/35", "1/8", "3/31", "2/9", "5/108" ]

Three different dice are thrown at the same time. Therefore, total number of possible outcomes will be 63 = (6 × 6 × 6) = 216. Number of events of getting a total of atmost 5 = 10 i.e. (1, 1, 1), (1, 1, 2), (1, 2, 1), (2, 1, 1), (1, 1, 3), (1, 3, 1), (3, 1, 1), (2, 2, 1) and (1, 2, 2). Therefore, probability of getting a total of atmost 5 P(E) = Number of favorable outcomes/Total number of possible outcome = 10/216 = 5/108 The answer is: E

E

mathematics

A no.when divided by 221 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?

[ "3", "6", "9", "10", "12" ]

221 + 43 = 264/17 = 9 (Remainder) C The answer is: C

C

mathematics

Nicole cycles at a constant rate of 10 kilometers per hour, and is passed by Jessica, who cycles at a constant rate of 20 kilometers per hour. If Jessica cycles at her constant rate for x minutes after passing Nicole, then stops to wait for her, how many minutes will Jessica have to wait for Nicole to catch up to her?

[ "a) x minutes", "b) x/2 minutes", "c) 2x/3 minutes", "d) 3x/2 minutes", "e) 2x minutes" ]

Speed of nicole = 20km/h or 20/60 km/min = 1/3 km/min. Once jessica passed the nicole, the distance between the nicole and jessica will increase at the rate of (30-20) = 10km/h or 1/6 km/min now jessica is cycling for x minutes after passing the nicole, so in those x minutes distance between jessica and nicole would be (1/6)*x = x/6 km. So, the time taken by nicole to travel x/6 km = (x/6)/(1/3) = x/2. hence answer should be B The answer is: B

B

mathematics

Six years hence,a fathers age will be three times his son's age and three years ago the fathers age is nine times as old as his son. the fathers present age is

[ "24 years", "28 years", "30 years", "40 years", "45 years" ]

Let "f" nd "s" be the father's nd son's present age respectively (f+6) = 3(s+6) f=3s+18-6 f=3s+12 f-3 = 9(s-3) f = 9s-27+3 f=9s-24 Equate "f" 9s-24 = 3s+12 6s = 36 s=6 f=3(6)+12 f=30 ANSWER:C The answer is: C

C

mathematics

If x and y are distinct prime numbers less than ten, what must be true about the product of x and y?

[ "xy is even", "xy is odd", "xy < 0", "xy < 36", "xy > 6" ]

Prime numbers less than 10 = 2, 3, 5, 7. x and y can take any oth the values On checking the options A. xy is even xy can be even or odd both B. xy is odd xy can be even or odd both C. xy < 0 Product of two prime numbers can never be < 0 Prime numbers are always positive D. xy < 36 The maximum value of multiplication can be 5*7 = 35. Hence this is true always E. xy > 6 x = 2, y = 3 In this case, xy = 6. FALSE Correct Option: D The answer is: D

D

mathematics

At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/3 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades account for 1/4 of all the students. If there are an equal number of students in the third and fourth grades, then the number of students in third grade is how many greater or fewer than the number of students in kindergarten?

[ "12 greater", "17 fewer", "92 fewer", "36 fewer", "44 fewer" ]

Soln>> from the given ratio of 16:1 u can derive that ter are 480 students KG= 1/3* 480 =160 5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder) 1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students) equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number (344 is the sum of remaining students) thus 160-68 =92>>> therfore answer is 92 fewer C The answer is: C

C

mathematics

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 hours, it must travel at a speed of:

[ "300 kmph", "360 kmph", "600 kmph", "720 kmph", "750 kmph" ]

Explanation: Distance = (240 x 5) = 1200 km. Speed = Distance/Time Speed = 1200/(5/3) km/hr. Required speed =(1200 X 3/5)km/hr = 720 km/hr. ANSWER IS D The answer is: D

D

mathematics

What is the remainder when 3^30 is divided by 5?

[ "0", "1", "2", "3", "4" ]

The units digit of powers of 3 follow a repeating cycle of four: {3, 9, 7, 1} 30 has the form 4k+2, so the units digit of 3^30 is 9. The remainder when dividing by 5 is 4. The answer is E. The answer is: E

E

mathematics

Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a + b ?

[ "110", "100", "190", "200", "210" ]

Answer is 10 Yes! there is really a faster way to solve it. Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2 Here A = sum of even ints from 2 to 20, inclusive number of even ints = 10, first int + last int = 2+20 = 22 A = 10*22 / 2 = 110 B = sum of odd ints from 1 to 19, inclusive number of odd ints = 10, first int + last int = 1+19 = 20 A = 10*20 / 2 = 100 A+B = 110 + 100 = 210 Ans :E The answer is: E

E

mathematics

In a club there are no more than 20 persons. What is the smallest number of fruits that must be brought to the club so that each person receives the same number of fruits?

[ "26", "75", "80", "45", "33" ]

The number of persons is not specified. We are just given that there are no more than 20 persons. If we assume that number of persons is 15 then answer will be B. If we assume that number of persons is 20 then answer will be C because only 80 is divisible by 20. The answer is: C

C

mathematics

Which of the following is closest to (-2/3)^199？

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

(-2/3)^4 = 16/81 which is already less than 1/2. For larger exponents, the expression will get closer and closer to zero. The answer is C. The answer is: C

C

mathematics

X, Y, W and Z are intezers and the expressing X - Y - Z is even and Y - W - Z is odd. If X is even then which of

[ "W must be odd", "J must be odd", "Y must be odd", "Z must be odd", "F must be odd" ]

Ans. If X is even and X - Y - Z is even then Y and Z both should be odd or both should be even. If Y - W - Z is odd, and Y and Z are also odd W should be odd If Y - W - Z is even, and Y and Z are even then W should be odd. W must be ODD Answer:A The answer is: A

A

mathematics

On the x-y coordinate plane there is a parabola, y=x(6-x). Which of the following points is in the region that is enclosed by this parabola and the x-axis? I. (1, 6) II. (3, 11) III. (5, 4)

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

Since co-efficient of x^2 is negative, the parabola will be downward facing. So the parabola and the x axis will enclose some points where the y-values of the parabola are positive. When x = 1, y = 5 lies on the parabola, so (1, 6) will not be enclosed by the parabola and x axis. When x = 3, y = 9 lies on the parabola, so (3, 11) will not be enclosed by the parabola and x axis. When x = 5, y = 5 lies on the parabola, so (5, 4) will be enclosed by the parabola and x axis. The answer is C. The answer is: C

C

mathematics

The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.

[ "290 sq cm", "800 sq cm", "209 sq cm", "Cannot be determined", "200 sq cm" ]

Explanation: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively. 4a = 2(l + b) 2a = l + b l . b = 480 We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found . Area of the square cannot be found. Answer: Option D The answer is: D

D

mathematics

Five fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?

[ "6", "8", "12", "16", "20" ]

5*4 = 20 The answer is E. The answer is: E

E

mathematics

Abhijit started a business investing 70000. Anuja joined him after 4 months with an amount of 105000 and Sunil joined them with 1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Abhijit, Anuja and Sunil respectively, three years after Abhijit started the business?

[ "9: 13: 26", "9 :12 :13", "8 :14: 24", "12:14:16", "8 :15: 12" ]

Ratio of their investments = 70 × 36 : 105 × 32: 140 × 26 = 9 : 12 : 13 Answer B The answer is: B

B

mathematics

If w,x,y and z are distinct odd positive integers,then the maximum value of the expression (w^2+x^2)*(y^2+z^2) can be divisible by?

[ "2", "3", "5", "8", "10" ]

ANY ODD NUMBER SQUARE WILL GIVE ODD NUMBER ONLY.. SIMILARLY WEN WE ADD 2 ODD NUMBERS WE WILL GET EVEN NUMBER.. WEN WE MULTIPLY 2 EVEN OWE WILL GET EVEN NUBER.. SO THE RESULT OF THE ABOVE EXPRESSION IS AN EVEN NUMBER ONLY.. HENCE IT IS DIVISIBLE BY 2... ANSWER:A The answer is: A

A

mathematics

The difference of two numbers is 20% of the larger number. If the smaller number is 12, the larger one is :

[ "15", "16", "18", "20", "None of these" ]

Let the larger number be x. Then, x -12 = 20% of x<>x-(x/5)=12 4x/5=12<=> x=(12∗5)/5=15. Answer :A The answer is: A

A

mathematics

When 6 fair coins are tossed simultaneously, in how many outcomes will the first and the last coin turn up heads?

[ "1", "3", "16", "31", "30" ]

Total outcome is 2^6 = 64 Favourable cases = H_ _ _ _ H The second, third, fourth and fifth places can be occupied by either H or T There are 2^4 =16 ways that can be done. Hence, the correct option is C The answer is: C

C

mathematics

Tough and Tricky questions: Word Problems. In a rare coin collection, one in six coins is gold, and all coins are either gold or silver. If 10 silver coins were to be subsequently traded for an additional 10 gold coins, the ratio of gold coins to silver coins would be 1 to 5. Based on this information, how many gold coins would there be in this collection after the proposed trade?

[ "50", "60", "180", "200", "300" ]

The correct answer is D. The answer is: D

D

mathematics

If Ram and Gohul can do a job in 10 days and 15 days independently. How many days would they take to complete the same job working simultaneously?

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

If Total Work is X. Ram rate of working=X/10 per day. Gohul rate of working=X/15 per day. Rate of work=(x/10)+(x/15)=30X/5X =6 days Answer is option E The answer is: E

E

mathematics

A train 125 m long passes a man running at 5 km/hr in the same direction in which the train is going in 10 sec. The speed of the train is?

[ "33 km/hr", "50 km/hr", "77 km/hr", "65 km/hr", "99 km/hr" ]

Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5 = 45 km/hr Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 => x = 50 km/hr. Answer:B The answer is: B

B