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	When a=4+(2/4) and b=4-(2/4), (2^a^2)/(2^b^2)=?	[ "260", "256", "240", "210", "225" ]	--> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/4 and a+b=8, 2^(a-b)(a+b)=2^(4/4)(8)=2^8=256 Therefore, the answer is B The answer is: B	B
mathematics	There are two box,one containing 39 red balls and the other containing 26 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is	[ ".60", ".50", ".70", ".80", ".90" ]	Here we are allowed to transfer the balls between the two boxes, so we keep only one red ball in first box and move all the remaining balls to the second box, so that we get maximum probability of drawing red ball from first box So first box--- only one red ball second box--- 38 red and 26 green Probability of choosing any box is 1/ 2. probability of choosing the red ball from first box is 1 probability of choosing the red ball from second box is 38/64 So probability of taking one red ball = [(1/2)×(1)]+[(1/2)*(38/64)]≃0.8 ANSWER:D The answer is: D	D
mathematics	If a + b - c = 2d, and if a - b + c =-2e, then a =	[ "2(d + e)", "d – e", "(d + e)/2", "d-2e", "e-d" ]	Add both equations: a + b - c = 2d a - b + c =-2e a+b-c+a-b+c=2d-2e 2a=2d-2e a=(d-e) Ans:B The answer is: B	B
mathematics	The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?	[ "75 kg", "65 kg", "55 kg", "85 kg", "93 kg" ]	Total weight increased = (8 x 3.5) kg = 28 kg. Weight of new person = (65 + 28) kg = 93 kg. Answer: E The answer is: E	E
mathematics	One half of a two digit number exceeds its one third by 7. What is the sum of the digits of the number?	[ "A)3", "B)5", "C)7", "D)9", "E)10" ]	x/2 – x/3 = 7 => x =46 4 + 6 = 10 ANSWER:E The answer is: E	E
mathematics	For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 94 Θ 33 ) Θ 17 ) - ( 96 Θ (33 Θ 17)) ?	[ "-10", "-2", "8", "13", "17" ]	(( 94 Θ 33 ) Θ 17 ) The remainder of 98 divided by 33 is 28; The remainder of 28 divided by 17 is 11; ( 96 Θ (33 Θ 17)) The remainder of 33 divided by 17 is 16; The remainder of 96 divided by 16 is 0. 11 - 0 = 11. Answer: D. The answer is: D	D
mathematics	J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?	[ "93.5", "90", "6.75", "6.25", "2" ]	Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables. Let, P = 400 then J = (75/100)400 = 300 also J = (80/100)T i.e. T = 300100/80 = 375 and T = [1-(r/100)]P i.e. 100-r = 100T/P = 100375/400 = 93.75 i.e. r = 6.25 Answer: Option D The answer is: D	D
mathematics	A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?	[ "971", "973", "268", "646", "365" ]	840 = P [1 + (10*3)/100] P = 646 Answer: D The answer is: D	D
mathematics	On a two-dimensional coordinate plane, the line A = x^2 - x^3 touches the x-axis in how many places?	[ "0", "1", "2", "3", "4" ]	Apparently it's A = x^2 - x^3 instead of A = x^2 - A^3. In this case: the x-intercept is the value(s) of x for A = 0. 0 = x^2 - x^3; 0 = x^2(1 - x); x = 0 or x = 1. Answer: C. The answer is: C	C
mathematics	Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?	[ "124%", "120%", "96%", "80%", "84%" ]	Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 84 (40 percent more than Tim's income). Thus, Mary's income (84) is 84% of Juan's income (100). Answer: E. The answer is: E	E
mathematics	A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?	[ "1/190", "1/20", "1/9", "1/10", "1/92" ]	The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. The answer is: C	C
mathematics	If 9 is added to twice a number and this sum is multiplied by 3, the result is the same as if the number is multiplied by 4 and 13 is added to the product. What is the number?	[ "-7", "-8", "-9", "-10", "-11" ]	let the number be x; 3(9+2x)=4x+13; x=-7 ANSWER:A The answer is: A	A
mathematics	Look at this series: 2, 1, (1/2), (1/4), (1/8), ... What number should come next?	[ "(1/3)", "(1/5)", "(1/6)", "(1/10)", "(1/16)" ]	This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result. 4/2 = 2 2/2 = 1 1/2 = 1/2 (1/2)/2 = 1/4 (1/4)/2 = 1/8 (1/8)/2= 1/16 and so on. Answer is E The answer is: E	E
mathematics	In a division sum, the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:	[ "72", "76", "100", "113", "112" ]	Diver = (53)+3 = 18 3 Quotient = 18 Quotient = 6 Dividend = (Divisor * Quotient) + Remainder Dividend = (18* 6) + 5 = 113 D The answer is: D	D
mathematics	The principal that amounts to Rs. 3913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?	[ "s. 3096", "s. 4076", "s. 4085", "s. 4096", "s. 5096" ]	Principal = [4913 / (1 + 25/(4 * 100))3] = 3913 * 16/17 * 16/17 * 16/17 = Rs. 3096. ANSWER:A The answer is: A	A
mathematics	In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?	[ "2.5 sec", "3.9 sec", "2.9 sec", "2.7 sec", "2.3 sec" ]	Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. Answer:A The answer is: A	A
mathematics	If each permutation of the digits 1,2,3,4,5,6 are listed in the increasing order of magnitude, then 289thterm will be	[ "361452", "321546", "321456", "341256", "None of these" ]	Explanation : Let's see how many numbers can be formed with the left most digit as 1 The digit '1' is placed at the 1st position (only 1 way of doing this) Since one digit is placed at the 1st position, any of the remaining 5 digits can be placed at 2nd position. Since one digit is placed at the 1st position and another digit is placed at the 2nd position, any of the remaining 4 digits can be placed at the 3rd position. So on ... 1 5 4 3 2 1 i.e., total number of ways = (1)( 5)( 4)( 3)( 2)( 1) = 120 i.e., total count of numbers which can be formed with the left most digit as 1 = 120 Similarly, total count of numbers which can be formed with the left most digit as 2 = 120 Similarly, total count of numbers which can be formed with the left most digit as 3 = 120 i.e., 240 numbers (=120 + 120) can be formed (with left most digit as 1) or (with left most digit as 2) Similarly, 360 numbers (=120 + 120 + 120) can be formed (with left most digit as 1) or (with left most digit as 2) or (with left most digit as 3) Hence, the left most digit of the 249th number = 3 Now, let's find out how many numbers can be formed with the left most digit as 3 and next digit as 1 The digit '3' is placed at the 1st position (only 1 way of doing this) The digit '1' is placed at the 2nd position (only 1 way of doing this) Any of the remaining 4 digits can be placed at 3rd position. Since 3 digits are placed in the first three positions, any of the remaining 3 digits can be placed at the 4th position. Since 4 digits are placed in the first four positions, any of the remaining 2 digits can be placed at the 5th position. Since 5 digits are placed in the first five positions, the remaining 1 digit can be placed at the 6th position. 1 1 4 3 2 1 i.e., total number of ways = (1)(1)(4)(3)(2)(1) = 24 i.e., Total count of numbers which can be formed (with the left most digit as 3) and (next digit as 1) = 24 Similarly, total count of numbers which can be formed (with the left most digit as 3) and (next digit as 2) = 24 Hence, 120 + 120 + 24 + 24 = 288 numbers can be formed (with left most digit as 1) or (with left most digit as 2) or (with left most digit as 3 and next digit as 1) or (with left most digit as 3 and next digit as 2) Hence, the 289th number is the minimum value number which is formed with the left most digit as 3 and next digit as 4. i.e., the number is 341256 Answer : D The answer is: D	D
mathematics	In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?	[ "7.25", "8.5", "8", "9.15", "10" ]	Explanation : Required run rate = (324 - 4.2 20 ) = 240/ 30 = 8. Answer : C The answer is: C	C
mathematics	The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?	[ "6.99%", "6.89%", "6.08%", "6.09%", "6.19%" ]	Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% Answer:D The answer is: D	D
mathematics	The vertex of a rectangle are (1, 0), (5, 0), (1, 1) and (5, 1) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?	[ "1/2", "2", "1/6", "3", "1/4" ]	If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 0.5). The slope of a line passing through (0,0) and (3, 0.5) is 0.5/3 = 1/6. The answer is C. The answer is: C	C
mathematics	The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder T of Y divided by 5?	[ "T=1.", "T=2.", "3.", "4.", "5." ]	X divided by 10 gives reminder of 2. X can be 2/12/22.... X+Y divided by 5 is 4. X + Y can be 4/ 9/ 19.... If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2 Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2 Hence the answer must be 2 (B) Also.... x+y=5m+4 and x=10K+2 hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B The answer is: B	B
mathematics	Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.	[ "1.9328", "1.9832", "1.9823", "1.9382", "None of them" ]	Sum of decimal places = (2 + 2) = 4 2.68 * 0.74 = 1.9832. Answer is B. The answer is: B	B
mathematics	On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out sand-dunes, 1 has treasure and only 2 out of 7 sand dunes formed have lucky coupons. Find the probability that the blown-out sand dune will contain both the things.	[ "2/25", "4/75", "7/75", "3/79", "4/5" ]	Probability of sand dune blown out = 2/3 Probability that it has treasure = 1/5 Probability that it has lucky coupon = 2/7 total probability = 2/3 * 1/5 * 2/7 = 3/79 ANSWER:D The answer is: D	D
mathematics	A team P of 20 engineers can complete work or task in 32 days. Another team Q of 16 engineers can complete same task in 30 days.Then the ratio of working capacity of 1 member of P to the 1 member of Q is a. 3 : 2	[ "22", "34", "77", "29", "21" ]	Explanation: Let the capacity of an engineer in P = x units, and in Q = y units. Working capacity of P = x × 32 × 20 Working capacity of Q = y × 16 × 30 As the total work is same, we equate the above equations. ⇒ x × 32 × 20 = y × 16 × 30 ⇒ xy=16×3032×20=34 Answer: B The answer is: B	B
mathematics	Two trains of equal lengths take 10 sec and 15 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?	[ "16 sec", "12 sec", "41 sec", "09 sec", "15 sec" ]	Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 =12 sec. Answer: B The answer is: B	B
mathematics	If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .	[ "90 seconds", "150 seconds", "60 seconds", "100 seconds", "120 seconds" ]	2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B The answer is: B	B
mathematics	A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 350 bolts?	[ "84", "72", "120", "144", "180" ]	Old Machine 100 bolts in 60 mins so, 5/3 bolts in 1 min New Machine 150 bolts in 60 mins so, 5/2 bolts in 1 min together, 5/3 + 5/2 = 25/6 bolts in 1 min so, for 350 bolts 350 * 6 / 25 = 84 mins Ans A The answer is: A	A
mathematics	One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?	[ "70 1/7 min", "94 1/7 min", "110 1/7 min", "112 1/7 min", "131 1/7 min" ]	First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) Now the 4 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 = 5/2 so they complete one robot in 2/5th of an hour - (3) Now the 5 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2+1/2 = 3 so they complete one robot in 1/3th of an hour - (4) Now the 6 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2 so they complete one robot in 2/5th of an hour - (5) And now we have 7 robots So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes Answer - E The answer is: E	E
mathematics	Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?	[ "10", "12", "14", "16", "18" ]	Part filled A in 1 hr= (1/16) Part filled B in 1 hr= (1/24) Part filled by (A+B) together in 1 hr=(1/16)+(1/24)=5/48 So, The tank will be full in 48/5 hrs Time taken to fill Exact quarter tank = (48/5) * (5/4) = 12 hrs Answer : B The answer is: B	B
mathematics	The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half?	[ "44.2", "47.8", "50.5", "53.6", "56.9" ]	The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. The answer is: B	B
mathematics	If 1,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?	[ "1,000", "100", "1,000,000", "10", "10,000" ]	Given that 1,000 microns = 1 decimeter =1,000,000,000 angstroms So, 1 micron = 1,000,000,000/1,000 =1,000,000 Answer : C The answer is: C	C
mathematics	Which of the following does NOT have a divisor greater than 1 that is the square of an integer?	[ "28", "32", "49", "62", "25" ]	Prime Factorization 28=227=2^27. Includes a perfect square of 4. 32=22222=4^22. Includes the perfect square of 16. 49=77. Is a perfect square. 62=231. No perfect square here, so a possibility. 25= 55. Is a perfect square. All but 62 have perfect squares as a factor so D is the correct answer. 28=227=2^27. Perfect square of 4. 32=22222=4^22. Perfect square of 16. 49=77. Perfect square. 62=231. No perfect square. 25= 55. Perfect square. The answer is: D	D
mathematics	A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 10% while selling. What is his percentage profit?	[ "10.22%", "20.22%", "21.22%", "20%", "Can't be calculated" ]	The owner buys 100kg but actually gets 120kg; The owner sells 100kg but actually gives 90kg; Profit: (120-90)/90*100=20% Answer: D. The answer is: D	D
mathematics	Find the value of x. (47% of 1442 - 36% of 1412) + 61 = x?	[ "1", "2", "3", "4", "5" ]	B) 2 The answer is: B	B
mathematics	Set A of 8 positive integers may have the same element and have 36. And set B of 8 positive integers must have different elements and have 36. When m and n are the greatest possible differences between 36 and other elements’ sums in set A and set B, respectively, m-n=?	[ "20", "21", "23", "25", "26" ]	This is maximum-minimum. Hence, 36-(1+1+1+1+1+1+1)=29 and 36-(1+2+3+4+5+6+7)=8. So, 29-8=21. The correct answer is B. The answer is: B	B
mathematics	If A lends Rs.2000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?	[ "90", "122.5", "132.5", "114.5", "212.5" ]	(20001.53)/100 => 90 ANSWER:A The answer is: A	A
mathematics	75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 28% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?	[ "25%", "30%", "50%", "55%", "75%" ]	Let x be the number of non-smoking rooms. Let N be the total number of rooms at the inn. 40% of non-smoking rooms have a king-sized bed. 0.4x = 0.28N x = 0.7N The percentage of rooms which permit smoking is 1 - 0.7 = 30% The answer is B. The answer is: B	B
mathematics	The difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is	[ "72", "60", "32", "96", "65" ]	Explanation: Let the larger number be x. Then, x - 48 = 1/3 x x - x/3 = 48 => 2x/3 = 48 => x = 72 Answer: Option A The answer is: A	A
mathematics	Two pipes A and B can separately fill a cistern in 24 minutes and 48 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 12 minutes. In how much time, the third pipe alone can empty the cistern?	[ "90 min", "48 min", "54 min", "120 min", "130 min" ]	1/12-(1/24+1/48)=-1/48 third pipe can empty in 48 minutes ANSWER:B The answer is: B	B
mathematics	A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?	[ "150", "872", "250", "288", "212" ]	Speed = 60(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed Time (50/3) * 15 = 250 meter Answer:C The answer is: C	C
mathematics	A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?	[ "118", "88", "90", "42", "22" ]	SP of 1m of cloth = 8925/85 = Rs. 125 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 125 - Rs. 7 = Rs. 118 Answer:A The answer is: A	A
mathematics	A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?	[ "9801", "10,000", "14,400", "12,696", "can not be determined" ]	Let the side for growing cabbages this year be X ft. Thus the area is X^2. Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2. The area would have increased by 197 sq ft as each cabbage takes 1 sq ft space. X^2 - Y^2 = 197 (X + Y)(X - Y) = 197 197 is a prime number and thus it will be (99+98)*(99-98). Thus X = 99 and Y = 98 X^2 = 99^2 = 9801 The answer is A. The answer is: A	A
mathematics	If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?	[ "1/4", "3/8", "1/2", "5/8", "3/4" ]	total nos of ways in which we can choose n = 96 n(n + 1)(n + 2) will be divisible by 8? case 1: n = odd then n+2 =odd & n+1 will be even i.e this needs get divided by 8, hence is a multiple of 8 so we have 8..96 = 12 multiples to fill the n+1 pos hence 12 ways case 2: n is even then n+2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n= 2....96 (all even nos) i.e 48 nos total = 48+12 =60 ways so reqd P =60/96 =5/8; ANSWER:D The answer is: D	D
mathematics	The length of a rectangular floor is more than its breadth by 100%. If Rs. 600 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?	[ "15.0m.", "14.4m.", "12.0m.", "16.2m.", "16.5m." ]	Let the length and the breadth of the floor be l m and b m respectively. l = b + 100% of b = l + 1b = 2b Area of the floor = 600/3 = 200 sq m l b = 200i.e., l * l/2 = 108 l2 = 216 => l = 14.4m. ANSWER:B The answer is: B	B
mathematics	Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)	[ "6/k", "8/k", "83k", "2/k", "1/k" ]	Part of the book he can read in 1 minute = 1/k Part of the book he can read in 8 minutes =8/k. Answer: B The answer is: B	B
mathematics	How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?	[ "14", "13", "12", "11", "10" ]	The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A The answer is: A	A
mathematics	Find the invalid no.from the following series 13, 18, 25, 30, 37, 40	[ "30", "35", "40", "47", "50" ]	The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong. C The answer is: C	C
mathematics	Which answer is closest to the √17?	[ "a 4.1", "b 4.2", "c 4.4", "d 4.5", "e 4.6" ]	Try filling the numbers into the y's. y x y = 4.1 x 4.1= 16.81 4.2 x 4.2 = 17.64 Answer: A The answer is: A	A
mathematics	If the number 517324 is completely divisible by 9, then the smallest whole number in the place of will be:	[ "3", "1", "5", "4", "2" ]	Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9. x = 5. C The answer is: C	C
mathematics	Last year, sales at Company Zora were 10% greater in February than in January, 10% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?	[ "March", "April", "May", "June", "February" ]	Jan = $100 10% greater in February than in January ---> Feb = $110 10% less in March than in Feb ---> Mar = $99 20% greater in April than in March ---> Apr = $118.80 10% less in May than in April ---> May $106.92 10% greater in June than in May --->Jun = $117.61 Answer : A The answer is: A	A
mathematics	A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?	[ "120 sec", "198 sec", "178 sec", "665 sec", "276 sec" ]	Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) } = LCM (60, 40) = 120 sec. Answer:A The answer is: A	A
mathematics	The equation of line q is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q?	[ "48", "50", "60", "75", "100" ]	This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.510075=0.5125 x => x=60; SO answer is 60=C The answer is: C	C
mathematics	In how many years will a sum of money doubles itself at 5% per annum on simple interest?	[ "29%", "20%", "07%", "50%", "23%" ]	P = (P5R)/100 R = 20% Answer:B The answer is: B	B
mathematics	If 30% of a number is equal to one-third of another number, what is the ratio of first number to the second number ?	[ "2:5", "3:7", "10:9", "7:3", "None of these" ]	Explanation : Let 30% of A=1/3B Then, 30A/100=1B/3 => 3A/10=B/3 => A:B= 10 : 9 Answer : C The answer is: C	C
mathematics	If X is the set of prime single-digit numbers and Y is a set containing each of the numbers in set X raised to the power of 2, how much greater is the median of set Y than the median of set X?	[ "2", "4", "9", "13", "17" ]	set X={2,3,5,7} set of prime single digit numbers set Y={4,9.25.49} each of the numbers in set X raised to the power of 2 Median set X= (3+5)/2= 4 Median set Y= (9+25)/2= 17 Required set Y - set X= 13 ANSWER:D The answer is: D	D
mathematics	The average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?	[ "107 kg", "80 kg", "120 kg", "90 kg", "100" ]	Solution Total weight increased = (10 x 4.2)kg = 42 kg. Weight of new person = (65 + 42)kg = 107kg. Answer A The answer is: A	A
mathematics	The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?	[ "33%", "28.02%", "37.5%", "30.5%", "22%" ]	C 37.5% Let marked price = $100. Then, C.P. = $64, S.P. = $88 Gain % = 24/64 * 100 = 37.5%. The answer is: C	C
mathematics	If 13 = 13w/(1-w) ,then (w)2 =	[ "1/4", "1/2", "1", "2", "3" ]	13-13w=13w 26w=13 w=1/2 2w2=1/22=1 ANSWER:C The answer is: C	C
mathematics	A box contains 15 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first twenty natural numbers. What is the chance that it is a multiple of either 4 or 15?	[ "17/10", "1/10", "7/10", "1/5", "3/10" ]	The probability that the number is a multiple of 4 is 5/20. (Since 45 = 20). Similarly the probability that the number is a multiple of 15 is 1/20. {Since 151 = 15). Neither 4 nor 15 has common multiple from 1 to 20. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 4 or 15 is (5+1)/20 = 3/10. ANSWER:E The answer is: E	E
mathematics	The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is	[ "124345 m", "233234 m", "153600 m", "123567 m", "168999 m" ]	Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m C The answer is: C	C
mathematics	If an article is sold at 20% profit instead of 14% profit, then the profit would be Rs. 180 more. What is the cost price?	[ "Rs.1000", "Rs. 2000", "Rs. 3000", "Rs. 4000", "Rs.5200" ]	Explanation: Let the cost price of an article be Rs. x. (20% of x) - (14% of x) = 180 20x/100 - 14x/100 = 105 => 6x = 180 * 100 => x = 3000 Cost price = Rs. 3000 Answer:C The answer is: C	C
mathematics	A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m3) is:	[ "4830", "5184", "6420", "8960", "7960" ]	Clearly, l = (48 - 12)m = 36 m, b = (36 -12)m = 24 m, h = 8 m. Volume of the box = (36 x 24 x 12) m3 = 5184 m3. Answer: Option B The answer is: B	B
mathematics	A bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?	[ "0.004%", "0.04%", "0.40%", "5%", "40%" ]	Total amount of water evaporated each day during a 50-day period = .008 * 50 =.010 * 100/2 = 1.0/2 = .5 percent of the original amount of water evaporated during this period = (.5/10) * 100% = 5 % Answer D The answer is: D	D
mathematics	A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn?	[ "188", "258", "376", "470", "517" ]	consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn R= 4 * 94 = 376 correct option - C The answer is: C	C
mathematics	The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 36 years, then find the age of the person sitting in the middle of the row?	[ "9 years", "29 years", "18 years", "13 years", "17 years" ]	Total age seven persons = (28 * 7)years Total age of the first three persons and the last three persons are (25 * 3) years and (36 * 3) years respectively. Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 36 * 3 = 196 - 75 - 108 = 13 years. ANSWER:D The answer is: D	D
mathematics	The largest four digit number which is a multiple of 8, 10,12 and 15 is:	[ "9960", "9950", "9940", "9930", "9920" ]	lcm=120 9999/120=83 83*120=9960 ANSWER:A The answer is: A	A
mathematics	The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?	[ "1,010", "1,164", "1,240", "1,316", "2,109" ]	First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively. Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2. Plug values of n = 18 and c = 1/2 into the equation and simplify to get the answer 2109. Option E. The answer is: E	E
mathematics	If it takes a tub 6 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?	[ "48 seconds", "1 minute, 12 seconds", "1 minute, 50 seconds", "2 minutes, 24 seconds", "4 minutes, 12 seconds" ]	If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained. If it takes 6 minutes to drain 5/7 th of tub it takes 6(7/5) minutes to drain the entire tub and 6(7/5)*(2/7) min to drain 2/7 th of the tub which is 2.4 minutes or 12/5 minutes or 2 minute 24 seconds So answer is D The answer is: D	D
mathematics	Three workers have a productivity ratio of 1 to 2 to 4. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?	[ "12 to 1", "6 to 1", "5 to 1", "20 to 3", "1 to 5" ]	The fastest worker who does 4 units of job worked for all 10 hours, so he did 410=40 units of job; The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 16=6 units of job; The ratio thus is 40 to 6, or 20 to 3. Answer: D The answer is: D	D
mathematics	Series B(n) is such that iB(i) = jB(j) for any pair of positive integers (i, j). If B(1) is a positive integer, which of the following is possible? I. 2*B(100) = B(99) + B(98) II. B(1) is the only integer in the series III. The series does not contain negative numbers	[ "I only", "II only", "IIII only", "IIIII only", "I, IIIII" ]	First thing I want to understand is this relation: iB(i) = jB(j) for any pair of positive integers. I will take examples to understand it. When i = 1 and j = 2, B(1) = 2B(2) So B(2) = B(1)/2 When i = 1 and j = 3, B(1) = 3B(3) So B(3) = B(1)/3 I see it now. The series is: B(1), B(1)/2, B(1)/3, B(1)/4 and so on... II and III are easily possible. We can see that without any calculations. II. B(1) is the only integer in the series If B(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except B(1) III. The series does not contain negative numbers Again, same series as above applies. In fact, since B(1) is a positive integer, this must be true. I. 2B(100) = B(99) + B(98) 2B(1)/100 = B(1)/99 + B(1)/98 (cancel B(1) from both sides) 2/100 = 1/99 + 1/98 Not true hence this is not possible Answer (D) The answer is: D	D
mathematics	A train passes a platform in 32 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is	[ "180 meter", "240 meter", "200 meter", "260 meter", "None of these" ]	Explanation: Speed of the train = 54 km/hr = (54×10)/32 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 32 => 300+L = 15×32 =480 => L = 480-300 = 180 meter Answer: Option A The answer is: A	A
mathematics	The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.	[ "38", "40", "45", "48", "49" ]	Let the price of gift pack be 'aa' Then number of packs bought =a+1=a+1 Hence total cost is a(a+1)a(a+1) It is given that 380<a(a+1)380<a(a+1) If a=19a=19, the total cost =19×20=380=19×20=380 Dexter would not have fallen short, If: a=20a=20, a(a+1)=420a(a+1)=420 So he would have fallen short by Rs 40. This is the minimum amount by which he may have fallen short. B) The answer is: B	B
mathematics	If x and y are different integers and x^2 = xy, which of the following must be true ? I. x = 0 II. y = 0 III. x = -y	[ "I only", "II only", "III only", "I and III only", "I, II, and III" ]	Re-arrange equation: x^2 - xy = 0 => x*(x-y) = 0 Therefore, either x=0 or x=y. We know that x and y are different, so x must be equal to 0. ANSWER:A The answer is: A	A
mathematics	Which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?	[ "x^2 + 5x + 6 > 0", "\|x + 2\| > 4", "9x - 7 < 3x + 14", "x^2 - 4x + 3 < 0", "(B) and (D)" ]	Factorizing x^2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0. This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative. Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x". ANSWER : D The answer is: D	D
mathematics	The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?	[ "252 kms", "152 kms", "552 kms", "752 kms", "152 kms" ]	Explanation: Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms) This is an A.P with first term, a=35, number of terms, n= 12,d=2. Required distance = 12/2[2 x 35+{12-1) x 2] =6(70+23) = 552 kms. Answer: C The answer is: C	C
mathematics	Sales price is $54, gross profit is 125% of cost, what is the value of gross profit?	[ "32", "30", "39", "40", "42" ]	Cost + Profit = Sales Cost + (125/100)Cost = 54 Cost = 24 Profit = 54 - 24 = 30 Answer (B) The answer is: B	B
mathematics	Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?	[ "100000", "100500", "105000", "Data inadequate", "None of these" ]	Let the investment of X in 1995 be x. ∴ Profit = x⁄5 ∴ Income = (x + x⁄5) = 6⁄5x Investment of company X in 1996 would be (x – 5000) From the question, (x - 500) × 126⁄100 = 6⁄5x ⇒ x = 105000 Answer C The answer is: C	C
mathematics	A sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?	[ "$3,000", "$3,150", "$4,000", "$2,500", "$5,000" ]	We're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600. Since the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales. Let's TEST Answer C: $4,000 Since 20% of $1,000 = $200 20% of $4,000 = 4($200) = $800 This is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure. Let's TEST Answer D: $2,500 Since 20% of $1,000 = $200 20% of $2,500 = 2.5($200) = $500 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: D The answer is: D	D
mathematics	A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1000. A's investment was	[ "s. 4,500", "s. 8,250", "s. 9,500", "s. 10,000", "s. 12,250" ]	A+B=15000 total profit=3000 3000-1000=2000 2000;1000=2:1 then 2*15000/3=10000 ANSWER:D The answer is: D	D
mathematics	If the circumference of a circle increases from 4pi to 8 pi, what change occurs in the area ?	[ "Area is quadrupled", "Area is tripled", "Area is doubles", "Area become half", "None of these" ]	Explanation: 2πR1=4π =>R1=22πR2=8π >R2=4Original Area =4π∗22=16πNew Area =4π∗42=64π So the area quadruples. Option A The answer is: A	A
mathematics	Among 700people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?	[ "20", "60", "80", "186", "210" ]	56%+44%-30%=70% who like either Strawberry, Apple, or both. That means 100%-70% = 30% do not like either Apple of Strawberry jam. 30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any) E The answer is: E	E
mathematics	Shane is playing a board game. For his first turn he moved ahead 3 spaces, for the second, 5 spaces and for the third, 1 space. For his next turn he had to go back 6 spaces. After that he got a card that said he could move two times the biggest forward move he had done so far. Now how many spaces from the beginning is Shane’s game piece?	[ "3", "13", "23", "33", "43" ]	You may want to draw this one. biggest move is 5, so two times biggest move is 10. 3 + 5 + 1 = 9 9 - 6 = 3 3 + 10 = 13, so he is 13 spaces from the beginning. correct answer B The answer is: B	B
mathematics	The ratio of three numbers is 6:7:5 and their sum is 108. The second number of the three numbers is?	[ "12", "42", "30", "36", "None of these" ]	Explanation: 6:7:5 Total parts = 18 18 parts --> 108 1 part ---->6 The second number of the three numbers is = 7 7 parts ----> 42 Answer: Option B The answer is: B	B
mathematics	In covering a distance of 24 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:	[ "4 kmph", "6 kmph", "6.25 kmph", "7.5 kmph", "7.8 kmph" ]	Let Abhay's speed be x km/hr. Then, 24/X - 24/2X = 3 6x = 24 x = 4 km/hr. Answer: Option A The answer is: A	A
mathematics	On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?	[ "40%", "50%", "60%", "80%", "90%" ]	Let T be the total number of passengers. Let x be the number of people with round trip tickets. 0.4T had round trip tickets and took their cars. 0.5x had round trip tickets and took their cars. 0.5x = 0.4T x = 0.8T The answer is D. The answer is: D	D
mathematics	The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N.	[ "797", "254", "597", "997", "297" ]	According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient divisor + remainder = 18 14 + 2 = 254 correc answer B The answer is: B	B
mathematics	for which value of n, 4^85+2^3373+4^n will be the perfect square ??	[ "1878", "1978", "1578", "2578", "3287" ]	given expression is in the form of a^2+2ab+b^2 4^85=2^2(85) 4^n=2^2n 2^3373=22^852^n 3373=85+1+n n=3373-86=3287 ANSWER:E The answer is: E	E
mathematics	The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?	[ "4", "5", "20", "24", "120" ]	If the president is sitting in the center, you only have 4 chairs left. There are 4 possibilities for 1st chair, 3 possibilities for 2nd chair, 2 possibilities for 3rd chair, and 1 for last chair. Multiply all those and you get 24. ANS:D. The answer is: D	D
mathematics	A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 24,000 earned at the end of 2 years from the starting of the business?	[ "A)7500", "B)7389", "C)7200", "D)7453", "E)7637" ]	A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 24000 * 3/10 = Rs.7200. Answer: C The answer is: C	C
mathematics	The sum of the first 50 positive even integers is 2550. What is the sum W of even integers from 102 to 200 inclusive?	[ "5100", "7550", "10100", "15500", "20100" ]	My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: W=2550+(100*50)=7550.B The answer is: B	B
mathematics	A sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent?	[ "25%", "20%", "15%", "10%", "5%" ]	6000 --- 1500 100 --- ? => 25% Answer: A The answer is: A	A
mathematics	Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?	[ "4: 45 p.m.", "2: 20 p.m.", "5: 20 p.m.", "5: 35 p.m.", "6: 00 p.m." ]	the distance travelled by the train A in first 20 minutes will be 10. The distance which will be remaining is 80. Now both trains are running in opposite direction.Their speed will be added so 40. Time at which they will meet =80/40=2 time of train B will be 0:20 +2=2:20 Hence answer is B.Hope i am correct The answer is: B	B
mathematics	A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:	[ "8.5 km/hr", "9 km/hr", "10 km/hr", "12.5 km/hr", "25km/hr" ]	Explanation: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr. Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr. Answer: C The answer is: C	C
mathematics	If 3 tic equals 6 tacs and 2 tacs equal 7 tocs, what is the ratio of one tic to one toc?	[ "7/1", "6/5", "5/6", "3/10", "1/15" ]	3Tic=6Tac and 2Tac=7Toc; 6Tic=12Tac and 12Tac=42Toc --> 6Tic=42*Toc --> Tic/Toc=42/6=7/1. Answer: A. The answer is: A	A
mathematics	John invests $x at the semi-annual constant compounded rate of 2 percent and also does $8,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??	[ "10000", "12000", "16160.8", "14000", "15000" ]	A = P(1+r/n)^nt A= total amount accrued P = principal deposited r = rate of interest in decimal form n = number of times per year, interest compounded t = time in number of years. . x(1+0.02/2)^2 - x = 8,000(1+0.04/4)^4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal) => x[(1.01)^2 - 1] = 8,000[(1.01)^4 - 1] => x[(1.01)^2 - 1] = 8,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides => x = 8,000(1.0201+1) =16160.8 Hence answer is C. The answer is: C	C
mathematics	Find the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.	[ "s.8500", "s.8000", "s.7500", "s.8800", "s.6500" ]	P = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years. S.I. = (PRT)/100 = Rs.(70,400(50/3)(3/4)*(1/100)) = Rs.8800 Answer is D. The answer is: D	D
mathematics	The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?	[ "323", "377", "344", "239", "112" ]	Explanation: Let the four numbers be x, x + 2, x + 4 and x + 6. => x + x + 2 + x + 4 + x + 6 = 36 => 4x + 12 = 36 => x = 6 The numbers are 6, 8, 10 and 12. Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344. Answer: C The answer is: C	C
mathematics	80% of 5/8 =	[ "0.2", "0.5", "0.6", "0.75", "1.0" ]	Should be simple. 0.8*5/8 = 4/8 = 1/2 = 0.5 Correct Option : B The answer is: B	B
mathematics	What is the unit digit in 8^100?	[ "0", "1", "6", "3", "5" ]	Unit digit in 8^100 = unit digit in [(8^4)^25 ] But unit digit in 8^4=6 unit digit 8^100= 6 Answer is C The answer is: C	C
mathematics	Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.1 more than the next one below it in size. What was the cost, in dollars, of the largest pot?	[ "$1.62", "$1.85", "$2.00", "$2.15", "$2.30" ]	This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS. We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot. Since the total price is $8.25 (a 10-cent increment) and the the difference in sequential prices of the pots is 10 cents, the largest pot PROBABLY has a price that is a 10-cent increment. From the answer choices, I would then TEST Answer A first IF.... The largest pot = $1.625 1.125 1.225 1.325 1.425 1.525 1.625 Total = $8.25 So this MUST be the answer. A The answer is: A	A

mathematics

When a=4+(2/4) and b=4-(2/4), (2^a^2)/(2^b^2)=?

[ "260", "256", "240", "210", "225" ]

--> (2^a^2)/(2^b^2) ={(2)^(a^2-b^2)}=2^(a-b)(a+b). Since a-b=4/4 and a+b=8, 2^(a-b)(a+b)=2^(4/4)(8)=2^8=256 Therefore, the answer is B The answer is: B

B

mathematics

There are two box,one containing 39 red balls and the other containing 26 green balls. You are allowed to move the balls between the boxes so that when you choose a box at random and a ball at random from the chosen box, the probability of getting a red ball is maximized. This maximum probability is

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

Here we are allowed to transfer the balls between the two boxes, so we keep only one red ball in first box and move all the remaining balls to the second box, so that we get maximum probability of drawing red ball from first box So first box--- only one red ball second box--- 38 red and 26 green Probability of choosing any box is 1/ 2. probability of choosing the red ball from first box is 1 probability of choosing the red ball from second box is 38/64 So probability of taking one red ball = [(1/2)×(1)]+[(1/2)*(38/64)]≃0.8 ANSWER:D The answer is: D

D

mathematics

If a + b - c = 2d, and if a - b + c =-2e, then a =

[ "2(d + e)", "d – e", "(d + e)/2", "d-2e", "e-d" ]

Add both equations: a + b - c = 2d a - b + c =-2e a+b-c+a-b+c=2d-2e 2a=2d-2e a=(d-e) Ans:B The answer is: B

B

mathematics

The average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?

[ "75 kg", "65 kg", "55 kg", "85 kg", "93 kg" ]

Total weight increased = (8 x 3.5) kg = 28 kg. Weight of new person = (65 + 28) kg = 93 kg. Answer: E The answer is: E

E

mathematics

One half of a two digit number exceeds its one third by 7. What is the sum of the digits of the number?

[ "A)3", "B)5", "C)7", "D)9", "E)10" ]

x/2 – x/3 = 7 => x =46 4 + 6 = 10 ANSWER:E The answer is: E

E

mathematics

For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 94 Θ 33 ) Θ 17 ) - ( 96 Θ (33 Θ 17)) ?

[ "-10", "-2", "8", "13", "17" ]

(( 94 Θ 33 ) Θ 17 ) The remainder of 98 divided by 33 is 28; The remainder of 28 divided by 17 is 11; ( 96 Θ (33 Θ 17)) The remainder of 33 divided by 17 is 16; The remainder of 96 divided by 16 is 0. 11 - 0 = 11. Answer: D. The answer is: D

D

mathematics

J is 25% less than P and 20% less than T. T is r% less than P. What is the value of r?

[ "93.5", "90", "6.75", "6.25", "2" ]

Usually We can solve every question of this type by choosing appropriate value of the Variable and deriving the value of other related variables. Let, P = 400 then J = (75/100)*400 = 300 also J = (80/100)*T i.e. T = 300*100/80 = 375 and T = [1-(r/100)]*P i.e. 100-r = 100*T/P = 100*375/400 = 93.75 i.e. r = 6.25 Answer: Option D The answer is: D

D

mathematics

A certain sum of money at simple interest amounted Rs.840 in 10 years at 3% per annum, find the sum?

[ "971", "973", "268", "646", "365" ]

840 = P [1 + (10*3)/100] P = 646 Answer: D The answer is: D

D

mathematics

On a two-dimensional coordinate plane, the line A = x^2 - x^3 touches the x-axis in how many places?

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

Apparently it's A = x^2 - x^3 instead of A = x^2 - A^3. In this case: the x-intercept is the value(s) of x for A = 0. 0 = x^2 - x^3; 0 = x^2(1 - x); x = 0 or x = 1. Answer: C. The answer is: C

C

mathematics

Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

[ "124%", "120%", "96%", "80%", "84%" ]

Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 84 (40 percent more than Tim's income). Thus, Mary's income (84) is 84% of Juan's income (100). Answer: E. The answer is: E

E

mathematics

A box contains 5 pairs of shoes (10 shoes in total). If two shoes are selected at random, what it is the probability that they are matching shoes?

[ "1/190", "1/20", "1/9", "1/10", "1/92" ]

The problem with your solution is that we don't choose 1 shoe from 20, but rather choose the needed one AFTER we just took one and need the second to be the pair of it. So, the probability would simply be: 1/1*1/9(as after taking one at random there are 9 shoes left and only one is the pair of the first one)=1/9 Answer: C. The answer is: C

C

mathematics

If 9 is added to twice a number and this sum is multiplied by 3, the result is the same as if the number is multiplied by 4 and 13 is added to the product. What is the number?

[ "-7", "-8", "-9", "-10", "-11" ]

let the number be x; 3(9+2x)=4x+13; x=-7 ANSWER:A The answer is: A

A

mathematics

Look at this series: 2, 1, (1/2), (1/4), (1/8), ... What number should come next?

[ "(1/3)", "(1/5)", "(1/6)", "(1/10)", "(1/16)" ]

This is a simple division series; each number is one-half of the previous number. In other terms to say, the number is divided by 2 successively to get the next result. 4/2 = 2 2/2 = 1 1/2 = 1/2 (1/2)/2 = 1/4 (1/4)/2 = 1/8 (1/8)/2= 1/16 and so on. Answer is E The answer is: E

E

mathematics

In a division sum, the remainder is 5 and the divisor is 3 times the quotient and is obtained by adding 3 to the thrice of the remainder. The dividend is:

[ "72", "76", "100", "113", "112" ]

Diver = (5*3)+3 = 18 3* Quotient = 18 Quotient = 6 Dividend = (Divisor * Quotient) + Remainder Dividend = (18* 6) + 5 = 113 D The answer is: D

D

mathematics

The principal that amounts to Rs. 3913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?

[ "s. 3096", "s. 4076", "s. 4085", "s. 4096", "s. 5096" ]

Principal = [4913 / (1 + 25/(4 * 100))3] = 3913 * 16/17 * 16/17 * 16/17 = Rs. 3096. ANSWER:A The answer is: A

A

mathematics

In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?

[ "2.5 sec", "3.9 sec", "2.9 sec", "2.7 sec", "2.3 sec" ]

Speed = 144 * 5/18 = 40 m/sec Time taken = 100/40 = 2.5 sec. Answer:A The answer is: A

A

mathematics

If each permutation of the digits 1,2,3,4,5,6 are listed in the increasing order of magnitude, then 289thterm will be

[ "361452", "321546", "321456", "341256", "None of these" ]

Explanation : Let's see how many numbers can be formed with the left most digit as 1 The digit '1' is placed at the 1st position (only 1 way of doing this) Since one digit is placed at the 1st position, any of the remaining 5 digits can be placed at 2nd position. Since one digit is placed at the 1st position and another digit is placed at the 2nd position, any of the remaining 4 digits can be placed at the 3rd position. So on ... 1 5 4 3 2 1 i.e., total number of ways = (1)( 5)( 4)( 3)( 2)( 1) = 120 i.e., total count of numbers which can be formed with the left most digit as 1 = 120 Similarly, total count of numbers which can be formed with the left most digit as 2 = 120 Similarly, total count of numbers which can be formed with the left most digit as 3 = 120 i.e., 240 numbers (=120 + 120) can be formed (with left most digit as 1) or (with left most digit as 2) Similarly, 360 numbers (=120 + 120 + 120) can be formed (with left most digit as 1) or (with left most digit as 2) or (with left most digit as 3) Hence, the left most digit of the 249th number = 3 Now, let's find out how many numbers can be formed with the left most digit as 3 and next digit as 1 The digit '3' is placed at the 1st position (only 1 way of doing this) The digit '1' is placed at the 2nd position (only 1 way of doing this) Any of the remaining 4 digits can be placed at 3rd position. Since 3 digits are placed in the first three positions, any of the remaining 3 digits can be placed at the 4th position. Since 4 digits are placed in the first four positions, any of the remaining 2 digits can be placed at the 5th position. Since 5 digits are placed in the first five positions, the remaining 1 digit can be placed at the 6th position. 1 1 4 3 2 1 i.e., total number of ways = (1)(1)(4)(3)(2)(1) = 24 i.e., Total count of numbers which can be formed (with the left most digit as 3) and (next digit as 1) = 24 Similarly, total count of numbers which can be formed (with the left most digit as 3) and (next digit as 2) = 24 Hence, 120 + 120 + 24 + 24 = 288 numbers can be formed (with left most digit as 1) or (with left most digit as 2) or (with left most digit as 3 and next digit as 1) or (with left most digit as 3 and next digit as 2) Hence, the 289th number is the minimum value number which is formed with the left most digit as 3 and next digit as 4. i.e., the number is 341256 Answer : D The answer is: D

D

mathematics

In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?

[ "7.25", "8.5", "8", "9.15", "10" ]

Explanation : Required run rate = (324 - 4.2 20 ) = 240/ 30 = 8. Answer : C The answer is: C

C

mathematics

The effective annual rate of interest corresponding to a nominal rate of 6% per annum payable half-yearly is?

[ "6.99%", "6.89%", "6.08%", "6.09%", "6.19%" ]

Amount of Rs. 100 for 1 year when compounded half-yearly = [100 * (1 + 3/100)2] = Rs. 106.09 Effective rate = (106.09 - 100) = 6.09% Answer:D The answer is: D

D

mathematics

The vertex of a rectangle are (1, 0), (5, 0), (1, 1) and (5, 1) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?

[ "1/2", "2", "1/6", "3", "1/4" ]

If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 0.5). The slope of a line passing through (0,0) and (3, 0.5) is 0.5/3 = 1/6. The answer is C. The answer is: C

C

mathematics

The remainder when dividing the expression (X + Y) by 5 is 4. The remainder of X divided by 10 is 2. What is the remainder T of Y divided by 5?

[ "T=1.", "T=2.", "3.", "4.", "5." ]

X divided by 10 gives reminder of 2. X can be 2/12/22.... X+Y divided by 5 is 4. X + Y can be 4/ 9/ 19.... If X+Y= 4 and X is 2 then Y = 2 and Y/5 will give a reminder of 2 Similarly, if X+Y= 9 and X = 2, then y/5 will give a reminder of 2 Hence the answer must be 2 (B) Also.... x+y=5m+4 and x=10K+2 hence 10k+2+y=5m+4 or y=5(m-2k)+2, m-2k being a constant remainder is 2 hence answer is B The answer is: B

B

mathematics

Given that 268 * 74 = 19832, find the values of 2.68 * 0.74.

[ "1.9328", "1.9832", "1.9823", "1.9382", "None of them" ]

Sum of decimal places = (2 + 2) = 4 2.68 * 0.74 = 1.9832. Answer is B. The answer is: B

B

mathematics

On a windy day, out of every 3 sand dunes formed, only 1 remains. Out of 5 blown-out sand-dunes, 1 has treasure and only 2 out of 7 sand dunes formed have lucky coupons. Find the probability that the blown-out sand dune will contain both the things.

[ "2/25", "4/75", "7/75", "3/79", "4/5" ]

Probability of sand dune blown out = 2/3 Probability that it has treasure = 1/5 Probability that it has lucky coupon = 2/7 total probability = 2/3 * 1/5 * 2/7 = 3/79 ANSWER:D The answer is: D

D

mathematics

A team P of 20 engineers can complete work or task in 32 days. Another team Q of 16 engineers can complete same task in 30 days.Then the ratio of working capacity of 1 member of P to the 1 member of Q is a. 3 : 2

[ "22", "34", "77", "29", "21" ]

Explanation: Let the capacity of an engineer in P = x units, and in Q = y units. Working capacity of P = x × 32 × 20 Working capacity of Q = y × 16 × 30 As the total work is same, we equate the above equations. ⇒ x × 32 × 20 = y × 16 × 30 ⇒ xy=16×3032×20=34 Answer: B The answer is: B

B

mathematics

Two trains of equal lengths take 10 sec and 15 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?

[ "16 sec", "12 sec", "41 sec", "09 sec", "15 sec" ]

Speed of the first train = 120/10 = 12 m/sec. Speed of the second train = 120/5 = 8 m/sec. Relative speed = 12 + 8 = 20 m/sec. Required time = (120 + 120)/20 =12 sec. Answer: B The answer is: B

B

mathematics

If two-third of a bucket is filled in 100 seconds then the time taken to fill the bucket completely will be .

[ "90 seconds", "150 seconds", "60 seconds", "100 seconds", "120 seconds" ]

2/3 filled in 100 seconds 1/3 filled in 50 secs then 2/3+1/3=100 + 50 seconds = 150 seconds ANSWER: B The answer is: B

B

mathematics

A metal company's old machine makes bolts at a constant rate of 100 bolts per hour. The company's new machine makes bolts at a constant rate of 150 bolts per hour. If both machines start at the same time and continue making bolts simultaneously, how many minutes will it take the two machines to make a total of 350 bolts?

[ "84", "72", "120", "144", "180" ]

Old Machine 100 bolts in 60 mins so, 5/3 bolts in 1 min New Machine 150 bolts in 60 mins so, 5/2 bolts in 1 min together, 5/3 + 5/2 = 25/6 bolts in 1 min so, for 350 bolts 350 * 6 / 25 = 84 mins Ans A The answer is: A

A

mathematics

One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 7 robots altogether, if the robots build only one robot at a time?

[ "70 1/7 min", "94 1/7 min", "110 1/7 min", "112 1/7 min", "131 1/7 min" ]

First the 2 robots work at the rate of 1 + 1/2 = 3/2 so they complete one robot in 2/3 rd of an hour = 40 minutes - (1) Now the 3 robots work together at the rate of 1 + 1/2 + 1/2 = 4/2 = 2/1 so they complete one robot in 1/2 an hour,i.e 30 minutes - (2) Now the 4 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 = 5/2 so they complete one robot in 2/5th of an hour - (3) Now the 5 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2+1/2 = 3 so they complete one robot in 1/3th of an hour - (4) Now the 6 robots work together at the rate of 1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2 so they complete one robot in 2/5th of an hour - (5) And now we have 7 robots So Total = (1) + (2) + (3)+(4)+(5) = 131 1/7minutes Answer - E The answer is: E

E

mathematics

Pipe A can fill a tank in 16 hrs and pipe B can fill it in 24 hrs. If both the pipes are opened in the empty tank. In how many hours will it be fill 5/4th of that tank?

[ "10", "12", "14", "16", "18" ]

Part filled A in 1 hr= (1/16) Part filled B in 1 hr= (1/24) Part filled by (A+B) together in 1 hr=(1/16)+(1/24)=5/48 So, The tank will be full in 48/5 hrs Time taken to fill Exact quarter tank = (48/5) * (5/4) = 12 hrs Answer : B The answer is: B

B

mathematics

The average (arithmetic mean) of eight numbers is 43.2. If the sum of half of these numbers is 154.4, what is the average of the other half?

[ "44.2", "47.8", "50.5", "53.6", "56.9" ]

The average of this half is 154.4/4 = 38.6 This is 4.6 below the overall average, thus the average of the other half of the numbers must be 4.6 above the overall age, that is 43.2+4.6 = 47.8 The answer is B. The answer is: B

B

mathematics

If 1,000 microns = 1 decimeter, and 1,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?

[ "1,000", "100", "1,000,000", "10", "10,000" ]

Given that 1,000 microns = 1 decimeter =1,000,000,000 angstroms So, 1 micron = 1,000,000,000/1,000 =1,000,000 Answer : C The answer is: C

C

mathematics

Which of the following does NOT have a divisor greater than 1 that is the square of an integer?

[ "28", "32", "49", "62", "25" ]

Prime Factorization 28=2*2*7=2^2*7. Includes a perfect square of 4. 32=2*2*2*2*2=4^2*2. Includes the perfect square of 16. 49=7*7. Is a perfect square. 62=2*31. No perfect square here, so a possibility. 25= 5*5. Is a perfect square. All but 62 have perfect squares as a factor so D is the correct answer. 28=2*2*7=2^2*7. Perfect square of 4. 32=2*2*2*2*2=4^2*2. Perfect square of 16. 49=7*7. Perfect square. 62=2*31. No perfect square. 25= 5*5. Perfect square. The answer is: D

D

mathematics

A shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20% while buying and by 10% while selling. What is his percentage profit?

[ "10.22%", "20.22%", "21.22%", "20%", "Can't be calculated" ]

The owner buys 100kg but actually gets 120kg; The owner sells 100kg but actually gives 90kg; Profit: (120-90)/90*100=20% Answer: D. The answer is: D

D

mathematics

Find the value of x. (47% of 1442 - 36% of 1412) + 61 = x?

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

B) 2 The answer is: B

B

mathematics

Set A of 8 positive integers may have the same element and have 36. And set B of 8 positive integers must have different elements and have 36. When m and n are the greatest possible differences between 36 and other elements’ sums in set A and set B, respectively, m-n=?

[ "20", "21", "23", "25", "26" ]

This is maximum-minimum. Hence, 36-(1+1+1+1+1+1+1)=29 and 36-(1+2+3+4+5+6+7)=8. So, 29-8=21. The correct answer is B. The answer is: B

B

mathematics

If A lends Rs.2000 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is?

[ "90", "122.5", "132.5", "114.5", "212.5" ]

(2000*1.5*3)/100 => 90 ANSWER:A The answer is: A

A

mathematics

75% of the guestrooms at the Stagecoach Inn have a queen-sized bed, and each of the remaining rooms has a king-sized bed. Of the non-smoking rooms, 60% have a queen-sized bed. If 28% of the rooms at the Stagecoach Inn are non-smoking rooms with king-sized beds, what percentage of the rooms permit smoking?

[ "25%", "30%", "50%", "55%", "75%" ]

Let x be the number of non-smoking rooms. Let N be the total number of rooms at the inn. 40% of non-smoking rooms have a king-sized bed. 0.4x = 0.28N x = 0.7N The percentage of rooms which permit smoking is 1 - 0.7 = 30% The answer is B. The answer is: B

B

mathematics

The difference between the two numbers is 1/3 of the larger number. If the smaller one is 48 the larger one is

[ "72", "60", "32", "96", "65" ]

Explanation: Let the larger number be x. Then, x - 48 = 1/3 x x - x/3 = 48 => 2x/3 = 48 => x = 72 Answer: Option A The answer is: A

A

mathematics

Two pipes A and B can separately fill a cistern in 24 minutes and 48 minutes respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 12 minutes. In how much time, the third pipe alone can empty the cistern?

[ "90 min", "48 min", "54 min", "120 min", "130 min" ]

1/12-(1/24+1/48)=-1/48 third pipe can empty in 48 minutes ANSWER:B The answer is: B

B

mathematics

A train running at the speed of 60 km/hr crosses a pole in 15 seconds. Find the length of the train?

[ "150", "872", "250", "288", "212" ]

Speed = 60*(5/18) m/sec = 50/3 m/sec Length of Train (Distance) = Speed * Time (50/3) * 15 = 250 meter Answer:C The answer is: C

C

mathematics

A trader sells 80 meters of cloth for Rs. 10000 at the profit of Rs. 7 per metre of cloth. What is the cost price of one metre of cloth?

[ "118", "88", "90", "42", "22" ]

SP of 1m of cloth = 8925/85 = Rs. 125 CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth = Rs. 125 - Rs. 7 = Rs. 118 Answer:A The answer is: A

A

mathematics

A gardener grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 197 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?

[ "9801", "10,000", "14,400", "12,696", "can not be determined" ]

Let the side for growing cabbages this year be X ft. Thus the area is X^2. Let the side for growing cabbages last year be Y ft. Thus, the area was Y^2. The area would have increased by 197 sq ft as each cabbage takes 1 sq ft space. X^2 - Y^2 = 197 (X + Y)(X - Y) = 197 197 is a prime number and thus it will be (99+98)*(99-98). Thus X = 99 and Y = 98 X^2 = 99^2 = 9801 The answer is A. The answer is: A

A

mathematics

If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

[ "1/4", "3/8", "1/2", "5/8", "3/4" ]

total nos of ways in which we can choose n = 96 n(n + 1)(n + 2) will be divisible by 8? case 1: n = odd then n+2 =odd & n+1 will be even i.e this needs get divided by 8, hence is a multiple of 8 so we have 8..96 = 12 multiples to fill the n+1 pos hence 12 ways case 2: n is even then n+2 will be even & the product will be divisible by 24 & thus 8 so nos of values that can be used for n= 2....96 (all even nos) i.e 48 nos total = 48+12 =60 ways so reqd P =60/96 =5/8; ANSWER:D The answer is: D

D

mathematics

The length of a rectangular floor is more than its breadth by 100%. If Rs. 600 is required to paint the floor at the rate of Rs. 3 per sq m, then what would be the length of the floor?

[ "15.0m.", "14.4m.", "12.0m.", "16.2m.", "16.5m." ]

Let the length and the breadth of the floor be l m and b m respectively. l = b + 100% of b = l + 1b = 2b Area of the floor = 600/3 = 200 sq m l b = 200i.e., l * l/2 = 108 l2 = 216 => l = 14.4m. ANSWER:B The answer is: B

B

mathematics

Varma can read a book in k minutes. What part of the book can he read in 8 minutes?(k>8)

[ "6/k", "8/k", "83k", "2/k", "1/k" ]

Part of the book he can read in 1 minute = 1/k Part of the book he can read in 8 minutes =8/k. Answer: B The answer is: B

B

mathematics

How many positive integers less than 20 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3?

[ "14", "13", "12", "11", "10" ]

The numbers must be of the form 2a+3b,2a+3b, where aa and bb are positive integers. The smallest number is 5=2∗1+3∗1.5=2∗1+3∗1. Starting with 55, we can get all the other numbers by adding either 22 or 33 to the already existing numbers on our list. Adding either 22 or 33 to 2a+3b2a+3b will give another number of the same form. So, after 55, we get 5+2=7,5+3=8,7+2=9,8+2=10,...5+2=7,5+3=8,7+2=9,8+2=10,... We will get all the numbers up to 1919 inclusive, except 1,2,3,4,1,2,3,4,and 6,6, because once we have 77 and 8,8, by adding 22 all the time we can get any odd or even number. We get a total of 19−5=1419−5=14 numbers. Answer A The answer is: A

A

mathematics

Find the invalid no.from the following series 13, 18, 25, 30, 37, 40

[ "30", "35", "40", "47", "50" ]

The differences between two successive terms from the beginning are 7, 5, 7, 5, 7, 5. So, 40 is wrong. C The answer is: C

C

mathematics

Which answer is closest to the √17?

[ "a 4.1", "b 4.2", "c 4.4", "d 4.5", "e 4.6" ]

Try filling the numbers into the y's. y x y = 4.1 x 4.1= 16.81 4.2 x 4.2 = 17.64 Answer: A The answer is: A

A

mathematics

If the number 517*324 is completely divisible by 9, then the smallest whole number in the place of * will be:

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

Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 9. x = 5. C The answer is: C

C

mathematics

Last year, sales at Company Zora were 10% greater in February than in January, 10% less in March than in Feb, 20% greater in April than in March, 10% less in May than in April, and 10% greater in June than in May. In which month were sales closest to Jan?

[ "March", "April", "May", "June", "February" ]

Jan = $100 10% greater in February than in January ---> Feb = $110 10% less in March than in Feb ---> Mar = $99 20% greater in April than in March ---> Apr = $118.80 10% less in May than in April ---> May $106.92 10% greater in June than in May --->Jun = $117.61 Answer : A The answer is: A

A

mathematics

A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?

[ "120 sec", "198 sec", "178 sec", "665 sec", "276 sec" ]

Time taken to meet for the first time at the starting point = LCM { length of the track / speed of A , length of the track / speed of B} = LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) } = LCM (60, 40) = 120 sec. Answer:A The answer is: A

A

mathematics

The equation of line q is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line q?

[ "48", "50", "60", "75", "100" ]

This can be solve in two steps and without any complex calculation. Given : equation of line q as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0). This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet) So a perpendicular from the (0,0) to hypotenuse will be the answer. Area of triangle= 0.5*100*75=0.5*125* x => x=60; SO answer is 60=C The answer is: C

C

mathematics

In how many years will a sum of money doubles itself at 5% per annum on simple interest?

[ "29%", "20%", "07%", "50%", "23%" ]

P = (P*5*R)/100 R = 20% Answer:B The answer is: B

B

mathematics

If 30% of a number is equal to one-third of another number, what is the ratio of first number to the second number ?

[ "2:5", "3:7", "10:9", "7:3", "None of these" ]

Explanation : Let 30% of A=1/3B Then, 30A/100=1B/3 => 3A/10=B/3 => A:B= 10 : 9 Answer : C The answer is: C

C

mathematics

If X is the set of prime single-digit numbers and Y is a set containing each of the numbers in set X raised to the power of 2, how much greater is the median of set Y than the median of set X?

[ "2", "4", "9", "13", "17" ]

set X={2,3,5,7} set of prime single digit numbers set Y={4,9.25.49} each of the numbers in set X raised to the power of 2 Median set X= (3+5)/2= 4 Median set Y= (9+25)/2= 17 Required set Y - set X= 13 ANSWER:D The answer is: D

D

mathematics

The average weight of 10 persons increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

[ "107 kg", "80 kg", "120 kg", "90 kg", "100" ]

Solution Total weight increased = (10 x 4.2)kg = 42 kg. Weight of new person = (65 + 42)kg = 107kg. Answer A The answer is: A

A

mathematics

The cost price of an book is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?

[ "33%", "28.02%", "37.5%", "30.5%", "22%" ]

C 37.5% Let marked price = $100. Then, C.P. = $64, S.P. = $88 Gain % = 24/64 * 100 = 37.5%. The answer is: C

C

mathematics

If 13 = 13w/(1-w) ,then (w)2 =

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

13-13w=13w 26w=13 w=1/2 2w*2=1/2*2=1 ANSWER:C The answer is: C

C

mathematics

A box contains 15 mangoes out of which 8 are spoilt. If eight mangoes are chosen at random, find the probability that A number is selected at random from first twenty natural numbers. What is the chance that it is a multiple of either 4 or 15?

[ "17/10", "1/10", "7/10", "1/5", "3/10" ]

The probability that the number is a multiple of 4 is 5/20. (Since 4*5 = 20). Similarly the probability that the number is a multiple of 15 is 1/20. {Since 15*1 = 15). Neither 4 nor 15 has common multiple from 1 to 20. Hence these events are mutually exclusive events. Therefore chance that the selected number is a multiple of 4 or 15 is (5+1)/20 = 3/10. ANSWER:E The answer is: E

E

mathematics

The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 minutes, then the area of the park (in sq. m) is

[ "124345 m", "233234 m", "153600 m", "123567 m", "168999 m" ]

Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m. 60 Let length = 3x metres and breadth = 2x metres. Then, 2(3x + 2x) = 1600 or x = 160. Length = 480 m and Breadth = 320 m. Area = (480 x 320) m2 = 153600 m C The answer is: C

C

mathematics

If an article is sold at 20% profit instead of 14% profit, then the profit would be Rs. 180 more. What is the cost price?

[ "Rs.1000", "Rs. 2000", "Rs. 3000", "Rs. 4000", "Rs.5200" ]

Explanation: Let the cost price of an article be Rs. x. (20% of x) - (14% of x) = 180 20x/100 - 14x/100 = 105 => 6x = 180 * 100 => x = 3000 Cost price = Rs. 3000 Answer:C The answer is: C

C

mathematics

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 6 m, the volume of the box (in m3) is:

[ "4830", "5184", "6420", "8960", "7960" ]

Clearly, l = (48 - 12)m = 36 m, b = (36 -12)m = 24 m, h = 8 m. Volume of the box = (36 x 24 x 12) m3 = 5184 m3. Answer: Option B The answer is: B

B

mathematics

A bowl was filled with 10 ounces of water, and 0.010 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?

[ "0.004%", "0.04%", "0.40%", "5%", "40%" ]

Total amount of water evaporated each day during a 50-day period = .008 * 50 =.010 * 100/2 = 1.0/2 = .5 percent of the original amount of water evaporated during this period = (.5/10) * 100% = 5 % Answer D The answer is: D

D

mathematics

A farmer used 1,034 acres of land for beans, wheat, and corn in the ratio of 5 : 2 : 4, respectively. How many R acres were used for corn?

[ "188", "258", "376", "470", "517" ]

consider 5x acres of land used for bean consider 2x acres of land used for wheat consider 4x acres of land used for corn Total given is 1034 acres 11x =1034 x = 94 land used for corn R= 4 * 94 = 376 correct option - C The answer is: C

C

mathematics

The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 36 years, then find the age of the person sitting in the middle of the row?

[ "9 years", "29 years", "18 years", "13 years", "17 years" ]

Total age seven persons = (28 * 7)years Total age of the first three persons and the last three persons are (25 * 3) years and (36 * 3) years respectively. Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 36 * 3 = 196 - 75 - 108 = 13 years. ANSWER:D The answer is: D

D

mathematics

The largest four digit number which is a multiple of 8, 10,12 and 15 is:

[ "9960", "9950", "9940", "9930", "9920" ]

lcm=120 9999/120=83 83*120=9960 ANSWER:A The answer is: A

A

mathematics

The sum of the first n positive perfect squares, where n is a positive integer, is given by the formula n^3/3 + c*n^2 + n/6, where c is a constant. What is the sum of the first 18 positive perfect squares?

[ "1,010", "1,164", "1,240", "1,316", "2,109" ]

First we need to find the constant 'c'. The easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively. Hence LHS = 1+4 and plug n=2 for RHS and simplify to get c = 1/2. Plug values of n = 18 and c = 1/2 into the equation and simplify to get the answer 2109. Option E. The answer is: E

E

mathematics

If it takes a tub 6 minutes to drain 5/7 of its content, how much more time will it take for the tub to be empty?

[ "48 seconds", "1 minute, 12 seconds", "1 minute, 50 seconds", "2 minutes, 24 seconds", "4 minutes, 12 seconds" ]

If 5/7 of tub's content is drained 2/7 th of tub still needs to be drained. If it takes 6 minutes to drain 5/7 th of tub it takes 6*(7/5) minutes to drain the entire tub and 6*(7/5)*(2/7) min to drain 2/7 th of the tub which is 2.4 minutes or 12/5 minutes or 2 minute 24 seconds So answer is D The answer is: D

D

mathematics

Three workers have a productivity ratio of 1 to 2 to 4. All three workers are working on a job for 4 hours. At the beginning of the 5th hour, the slowest worker takes a break. The slowest worker comes back to work at the beginning of the 9th hour and begins working again. The job is done in ten hours. What was the ratio of the work performed by the fastest worker as compared to the slowest?

[ "12 to 1", "6 to 1", "5 to 1", "20 to 3", "1 to 5" ]

The fastest worker who does 4 units of job worked for all 10 hours, so he did 4*10=40 units of job; The slowest worker who does 1 unit of job worked for only 4+2=6 hours (first 4 hours and last 2 hours), so he did 1*6=6 units of job; The ratio thus is 40 to 6, or 20 to 3. Answer: D The answer is: D

D

mathematics

Series B(n) is such that i*B(i) = j*B(j) for any pair of positive integers (i, j). If B(1) is a positive integer, which of the following is possible? I. 2*B(100) = B(99) + B(98) II. B(1) is the only integer in the series III. The series does not contain negative numbers

[ "I only", "II only", "IIII only", "IIIII only", "I, IIIII" ]

First thing I want to understand is this relation: i*B(i) = j*B(j) for any pair of positive integers. I will take examples to understand it. When i = 1 and j = 2, B(1) = 2*B(2) So B(2) = B(1)/2 When i = 1 and j = 3, B(1) = 3*B(3) So B(3) = B(1)/3 I see it now. The series is: B(1), B(1)/2, B(1)/3, B(1)/4 and so on... II and III are easily possible. We can see that without any calculations. II. B(1) is the only integer in the series If B(1) = 1, then series becomes 1, 1/2, 1/3, 1/4 ... all fractions except B(1) III. The series does not contain negative numbers Again, same series as above applies. In fact, since B(1) is a positive integer, this must be true. I. 2*B(100) = B(99) + B(98) 2*B(1)/100 = B(1)/99 + B(1)/98 (cancel B(1) from both sides) 2/100 = 1/99 + 1/98 Not true hence this is not possible Answer (D) The answer is: D

D

mathematics

A train passes a platform in 32 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is

[ "180 meter", "240 meter", "200 meter", "260 meter", "None of these" ]

Explanation: Speed of the train = 54 km/hr = (54×10)/32 m/s = 15 m/s Length of the train = speed × time taken to cross the man = 15×20 = 300 m Let the length of the platform = L Time taken to cross the platform = (300+L)/15 => (300+L)/15 = 32 => 300+L = 15×32 =480 => L = 480-300 = 180 meter Answer: Option A The answer is: A

A

mathematics

The no. of gift pack bought by Dexter is 1 more than the price, in rupees, of each gift pack. The amount of Rs.380 which Dexter had, fell short of the required amount. What is theamount by which he might have fallen short.

[ "38", "40", "45", "48", "49" ]

Let the price of gift pack be 'aa' Then number of packs bought =a+1=a+1 Hence total cost is a(a+1)a(a+1) It is given that 380<a(a+1)380<a(a+1) If a=19a=19, the total cost =19×20=380=19×20=380 Dexter would not have fallen short, If: a=20a=20, a(a+1)=420a(a+1)=420 So he would have fallen short by Rs 40. This is the minimum amount by which he may have fallen short. B) The answer is: B

B

mathematics

If x and y are different integers and x^2 = xy, which of the following must be true ? I. x = 0 II. y = 0 III. x = -y

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

Re-arrange equation: x^2 - xy = 0 => x*(x-y) = 0 Therefore, either x=0 or x=y. We know that x and y are different, so x must be equal to 0. ANSWER:A The answer is: A

A

mathematics

Which of the following inequalities has (have) a finite range of values of "x" satisfying it (them)?

[ "x^2 + 5x + 6 > 0", "|x + 2| > 4", "9x - 7 < 3x + 14", "x^2 - 4x + 3 < 0", "(B) and (D)" ]

Factorizing x^2 - 4x + 3 < 0 we get, (x - 3)(x - 1) < 0. This inequality will hold good when one of the terms (x - 3) or (x - 1) is positive and the other is negative. Evaluating both the options, we get 1 < x < 3. i.e., a finite range of values for "x". ANSWER : D The answer is: D

D

mathematics

The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?

[ "252 kms", "152 kms", "552 kms", "752 kms", "152 kms" ]

Explanation: Total distance travelled in 12 hours =(35+37+39+.....upto 12 terms) This is an A.P with first term, a=35, number of terms, n= 12,d=2. Required distance = 12/2[2 x 35+{12-1) x 2] =6(70+23) = 552 kms. Answer: C The answer is: C

C

mathematics

Sales price is $54, gross profit is 125% of cost, what is the value of gross profit?

[ "32", "30", "39", "40", "42" ]

Cost + Profit = Sales Cost + (125/100)Cost = 54 Cost = 24 Profit = 54 - 24 = 30 Answer (B) The answer is: B

B

mathematics

Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 5000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?

[ "100000", "100500", "105000", "Data inadequate", "None of these" ]

Let the investment of X in 1995 be x. ∴ Profit = x⁄5 ∴ Income = (x + x⁄5) = 6⁄5x Investment of company X in 1996 would be (x – 5000) From the question, (x - 500) × 126⁄100 = 6⁄5x ⇒ x = 105000 Answer C The answer is: C

C

mathematics

A sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. How many dollars’ worth of sales does she need to make in order to bring her total weekly income to $600?

[ "$3,000", "$3,150", "$4,000", "$2,500", "$5,000" ]

We're told that a sales representative receives a salary of $100 per week and earns a commission of 20% on all sales she makes. We're asked how many dollars’ worth of sales will bring her total weekly income to $600. Since the salesperson receives a $100 salary, the remaining $500 has to be accounted for by the 20% commission. Since those numbers are rather specific, we're likely dealing with a 'round number' for total sales. Let's TEST Answer C: $4,000 Since 20% of $1,000 = $200 20% of $4,000 = 4($200) = $800 This is TOO HIGH (it's supposed to be $500), so we need a LOWER total sales figure. Let's TEST Answer D: $2,500 Since 20% of $1,000 = $200 20% of $2,500 = 2.5($200) = $500 This is an exact MATCH for what we were told, so this MUST be the answer. Final Answer: D The answer is: D

D

mathematics

A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 3,000 B's share was Rs. 1000. A's investment was

[ "s. 4,500", "s. 8,250", "s. 9,500", "s. 10,000", "s. 12,250" ]

A+B=15000 total profit=3000 3000-1000=2000 2000;1000=2:1 then 2*15000/3=10000 ANSWER:D The answer is: D

D

mathematics

If the circumference of a circle increases from 4pi to 8 pi, what change occurs in the area ?

[ "Area is quadrupled", "Area is tripled", "Area is doubles", "Area become half", "None of these" ]

Explanation: 2πR1=4π =>R1=22πR2=8π >R2=4Original Area =4π∗22=16πNew Area =4π∗42=64π So the area quadruples. Option A The answer is: A

A

mathematics

Among 700people, 56% like strawberry jam, 44% like apple jam, and 40% like raspberry jam. If 30% of the people like both strawberry and apple jam, what is the largest possible number of people who like raspberry jam but do not like either strawberry or apple jam?

[ "20", "60", "80", "186", "210" ]

56%+44%-30%=70% who like either Strawberry, Apple, or both. That means 100%-70% = 30% do not like either Apple of Strawberry jam. 30% is the most possible that like raspberry jam but do not like either strawberry or apple (assuming nobody in the group does not like any) E The answer is: E

E

mathematics

Shane is playing a board game. For his first turn he moved ahead 3 spaces, for the second, 5 spaces and for the third, 1 space. For his next turn he had to go back 6 spaces. After that he got a card that said he could move two times the biggest forward move he had done so far. Now how many spaces from the beginning is Shane’s game piece?

[ "3", "13", "23", "33", "43" ]

You may want to draw this one. biggest move is 5, so two times biggest move is 10. 3 + 5 + 1 = 9 9 - 6 = 3 3 + 10 = 13, so he is 13 spaces from the beginning. correct answer B The answer is: B

B

mathematics

The ratio of three numbers is 6:7:5 and their sum is 108. The second number of the three numbers is?

[ "12", "42", "30", "36", "None of these" ]

Explanation: 6:7:5 Total parts = 18 18 parts --> 108 1 part ---->6 The second number of the three numbers is = 7 7 parts ----> 42 Answer: Option B The answer is: B

B

mathematics

In covering a distance of 24 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

[ "4 kmph", "6 kmph", "6.25 kmph", "7.5 kmph", "7.8 kmph" ]

Let Abhay's speed be x km/hr. Then, 24/X - 24/2X = 3 6x = 24 x = 4 km/hr. Answer: Option A The answer is: A

A

mathematics

On a certain transatlantic crossing, 40 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship. If 50 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

[ "40%", "50%", "60%", "80%", "90%" ]

Let T be the total number of passengers. Let x be the number of people with round trip tickets. 0.4T had round trip tickets and took their cars. 0.5x had round trip tickets and took their cars. 0.5x = 0.4T x = 0.8T The answer is D. The answer is: D

D

mathematics

The division of a whole number N by 14 gives a quotient of 18 and a remainder of 2. Find N.

[ "797", "254", "597", "997", "297" ]

According to the division process of whole numbers, N can be written, using multiplication, as follows N = quotient *divisor + remainder = 18* 14 + 2 = 254 correc answer B The answer is: B

B

mathematics

for which value of n, 4^85+2^3373+4^n will be the perfect square ??

[ "1878", "1978", "1578", "2578", "3287" ]

given expression is in the form of a^2+2ab+b^2 4^85=2^2(85) 4^n=2^2n 2^3373=2*2^85*2^n 3373=85+1+n n=3373-86=3287 ANSWER:E The answer is: E

E

mathematics

The president of a country and 4 other dignitaries are scheduled to sit in a row on the 5 chairs represented above. If the president must sit in the center chair, how many different seating arrangements are possible for the 5 people?

[ "4", "5", "20", "24", "120" ]

If the president is sitting in the center, you only have 4 chairs left. There are 4 possibilities for 1st chair, 3 possibilities for 2nd chair, 2 possibilities for 3rd chair, and 1 for last chair. Multiply all those and you get 24. ANS:D. The answer is: D

D

mathematics

A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 24,000 earned at the end of 2 years from the starting of the business?

[ "A)7500", "B)7389", "C)7200", "D)7453", "E)7637" ]

A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3 B's share = 24000 * 3/10 = Rs.7200. Answer: C The answer is: C

C

mathematics

The sum of the first 50 positive even integers is 2550. What is the sum W of even integers from 102 to 200 inclusive?

[ "5100", "7550", "10100", "15500", "20100" ]

My solution is: First 50 even integers: 2 4 6 8 <...> Integers from 102 to 200 102 104 106 108 <...> We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then: W=2550+(100*50)=7550.B The answer is: B

B

mathematics

A sum of money deposited at C.I. amounts to Rs.6000 in 6 years and to Rs.7500 in 7 years. Find the rate percent?

[ "25%", "20%", "15%", "10%", "5%" ]

6000 --- 1500 100 --- ? => 25% Answer: A The answer is: A

A

mathematics

Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 0: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

[ "4: 45 p.m.", "2: 20 p.m.", "5: 20 p.m.", "5: 35 p.m.", "6: 00 p.m." ]

the distance travelled by the train A in first 20 minutes will be 10. The distance which will be remaining is 80. Now both trains are running in opposite direction.Their speed will be added so 40. Time at which they will meet =80/40=2 time of train B will be 0:20 +2=2:20 Hence answer is B.Hope i am correct The answer is: B

B

mathematics

A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:

[ "8.5 km/hr", "9 km/hr", "10 km/hr", "12.5 km/hr", "25km/hr" ]

Explanation: Man's rate in still water = (15 - 2.5) km/hr = 12.5 km/hr. Man's rate against the current = (12.5 - 2.5) km/hr = 10 km/hr. Answer: C The answer is: C

C

mathematics

If 3 tic equals 6 tacs and 2 tacs equal 7 tocs, what is the ratio of one tic to one toc?

[ "7/1", "6/5", "5/6", "3/10", "1/15" ]

3Tic=6*Tac and 2*Tac=7*Toc; 6*Tic=12*Tac and 12*Tac=42*Toc --> 6*Tic=42*Toc --> Tic/Toc=42/6=7/1. Answer: A. The answer is: A

A

mathematics

John invests $x at the semi-annual constant compounded rate of 2 percent and also does $8,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??

[ "10000", "12000", "16160.8", "14000", "15000" ]

A = P(1+r/n)^nt A= total amount accrued P = principal deposited r = rate of interest in decimal form n = number of times per year, interest compounded t = time in number of years. . x(1+0.02/2)^2 - x = 8,000(1+0.04/4)^4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal) => x[(1.01)^2 - 1] = 8,000[(1.01)^4 - 1] => x[(1.01)^2 - 1] = 8,000[(1.01)^2+1][(1.01)^2-1] --> Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides => x = 8,000(1.0201+1) =16160.8 Hence answer is C. The answer is: C

C

mathematics

Find the simple interest on Rs. 70,400 at 16 2/3% per annum for 9 months.

[ "s.8500", "s.8000", "s.7500", "s.8800", "s.6500" ]

P = Rs.70400,R = 50/3% p.a and T = 9/12 years = 3/4years. S.I. = (P*R*T)/100 = Rs.(70,400*(50/3)*(3/4)*(1/100)) = Rs.8800 Answer is D. The answer is: D

D

mathematics

The sum of four consecutive even numbers is 36. Find the sum of the squares of these numbers?

[ "323", "377", "344", "239", "112" ]

Explanation: Let the four numbers be x, x + 2, x + 4 and x + 6. => x + x + 2 + x + 4 + x + 6 = 36 => 4x + 12 = 36 => x = 6 The numbers are 6, 8, 10 and 12. Sum of their squares = 62 + 82 + 102 + 122 = 36 + 64 + 100 + 144 = 344. Answer: C The answer is: C

C

mathematics

80% of 5/8 =

[ "0.2", "0.5", "0.6", "0.75", "1.0" ]

Should be simple. 0.8*5/8 = 4/8 = 1/2 = 0.5 Correct Option : B The answer is: B

B

mathematics

What is the unit digit in 8^100?

[ "0", "1", "6", "3", "5" ]

Unit digit in 8^100 = unit digit in [(8^4)^25 ] But unit digit in 8^4=6 unit digit 8^100= 6 Answer is C The answer is: C

C

mathematics

Mark bought a set of 6 flower pots of different sizes at a total cost of $8.25. Each pot cost 0.1 more than the next one below it in size. What was the cost, in dollars, of the largest pot?

[ "$1.62", "$1.85", "$2.00", "$2.15", "$2.30" ]

This question can be solved with a handful of different Algebra approaches (as has been shown in the various posts). Since the question asks for the price of the largest pot, and the answers are prices, we can TEST THE ANSWERS. We're told that there are 6 pots and that each pot costs 25 cents MORE than the next. The total price of the pots is $8.25. We're asked for the price of the largest (most expensive) pot. Since the total price is $8.25 (a 10-cent increment) and the the difference in sequential prices of the pots is 10 cents, the largest pot PROBABLY has a price that is a 10-cent increment. From the answer choices, I would then TEST Answer A first IF.... The largest pot = $1.625 1.125 1.225 1.325 1.425 1.525 1.625 Total = $8.25 So this MUST be the answer. A The answer is: A

A