regisss/math_qa huggingface dataset:
Problem: 15 men take 21 days of 8 hrs . each to do a piece of work . how many days of 4 hrs . each would it take for 21 women if 3 women do as much work as 2 men ?
Options: a ) 30 , b ) 20 , c ) 15 , d ) 25 , e ) 45
Rationale: "let 1 man does 1 unit / hr of work 15 m in 21 days of 8 hrs will do ( 15 * 21 * 8 ) units 3 w = 2 m 1 w = ( 2 / 3 ) units / hr 21 w with 4 hrs a day will take ( 15 * 21 * 8 ) / ( 21 * 4 * ( 2 / 3 ) ) days = > 45 days answer : e"
Answer: e
Problem: from a group of 4 boys and 4 girls , 6 children are to be randomly selected . what is the probability that 3 boys and 3 girls will be selected ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 5 , d ) 4 / 7 , e ) 5 / 9
Rationale: "the total number of ways to choose 6 children from 8 is 8 c 6 = 28 the number of ways to choose 3 boys and 3 girls is 4 c 3 * 4 c 3 = 4 * 4 = 16 p ( 3 boys and 3 girls ) = 16 / 28 = 4 / 7 the answer is d ."
Answer: d
Problem: on dividing 21 by a number , the quotient is 10 and the remainder is 1 . find the divisor .
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 7
Rationale: "d = ( d - r ) / q = ( 21 - 1 ) / 10 = 20 / 10 = 2 b"
Answer: b
Problem: if length of a rectangle is equal to side of a square and breadth of rectangle is half of length . if area of square is 36 sq . m . calculate the area of rectangle ?
Options: a ) 18
b ) 20
c ) 27
d ) 32
e ) 25
Rationale: side of square = √ 36 = 6 m . length = 6 m and breadth = 3 m area of rectangle = 6 * 3 = 18 sq . m answer a
Answer: a
Problem: the price of a t . v . set worth rs . 70000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 22678 , b ) 26699 , c ) 69000 , d ) 19000 , e ) 26711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 70000 - 1000 ) = rs . 69000 answer : c"
Answer: c
Problem: the original price of a suit is $ 200 . the price increased 20 % , and after this increase , the store published a 20 % off coupon for a one - day sale . given that the consumers who used the coupon on sale day were getting 20 % off the increased price , how much did these consumers pay for the suit ?
Options: a ) $ 192 , b ) $ 198 , c ) $ 200 , d ) $ 208 , e ) $ 216
Rationale: "0.8 * ( 1.2 * 200 ) = $ 192 the answer is a ."
Answer: a
Problem: 998 x 998 = ?
Options: a ) 996000 , b ) 1000000 , c ) 996004 , d ) 4000 , e ) 996008
Rationale: "998 x 998 = ( 998 ) 2 = ( 1000 - 2 ) 2 = ( 1000 ) 2 + ( 2 ) 2 - ( 2 x 1000 x 2 ) = 1000000 + 4 - 4000 = 1000004 - 4000 = 996004 . c )"
Answer: c
Problem: steve traveled the first 2 hours of his journey at 55 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
Options: a ) 60 mph , b ) 56.67 mph , c ) 70 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "distance traveled in 2 hours = 2 * 55 = 110 m distance traveled in 3 hours = 3 * 80 = 240 m total distance covered = 240 + 110 = 350 m total time = 2 + 3 = 5 h hence avg speed = total distance covered / total time taken = 350 / 5 = 70 mph answer : c"
Answer: c
Problem: in a basketball game , dhoni scored 30 points more than dravid , but only half as many points as shewag . if the 3 players scored a combined total of 150 points , how many points did dhoni score ?
Options: a ) 50 , b ) 52 , c ) 35 , d ) 40 , e ) 45
Rationale: let dravid scored point = x then dhoni scored = x + 30 shewag scored = 2 * ( x + 30 ) = 2 x + 60 as given , x + x + 30 + 2 x + 60 = 150 points 4 x + 90 = 150 x = 150 - 90 / 4 = 15 so dhoni scored = x + 30 i . e ) 15 + 30 = 45 answer : e
Answer: e
Problem: on a partly cloudy day , milton decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets cloudy , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 7 , e ) 1 / 3
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : d
Answer: d
Problem: if the sample interest on a sum of money 10 % per annum for 2 years is $ 1200 , find the compound interest on the same sum for the same period at the same rate ?
Options: a ) $ 1260 , b ) $ 1520 , c ) $ 1356 , d ) $ 1440 , e ) $ 1210
Rationale: rate = 10 % time = 2 years s . i . = $ 1200 principal = 100 * 1200 / 10 * 2 = $ 6000 amount = 6000 ( 1 + 10 / 100 ) ^ 2 = $ 7260 c . i . = 7260 - 6000 = $ 1260 answer is a
Answer: a
Problem: if 35 % of a number is 12 less than 50 % of that number , then the number is ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 80 , e ) 70
Rationale: "let the number be x . then , 50 % of x - 35 % of x = 12 50 / 100 x - 35 / 100 x = 12 x = ( 12 * 100 ) / 15 = 80 . answer : d"
Answer: d
Problem: find the number of different prime factors of 441
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "explanation : l . c . m of 441 = 3 x 3 x 7 x 7 3 , 7 number of different prime factors is 2 . answer : option b"
Answer: b
Problem: rs 50000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?
Options: a ) 20000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
Rationale: let first parrt is x and second part is y then x + y = 50000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 50000 + y so y = 30000 then x = 50000 - 30000 = 20000 first part = 20000 answer : a
Answer: a
Problem: the average of 10 consecutive odd numbers is 22 . what is the sum of the first 3 numbers ?
Options: a ) 13 , b ) 45 , c ) 17 , d ) 220 , e ) 90
Rationale: "22 = ( n + n + 2 + n + 4 + . . . + ( n + 18 ) ) / 10 22 = ( 10 n + ( 2 + 4 + . . . + 18 ) ) / 10 220 = 10 n + 2 ( 1 + 2 + . . . + 9 ) 220 = 10 n + 2 ( 9 ) ( 10 ) / 2 220 = 10 n + 90 220 - 90 = 10 n 130 = 10 n n = 13 so the first three numbers are 13 , 15 , 17 13 + 15 + 17 = 45 option b"
Answer: b
Problem: a number when divided by a certain divisor left remainder 245 , when twice the number was divided by the same divisor , the remainder was 112 . find the divisor ?
Options: a ) 378 , b ) 365 , c ) 380 , d ) 456 , e ) 460
Rationale: "easy solution : n = dq 1 + 245 2 n = 2 dq 1 + 490 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 378 d * some integer = 378 checking all options only ( a ) syncs with it . answer a"
Answer: a
Problem: 4 out of 8 employees are capable of doing a certain task . sixty percent of the 5 employees , including the 4 who are capable , are assigned to a project involving this task . what percentage of employees assigned to the project are not capable ?
Options: a ) 43.33 % , b ) 33.33 % , c ) 13.33 % , d ) 38.33 % , e ) none
Rationale: given 50 % of 8 employees including 4 who are capable of doing task . 60 % of 5 employeees = 50 / 100 * 4 = 4 employees = = = > 4 employees who are capable of doing the task and no one employee who is not capable . percentage of employees assigned who are not capable answer : e
Answer: e
Problem: 85 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: "answer = a please refer diagram below 85 - 10 = 75"
Answer: a
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places
Options: a ) 34 , b ) 35 , c ) 56 , d ) 67 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 16 + 14 ) = 60 cm parameter of the square = 60 cm i . e . 4 a = 60 a = 15 diameter of the semicircle = 15 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 15 ) = 1 / 2 ( 22 / 7 ) ( 15 ) = 330 / 14 = 23.57 cm to two decimal places answer : option e"
Answer: e
Problem: a flagstaff 17.5 m high casts a shadow of length 40.25 m . the height of the building , which casts a shadow of length 28.75 m under similar conditions will be :
Options: a ) 10 m , b ) 12.5 m , c ) 17.5 m , d ) 21.25 m , e ) none
Rationale: "let height of the building be x meters 40.25 : 28.75 : : 17.5 < = > 40.25 x x = 28.75 x 17.5 x = 28.75 x 17.5 / 40.25 x = 12.5 answer : option b"
Answer: b
Problem: x can do a piece of work in 4 hours ; y and z together can do it in 3 hours , while x and z together can do it in 2 hours . how long will y alone take to do it ?
Options: a ) 5 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) 15 hours
Rationale: x 1 hour ' s work = 1 / 4 ; y + z ' s hour ' s work = 1 / 3 x + y + z ' s 1 hour ' s work = 1 / 4 + 1 / 3 = 7 / 12 y ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 . y alone will take 12 hours to do the work . c
Answer: c
Problem: how many liters of water must be evaporated from 50 liters of a 6 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "6 % of a 50 liter solution is 3 l which is 10 % of the solution at the end . the solution at the end must be 30 l . we need to evaporate 20 liters . the answer is a ."
Answer: a
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 40 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: "total men in company 40 % means total women in company 60 % ( assume total people in company 100 % ) no of men employees attended picnic = 40 x ( 20 / 100 ) = 8 no of women employees attended picnic = 60 x ( 40 / 100 ) = 24 total percentage of employees attended the picnic = 8 + 24 = 32 % answer : a"
Answer: a
Problem: 7 log 7 ( 8 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 8
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 7 log 7 ( 8 ) = 8 correct answer e"
Answer: e
Problem: excluding stoppages , the speed of a bus is 84 kmph and including stoppages , it is 70 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 min , b ) 10 min , c ) 15 min , d ) 14 min , e ) 13 min
Rationale: "due to stoppages , it covers 14 km less . time taken to cover 14 km = ( 14 / 84 x 60 ) min = 10 min answer : b"
Answer: b
Problem: 40 is what percent of 160 ?
Options: a ) 35 % , b ) 40 % , c ) 45 % , d ) 50 % , e ) 25 %
Rationale: 40 / 160 × 100 = 25 % answer : e
Answer: e
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.50 $ , b ) 380.50 $ , c ) 425.50 $ , d ) 450.50 $ , e ) 465.60 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 57 ) = 465.60 hence answer will be ( e )"
Answer: e
Problem: the l . c . m of 22 , 54 , 108 , 135 and 198 is
Options: a ) 5942 , b ) 2887 , c ) 5940 , d ) 2888 , e ) 28881
Rationale: answer : c ) 5940
Answer: c
Problem: the sale price sarees listed for rs . 280 after successive discount is 12 % and 8 % is ?
Options: a ) 288 , b ) 226 , c ) 250 , d ) 230 , e ) 262
Rationale: "280 * ( 88 / 100 ) * ( 92 / 100 ) = 226 answer : b"
Answer: b
Problem: a girl sitting in a train which is travelling at 40 kmph observes that a goods train travelling in a opposite direction , takes 12 seconds to pass him . if the goods train is 1120 m long , find its speed .
Options: a ) 295 , b ) 296 , c ) 297 , d ) 298 , e ) 299
Rationale: relative speed = ( 1120 / 12 ) m / s = ( 1120 / 12 ) * ( 18 / 5 ) = 336 kmph speed of goods train = 336 - 40 = 296 kmph answer is b
Answer: b
Problem: a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction t of the sum of the 21 numbers in the list ?
Options: a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
Rationale: "this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction t of n to the total would be 4 a / 24 a or 1 / 6 answer b"
Answer: b
Problem: 107 x 107 + 93 x 93 = ?
Options: a ) 19578 , b ) 19418 , c ) 20098 , d ) 21908 , e ) none of them
Rationale: "= ( 107 ) ^ 2 + ( 93 ) ^ 2 = ( 100 + 7 ) ^ 2 + ( 100 - 7 ) ^ 2 = 2 x [ ( 100 ) ^ 2 + 7 ^ 2 ] = 2 [ 10000 + 49 ] = 2 x 10049 = 20098 answer is c"
Answer: c
Problem: a sum was put at simple interest at certain rate for 3 years . had it been put at 1 % higher rate it would have fetched rs . 66 more . the sum is : a . rs . 2,400 b . rs . 2,100 c . rs . 2,200 d . rs . 2,480
Options: a ) 2000 , b ) 2100 , c ) 2200 , d ) 2300 , e ) 2400
Rationale: "1 percent for 3 years = 66 1 percent for 1 year = 22 = > 100 percent = 2200 answer : c"
Answer: c
Problem: the difference between the place value and the face value of 6 in the numeral 856973 is
Options: a ) 973 , b ) 6973 , c ) 5994 , d ) 6084 , e ) none of these
Rationale: "( place value of 6 ) - ( face value of 6 ) = ( 6000 - 6 ) = 5994 answer : option c"
Answer: c
Problem: 60 % of a number is added to 180 , the result is the same number . find the number ?
Options: a ) 300 , b ) 277 , c ) 266 , d ) 99 , e ) 450
Rationale: ": ( 60 / 100 ) * x + 180 = x 2 x = 900 x = 450 answer : e"
Answer: e
Problem: andrew travelling to 7 cities . gasoline prices varied from city to city . $ 1.75 , $ 1.61 , $ 1.79 , $ 2.11 , $ 1.96 , $ 2.09 , $ 1.82 . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.82 , c ) $ 1.92 , d ) $ 2.13 , e ) $ 2.15
Rationale: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.82 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.82 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b
Answer: b
Problem: if 625 ( 5 ^ x ) = 1 then x =
Options: a ) – 2 , b ) - 4 , c ) 0 , d ) - 1 , e ) 2
Rationale: "5 ^ x = 1 / 625 5 ^ x = 1 / 5 ^ 4 5 ^ x = 5 ^ - 4 x = - 4 b"
Answer: b
Problem: find the least number of complete years in which a sum of money put out at 45 % compound interest will be more than double of itself ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "2 years answer : a"
Answer: a
Problem: the speed of the boat in still water in 12 kmph . it can travel downstream through 45 kms in 3 hrs . in what time would it cover the same distance upstream ?
Options: a ) 8 hours , b ) 6 hours , c ) 4 hours , d ) 5 hours , e ) 6 hours
Rationale: still water = 12 km / hr downstream = 45 / 3 = 15 km / hr upstream = > > still water = ( u + v / 2 ) = > > 12 = u + 15 / 2 = 9 km / hr so time taken in upstream = 45 / 9 = 5 hrs answer : d
Answer: d
Problem: the avg weight of a , b & c is 55 kg . if d joins the group , the avg weight of the group becomes 60 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 58 kg . what is the weight of a ?
Options: a ) 56 , b ) 65 , c ) 75 , d ) 86 , e ) 90
Rationale: "a + b + c = 3 * 55 = 165 a + b + c + d = 4 * 60 = 240 - - - - ( i ) so , d = 75 & e = 75 + 3 = 78 b + c + d + e = 58 * 4 = 232 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 240 – 232 = 8 a = e + 8 = 78 + 8 = 86 answer : d"
Answer: d
Problem: a train 120 m in length crosses a telegraph post in 12 seconds . the speed of the train is ?
Options: a ) 16 kmph , b ) 88 kmph , c ) 36 kmph , d ) 18 kmph , e ) 19 kmph
Rationale: "s = 120 / 12 * 18 / 5 = 36 kmph answer : c"
Answer: c
Problem: a small table has a length of 12 inches and a breadth of b inches . cubes are placed on the surface of the table so as to cover the entire surface . the maximum side of such cubes is found to be 4 inches . also , a few such tables are arranged to form a square . the minimum length of side possible for such a square is 32 inches . find b .
Options: a ) 8 , b ) 16 , c ) 24 , d ) 32 , e ) 48
Rationale: "from the info that the maximum sides of the cubes is 4 , we know that the gcf of 12 ( = 2 ^ 2 * 3 ) andbis 4 ( = 2 ^ 2 ) , sob = 2 ^ x , where x > = 2 . from the second premise , we know that the lcm of 12 ( 2 ^ 2 * 3 ) andbis 32 ( 2 ^ 5 ) , sob = 2 ^ 5 combining 2 premises shows the answer is d ( 32 ) ."
Answer: d
Problem: if ' a ' completes a piece of work in 3 days , which ' b ' completes it in 5 days and ' c ' takes 10 days to complete the same work . how long will they take to complete the work , if they work together ?
Options: a ) 1.5 days , b ) 4.5 days , c ) 7 days , d ) 9.8 days , e ) 9 days
Rationale: explanation : hint : a ' s one day work = 1 / 3 b ' s one day work = 1 / 5 c ' s one day work = 1 / 10 ( a + b + c ) ' s one day work = 1 / 3 + 1 / 5 + 1 / 10 = 1 / 1.5 hence , a , b & c together will take 1.5 days to complete the work . answer is a
Answer: a
Problem: a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 105 liters of drink a to convert it to drink b ?
Options: a ) 14 , b ) 21 , c ) 28 , d ) 35 , e ) 42
Rationale: "in 105 liters of drink a , there are 60 liters of milk and 45 liters of juice . with 60 liters of milk , we need a total of 80 liters of juice to make drink b . we need to add 35 liters of juice . the answer is d ."
Answer: d
Problem: at what rate percent per annum will a sum of money double in 9 years .
Options: a ) 12.5 % , b ) 13.5 % , c ) 11.5 % , d ) 11.1 % , e ) 21.5 %
Rationale: "let principal = p , then , s . i . = p and time = 8 years rate = [ ( 100 x p ) / ( p x 9 ) ] % = 11.1 % per annum . answer : d"
Answer: d
Problem: evaluate : 30 - 12 ÷ 3 × 2 =
Options: a ) 11 , b ) 22 , c ) 33 , d ) 44 , e ) 55
Rationale: "according to order of operations , 12 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 3 × 2 = 4 × 2 = 8 hence 30 - 12 ÷ 3 × 2 = 30 - 8 = 22 correct answer is b ) 22"
Answer: b
Problem: if n is a prime number greater than 11 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 11 , square it and see what would be the remainder upon division of it by 12 . n = 17 - - > n ^ 2 = 289 - - > remainder upon division 289 by 12 is 1 . answer : b ."
Answer: b
Problem: if a * b = 2 a - 3 b + ab , then 3 * 5 + 5 * 3 is equal to :
Options: a ) 22 , b ) 37 , c ) 38 , d ) 398 , e ) 72
Rationale: "explanation : 3 * 5 + 5 * 3 = ( 2 * 3 - 3 * 5 + 3 * 5 ) + ( 2 * 5 - 3 * 3 + 5 * 3 ) = ( 6 + 10 - 9 + 15 ) = 22 . answer : a ) 22"
Answer: a
Problem: noelle walks from point a to point b at an average speed of 3 kilometers per hour . at what speed , in kilometers per hour , must noelle walk from point b to point a so that her average speed for the entire trip is 4 kilometers per hour ?
Options: a ) 5.75 , b ) 6 , c ) 7.25 , d ) 7.5 , e ) 7.75
Rationale: "let ' s suppose that speed while returning was xkm / h since the distance is same , we can apply the formula of avg speed avg speed = 2 s 1 s 2 / s 1 + s 2 4 = 2 * 3 * x / 3 + x x = 6 b is the answer"
Answer: b
Problem: the product of x and y is a constant . if the value of x is increased by 40 % , by what percentage must the value of y be decreased ?
Options: a ) 34 % , b ) 36 % , c ) 28.57 % , d ) 30 % , e ) 32 %
Rationale: x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.4 x ( 140 ) i . e . 140 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 140 = 71.43 i . e . y decreases from 100 to 71.43 i . e . decrease of 28.57 % c
Answer: c
Problem: if a and b are the roots of the equation x 2 - 6 x + 6 = 0 , then the value of a 2 + b 2 is :
Options: a ) 36 , b ) 24 , c ) 17 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 6 product of roots = ab = 6 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 36 - 12 = 24 answer b"
Answer: b
Problem: a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 3 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters per second faster than her speed flying to the rose . the bee flies how many meters per second from the daisy to the rose ?
Options: a ) 4.2 , b ) 5.2 , c ) 6 , d ) 8 , e ) 10
Rationale: "let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 3 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 4.2 m / s a"
Answer: a
Problem: 6 persons in an organization including x and y were to be divided in two groups of 3 members each . the total number of groups containing both x and y is what fraction of the total number of groups which can be formed ?
Options: a ) 1 / 4 , b ) 1 / 70 , c ) 3 / 14 , d ) 3 / 10 , e ) 11 / 14
Rationale: the fraction is nothing but the probability . . number to choose 3 out of 6 = 6 c 3 number to choose x and y and 2 from remaining 4 = 4 c 2 . . prob of a and b choosen = 4 c 2 / 6 c 3 = 3 / 10 answer : d
Answer: d
Problem: having scored 94 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 24
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 94 = 19 ( n + 4 ) = > n = 18 so , average score after 19 th innings = x + 4 = 22 . answer : d"
Answer: d
Problem: ratio between rahul and deepak is 4 : 2 , after 6 years rahul age will be 22 years . what is deepak present age
Options: a ) 9 , b ) 3 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : present age is 4 x and 2 x , = > 4 x + 22 = 26 = > x = 1 so deepak age is = 2 ( 1 ) = 2 answer : option d"
Answer: d
Problem: a train 150 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 288 , b ) 236 , c ) 350 , d ) 299 , e ) 266
Rationale: d = 72 * 5 / 18 = 25 = 500 – 150 = 299 . answer : c
Answer: c
Problem: the present worth of a certain bill due sometime hence is rs . 1296 and the true discount is rs . 72 . what is the banker ' s discount ?
Options: a ) rs . 76 , b ) rs . 72 , c ) rs . 74 , d ) rs . 4 , e ) none of these
Rationale: explanation : bg = ( td ) 2 / pw = 722 / 1296 = 72 × 72 / 1296 = 12 × 12 / 36 = 12 / 3 = rs . 4 bg = bd – td = > 4 = bd - 72 = > bd = 72 + 4 = rs . 76 answer : option a
Answer: a
Problem: the grade point average of the entire class is 88 . if the average of one third of the class is 94 , what is the average of the rest of the class ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 88 x = ( 1 / 3 ) 94 x + ( 2 / 3 ) ( p ) x 264 = 94 + 2 p 2 p = 170 p = 85 . the answer is d ."
Answer: d
Problem: a truck covers a distance of 376 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 14 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 376 / 8 = 47 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 47 + 18 ) = 65 kmph distance travelled by car = 376 + 14 = 390 km time taken by car = distance / speed = 390 / 65 = 6 hours . answer – a"
Answer: a
Problem: the ratio of the ages of maala and kala is 3 : 5 . the total of their ages is 3.2 decades . the proportion of their ages after 0.8 decades will be [ 1 decade = 10 years ]
Options: a ) 6 : 5 , b ) 5 : 7 , c ) 4 : 5 , d ) 7 : 9 , e ) 3 : 6
Rationale: let , maala ’ s age = 3 a and kala ’ s age = 5 a then 3 a + 5 a = 32 a = 4 maala ’ s age = 12 years and kala ’ s age = 20 years proportion of their ages after 8 is = ( 12 + 8 ) : ( 20 + 8 ) = 20 : 28 = 5 : 7 answer : b
Answer: b
Problem: mike took a taxi to the airport and paid $ 2.50 to start plus $ 0.25 per mile . annie took a different route to the airport and paid $ 2.50 plus $ 5.00 in bridge toll fees plus $ 0.25 per mile . if each was charged exactly the same amount , and annie ' s ride was 18 miles , how many miles was mike ' s ride ?
Options: a ) 30 , b ) 34 , c ) 38 , d ) 42 , e ) 48
Rationale: "the cost of annie ' s ride was 2.5 + 5 + ( 0.25 * 18 ) = $ 12 let x be the distance of mike ' s ride . the cost of mike ' s ride is 2.5 + ( 0.25 * x ) = 12 0.25 * x = 9.5 x = 38 miles the answer is c ."
Answer: c
Problem: a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 55 percent .
Options: a ) 145 , b ) 150 , c ) 175 , d ) 165 , e ) 130
Rationale: 1 hr = 20 percent . thus 15 min = 5 percent . now to charge 55 percent 165 min . answer : d
Answer: d
Problem: in a box of 11 pens , a total of 3 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 28 / 55 , b ) 19 / 33 , c ) 7 / 11 , d ) 4 / 7 , e ) 3 / 5
Rationale: "p ( neither pen is defective ) = 8 / 11 * 7 / 10 = 28 / 55 the answer is a ."
Answer: a
Problem: an engineer designed a ball so that when it was dropped , it rose with each bounce exactly one - half as high as it had fallen . the engineer dropped the ball from a 32 - meter platform and caught it after it had traveled 46.5 meters . how many times did the ball bounce ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "going down = 32 m going up = 16 - - > total = 48 going down = 16 - - > total = 64 going up = 8 - - > total = 72 going down = 8 - - > total = 80 going up = 4 - - > total = 84 going down = 4 - - > total = 86 going up = 2 - - > total = 88 ( caught ) no of bounces = 4 answer : a"
Answer: a
Problem: there are two cars . one is 90 miles north of the other . simultaneously , the car to the north is driven westward at 25 miles per hour and the other car is driven eastward at 35 miles per hour . how many miles apart are the cars after 2 hours ?
Options: a ) 120 , b ) 130 , c ) 140 , d ) 150 , e ) 160
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 90 and a height of 120 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 90 lines up with the ' 3 ' and the 120 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 30 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 90 / 120 / 150 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : d"
Answer: d
Problem: a rectangular box measures internally 1.6 m long , 1 m broad and 60 cm deep . the number of cubical box each of edge 20 cm that can be packed inside the box is :
Options: a ) 30 , b ) 60 , c ) 90 , d ) 120 , e ) 140
Rationale: "explanation : number of blocks = ( 160 x 100 x 60 / 20 x 20 x 20 ) = 120 answer : d"
Answer: d
Problem: a certain meter records voltage between 0 and 10 volts inclusive . if the average value of 3 recordings on the meter was 9 volts , what was the smallest possible recording in volts ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: "if average of 3 is 9 so sum of 3 should be 27 3 recording can be from 0 - 10 inclusive to find one smallest other two should be highest so , lets assume three var are a , b , c say a is smallest and give b and c greatest readings say 10 and 10 so a has to be 7 e"
Answer: e
Problem: bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p & q , having each turn together to fill the empty drum ?
Options: a ) 45 , b ) 53 , c ) 54 , d ) 46 , e ) 63
Rationale: if caoacity of q is x units , then capacity of p is 3 x and capacity of drum is 60 * 3 x = 180 x . it will take 180 x / 4 x = 45 turns it will take for both the buckets p & q , having each turn together to fill the empty drum . answer : a
Answer: a
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 40 now , the son age 5 years back was
Options: a ) 14 , b ) 17 , c ) 15 , d ) 19 , e ) 99
Rationale: "let the son ' s present age be x years . then , ( 40 - x ) = x x = 20 . son ' s age 5 years back = ( 20 - 5 ) = 15 years answer : c"
Answer: c
Problem: the h . c . f . of two numbers is 30 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 276 , b ) 299 , c ) 420 , d ) 345 , e ) 365
Rationale: "clearly , the numbers are ( 30 x 13 ) and ( 30 x 14 ) . larger number = ( 30 x 14 ) = 420 . answer : option c"
Answer: c
Problem: find compound interest on rs . 7500 at 4 % per year for 2 years , compounded annually .
Options: a ) 812 , b ) 712 , c ) 412 , d ) 512 , e ) 612
Rationale: "amount = rs [ 7500 * ( 1 + ( 4 / 100 ) 2 ] = rs ( 7500 * ( 26 / 25 ) * ( 26 / 25 ) ) = rs . 8112 . therefore , compound interest = rs . ( 8112 - 7500 ) = rs . 612 . answer is e ."
Answer: e
Problem: a man whose speed is 5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 7 , b ) 4 , c ) 6 , d ) 9 , e ) 4.55
Rationale: "m = 5.0 s = 1.5 ds = 6.5 us = 3.5 as = ( 2 * 6 * 3 ) / 10 = 4.55 answer : e"
Answer: e
Problem: in an election only two candidates contested . a candidate secured 70 % of the valid votes and won by a majority of 178 votes . find the total number of valid votes ?
Options: a ) 445 , b ) 570 , c ) 480 , d ) 520 , e ) 550
Rationale: let the total number of valid votes be x . 70 % of x = 70 / 100 * x = 7 x / 10 number of votes secured by the other candidate = x - 7 x / 100 = 3 x / 10 given , 7 x / 10 - 3 x / 10 = 178 = > 4 x / 10 = 178 = > 4 x = 1780 = > x = 445 . answer : a
Answer: a
Problem: what is the angle between the hands of a clock when time is 10 : 30 ?
Options: a ) 65 deg , b ) 75 deg , c ) 45 deg , d ) 15 deg , e ) 135 deg
Rationale: "angle between two hands = 30 h - 11 / 2 m = 30 * 10 - 30 * 11 / 2 = 300 - 165 = 135 deg answer : e"
Answer: e
Problem: at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 10.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be d .
Answer: d
Problem: if jake loses 5 pounds , he will weigh thrice as much as his sister . together they now weigh 285 pounds . what is jake ' s present weight , in pounds ?
Options: a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 215
Rationale: "this problem can be solved as a simple word problem in which we must convert words to math . before we create our equations , we want to define some variables . j = jake ’ s current weight , in pounds s = sister ’ s current weight , in pounds we are told that “ if jake loses 8 pounds , he will weigh twice as much as his sister . we put this into an equation : j – 5 = 3 s j = 3 s + 5 ( equation 1 ) next , we are told that “ together they now weigh 275 pounds . ” we can also put this into an equation . j + s = 285 ( equation 2 ) to solve this equation , we can substitute 2 s + 8 from equation 1 for the variable j in equation 2 : 3 s + 5 = 285 - s 4 s = 280 s = 70 j + 70 = 285 j = 215 answer : e"
Answer: e
Problem: 6 computers , each working at the same constant rate , together can process a certain amount of data in 9 days . how many additional computers , each working at the same constant rate , will be needed to process the same amount of data in 6 days ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 9 , e ) 12
Rationale: explanation : if six computers require 9 days to process the data , thats a total of 54 computer - days the product of 6 and 9 . if you change the number of computers or the number of days , 54 will have to remain the product , whether that means 54 days of one computer or one day with 54 computers . in 6 days , the number of computers is : 6 c = 54 c = 9 9 computers is 3 more than the 6 that it took to do the job in 9 days , so the correct choice is ( a ) .
Answer: a
Problem: the radius of a cylindrical vessel is 7 cm and height is 4 cm . find the whole surface of the cylinder ?
Options: a ) 484 , b ) 771 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 4 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 11 ) = 484 answer : a"
Answer: a
Problem: mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.00 . each pot cost 0.25 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.75 , b ) $ 1.96 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: "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 $ 8.00 ( a 25 - cent increment ) and the the difference in sequential prices of the pots is 25 cents , the largest pot probably has a price that is a 25 - cent increment . from the answer choices , i would then test answer c first ( since answers b and d are not in 25 - cent increments ) . if . . . . the largest pot = $ 1.958 0.708 0.958 1.208 1.458 1.708 1.958 total = $ 8.00 so this must be the answer . b"
Answer: b
Problem: determine the value of ( 27 / 31 * 31 / 27 ) * 3
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) none
Rationale: "solution : both fractions should be reduced before performing arithmetic operations . we get ( 27 / 31 * 31 / 27 ) 3 = 1 * 3 = 3 answer d"
Answer: d
Problem: a rectangular grassy plot 110 m by 65 cm has a gravel path . 5 cm wide all round it on the inside . find the cost of gravelling the path at 80 paise per sq . mt
Options: a ) 680 , b ) 378 , c ) 267 , d ) 299 , e ) 271
Rationale: "explanation : area of theplot = 110 * 65 = 7150 sq m area of the plot excluding the path = ( 110 - 5 ) * ( 65 - 5 ) = 6300 sq m area of the path = 7150 - 6300 = 850 sq m cost of gravelling the path = 850 * 80 / 100 = 680 rs answer : a ) 680 rs"
Answer: a
Problem: in a dairy farm , 16 cows eat 16 bags of husk in 16 days . in how many days one cow will eat one bag of husk ?
Options: a ) 16 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: explanation : one bag of husk = 16 cows per day ⇒ 16 × 1 × 16 = 1 × 16 × x for one cow = 16 days answer : a
Answer: a
Problem: in 12 pumps can raise 1218 tons of water in 11 days of 9 hrs each , how many pumps will raise 2030 tons of water in 12 days of 11 hrs each ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 22
Rationale: explanation : pumps work time 12 1218 99 x 2030 132 = > 1218 / ( 912 * 99 ) = 2020 / ( x × 132 ) = > x = 15 pumps answer : option b
Answer: b
Problem: if the probability of rain on any given day in chicago during the summer is 20 % , independent of what happens on any other day , what is the probability of having exactly 3 rainy days from july 4 through july 7 inclusive ?
Options: a ) 2 / 25 , b ) 3 / 125 , c ) 7 / 125 , d ) 12 / 625 , e ) 16 / 625
Rationale: "one possible case is : rainy - rainy - rainy - not rainy . the probability of this case is 1 / 5 * 1 / 5 * 1 / 5 * 4 / 5 = 4 / 625 the number of possible cases is 4 c 3 = 4 . p ( exactly 3 rainy days ) = 4 * 4 / 625 = 16 / 625 the answer is e ."
Answer: e
Problem: find the product of the local value and absolute value of 2 in 564823
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 18000
Rationale: "explanation : place value = local value face value = absolute value the place value of 2 in 564823 is 2 x 10 = 20 the face value of 2 in 564823 is nothing but 2 . = > 20 x 2 = 40 answer : option a"
Answer: a
Problem: the present population of a town is 60,000 . the population increases annually at 10 % . find the population after 3 years .
Options: a ) 86000 , b ) 79860 , c ) 76300 , d ) 82900 , e ) none of these
Rationale: "explanation : solution : the required population is 60000 ( 1 + 10 / 100 ) ^ 3 = 60000 * 110 / 100 * 110 / 100 * 110 / 100 = 79,860 answer : b"
Answer: b
Problem: 32.32 / 2000 is equal to :
Options: a ) 1.012526 , b ) 0.012625 , c ) 0.12526 , d ) 0.01616 , e ) 0.12725
Rationale: "25.25 / 2000 = 2525 / 200000 = 0.01616 answer : d"
Answer: d
Problem: george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 5 % of the money for taxi fare and buys 25 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 30 , c ) 20 , d ) 22.5 , e ) 12
Rationale: let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 5 % of 200 = 10 for taxi fare , so he is left with 190 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 90 ( 190 - 100 ) no of oranges he can buy = 90 / 4 = > 22,5 so , george can buy 20 oranges . d
Answer: d
Problem: if 4 spiders make 4 webs in 4 days , then 1 spider will make 1 web in how many days ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 4 , e ) 6
Rationale: "explanation : let the required number days be x . less spiders , more days ( indirect proportion ) less webs , less days ( direct proportion ) spiders 1 : 4 | | : : 4 : 1 webs 4 : 1 | = > 1 * 4 * x = 4 * 1 * 4 = > x = 4 answer : d"
Answer: d
Problem: in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 36 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 65.80 % , c ) 68.57 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 36 % of 1100 ) + ( 32 % of 900 ) = 396 + 288 = 684 failed = 2000 - 684 = 1316 failed % = [ ( 1316 / 2000 ) x 100 ] % = 65.8 % . answer : b"
Answer: b
Problem: john left home and drove at the rate of 50 mph for 2 hours . he stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination . how many miles did john drive ?
Options: a ) 235 miles . , b ) 245 miles . , c ) 255 miles . , d ) 265 miles . , e ) 275 miles .
Rationale: "the total distance d traveled by john is given by d = 50 * 2 + 3 * 55 = 265 miles . answer d"
Answer: d
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 88 kg , e ) 96 kg
Rationale: "volume of water displaced = ( 3 x 2 x 0.01 ) m 3 = 0.06 m 3 . mass of man = volume of water displaced x density of water = ( 0.06 x 1000 ) kg = 60 kg . answer : option b"
Answer: b
Problem: one of the longest sides of the triangle is 20 m , the other side is 10 m . area of the triangle is 80 m ^ 2 . what is the another side of the triangle ?
Options: a ) 2 sqrt ( 61 )
b ) 2 sqrt ( 62 )
c ) 2 sqrt ( 63 )
d ) 2 sqrt ( 64 )
e ) 2 sqrt ( 65 )
Rationale: base of triangle is 20 and area is 80 therefore height = 2 * 80 / 20 = 8 . now one side of triangle is of 10 . so we can get the point were the base is divided by applying pythagoras therm so division pt = sqrt ( 10 ^ 2 - 8 ^ 2 ) = sqrt ( 36 ) = 6 threfore other half is 14 . now second side = sqrt ( 14 ^ 2 + 8 ^ 2 ) = sqrt ( 260 ) = 2 sqrt ( 65 ) answer : e
Answer: e
Problem: anne earned $ 3 an hour baby - sitting , and $ 4 an hour working in the garden . last week she did baby - sitting for 5 hours and garden work for 3 hours . how much more money does she need to buy a game that costs $ 35 ?
Options: a ) $ 8 , b ) $ 12 , c ) $ 6 , d ) $ 21 , e ) $ 10
Rationale: 5 x $ 3 = $ 15 for baby - sitting 3 x $ 4 = $ 12 for garden work $ 15 + $ 12 = $ 27 she has $ 35 - $ 27 = $ 8 more needed to buy the game correct answer a
Answer: a
Problem: if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c â ˆ ’ a ?
Options: a ) 25 , b ) 70 , c ) 90 , d ) 140 , e ) it can not be determined from the information given
Rationale: "the arithmetic mean of a and b = ( a + b ) / 2 = 45 - - a + b = 90 - - 1 similarly for b + c = 160 - - 2 subtracting 1 from 2 we have c - a = 70 ; answer : b"
Answer: b
Problem: a envelop weight 8.2 gm , if 800 of these envelop are sent with an advertisement mail . how much wieght ?
Options: a ) 6.56 kg , b ) 6.8 kg , c ) 6.7 kg , d ) 6.9 kg , e ) 7.8 kg
Rationale: "800 * 8.2 6560.0 gm 6.56 kg answer : a"
Answer: a
Problem: if a coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 4 flips and not on the last flip ?
Options: a ) 1 / 8 , b ) 1 / 32 , c ) 1 / 4 , d ) 1 / 2 , e ) 1 / 16
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Answer: b
Problem: the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 990 square meters , what is the depth of the channel ( in meters ) ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "1 / 2 * d * ( 14 + 8 ) = 990 d = 90 the answer is e ."
Answer: e
Problem: income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 14000 , then find his savings ?
Options: a ) 3600 , b ) 2800 , c ) 3608 , d ) 3602 , e ) 3603
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 14000 = > x = 2800 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 2800 . answer : b"
Answer: b
Problem: two employees x and y are paid a total of rs . 750 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.90 , b ) s . 250.90 , c ) s . 290.90 , d ) s . 300.90 , e ) s . 340.90
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 750 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 750 ⇒ y [ 12 / 10 + 1 ] = 750 ⇒ 22 y / 10 = 750 ⇒ 22 y = 7500 ⇒ y = 7500 / 22 = rs . 340.90 e )"
Answer: e
Problem: the difference between compound interest and simple interest on a certain amount of money at 5 % per annum for 2 years is 19 . find the sum :
Options: a ) 4500 , b ) 7600 , c ) 5000 , d ) 6000 , e ) none of these
Rationale: "sol . ( d ) let the sum be 100 . therefore , si = 100 × 5 × 2100 = 10100 × 5 × 2100 = 10 and ci = 100 ( 1 + 5100 ) 2 − 100100 ( 1 + 5100 ) 2 − 100 ∴ = 100 × 21 × 2120 × 20 − 100 = 414 = 100 × 21 × 2120 × 20 − 100 = 414 difference of ci and si = 41 ⁄ 4 - 10 = 1 ⁄ 4 if the difference is 1 ⁄ 4 , the sum = 100 = > if the difference is 19 , the sum = 400 × 19 = 7600 answer b"
Answer: b
Problem: 1398 x 1398 = ?
Options: a ) 1624404 , b ) 1851404 , c ) 1951404 , d ) 1954404 , e ) none of these
Rationale: "explanation : 1398 x 1398 = ( 1398 ) 2 = ( 1400 - 2 ) 2 = 14002 - ( 2 × 1400 × 2 ) + 22 = 1960000 - 5600 + 4 = 1954404 . answer : option d"
Answer: d
Problem: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 60 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 10 , e ) 16
Rationale: "machine b produces 100 part in 60 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 60 / 2 = 30 minutes . now , machine a produces 100 parts in 30 minutes which is 100 / 30 = 10 / 3 parts / minute . 10 / 3 parts x a total of 6 minutes = 20 a"
Answer: a
Problem: if the area of a square with sides of length 3 centimeters is equal to the area of a rectangle with a width of 4 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4 , b ) 8 , c ) 12 , d ) 3 , e ) 18
Rationale: "let length of rectangle = l 3 ^ 2 = l * 4 = > l = 9 / 4 = 3 answer d"
Answer: d
Problem: if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 12 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: there are several algebraic ways to solve this question , but the easiest way is as follows : since we can not have two correct answers just pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 12 . n = 7 - - > n ^ 2 = 49 - - > remainder upon division 49 by 12 is 1 . answer : b .
Answer: b
Problem: set j consists of 5 consecutive even numbers . if the smallest term in the set is - 2 , what is the range of the positive integers in set j ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: since there are only 5 integers , another approach is the just list all 5 . we get : - 2 , 0,2 , 4 , 6 range of positive integers = 6 - 2 = 4 answer : c
Answer: c
Problem: what is the greatest positive integer n such that 3 ^ n is a factor of 36 ^ 450 ?
Options: a ) 100 , b ) 200 , c ) 300 , d ) 600 , e ) 900
Rationale: "36 = 3 ^ 2 * 2 ^ 2 . 36 ^ 450 = 3 ^ 900 * 2 ^ 900 the answer is e ."
Answer: e
Problem: the sum of all the integers g such that - 26 < g < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 g = - 49 . d is the answer ."
Answer: d
Problem: a sum of money at simple interest amounts to $ 680 in 3 years and to $ 710 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 590 , d ) $ 549 , e ) $ 675
Rationale: "c $ 590 s . i . for 1 year = $ ( 710 - 680 ) = $ 30 . s . i . for 3 years = $ ( 30 x 3 ) = $ 90 . principal = $ ( 680 - 90 ) = $ 590 ."
Answer: c
Problem: a student chose a number , multiplied it by 2 , then subtracted 180 from the result and got 104 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 142 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 180 = 104 2 x = 284 x = 142 correct answer d"
Answer: d
Problem: two brothers take the same route to school on their bicycles , one gets to school in 25 minutes and the second one gets to school in 36 minutes . the ratio of their speeds is
Options: a ) 4 : 5 , b ) 1 : 2 , c ) 6 : 7 , d ) 5 : 6 , e ) none
Rationale: solution let us name the brothers as a and b . = ( a ' s speed ) : ( b ' s speed ) = â ˆ š b : â ˆ š a = â ˆ š 25 : â ˆ š 36 = 5 : 6 answer d
Answer: d