regisss/math_qa huggingface dataset:
Problem: two goods train each 500 m long , are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively find the time taken by the slower train to pass the driver of the faster one .
Options: a ) 12 sec , b ) 24 sec , c ) 48 sec , d ) 60 sec , e ) none
Rationale: solution relative speed = ( 45 + 30 ) km / hr = ( 75 x 5 / 18 ) m / sec = ( 125 / 6 ) m / sec total distance covered = ( 500 + 500 ) m = 1000 m required time = ( 1000 x 6 / 125 ) sec = 48 sec answer c
Answer: c
Problem: the population of a village is 14300 . it increases annually at the rate of 15 % p . a . what will be its population after 2 years ?
Options: a ) 18911 , b ) 18788 , c ) 19898 , d ) 14000 , e ) 14400
Rationale: formula : ( after = 100 denominator ago = 100 numerator ) 14300 × 115 / 100 × 115 / 100 = 18911 a
Answer: a
Problem: what is the sum of all possible solutions to | x - 3 | ^ 2 + | x - 3 | = 20 ?
Options: a ) - 1 , b ) 6 , c ) 7 , d ) 12 , e ) 14
Rationale: "first of all | x - 3 | ^ 2 = ( x - 3 ) ^ 2 , so we have : ( x - 3 ) ^ 2 + | x - 3 | = 20 . when x < 3 , x - 3 is negative , thus | x - 3 | = - ( x - 3 ) . in this case we ' ll have ( x - 3 ) ^ 2 - ( x - 3 ) = 20 - - > x = - 1 or x = 8 . discard x = 8 because it ' s not in the range we consider ( < 3 ) . when x > = 3 , x - 3 is non - negative , thus | x - 3 | = x - 3 . in this case we ' ll have ( x - 3 ) ^ 2 + ( x - 3 ) = 20 - - > x = - 2 or x = 7 . discard x = - 2 because it ' s not in the range we consider ( > = 3 ) . thus there are two solutions : x = - 1 and x = 7 - - > the sum = 6 . answer : b ."
Answer: b
Problem: if x / 5 + 9 / x = 14 / 5 , what are the values of 3 x - 7 ?
Options: a ) 8 and 9 , b ) 8 and 20 , c ) 17 and 21 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing b is the answer 8 or 20
Answer: b
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 23 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 3 : 1 , d ) 1 : 3 , e ) 1 : 4
Rationale: "speed = x and y resp length of first = 27 x length of second train = 17 y related speed = x + y time taken to cross each other = 23 s 27 x + 17 y / x + y = 23 27 x + 17 y = 23 ( x + y ) 4 x = 6 y x / y = 6 / 4 = 3 / 2 answer b"
Answer: b
Problem: a closed cylindrical tank contains 36 pie cubic feet of water and its filled to half its capacity . when the tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . when the tank is placed on its side on level ground , what is the height , in feet , of the surface of the water above the ground ?
Options: a ) 0 feet
b ) 1 feet
c ) 2 feet
d ) 3 feet
e ) 4 feet
Rationale: 36 pie cubic feet of water and its filled to half tank ' s capacity . . . volume of tank = 72 pie cubic feet height of tank = 4 * 2 = 8 feet ( since tank is placed upright on its circular base on level ground , the height of water in the tank is 4 feet . ) 72 pie = pie * r 2 * 8 r 2 = 9 r = 3 feet answer : d
Answer: d
Problem: the ratio of two speeds of two trains is 3 to 4 . if each of the trains slows its speed 5 km / hr , what will be the ratio of these two train speeds ?
Options: a ) 3 / 4 , b ) 8 / 9 , c ) 18 / 19 , d ) 23 / 24 , e ) it can not be determined from the information given
Rationale: 3 / 4 = 3 x / 4 x we need to find out ( 3 x + 5 ) / ( 4 x + 5 ) off course we can not solve this to arrive at any rational number hence e .
Answer: e
Problem: shopkeeper rise price by 33 % and gives successive discount of 10 % and 15 % . what is overall % gain or loss ?
Options: a ) 1.745 % , b ) 4.745 % , c ) 3.745 % , d ) 6.745 % , e ) 7.745 %
Rationale: "let d initial price be 100 33 % rise now price = 133 / 100 * 100 = 133 10 % discount then price = 133 * 90 / 100 = 119.7 15 % discount then price = 119.7 * 85 / 100 = 101.745 so gain = 101.745 - 100 = 1.745 gain % = gain * 100 / cp = = > 1.745 * 100 / 100 = 1.745 % answer : a"
Answer: a
Problem: in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 3 : 7 : 13 . if the shop carries 352 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 3 x , 7 x and 13 x total dogs and bunnies = 16 x . and we are given that 16 x = 352 . hence x = 22 . dogs = 3 x = 3 * 22 = 66 ( option b )"
Answer: b
Problem: a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ?
Options: a ) 48 , b ) 75 , c ) 60 , d ) 54 , e ) 45
Rationale: "answer let the number be x . x / 15 = 240 / x x ^ 2 = 240 * 15 = 3600 x = √ 3600 = 60 correct option : c"
Answer: c
Problem: when the price of an article was reduced by 25 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 35 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 25 % , the new price is 0.75 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.75 p ) ( 1.8 n ) = 1.35 np , which is 1.35 times the old revenue , so is 35 % greater . answer : a"
Answer: a
Problem: 5 years ago , the average age of a and b was 15 years . average age of a , b and c today is 20 years . how old will c be after 14 years ?
Options: a ) 30 , b ) 34 , c ) 40 , d ) 50 , e ) 60
Rationale: explanation : ( a + b ) , five years ago = ( 15 * 2 ) = 30 years . ( a + b ) , now = ( 30 + 5 * 2 ) years = 40 years . ( a + b + c ) , now = ( 20 x 3 ) years = 60 years . c , now = ( 60 - 40 ) years = 20 years . c , after 14 years = ( 20 + 14 ) years = 34 years . answer : b
Answer: b
Problem: one fourth of a solution that was 10 % sugar by weight was replaced with by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.16 - - > x = 0.34 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.16 - - > x = 0.34 . answer : a ."
Answer: a
Problem: from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a black card and the second card is a king or queen ?
Options: a ) 1 / 52 , b ) 1 / 13 , c ) 1 / 26 , d ) 3 / 26 , e ) 17 / 26
Rationale: "p ( black card ) = 1 / 2 p ( king or queen ) = 2 / 13 p ( black card then a king / queen ) = 1 / 2 * 2 / 13 = 1 / 13 the answer is b ."
Answer: b
Problem: a man whose bowling average is 22.2 , takes 4 wickets for 36 runs and thereby decreases his average by 1.2 . the number of wickets , taken by him before his last match is :
Options: a ) 14 , b ) 22 , c ) 38 , d ) 40 , e ) 50
Rationale: "explanation : let the number of wickets taken before the last match is x . then , ( 22.2 x + 36 ) / ( x + 4 ) = 21 = > 22.2 x + 36 = 21 x + 84 = > 1.2 x = 48 = > x = 48 / 1.2 = 40 answer : d"
Answer: d
Problem: a can give b 100 meters start and c 120 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 10.22 meters , b ) 11.22 meters , c ) 22.22 meters , d ) 33.22 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 880 meters . therefore , b runs 900 meters while c runs 880 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 880 ) / 900 = 977.778 meters thus , b can give c ( 1000 - 977.77 ) = 22.22 meters start answer : c"
Answer: c
Problem: a train 450 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 60 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 450 × 2 / 15 ) sec = 60 sec answer : e"
Answer: e
Problem: a rectangular with dimensions 35 inches by 45 inches is to be divided into squares of equal size . which of the following could be a length of a side of the squares ?
Options: a ) a ) 4 inches
b ) b ) 6 inches
c ) c ) 5 inches
d ) d ) 8 inches
e ) e ) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where l = w you can solve this using gcf 35 = 5 * 7 45 = 3 * 3 * 5 gcf = 5 p . s you can make squares with side of 5 answer : c
Answer: c
Problem: find the greatest number which leaves the same remainder when it divides 25 , 50 and 120 .
Options: a ) 18 , b ) 5 , c ) 12 , d ) 16 , e ) none of these
Rationale: "120 - 50 = 70 50 - 25 = 25 120 - 25 = 95 the h . c . f of 25 , 70 and 95 is 5 . answer : b"
Answer: b
Problem: o ( x ) represents the least odd integer greater than x , whereas o ( x ) represents the greatest odd integer less than x . likewise , e ( x ) represents the least even integer greater than x , whereas e ( x ) represents the greatest even integer less than x . according to these definitions , the value of o ( 11.6 ) + e ( – 10.4 ) + o ( – 9.2 ) + e ( 9.5 ) is :
Options: a ) - 3 , b ) - 1 , c ) 0 , d ) 1 , e ) 3
Rationale: "o ( 11.6 ) + e ( – 10.4 ) + o ( – 9.2 ) + e ( 9.5 ) = 13 + ( - 10 ) + ( - 11 ) + 8 = 0 the answer is c ."
Answer: c
Problem: what is the smallest positive integer k such that the product of 2205 x k is a perfect square ?
Options: a ) 5 , b ) 9 , c ) 15 , d ) 25 , e ) 63
Rationale: "a perfect square , is just an integer that can be written as the square of some other integer . for example 16 = 4 ^ 2 , is a perfect square . now , 2205 = 3 ^ 2 * 7 ^ 7 * 5 , so if k = 5 then 2205 k = ( 3 * 7 * 5 ) ^ 2 , which is a perfect square ( basically the least positive value of k must complete only the power of 7 to even power as powers of other primes are already even ) . answer : a ."
Answer: a
Problem: the function f ( p ) represents the number of ways that prime numbers can be uniquely summed to form a certain number p such that p = a + b + c + d … where those summed variables are each prime and a ≤ b ≤ c ≤ d . . . for instance f ( 8 ) = 3 and the unique ways are 2 + 2 + 2 + 2 and 2 + 3 + 3 and 3 + 5 . what is f ( 12 ) ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: so we can start with 2 and check whether sum of two primes is primes is even . 1 ) 2 ( 6 times ) 2 ) 2 ( 3 times ) + 3 ( 2 times ) 3 ) 2 ( 2 times ) + 3 + 5 4 ) 2 + 3 + 7 5 ) 2 + 5 + 5 6 ) 3 ( 4 times ) 7 ) 5 + 7 answer : d
Answer: d
Problem: in what time will a train 175 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.58 sec , b ) 2.91 sec , c ) 4.37 sec , d ) 2.9 sec , e ) 1.8 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 175 / 40 = 4.37 sec . answer : c"
Answer: c
Problem: a student chose a number , multiplied it by 5 , then subtracted 275 from the result and got 135 . what was the number he chose ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 86 , e ) 88
Rationale: "let x be the number he chose , then 5 ⋅ x − 275 = 135 5 x = 410 x = 82 correct answer b"
Answer: b
Problem: in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
Options: a ) 36 , b ) 34 , c ) 32 , d ) 30 , e ) 28
Rationale: "let c be the capacity of the can . ( 3 / 5 ) * ( c - 6 ) + 6 = ( 2 / 3 ) * c 9 c - 54 + 90 = 10 c c = 36 the answer is a ."
Answer: a
Problem: susan drives from city a to city b . after two hours of driving she noticed that she covered 80 km and calculated that , if she continued driving at the same speed , she would end up been 15 minutes late . so she increased her speed by 10 km / hr and she arrived at city b 36 minutes earlier than she planned . find the distance between cities a and b .
Options: a ) 223 , b ) 376 , c ) 250 , d ) 378 , e ) 271
Rationale: let xx be the distance between a and b . since susan covered 80 km in 2 hours , her speed was v = 802 = 40 v = 802 = 40 km / hr . if she continued at the same speed she would be 1515 minutes late , i . e . the planned time on the road is x 40 − 1560 x 40 − 1560 hr . the rest of the distance is ( x − 80 ) ( x − 80 ) km . v = 40 + 10 = 50 v = 40 + 10 = 50 km / hr . so , she covered the distance between a and b in 2 + x − 80502 + x − 8050 hr , and it was 36 min less than planned . therefore , the planned time was 2 + x − 8050 + 36602 + x − 8050 + 3660 . when we equalize the expressions for the scheduled time , we get the equation : x 40 − 1560 = 2 + x − 8050 + 3660 x 40 − 1560 = 2 + x − 8050 + 3660 x − 1040 = 100 + x − 80 + 3050 x − 1040 = 100 + x − 80 + 3050 x − 104 = x + 505 x − 104 = x + 505 5 x − 50 = 4 x + 2005 x − 50 = 4 x + 200 x = 250 x = 250 so , the distance between cities a and b is 250 km . answer : c
Answer: c
Problem: a train running at the speed of 40 km / hr crosses a pole in 9 sec . what is the length of the train ?
Options: a ) 100 m , b ) 150 m , c ) 187 m , d ) 167 m , e ) 197 m
Rationale: "speed = 40 * 5 / 18 = 100 / 9 m / sec length of the train = speed * time = 100 / 9 * 9 = 100 m answer : a"
Answer: a
Problem: what is the remainder if 7 ^ 16 is divided by 100 ?
Options: a ) 3 , b ) 4 , c ) 2 , d ) 1 , e ) 5
Rationale: "7 ^ 16 can be written as ( 7 ^ 4 ) ^ 4 if we divide 7 ^ 4 by 100 the reminder is 1 so , ( 7 ^ 4 ) ^ 4 by 100 , the reminder is 1 ^ 4 = 1 answer : d"
Answer: d
Problem: a large box contains 17 small boxes and each small box contains 25 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) 250 , b ) 350 , c ) 425 , d ) 550 , e ) 650
Rationale: "the number of chocolate bars is equal to 17 * 25 = 425 correct answer c"
Answer: c
Problem: what is the product of all the possible values of x if x ^ 2 + 5 x + 6 ?
Options: a ) 12 , b ) 18 , c ) 15 , d ) 6 , e ) 9
Rationale: explanation : = > y = x ^ 2 + 5 x + 6 = > y = ( x + 2 ) ( x + 3 ) = > x = - 2 , x = - 3 product x = ( - 2 ) ( - 3 ) = 6 answer option 6 answer : d
Answer: d
Problem: jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 6 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 5 : 1 , b ) 30 : 2 , c ) 15 : 2 , d ) 20 : 2 , e ) 25 : 2
Rationale: "u / i = 6 / 2 i / b = 5 / 1 since i is multiple of both 2 ( as per first ratio ) and 5 ( as per second ratio ) so let ' s assume that i = 10 i . e . multiplying teh first ratio by 5 and second ration by 2 in each numerator and denominator then , u : i : b = 30 : 18 : 2 i . e . u : b = 30 : 2 answer : option b"
Answer: b
Problem: a man walking at a constant rate of 9 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 3 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 3 * 15 / 60 = 15 / 20 miles and the man walks the distance mm , which is 3 * 9 / 60 = 9 / 20 mile . the difference of 15 / 20 - 9 / 20 = 3 / 10 miles ( mw ) will be covered by the man in ( 3 / 10 ) / 9 = 1 / 30 of an hour , which is 2 minutes . answer b .
Answer: b
Problem: in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 20 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
Options: a ) 2 % , b ) 5 % , c ) 8 % , d ) 10 % , e ) 12 %
Rationale: "since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 20 % of democrats ( 40 * 0.2 = 8 ) voted for candidate x , means that out of total of 100 voters ; 56 ( 48 + 8 ) voters voted for candidate x and 44 voted for candidate y . thus we can infer that candidate x is expected to win the election by 12 ( 56 - 44 ) votes . therefore candidate x is expected to win the election by ( 12 / 100 ) votes which is equivalent to 12 % . i think the answer is e ."
Answer: e
Problem: a school has received 50 % of the amount it needs for a new building by receiving a donation of $ 400 each from people already solicited . people already solicited represent 40 % of the people from whom the school will solicit donations . how much average contribution is requited from the remaining targeted people to complete the fund raising exercise ?
Options: a ) $ 400 , b ) $ 177.78 , c ) $ 320 , d ) $ 277 , e ) $ 200
Rationale: "let us suppose there are 100 people . 40 % of them donated $ 16000 ( 400 * 40 ) $ 16000 is 50 % of total amount . so total amount = 16000 * 100 / 50 remaining amount is 50 % of total amount . 50 % of total amount = 16000 * ( 100 / 50 ) * ( 50 / 100 ) = 16000 this amount has to be divided by 50 ( remaining people are 50 ) so per head amount is 16000 / 50 = 320 answer : c"
Answer: c
Problem: the sides of a square region , measured to the nearest centimeter , are 10 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 96.25 sq cm , b ) 98.25 sq cm , c ) 92.25 sq cm , d ) 100.25 sq cm , e ) 90.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 9.5 is equidistant from both 9 and 10 ) the answer still should be : 9.5 ^ 2 = 90.25 . answer : e"
Answer: e
Problem: p software has coding line 5 % more than n , n software has coding line 1 / 2 more than m . m software has 100 lines of coding . find p lines .
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 158
Rationale: "m s / w has 100 line of code n s / w has = 100 + 100 * 1 / 2 = 150 line of code p s / w 5 % more n ' code 150 + 7.5 = 157.5 or 158 line of code answer : e"
Answer: e
Problem: in a garden , there are 10 rows and 15 columns of mango trees . the distance between the two trees is 2 metres and a distance of one metre is left from all sides of the boundary of the garden . the length of the garden is
Options: a ) 20 m , b ) 30 m , c ) 24 m , d ) 26 m , e ) 28 m
Rationale: "explanation : each row contains 15 plants . there are 14 gapes between the two corner trees ( 14 x 2 ) metres and 1 metre on each side is left . therefore length = ( 28 + 2 ) m = 30 m . answer : b"
Answer: b
Problem: if tim had lunch at $ 50.50 and he gave 10 % tip , how much did he spend ?
Options: a ) $ 30.60 , b ) $ 60.60 , c ) $ 70.60 , d ) $ 55.55 , e ) $ 50.60
Rationale: "the tip is 20 % of what he paid for lunch . hence tip = 20 % of 50.50 = ( 10 / 100 ) * 50.50 = $ 5.05 total spent 50.50 + 5.05 = $ 55.55 correct answer d"
Answer: d
Problem: a 240 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 260 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 240 / 9 = 500 / 9 x = 260 ans is 260 m answer : a"
Answer: a
Problem: company a imported 12,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 10 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?
Options: a ) 420 , b ) 480 , c ) 1050 , d ) 1680 , e ) 2100
Rationale: answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 10 % brass widgets leads to 4 % blue brass widgets out of the total 10,550 widgets . 12,000 / 100 * 4 = 480 . answer b .
Answer: b
Problem: mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: here when he step down 26 steps he has 30 seconds for remaining steps . if he step down 34 stairs he has only 18 sec . 30 - 18 = 12 12 secs for 8 steps . . 18 secs for 12 steps . 12 + 34 = 46 so ans is 46 . . answer : b
Answer: b
Problem: solution x is 30 % chemical a and 70 % chemical b by volume . solution y is 40 % chemical a and 60 % chemical b by volume . if a mixture of x and y is 36 % chemical a , what percent of the mixture is solution x ?
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "the volume of the mixture be x + y . 0.3 x + 0.4 y = 0.36 ( x + y ) x = 2 y / 3 x / ( x + y ) = ( 2 y / 3 ) / ( 5 y / 3 ) = 2 / 5 = 40 % . the answer is c ."
Answer: c
Problem: jim ’ s taxi service charges an initial fee of $ 2.45 at the beginning of a trip and an additional charge of $ 0.35 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.45 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.6
Rationale: "let the fixed charge of jim ’ s taxi service = 2.45 $ and charge per 2 / 5 mile ( . 4 mile ) = . 35 $ total charge for a trip of 3.6 miles = 2.45 + ( 3.6 / . 4 ) * . 35 = 2.45 + 9 * . 35 = 5.6 $ answer e"
Answer: e
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 24 % of the original number . what percent of the red candies remain ?
Options: a ) 12.5 % , b ) 16.7 % , c ) 22.5 % , d ) 27.5 % , e ) 33.3 %
Rationale: let x be the original number of each color so there are a total of 5 x candies . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.2 x red + yellow = 0.45 x red = 0.225 x , since red = yellow . the answer is c .
Answer: c
Problem: on selling 9 balls at rs . 720 , there is a loss equal to the cost price of 5 balls . the cost price of a ball is :
Options: a ) s . 145 , b ) s . 150 , c ) s . 155 , d ) s . 160 , e ) s . 180
Rationale: "( c . p . of 9 balls ) - ( s . p . of 9 balls ) = ( c . p . of 5 balls ) c . p . of 4 balls = s . p . of 9 balls = rs . 720 . c . p . of 1 ball = rs . 720 / 4 = rs . 180 . answer : option e"
Answer: e
Problem: boy sells a book for rs . 630 he gets a loss of 10 % , to gain 10 % , what should be the sp ?
Options: a ) 430 , b ) 450 , c ) 550 , d ) 770 , e ) 660
Rationale: "cost price = 630 / 90 x 100 = 700 to gain 10 % = 700 x 10 / 100 = 70 sp = cp + gain = 700 + 70 = 770 answer : d"
Answer: d
Problem: a and b can do a piece of work in 11 days . with the help of c they finish the work in 5 days . c alone can do that piece of work in ?
Options: a ) 15.5 days , b ) 19.5 days , c ) 17.5 days , d ) 9.2 days , e ) 18.5 days
Rationale: "c = 1 / 5 – 1 / 11 = 6 / 55 = > 9.2 days answer : d"
Answer: d
Problem: a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
Options: a ) 4 , b ) 6 , c ) 5 , d ) 17 , e ) 13
Rationale: "speed of train relative to man = ( 60 + 6 ) km / hr = 66 km / hr [ 66 * 5 / 18 ] m / sec = [ 55 / 3 ] m / sec . time taken to pass the man = [ 310 * 3 / 55 ] sec = 17 sec answer : d"
Answer: d
Problem: how many odd factors does 210 have ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: start with the prime factorization : 210 = 2 * 3 * 5 * 7 for odd factors , we put aside the factor of two , and look at the other prime factors . set of exponents = { 1 , 1 , 1 } plus 1 to each = { 2 , 2 , 2 } product = 2 * 2 * 2 = 8 therefore , there are 8 odd factors of 210 . in case you are curious , they are { 1 , 3 , 5 , 7 , 15 , 21 , 35 , and 105 } answer : e .
Answer: e
Problem: sarah operated her lemonade stand monday through friday over a two week period and made a total profit of 350 dollars . on hot days she sold cups of lemonade for a price that was 25 percent higher than the regular days . each cup she sold had a total cost of 75 cents and sarah did not incur any other costs . if every day she sold exactly 32 cups and 3 of the days were hot , then what was the price of 1 cup on a hot day ?
Options: a ) $ 1.50 , b ) $ 1.88 , c ) $ 2.14 , d ) $ 2.50 , e ) $ 3.25
Rationale: "7 regular days - - > sales = 7 * 32 * x = 224 x ; 3 hot days - - > sales = 3 * 32 * ( 1.25 x ) = 120 x ; total sales = 224 x + 120 x = 344 x . total cost = 10 * 32 * 0.75 = 240 . profit = 344 x - 240 = 350 - - > x = 1.715 . 1.25 x = ~ 2.14 . answer : c ."
Answer: c
Problem: what is the greatest prime factor of 2 ^ 8 - 1 ?
Options: a ) 11 , b ) 13 , c ) 17 , d ) 19 , e ) 23
Rationale: "2 ^ 8 - 1 = ( 2 ^ 4 - 1 ) ( 2 ^ 4 + 1 ) = 15 * 17 the answer is c ."
Answer: c
Problem: if x , y , and z are positive integers and 2 x = 3 y = 4 z , then the least possible value of x + y + z is
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 31
Rationale: "given 2 x = 3 y = 5 z x + y + z in terms of x = x + ( 2 x / 3 ) + ( 2 x / 5 ) = 31 x / 15 now checking with each of the answers and see which value gives a minimum integer value . a x = 15 / 31 * 40 , not an integer b , c , d can be ruled out similarly . e is minimum value as x = 15 * 31 / 31 = 15 answer is e"
Answer: e
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 7 ≤ x ≤ 1 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 432 , c ) 2,160 , d ) 3024 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 7 ( 9 horizontal dots and 7 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 7 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 6 c 1 , ( 7 - 1 = 6 as 1 vertical dot is already occupied by a ) . 9 c 1 * 7 c 1 * 8 c 1 * 6 c 1 = 3024 answer : d ."
Answer: d
Problem: a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?
Options: a ) 50 , b ) 60 , c ) 90 , d ) 48 , e ) 67
Rationale: c $ 90 let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 .
Answer: c
Problem: when n is divided by 48 , the remainder is 6 . what is the remainder when 4 n is divided by 8 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "let n = 6 ( leaves a remainder of 6 when divided by 48 ) 4 n = 4 ( 6 ) = 24 , which leaves a remainder of 0 when divided by 8 . answer a"
Answer: a
Problem: find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?
Options: a ) 2468 , b ) 2789 , c ) 2987 , d ) 3334 , e ) 3568
Rationale: if sum of the digits is divisible by 3 , the number is divisible by 3 . therefore , required number of non - negative integers is equal to count of numbers less than 10000 which are divisible by 3 . such numbers are ( 3 , 6 , 9 , . . . , 9999 ) ( arithmetic progression with first term = 3 , last term = 9999 , common difference = 3 ) . count of such numbers = 9999 3 = 3333 99993 = 3333 but zero is also divisible by 3 . this makes our total count 3334 d
Answer: d
Problem: a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got rs . 242 . what is the share of c ?
Options: a ) 33 , b ) 44 , c ) 55 , d ) 77 , e ) 99
Rationale: "the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = rs . 44 \ answer : b"
Answer: b
Problem: the present population of a town is 4320 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2100 , c ) 3500 , d ) 3000 , e ) 2050
Rationale: "p = 4320 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 4320 / ( 1 + 20 / 100 ) ^ 2 = 4320 / ( 6 / 5 ) ^ 2 = 3000 ( approximately ) answer is d"
Answer: d
Problem: if 12 men and 16 boys can do a piece of work in 7 days and 13 men together will 24 boys can do it in 4 days . compare the daily work done by a man with that of a boy .
Options: a ) 1 : 4 , b ) 1 : 2 , c ) 1 : 3 , d ) 2 : 1 , e ) 4 : 1
Rationale: "12 m + 16 b - - - - - 7 days 13 m + 24 b - - - - - - - 4 days 84 m + 112 b = 52 m + 96 b 32 m = 16 b = > 2 m = b m : b = 1 : 2 answer : b"
Answer: b
Problem: two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 6 days ?
Options: a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 3 , d ) 1 / 9 , e ) 2 / 6
Rationale: "a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 6 days = 6 ( 1 / 18 ) = 1 / 3 . answer c"
Answer: c
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.50 . if the company ’ s latest order required a truck with at least 432,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 3,375
Rationale: "number of boxes = total volume / volume of one box = 432,000 / ( 8 * 10 * 12 ) = 450 one box costs 7.50 , so 450 box will cost = 450 * 7.5 = 3375 e is the answer"
Answer: e
Problem: in how many ways 4 boys and 4 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 12 , d ) 576 , e ) none
Rationale: "solution : let the arrangement be , b g b g b g b g 4 boys can be seated in 4 ! ways . girl can be seated in 4 ! ways . required number of ways , = 4 ! * 4 ! = 576 . answer : option d"
Answer: d
Problem: two men a and b start from place x walking at 4 ½ kmph and 5 ¾ kmph respectively . how many km apart they are at the end of 4 ½ hours if they are walking in the same direction ?
Options: a ) 7 km , b ) 6 km , c ) 5 5 / 8 km , d ) 9 km , e ) 5 km
Rationale: "rs = 5 ¾ - 4 ½ = 1 ¼ t = 4 ½ h . d = 5 / 4 * 9 / 2 = 45 / 8 = 5 5 / 8 km answer : c"
Answer: c
Problem: kavi spends 50 % of his monthly salary on food and saves 80 % of the remaining amount . if his monthly salary is rs . 19000 , how much money does he save every month ?
Options: a ) rs . 2000 , b ) rs . 600 , c ) rs . 8000 , d ) rs . 3800 , e ) rs . 1200
Rationale: explanation : kavi ' s monthly income = rs . 19,000 he spends 50 % on food . the total money spent on food = 50 / 100 * 19000 = rs . 9500 now , his monthly remaining income = rs . 19000 – rs . 9500 = rs . 9500 out of rs . 9500 , he saves 40 % . amount saved = 40 / 100 * 9500 = rs . 3800 answer : d
Answer: d
Problem: a man can row upstream at 40 kmph and downstream at 52 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 40 , c ) 42 , d ) 46 , e ) 24
Rationale: "us = 40 ds = 52 m = ( 40 + 52 ) / 2 = 46 answer : d"
Answer: d
Problem: a can do a piece of work in 10 days and b alone can do it in 20 days . how much time will both take to finish the work ?
Options: a ) a ) 5.333 , b ) b ) 6 , c ) c ) 6.666 , d ) d ) 8.333 , e ) e ) 9
Rationale: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 10 x 20 / ( 10 + 20 ) = 200 / 30 = 6.666 days answer : c"
Answer: c
Problem: a ferry can transport 100 tons of vehicles . automobiles range in weight from 1,600 to 3,000 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 110 , b ) 128 , c ) 115 , d ) 130 , e ) 120
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1600 pounds here since , 1 ton = 2000 pounds 100 tons will be 200,000 pounds from the answer choices : let max number of vehicles be 120 total weight will be = 120 * 1600 = 192000 pounds , which is lesser than the maximum weight allowed . ans : e"
Answer: e
Problem: the simple interest on rs . 10 for 4 months at the rate of 3 paise per rupeeper month is
Options: a ) 1.2 , b ) 1.4 , c ) 2.25 , d ) 3.21 , e ) none
Rationale: "sol . s . i . = rs . [ 10 * 3 / 100 * 4 ] = rs . 1.20 answer a"
Answer: a
Problem: two trains are moving in the same direction at 72 kmph and 36 kmph . the faster train crosses a man in the slower train in 48 seconds . find the length of the faster train ?
Options: a ) 270 , b ) 288 , c ) 266 , d ) 299 , e ) 480
Rationale: "relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 27 sec = 48 * 10 = 480 m . the length of the faster train = 480 m . answer : e"
Answer: e
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 25 % of the original number . what percent of the red candies remain ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 40 %
Rationale: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = 1.25 x red + yellow = 0.5 x red = 0.25 x , since red = yellow . the answer is c ."
Answer: c
Problem: what is the units digit of ( 63 ^ 4 ) ( 41 ^ 7 ) ( 99 ^ 9 ) ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "the units digit of 63 ^ 4 is the units digit of 3 ^ 4 which is 1 . the units digit of 41 ^ 7 is the units digit of 1 ^ 7 which is 1 . the units digit of 99 ^ 9 is the units digit of 9 ^ 9 which is 9 . note the pattern : 9 ^ 1 = 9 , 9 ^ 2 = 81 , 9 ^ 3 = 729 , . . . the units digit alternates between 9 and 1 . the units digit of 1 * 1 * 9 is 9 . the answer is e ."
Answer: e
Problem: if - 4 and - 8 are negative integers , then - 4 * - 8 + 2 is
Options: a ) - 32 , b ) - 30 , c ) 34 , d ) - 24 , e ) - 10
Rationale: answer : c
Answer: c
Problem: the maximum number of students among them 1234 pens and 874 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 2 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1234 and 874 = 2 . answer : b"
Answer: b
Problem: a boatman selling a boat along river flow . if he sell boat in steal water at 3 m / sec and flow of river is 2 m / sec . how much time he will take to sell 100 m .
Options: a ) 30 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: net speed = 3 + 2 = 5 m / sec distance = 100 m time = 100 / 5 = 20 sec answer d
Answer: d
Problem: a man can row his boat with the stream at 12 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 2 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: explanation : ds = 12 us = 8 s = ? s = ( 12 - 8 ) / 2 = 2 kmph answer : a
Answer: a
Problem: jayant opened a shop investing rs . 30,000 . madhu joined him 2 months later , investing rs . 45,000 . they earned a profit of rs . 60,000 after completion of one year . what will be madhu ' s share of profit ?
Options: a ) rs . 27,000 , b ) rs . 24,000 , c ) rs . 30,000 , d ) rs . 36,000 , e ) none of these
Rationale: "30,000 * 12 = 45,000 * 8 1 : 1 madhu ' s share = 1 / 2 * 60,000 i . e . rs . 30,000 answer : c"
Answer: c
Problem: if the average ( arithmetic mean ) of a and b is 120 , and the average of b and c is 150 , what is the value of a − c ?
Options: a ) − 60 , b ) − 100 , c ) 100 , d ) 135 , e ) it can not be determined from the information given
Rationale: "a + b = 240 b + c = 300 a - c = - 60 . imo option a ."
Answer: a
Problem: a vessel of capacity 2 litre has 25 % of alcohol and another vessel of capacity 6 litre had 30 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 23 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "25 % of 2 litres = 0.5 litres 30 % of 6 litres = 1.8 litres therefore , total quantity of alcohol is 2.3 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 23 % answer : a"
Answer: a
Problem: if x / 4 years ago roger was 14 years old and x / 4 years from now he will be 4 x years old , how old will he be 3 x years from now ?
Options: a ) 32 , b ) 35 , c ) 30 , d ) 40 , e ) 27
Rationale: "assume the current age = a a - x / 4 = 14 ( i ) a + x / 4 = 4 x or a = 15 x / 4 ( ii ) putting the value of a from ( ii ) in ( i ) 15 x / 4 - x / 4 = 14 or 14 x / 4 = 14 therefore x = 4 and a = 15 3 x years from now , age will be 15 + 3 * 4 = 27 option e"
Answer: e
Problem: jack and jill work at a hospital with 4 other workers . for an internal review , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that jack and jill will both be chosen ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 15 , d ) 3 / 8 , e ) 2 / 3
Rationale: "total number of ways to choose 2 out of 6 workers = 6 ! / 2 ! 4 ! = 15 number of ways to choose both jack and jill = 1 probability = 1 / 15 c should be the answer"
Answer: c
Problem: a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 89 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d"
Answer: d
Problem: what least number must be added to 9879 , so that the sum is completely divisible by 10 ?
Options: a ) 3 , b ) 4 , c ) 1 , d ) 2 , e ) 6
Rationale: "if we divide 9879 by 10 remainder is 9 10 - 9 = 1 answer : c"
Answer: c
Problem: solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 450 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d"
Answer: d
Problem: a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 44 , c ) 99 , d ) 88 , e ) 11
Rationale: "750 - - - - 180 100 - - - - ? = > 44 % answer : b"
Answer: b
Problem: a , b and c invested rs . 6500 , rs . 1300 and rs . 7800 respectively , in a partnership business . find the share of b in profit of rs . 11700 after a year ?
Options: a ) 1300 , b ) 3877 , c ) 1170 , d ) 975 , e ) 7800
Rationale: "explanation : 6500 : 1300 : 7800 5 : 1 : 6 1 / 12 * 11700 = 975 answer : d"
Answer: d
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )"
Answer: b
Problem: evaluate 35 % of 450 + 45 % of 350
Options: a ) 232 , b ) 242 , c ) 315 , d ) 262 , e ) 272
Rationale: "explanation : = ( 35 / 100 ) * 450 + ( 45 / 100 ) * 350 = 315 option c"
Answer: c
Problem: when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 66.7 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ."
Answer: c
Problem: a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .
Options: a ) 10 kmph , b ) 20 kmph , c ) 30 kmph , d ) 40 kmph , e ) 50 kmph
Rationale: a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph
Answer: a
Problem: reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 5 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 300 12 r 2 = 300 r 2 = 25 r = 5 . answer : a"
Answer: a
Problem: if the number 872 , 152,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 872 , 152,24 x sum of digits at odd places = 8 + 2 + 5 + 2 + x = 17 + x ( i ) sum of digits at even places = 7 + 1 + 2 + 4 = 14 ( ii ) ( i ) - ( ii ) = 17 + x - 14 = x - 3 hence x should be = 3 to make this a multiple of 11 ( 0 ) option c"
Answer: c
Problem: darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 20 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 5.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 20 x = 5.5 minutes answer : a"
Answer: a
Problem: one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 150 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 60 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 150 2.5 h = 150 h = 60 . a is the answer ."
Answer: a
Problem: a furniture manufacturer has two machines , but only one can be used at a time . machine w is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine w can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: ' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d
Answer: d
Problem: what will be the remainder when 17 ^ 200 is divided by 18 ?
Options: a ) 3 , b ) 8 , c ) 5 , d ) 1 , e ) 7
Rationale: "when n is even , ( x ^ n - a ^ n ) is completely divisible by ( x - a ) . ( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) , ( 17 ^ 200 - 1 ) is completely divisible by 18 . on dividing 17 ^ 200 by 18 , we get 1 as remainder . answer is d"
Answer: d
Problem: calculate 469200 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691530800
Rationale: "answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e"
Answer: e
Problem: how many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 25 , d ) 23 , e ) 27
Rationale: "explanation : d = 100 + 130 = 230 s = 36 * 5 / 18 = 10 mps t = 230 / 10 = 23 sec answer : option d"
Answer: d
Problem: the average of first six prime numbers which are between 60 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 72.33
Rationale: "explanation : first six prime numbers which are between 60 and 90 = 61 , 67 , 71 , 73 , 79 , 83 average = ( 61 + 67 + 71 + 73 + 79 + 83 ) / 6 = 72.33 answer : e"
Answer: e
Problem: a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?
Options: a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years
Rationale: "c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b"
Answer: b