regisss/math_qa huggingface dataset:
Problem: how many integers between 362855 and 852755 have tens digit 1 and units digit 3 ?
Options: a ) 4,888 , b ) 4,898 , c ) 4,889 , d ) 4,869 , e ) 4,896
Rationale: there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 362,855 and 852,755 is 852,755 - 362,855 = 489,900 - one number per each hundred gives 133,900 / 100 = 4,889 numbers . answer : c .
Answer: c
Problem: the length of each side of square a is increased by 100 percent to make square b . if the length of the side of square b is increased by 80 percent to make square c , by what percent is the area of square c greater than the sum of the areas of squares a and b ?
Options: a ) 75 % , b ) 80 % , c ) 100 % , d ) 150 % , e ) 159.2 %
Rationale: "let length of each side of square a be 10 area of a = 10 ^ 2 = 100 since , length of each side of square a is increased by 100 percent to make square b length of each side of square b = 2 * 10 = 20 area of b = 20 ^ 2 = 400 since , length of the side of square b is increased by 80 percent to make square c length of each side of square c = 1.8 * 20 = 36 area of c = 36 ^ 2 = 1296 difference in areas of c and cummulative areas of a and b = 1296 - ( 400 + 100 ) = 796 percent is the area of square c greater than the sum of the areas of squares a and b = ( 796 / 500 ) * 100 % = 159.2 % answer e"
Answer: e
Problem: what are the last two digits of ( 301 * 401 * 503 * 604 * 646 * 547 * 448 * 349 ) ^ 2
Options: a ) 96 , b ) 76 , c ) 56 , d ) 44 , e ) 16
Rationale: "( ( 301 * 401 * 503 * 604 * 646 ) * ( 547 * 448 * 349 ) ) ^ 2 if you observe above digits , last digit are : 1,1 , 3,4 , 6,7 , 8,9 ; 1 & 5 are missing ; so i have rearranged them so that multiplication will be easy for me as initial 4 digits have last two digits as 01 , 01,03 , 04,46 and final three as 47 * 48 * 49 . solving for only last two digits and multiplying them we get : ( ( 03 * 04 * 46 ) ( 56 * 49 ) ) ^ 2 = ( 52 * 44 ) ^ 2 = 88 ^ 2 = 44 hence answer is d"
Answer: d
Problem: a corporation that had $ 10 billion in profits for the year paid out $ 200 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 200 million ) / ( 10 billion ) ] * 100 = [ ( 200 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 20 / 1000 ) * 100 = 2 % so answer is ( d )"
Answer: d
Problem: the 15 homes in a new development are each to be sold for one of 3 different prices so that the developer receives an average ( arithmetic mean ) of $ 200000 per home . if 4 of the homes are to be sold for $ 170000 each and 5 are to be sold for $ 200000 each , what will be the selling price of each of the remaining 8 homes ?
Options: a ) $ 200,000 , b ) $ 210,000 , c ) $ 215,000 , d ) $ 220,000 , e ) $ 230,000
Rationale: imo the answer has to be d . 5 houses are being sold for 200,000 . 4 houses are being sold for $ 30,000 less , resulting in a loss of $ 120,000 . to make the average selling price intact i . e . $ 200,000 , the remaining 8 houses must be sold at such a profit that it compensates for the loss of 120,000 . hence 8 x = 120,000 . x = 15,000 . the 8 houses are sold at $ 15,000 profit or at $ 215,000 . ( answer c )
Answer: c
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 200 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 4.4
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 200 / 45 = $ 4.4 answer : e ."
Answer: e
Problem: if each side of a square is increased by 25 % , find the percentage change in its area .
Options: a ) 46.25 % , b ) 56.25 % , c ) 56 % , d ) 50.25 % , e ) 36.25 %
Rationale: "let each side of the square be a . then , area = a 2 . new side = ( 125 a / 100 ) = ( 5 a / 4 ) . new area = ( 5 a / 4 ) 2 = ( 25 a 2 ) / 16 . increase in area = ( ( 25 a 2 ) / 16 ) - a 2 = ( 9 a 2 ) / 16 . increase % = [ ( ( 9 a 2 ) / 16 ) * ( 1 / a 2 ) * 100 ] % = 56.25 % . answer b 56.25 %"
Answer: b
Problem: at a summer camp with 1,500 participants , 1 / 2 of the campers are aged 10 to 12 . next year , the number of campers aged 10 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,500 campers will the 10 to 12 - year - olds represent ?
Options: a ) 62 , b ) 64 , c ) 65 , d ) 66 2 / 3 % , e ) 67
Rationale: "total - 1,500 participants campers are aged 10 to 12 = ( 1 / 2 ) * 1500 = 750 next year , campers are aged 10 to 12 = ( 4 / 3 ) * 750 = 1000 percentage = ( 1000 / 1500 ) * 100 = 66 2 / 3 % answer : option d"
Answer: d
Problem: a big container is 50 % full with water . if 20 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "20 liters is 25 % of the capacity c . 20 = 0.25 c c = 80 liters . the answer is a ."
Answer: a
Problem: 0.0007 ? = 0.01
Options: a ) 70 , b ) 7 , c ) 0.7 , d ) 0.07 , e ) none of these
Rationale: "explanation : required answer = 0.0007 / 0.01 = 0.07 / 1 = 0.07 . answer : option d"
Answer: d
Problem: a goods train runs at a speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: s = 260 + x / t 72 * 5 / 18 = 260 + x / 26 x = 260 answer : c
Answer: c
Problem: the area of a sector of a circle of radius 5 cm formed by an arc of length 4 cm is ?
Options: a ) 8.78 , b ) 8.67 , c ) 8.75 , d ) 10 , e ) 8.28
Rationale: "( 5 * 4 ) / 2 = 10 answer : d"
Answer: d
Problem: if an object travels 200 feet in 2 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 68 , b ) 54 , c ) 21 , d ) 48 , e ) 22
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 200 feet in 2 sec then it travels 200 / 2 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 100 feet in 1 hour = 360000 feet in 1 hr = 360000 / 5280 miles in 1 hour = 36000 / 528 miles / hr ~ 68 miles / hr answer - a"
Answer: a
Problem: a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 14 white mice in the experiment , how many brown mice are in the experiment ?
Options: a ) 12 , b ) 8 , c ) 28 , d ) 7 , e ) 27
Rationale: let total number of mice = m number of white mice = 2 / 3 m = 14 m = 21 number of brown mice = 1 / 3 m = 1 / 3 * 21 = > brown mice = 7 answer d
Answer: d
Problem: if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 12 ?
Options: a ) 1 / 48 , b ) 234 / 8 , c ) 1 / 24 , d ) 5 / 8 , e ) 3 / 4
Rationale: "i get 5 / 8 as well 1 to 96 inclusive means we have 48 odd and 48 even integers e o e / 12 = integer , therefore we have 48 / 96 numbers divisible by 8 o e o / 12 = not integer we can not forget multiples of 12 from 1 to 96 we have 8 numbers that are multiple of 12 therefore , 48 / 96 + 8 / 96 = 23 / 48 answer : b"
Answer: b
Problem: a theater box office sold an average ( arithmetic mean ) of 68 tickets per staff member to a particular movie . among the daytime staff , the average number sold per member was 80 , and among the evening staff , the average number sold was 60 . if there are no other employees , what was the ratio of the number of daytime staff members to the number of evening staff members ?
Options: a ) 2 : 3 , b ) 1 : 4 , c ) 5 : 6 , d ) 7 : 11 , e ) 3 : 7
Rationale: "deviation from the mean for the daytime staff = 80 - 68 = 12 . deviation from the mean for the evening staff = 68 - 60 = 8 . thus , the ratio of the number of daytime staff members to the number of evening staff members is 8 : 12 = 2 : 3 . the answer is a ."
Answer: a
Problem: if 7 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 12 , b ) 11 , c ) 10 , d ) 14 , e ) 13
Rationale: "7 ( log 2 ^ 2 * 5 ^ 2 ) = x 7 log ( 5 * 2 ) ^ 2 = x 7 * 2 log ( 5 * 2 ) = x 14 log 10 = x log 10 base 10 = 1 so 14 * 1 = x x = 14 answer : d"
Answer: d
Problem: a bag contains 6 black and 8 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 3 / 4 , b ) 4 / 7 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
Rationale: "let number of balls = ( 6 + 8 ) = 14 . number of white balls = 8 . p ( drawing a white ball ) = 8 / 14 = 4 / 7 . option b ."
Answer: b
Problem: we had $ 2800 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 3700 , b ) $ 4000 , c ) $ 4300 , d ) $ 4600 , e ) $ 4900
Rationale: "let x be the amount of money we started with . 0.7 x = 2800 x = 4000 the answer is b ."
Answer: b
Problem: ? x 48 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 534
Rationale: "let y x 48 = 173 x 240 then y = ( 173 x 240 ) / 48 = 173 x 5 = 865 . answer : c"
Answer: c
Problem: the ratio of the length and the breadth of a rectangle is 4 : 3 and the area of the rectangle is 6912 sq cm . find the ratio of the breadth and the area of the rectangle ?
Options: a ) 1 : 96
b ) 1 : 99
c ) 1 : 95
d ) 1 : 12
e ) 1 : 11
Rationale: let the length and the breadth of the rectangle be 4 x cm and 3 x respectively . ( 4 x ) ( 3 x ) = 6912 12 x 2 = 6912 x 2 = 576 = 4 * 144 = 22 * 122 ( x > 0 ) = > x = 2 * 12 = 24 ratio of the breadth and the areas = 3 x : 12 x 2 = 1 : 4 x = 1 : 96 . answer : a
Answer: a
Problem: after an ice began to melt out from the freezer , in the first hour lost 3 / 4 , in the second hour lost 3 / 4 of its remaining . if after two hours , the volume is 0.25 cubic inches , what is the original volume of the cubic ice , in cubic inches ?
Options: a ) 2.5 , b ) 3.0 , c ) 4.0 , d ) 6.5 , e ) 8.0
Rationale: "let initial volume of ice be = x ice remaining after 1 hour = x - 0.75 x = 0.25 x ice remaining after 2 hour = ( 1 / 4 ) x - ( 3 / 4 * 1 / 4 * x ) = ( 1 / 16 ) x ( 1 / 16 ) x = 0.25 x = 4 alternate solution : try to backsolve . initial volume = 4 after one hour - - > ( 1 / 4 ) 4 = 1 after two hours - - > ( 1 / 4 ) 1 = 0.25 answer : c"
Answer: c
Problem: log 3 n + log 6 n what is 3 digit number n that will be whole number
Options: a ) 629 , b ) 729 , c ) 829 , d ) 929 , e ) 216
Rationale: "no of values n can take is 1 6 ^ 3 = 216 answer : e"
Answer: e
Problem: of the total amount that rose spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 20 percent on food , and 30 percent on other items . if rose paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 2.8 % , b ) 4.4 % , c ) 4.6 % , d ) 5.2 % , e ) 6.0 %
Rationale: assume she has $ 200 to spend . tax clothing = 50 % = $ 100 = $ 4.00 food = 20 % = $ 40 = $ 0.00 items = 30 % = $ 60 = $ 4.80 total tax = $ 8.80 % of total amount = 8.8 / 200 * 100 = 4.4 % b )
Answer: b
Problem: 33 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 88 m , c ) 42 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 33 ⇔ = [ 33 * 20 * 20 * 7 / 22 ] = 4200 cm = 42 m . answer c"
Answer: c
Problem: in a certain game of dice , the player ’ s score is determined as a sum of 3 throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 216 , c ) 1 / 221 , d ) 1 / 84 , e ) 1 / 42
Rationale: to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 + 6 = 18 , because if he gets even one less than that so 17 , someone can get 18 and john will get nothing . p ( 18 ) = 1 / 6 ^ 3 = 1 / 216 . answer : b .
Answer: b
Problem: if the product of the integers w , x , y and z is 68 , and if 0 < w < x < y < z , what is the value of w + z ?
Options: a ) 10 , b ) 5 , c ) 16 , d ) 18 , e ) 21
Rationale: 24 = 1 * 2 * 3 * 4 so w = 1 , x = 2 , y = 3 , z = 4 w + z = 1 + 4 = 5 answer - b
Answer: b
Problem: what is the least number which when divided by 5 , 6 , 9 and 18 leaves remainder 4 in each care ?
Options: a ) 30 , b ) 44 , c ) 36 , d ) 56 , e ) 94
Rationale: "explanation : lcm of 5 , 6 , 9 and 18 is 90 required number = 90 + 4 = 94 answer : option e"
Answer: e
Problem: the speed of a railway engine is 63 km per hour when no compartment is attached , and the reduction in speed is directly proportional to the square root of the number of compartments attached . if the speed of the train carried by this engine is 24 km per hour when 9 compartments are attached , the maximum number of compartments that can be carried by the engine is :
Options: a ) 19 , b ) 18 , c ) 16 , d ) 17 , e ) 23
Rationale: the reduction in speed is directly proportional to the square root of the number of compartments attached does reduction mean amount subtracted ? or percentage decrease ? there are at least two interpretations , and the wording does not provide a clear interpretation between them . evidently what the question intends is the subtraction interpretation . what is subtracted from the speed is directly proportional to the square root of the number of compartments attached . in other words , if s = speed , and n = number of compartments , then s = 63 - k * sqrt ( n ) where k is a constant of the proportionality . in general , if a is directly proportional to b , we can write a = k * b and solve for k . if n = 9 , then s = 24 24 = 63 - k * sqrt ( 9 ) = 63 - 3 k k = 13 now , we need to know : what value of n makes s go to zero ? 0 = 63 - 13 * sqrt ( n ) 13 * sqrt ( n ) = 63 n = 23 with 24 compartments , the train does not budge . therefore , it would budge if there were one fewer cars . thus , 23 is the maximum number of cars the engine can pull and still move . e
Answer: e
Problem: in a class of 79 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 25 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 79 54 + not = 79 not = 79 - 54 = 25 so answer is c"
Answer: c
Problem: a train traveled the first d miles of its journey it an average speed of 60 miles per hour , the next d miles of its journey at an average speed of y miles per hour , and the final d miles of its journey at an average speed of 160 miles per hour . if the train ’ s average speed over the total distance was 98 miles per hour , what is the value of y ?
Options: a ) 68 , b ) 84 , c ) 90 , d ) 120 , e ) 125
Rationale: average speed = total distance traveled / total time taken 3 d / d / 60 + d / y + d / 160 = 98 solving for d and y , 15 y = 11 y + 480 4 y = 500 y = 125 answer e
Answer: e
Problem: a vessel of capacity 2 litre has 35 % of alcohol and another vessel of capacity 6 litre had 50 % 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 ) 31 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 37 % .
Rationale: "35 % of 2 litres = 0.7 litres 50 % of 6 litres = 3 litres therefore , total quantity of alcohol is 3.7 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 37 % e"
Answer: e
Problem: how many integers between 324,700 and 468,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,439
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 324,700 and 468,600 is 468,600 - 324,700 = 133,900 - one number per each hundred gives 143,900 / 100 = 1,439 numbers . answer : e ."
Answer: e
Problem: find the unknown term 8 , x , 62 , - 4 , - 12
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: 8 , x , 6,2 , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : d
Answer: d
Problem: what is the local value of 6 in the product of face value of 7 and local value of 8 in 7098060
Options: a ) 60 , b ) 600 , c ) 6000 , d ) 60000 , e ) 6
Rationale: ( face value of 7 ) x ( local value of 8 ) = 7 x 8000 = 56000 local value of 6 in 56000 = 6000 c
Answer: c
Problem: how many integers are divisible by 3 between 10 ! and 10 ! + 20 inclusive ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "0 ! is divisible by 3 - the way i look factorials is that any number included will also be divisible by the product . 10,9 , 8,7 , 6,5 , 4,3 , 2,1 are all divisors of 10 ! there are 6 numbers between 10 ! and 10 ! + 20 that are divisible by 3 . hence b : 7"
Answer: b
Problem: a cricket bat is sold for $ 850 , making a profit of $ 205 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 32 % , d ) 36 % , e ) 40 %
Rationale: "205 / ( 850 - 205 ) = 205 / 645 = 41 / 129 = 32 % . answer : c ."
Answer: c
Problem: what is the unit digit in 12 ^ 100 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 6
Rationale: unit digit in 12 ^ 100 = unit digit in [ ( 12 ^ 4 ) ^ 25 ] but unit digit in 12 ^ 4 = 6 unit digit 12 ^ 100 = 6 answer is e
Answer: e
Problem: for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 4 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "4 ” 3 = 9 - 4 = 5 answer : a"
Answer: a
Problem: a man buys an article for $ 10 . and sells it for $ 25 . find the gain percent ?
Options: a ) 25 % , b ) 50 % , c ) 20 % , d ) 150 % , e ) 300 %
Rationale: "c . p . = $ 10 s . p . = $ 25 gain = $ 15 gain % = 15 / 10 * 100 = 150 % answer is d"
Answer: d
Problem: a can do a piece of work in 12 days . when he had worked for 2 days b joins him . if the complete work was finished in 8 days . in how many days b alone can finish the work ?
Options: a ) 28 days , b ) 76 days , c ) 16 days , d ) 18 days , e ) 19 days
Rationale: 8 / 12 + 6 / x = 1 x = 18 days 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 6 x years from now ?
Options: a ) 32 , b ) 39 , c ) 30 , d ) 40 , e ) 28
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 6 x years from now , age will be 15 + 6 * 4 = 39 option b"
Answer: b
Problem: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing the same no . by 38
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 8
Rationale: "p ã · 44 = 432 = > p = 432 * 44 = 19008 p / 38 = 19008 / 38 = 500 , remainder = 8 e"
Answer: e
Problem: sue ' s trail mix is 30 % nuts and 70 % dried fruit . jane ' s trail mix is 60 % nuts and 40 % chocolate chips . if the combined mixture of sue and jane ' s trails mix contains 48 % nuts , what percent of the combined mixture is dried fruit ?
Options: a ) 20 % , b ) 24 % , c ) 28 % , d ) 32 % , e ) 36 %
Rationale: "48 % is 18 % - points above 30 % and 12 % - points below 60 % . so the ratio of sue ' s mix to jane ' s mix is 2 : 3 . 2 / 5 * 70 % = 28 % the answer is c ."
Answer: c
Problem: x can finish a work in 30 days . y can finish the same work in 15 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 10 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 30 work done by y in 1 day = 1 / 15 work done by y in 10 days = 10 / 15 = 2 / 3 remaining work = 1 – 2 / 3 = 1 / 3 number of days in which x can finish the remaining work = ( 1 / 3 ) / ( 1 / 30 ) = 10 b"
Answer: b
Problem: what is the sum of the numbers between 1 and 10 , inclusive ?
Options: a ) 85 , b ) 95 , c ) 100 , d ) 105 , e ) 55
Rationale: "sol . add all the numbers between 1 and 10 . final answer = e , 55 ."
Answer: e
Problem: a is thrice as good a work man as b and together they finish a piece of work in 12 days . the number of days taken by a alone to finish the work is :
Options: a ) 28 days . , b ) 14 days . , c ) 12 days . , d ) 16 days . , e ) 18 days .
Rationale: solution ( a ’ s 1 day ’ s work ) : ( b ’ s 1 day ’ s work ) = 3 : 1 . ( a + b ) ' s 1 day ’ s work = 1 / 12 divide 1 / 14 in the ratio 3 : 1 . ∴ a ’ s 1 day ’ s work = ( 1 / 12 x 2 / 3 ) = 1 / 16 hence , a alone can finish the work in 16 days . answer d
Answer: d
Problem: 300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 55 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
Options: a ) 7 , b ) 25 , c ) 35 , d ) 45 , e ) 75
Rationale: "out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 55 % = 99 responded as satisfied , so remaining satisfied are 120 - 99 = 21 so 21 is what percentage of 300 - 7 % so the answer should be a"
Answer: a
Problem: the average age of 9 men increases by 4 years when two women are included in place of two men of ages 36 and 32 years . find the average age of the women ?
Options: a ) 78 , b ) 26 , c ) 52 , d ) 54 , e ) 56
Rationale: "explanation : 36 + 32 + 9 * 4 = 104 / 2 = 52 answer : c"
Answer: c
Problem: 0.014 × 0.014 = ?
Options: a ) 0.000196 , b ) 0.00196 , c ) 19.6 , d ) 196 , e ) none
Rationale: "solution sum of decimals places = 6 . 14 × 14 = 196 . = s 0.014 × 0.014 = 0.000196 answer a"
Answer: a
Problem: of the land owned by a farmer , 90 percent was cleared for planting . of the cleared land , 30 percent was planted with soybeans and 60 percent of the cleared land was planted with wheat . if the remaining 540 acres of cleared land was planted with corn , how many acres did the farmer own ?
Options: a ) 7200 , b ) 6000 , c ) 3500 , d ) 5000 , e ) 6200
Rationale: 30 % od 90 % = 27 % , 60 % 0 f 90 % = 54 % so the remaining 90 - 27 - 54 = 9 % = 540 acres or 10 % of 90 % = 9 % - - > 540 / 9 * 100 = 6000 acres answer ( b )
Answer: b
Problem: three unbiased coins are tossed . what is the probability of getting at most two heads ?
Options: a ) 3 / 4 , b ) 1 / 4 , c ) 3 / 8 , d ) 7 / 8 , e ) none of these
Rationale: explanation : here s = { ttt , tth , tht , htt , thh , hth , hht , hhh } let e = event of getting at most two heads . then e = { ttt , tth , tht , htt , thh , hth , hht } . p ( e ) = n ( e ) / n ( s ) = 7 / 8 . answer is d
Answer: d
Problem: the wages earned by robin is 49 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 32.88 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 149 and $ 160 respectively . charles earns $ 49 more than robin who earns $ 149 . therefore , charles ' wage is 49 / 149 * 100 = 32.88 % . the correct choice is ( e )"
Answer: e
Problem: there are 59 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 29 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 59 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 59 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 29 answer : d"
Answer: d
Problem: a sum of salary is distributed among a , b , c , d in the proportion of 2 : 3 : 4 : 6 . if d gets $ 700 more than c , what is the b ' s share ?
Options: a ) $ 1050 , b ) $ 2500 , c ) $ 3000 , d ) $ 3400 , e ) $ 8000
Rationale: let the shares of a , b , c , d are 2 x , 3 x , 4 x , 6 x 6 x - 4 x = 700 x = 350 b ' s share = 3 x = $ 1050 answer is a
Answer: a
Problem: two 6 faced dice are thrown together . the probability that all the three show the same number on them is ?
Options: a ) 1 / 32 , b ) 1 / 6 , c ) 1 / 33 , d ) 1 / 38 , e ) 1 / 34
Rationale: "the three dice can fall in 6 * 6 = 36 ways . hence the probability is 6 / 36 = 1 / 6 answer : b"
Answer: b
Problem: the tax on a commodity is diminished by 27 % and its consumption increased by 16 % . the effect on revenue is ?
Options: a ) 18 , b ) 16 , c ) 5 , d ) 15 , e ) 4
Rationale: "100 * 100 = 10000 73 * 116 = 8468 - - - - - - - - - - - 10000 - - - - - - - - - - - 1532 100 - - - - - - - - - - - ? = > 15 % decrease answer : d"
Answer: d
Problem: 5 , 10 , 13 , 26 , 29 , 58 , 61 , ( . . . . )
Options: a ) 128 , b ) 64 , c ) 122 , d ) 125 , e ) 130
Rationale: "numbers are alternatively multiplied by 2 and increased by 3 5 ã — 2 = 10 10 + 3 = 13 13 ã — 2 = 26 26 + 3 = 29 29 ã — 2 = 58 58 + 3 = 61 61 ã — 2 = 122 answer c"
Answer: c
Problem: in a class , 7 students like to play basketball and 8 like to play cricket . 5 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 10 , b ) 15 , c ) 16 , d ) 18 , e ) 22
Rationale: draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 7 + 8 - 5 = 10 a )
Answer: a
Problem: a library has an average of 175 visitors on sundays and 75 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 165 * 5 + 75 * 25 ) / 30 = 2700 / 30 = 90 answer : b ) 90"
Answer: b
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 26 } + { 24 } ?
Options: a ) 23 , b ) 20 , c ) 27 , d ) 5 , e ) 2
Rationale: "soln : { 26 } + { 24 } = 26 * { 24 } + { 24 } = 27 * { 24 } answer : c"
Answer: c
Problem: in a mixed college 160 students are there in one class . out of this 160 students 3 / 8 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 100 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 3 / 8 = 60 total boys : 160 - 60 = 100 answer is d"
Answer: d
Problem: a beats b by 50 m in a race of 500 m , then b beats by c by 25 m in a race of 500 m . find the distance by which a beats c in a race of 400 ?
Options: a ) 55 m , b ) 56 m , c ) 57 m , d ) 58 m , e ) 59 m
Rationale: a beats b in 500 m race by 50 m so , for every 10 m race a beat b by 1 m . . so , in 400 m race a beat b by 40 m in a case of b & c , b beats c by 25 m in 500 m race . . so , b beats c by 1 m in 20 m race now , in a 400 m race b beats c by 18 m . . in a 400 m race , a beats b by 40 m & b beats c by 18 m . . so , a beats c by 58 m answer : d
Answer: d
Problem: a fellow borrowed a certain sum of money at 4 % per annum at simple interest and in 4 years the interest amounted to rs . 1260 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1500 , d ) 1060 , e ) 1110
Rationale: "p - 1260 = ( p * 4 * 4 ) / 100 p = 1500 answer : c"
Answer: c
Problem: if x ^ 2 + 1 / x ^ 2 = √ 20 what is the value of x ^ 4 + 1 / x ^ 4 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "important : i notice that if we square x ² , we get x ⁴ , and if we square 1 / x ² , we get 1 / x ⁴ , so let ' s see what happens if we take the equation x ² + 1 / x ² = √ 20 andsquareboth sides : ( x ² + 1 / x ² ) ² = 20 so , ( x ² + 1 / x ² ) ( x ² + 1 / x ² ) = 20 expand to get : x ⁴ + 1 + 1 + 1 / x ⁴ = 20 simplify : x ⁴ + 1 / x ⁴ = 18 answer : e"
Answer: e
Problem: the pilot of a small aircraft with a 40 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 5 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 7
Rationale: actual miles / gallon is = 480 / 40 = 12 miles / gallon . current engine miles / gallon is 5 miles / gallon . additional 7 miles / gallon is required to match the actual mileage . imo option e .
Answer: e
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 40 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 20 , at what time will they be reading the same page ?
Options: a ) 9 : 30 , b ) 9 : 00 , c ) 8 : 40 , d ) 7 : 50 , e ) 7 : 00
Rationale: "relative speed = jan - tom = 10 pages per hour = 1 / 6 page per minute time diff = 50 minutes by the time jan started tom already finished ( 30 / 60 ) * 50 = 25 pages time taken = 25 / ( 1 / 6 ) = 25 * 6 = 150 minutes = 7 : 50 answer : d"
Answer: d
Problem: what is the % change in the area of a rectangle when its length increases by 35 % and its width decreases by 35 % ?
Options: a ) 0 %
b ) 20 % increase
c ) 20 % decrease
d ) 12 % decrease
e ) insufficient data
Rationale: ( 135 / 10 ) * ( 65 / 10 ) = 8775 / 100 ~ 88 of original area 0.88 is a 12 % decrease from 100 / 100 - > d
Answer: d
Problem: what is the product between the place values of two 8 ' s in the numeral 780.38
Options: a ) 0.16 , b ) 0.64 , c ) 80.08 , d ) 64 , e ) 6.4
Rationale: required product = 80 x 0.08 = 6.4 answer is e
Answer: e
Problem: two numbers are 30 % and 37 % are less than a third number . how much percent is the second number less than the first ?
Options: a ) 19 % , b ) 80 % , c ) 10 % , d ) 90 % , e ) 15 %
Rationale: i ii iii 70 63 100 70 - - - - - - - - 7 100 - - - - - - ? = > 10 % answer : c
Answer: c
Problem: a train is 360 meter long is running at a speed of 30 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 87 , b ) 69 , c ) 60 , d ) 72 , e ) 21
Rationale: "speed = 30 km / hr = 30 * ( 5 / 18 ) m / sec = 25 / 3 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 3 / 25 ) = 60 seconds answer : c"
Answer: c
Problem: the total car population in a chennai is 9000 out of which 5000 are made by honda . out of every 100 honda cars , 90 are red in color , but only 60 % of the total car population is red . find the % of non - honda cars that are red
Options: a ) 22.5 % , b ) 21.5 % , c ) 20.5 % , d ) 12.5 % , e ) 10.5 %
Rationale: total honda brand red cars = 90 / 100 * 5000 = 4500 total red cars = 60 / 100 * 9000 = 5400 no . of non - honda cars = 9000 - 5000 = 4000 no . of non - honda red cars = 5400 - 4500 = 900 % of non - honda red cars = 900 / 4000 * 100 = 22.5 % answer : a
Answer: a
Problem: danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 29 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 14.5 minutes , b ) 29 minutes , c ) 35 minutes , d ) 58 minutes , e ) 87 minutes
Rationale: danny ' s time is 29 minutes . the time to reach halfway is 14.5 minutes . steve ' s time is 58 minutes . the time to reach halfway is 29 minutes . the time difference is 29 - 14.5 = 14.5 minutes the answer is a .
Answer: a
Problem: find the fraction which has the same ratio to 1 / 2 that 2 / 5 has to 3 / 7
Options: a ) 1 / 2 , b ) 2 / 12 , c ) 14 / 30 , d ) 3 / 8 , e ) 7 / 9
Rationale: "a : 1 / 2 = 2 / 5 : 3 / 7 as the product of the means is equal to the product of the extremes . a * 3 / 7 = 1 / 2 * 2 / 5 a * 3 / 7 = 2 / 10 a = 14 / 30 = > a = 14 / 30 answer : c"
Answer: c
Problem: the average of 7 consecutive numbers a , b , c , d , e , f and g is 9 . what percent of g is a ?
Options: a ) 42.0 , b ) 48.0 , c ) 50.0 , d ) 52.2 , e ) 54.0
Rationale: explanation : in such a case the middle number ( d ) is the average ∴ d = 9 and a = 6 and g = 12 required percentage = 6 / 12 x 100 = 50.0 answer : option c
Answer: c
Problem: a hen leaps 6 leaps for every 8 leaps of a duck , but 4 leaps of the duck are equal to 3 leaps of the hen . what is the ratio of the speed of the hen to that of the duck ?
Options: a ) 1 : 1 , b ) 3 : 8 , c ) 4 : 3 , d ) 8 : 9 , e ) 1 : 3
Rationale: given ; 4 duck = 3 hen ; or , duck / hen = 3 / 4 ; let hen ' s 1 leap = 4 meter and ducks 1 leap = 3 meter . then , ratio of speed of hen and duck = 4 * 6 / 3 * 8 = 1 : 1 ' ' answer : 1 : 1 ;
Answer: a
Problem: amar takes as much time in running 24 meters as a car takes in covering 60 meters . what will be the distance covered by amar during the time the car covers 2.2 km ?
Options: a ) 700 m , b ) 500 m , c ) 870 m , d ) 880 m , e ) 840 m
Rationale: "distance covered by amar = 24 / 60 ( 2.2 km ) = 2 / 5 ( 2200 ) = 880 m answer : d"
Answer: d
Problem: of the 600 residents of clermontville , 35 % watch the television show island survival , 40 % watch lovelost lawyers and 50 % watch medical emergency . if all residents watch at least one of these 3 shows and 18 % watch exactly 2 of these shows , then how many clermontville residents b watch all of the shows ?
Options: a ) 150 , b ) 108 , c ) 42 , d ) 21 , e ) - 21
Rationale: oa is d . 100 = a + b + c - ab - ac - bc + abc , which is the same as the following formula 100 = a + b + c + ( - ab - ac - bc + abc + abc + abc ) - 2 abc . the term between parantheses value 18 % so the equation to resolve is 100 = 35 + 40 + 50 - 18 - 2 abc therefore the value of abc is 3.5 % of 600 , b is 21 . d is the correct answer
Answer: d
Problem: the product of two numbers is 336 and the sum of their squares is 289 . the sum of the number is ?
Options: a ) a ) 23 , b ) b ) 25 , c ) c ) 27 , d ) d ) 31 , e ) e ) 35
Rationale: "let the numbers be x and y . then , xy = 336 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 336 ) = 961 x + y = 31 . option d"
Answer: d
Problem: the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 600 per sq . metre .
Options: a ) rs . 15,000 , b ) rs . 15,500 , c ) rs . 12,375 , d ) rs . 16,500 , e ) none
Rationale: "solution area of the floor = ( 5.5 x 3.75 ) m ² = 20.635 m ² cost of paying = rs . ( 600 x 20.625 ) = rs . 12,375 . answer c"
Answer: c
Problem: x and y together can completes a work in 12 days and y complete the same work in 24 days . then the number of days x required to complete the work will be ?
Options: a ) 15 days . , b ) 12 days . , c ) 24 days . , d ) 13 days . , e ) 16 days .
Rationale: x and y complete in one day = 1 / 12 part , y completes in one day = 1 / 24 parts . therefore x alone can do in one day = 1 / 24 part . therefore the work can be finished by x = 24 days . ans : c
Answer: c
Problem: if 204 ÷ 12.75 = 16 , then 2.04 ÷ 1.275 = ?
Options: a ) 16 , b ) 1.6 , c ) 0.16 , d ) 0.016 , e ) none of these
Rationale: explanation : ( 204 / 12.75 ) = 16 ⇒ ( 20.4 ) / ( 1.275 ) = 16 ( ∵ divided numerator and denominator by 10 ) ⇒ 2.04 / 1.275 = 1.6 ( ∵ divided lhs and rhs by 10 ) answer : option b
Answer: b
Problem: if n is an integer and 101 n ^ 2 is less than or equal to 3600 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 5 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 3600 n ^ 2 < = 3600 / 101 which will be less than 81 since 3600 / 100 = 36 which is the square of 9 next closest value of n where n ^ 2 < = 36 is 5 ans b"
Answer: b
Problem: the simple form of the ratio 4 / 3 : 3 / 7 is ?
Options: a ) 7 : 3 , b ) 10 : 3 , c ) 15 : 3 , d ) 25 : 3 , e ) 30 : 3
Rationale: "4 / 3 : 3 / 7 = 21 : 9 = 7 : 3 answer : a"
Answer: a
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 105 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 2400 , b ) $ 3200 , c ) $ 3500 , d ) $ 6400 , e ) $ 9600
Rationale: let x be the monthly salary 15 % of 1 / 5 * x = 105 x = 3500 answer c
Answer: c
Problem: what is 12 percent of 80 ?
Options: a ) 11.21 , b ) 9.6 , c ) 8.66 , d ) 12.23 , e ) 13.1
Rationale: "we assume that 80 is 100 % assume ' x ' is value we looking for here , 80 = 100 % and x = 12 % therefore , 80 / x = 100 % / 12 % 80 / x = 8.33 x = 9.6 b"
Answer: b
Problem: if the average ( arithmetic mean ) of 5 b , 6 b + 47 b , 8 b - 4 and 2 b is 140 , what is the value of b ?
Options: a ) 20 , b ) 22 , c ) 25 , d ) 30 , e ) 48
Rationale: am of 5 b , 6 b + 47 b , 8 b - 4 and 2 b = 5 b + 6 b + 4 + 7 b + 8 b - 4 + 2 b = 28 b / 5 given that 28 b / 5 = 140 b = 25 answer is c
Answer: c
Problem: you buy a piece of land with an area of â ˆ š 400 , how long is one side of the land plot ?
Options: a ) 28 , b ) 29 , c ) 30 , d ) 20 , e ) 32
Rationale: "try filling the numbers into the answer y x y = find the closest to 400 . answer d"
Answer: d
Problem: find the number , difference between number and its 3 / 5 is 62 .
Options: a ) 150 , b ) 153 , c ) 154 , d ) 155 , e ) 156
Rationale: "explanation : let the number = x , then , x - ( 3 / 5 ) x = 62 , = > ( 2 / 5 ) x = 62 = > 2 x = 62 * 5 , = > x = 155 answer : option d"
Answer: d
Problem: company kw is being sold , and both company a and company b were considering the purchase . the price of company kw is 90 % more than company a has in assets , and this same price is also 100 % more than company b has in assets . if companies a and b were to merge and combine their assets , the price of company kw would be approximately what percent of these combined assets ?
Options: a ) 66 % , b ) 75 % , c ) 86 % , d ) 97 % , e ) 150 %
Rationale: "let the price of company a ' s assets be 100 price of assets of kw is 90 % more than company a ' s assets which is 190 price of assets of kw is 100 % more than company b ' s assets which means price of company b ' s assets is half the price of kw = 95 a + b = 195 kw = 190 kw / ( a + b ) * 100 = 190 / 195 * 100 = 97.43 % or 97 % d"
Answer: d
Problem: if $ 200 invested at a certain rate of simple interest amounts to $ 240 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 210
Rationale: "200 amounts to 240 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 240 200 + 200 * ( r / 100 ) * ( 3 ) = 240 = > r = 20 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 210 answer is e ."
Answer: e
Problem: a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 60 to incur a loss 20 % ?
Options: a ) 30 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 60 * ( 100 % + 20 % ) = $ 72 number of articles to be sold for $ 72 to incur a 20 % loss : $ 72 / $ 2.40 = 30 thus , solution a is correct ."
Answer: a
Problem: a train 200 m long crosses a platform 200 m long in 40 sec ; find the speed of the train ?
Options: a ) 94 kmph , b ) 58 kmph , c ) 54 kmph , d ) 94 kmph , e ) 36 kmph
Rationale: "d = 200 + 200 = 400 t = 40 s = 400 / 40 * 18 / 5 = 36 kmph answer : e"
Answer: e
Problem: a shopkeeper sold 30 articles at the cost price of 25 articles . then find the profit % or lost %
Options: a ) 15 % , b ) 18 % , c ) 20 % loss , d ) 25 % , e ) 30 %
Rationale: "here 30 articles selling price = 25 articles cost price so the difference = 25 - 30 = - 5 % of loss = 5 * 100 / 25 = 20 % correct option is c"
Answer: c
Problem: the sum of three consecutive even numbers is 30 . find the middle number of the three ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 25 , e ) 34
Rationale: "three consecutive even numbers ( 2 p - 2 ) , 2 p , ( 2 p + 2 ) . ( 2 p - 2 ) + 2 p + ( 2 p + 2 ) = 30 6 p = 30 = > p = 5 . the middle number is : 5 p = 25 . answer : d"
Answer: d
Problem: if x is the median of the set { 9 / 2 , 10 / 3 , 27 / 9 , 21 / 5 , x } , x could be
Options: a ) 16 / 5 , b ) 17 / 5 , c ) 28 / 7 , d ) 30 / 7 , e ) 31 / 7
Rationale: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 10 / 3 = 3 . something , 27 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( c )"
Answer: c
Problem: james and david work at a grocery shop with 12 other workers . for an internal review , 2 of the 12 workers will be randomly chosen to be interviewed . what is the probability that james and david will both be chosen ?
Options: a ) 1 / 26 , b ) 1 / 36 , c ) 1 / 46 , d ) 1 / 66 , e ) 1 / 56
Rationale: probability that james and david will both be chosen out of 12 workers = ( 2 / 12 ) * ( 1 / 11 ) = 1 / 66 answer d
Answer: d
Problem: bookman purchased 40 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 300 , how many paperback copies were sold ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "the bookman had 10 hardback ad 40 - 10 = 30 paperback copies ; 14 copies were sold , hence 40 - 14 = 26 copies were left . let # of paperback copies left be p then 10 p + 20 ( 26 - p ) = 300 - - > 10 p = 220 - - > p = 22 # of paperback copies sold is 30 - 22 = 8 answer : c"
Answer: c
Problem: a candidate got 35 % of the votes and lost to the rival by 1800 votes . how many votes were cast ?
Options: a ) 5500 , b ) 6000 , c ) 6500 , d ) 7000 , e ) 7500
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1800 10 % = 600 100 % of the votes = 6000 answer : b"
Answer: b
Problem: a company conducted a survey about its two brands , a and b . x percent of respondents liked product a , ( x – 20 ) percent liked product b , 23 percent liked both products , and 23 percent liked neither product . what is the minimum number d of people surveyed by the company ?
Options: a ) 46 , b ) 80 , c ) d . 90 , d ) d . 100 , e ) 200
Rationale: 100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d .
Answer: d
Problem: two trains of equal length are running on parallel lines in the same directions at 46 km / hr . and 36 km / hr . the faster trains pass the slower train in 54 seconds . the length of each train is :
Options: a ) 82 m , b ) 50 m , c ) 75 m , d ) 80 m , e ) none of these
Rationale: "explanation : the relative speed of train is 46 - 36 = 10 km / hr = ( 10 x 5 ) / 18 = 25 / 9 m / s 10 × 518 = 259 m / s in 54 secs the total distance traveled is 54 x 25 / 9 = 150 m . therefore the length of each train is = 150 / 2 = 75 m . answer c"
Answer: c
Problem: if 11.25 m of a uniform steel rod weighs 42.75 kg . what will be the weight of 7 m of the same rod ?
Options: a ) 22.8 kg , b ) 26.6 kg , c ) 28 kg , d ) 26.5 kg , e ) none of these
Rationale: "explanation : let the required weight be x kg . then , less length , less weight ( direct proportion ) = > 11.25 : 7 : : 42.75 : x = > 11.25 x x = 7 x 42.75 = > x = ( 7 x 42.75 ) / 11.25 = > x = 26.6 answer : b"
Answer: b
Problem: if a farmer wants to plough a farm field on time , he must plough 160 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 600 , b ) 490 , c ) 448 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 160 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 160 x = 85 ( x + 2 ) + 40 75 x = 210 x = 2.8 so the farmer planned to have the work done in 6 days , and the area of the farm field is 160 ( 2.8 ) = 448 hectares correct answer c"
Answer: c
Problem: a chemist mixes one liter of pure water with x liters of a 60 % salt solution , and the resulting mixture is a 10 % salt solution . what is the value of x ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 1 , e ) 3
Rationale: "concentration of salt in pure solution = 0 concentration of salt in salt solution = 60 % concentration of salt in the mixed solution = 10 % the pure solution and the salt solution is mixed in the ratio of - - > ( 60 - 10 ) / ( 10 - 0 ) = 5 / 1 1 / x = 5 / 1 x = 1 / 5 answer : a"
Answer: a
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 36 pages per hour . if tom starts reading a novel at 4 : 00 , and jan begins reading an identical copy of the same book at 4 : 48 , at what time will they be reading the same page ?
Options: a ) 7 : 18 , b ) 7 : 48 , c ) 8 : 18 , d ) 8 : 48 , e ) 9 : 18
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 6 pages per hour , so it will take 4 hours to catch tom . the answer is d ."
Answer: d
Problem: bhatia , ashtikar and singh begin to play with rs 70 each . at the end the ratio of the amounts left with ashtikar and singh is 1 : 2 and of those with singh and bhatia is 4 : 1 . what is singh ' s gain ( in rs ) ?
Options: a ) 40 , b ) 45 , c ) 48 , d ) 50 , e ) 53
Rationale: we have b + a + s = 210 and s = 2 a , s = 4 b and a = 2 b solving these eqs we got that singh have rs . 120 in the end bhatia have 30 and astikar have 60 . so singh ' s profit is 120 - 70 = 50 answer : d
Answer: d
Problem: if x ^ 2 + ( 1 / x ^ 2 ) = 7 , x ^ 4 + ( 1 / x ^ 4 ) = ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 14 , e ) 47
Rationale: "- > x ^ 4 + ( 1 / x ^ 4 ) = ( x ^ 2 ) ^ 2 + ( 1 / x ^ 2 ) ^ 2 = ( x ^ 2 + 1 / x ^ 2 ) ^ 2 - 2 x ^ 2 ( 1 / x ^ 2 ) = 7 ^ 2 - 2 = 47 . thus , the answer is e ."
Answer: e
Problem: the floor of a rectangular room is 19 m long and 12 m wide . the room is surrounded by a veranda of width 2 m on all its sides . the area of the veranda is :
Options: a ) 144 m 2 , b ) 140 m 2 , c ) 108 m 2 , d ) 158 m 2 , e ) none of these
Rationale: "area of the outer rectangle = 23 ã — 16 = 368 m 2 area of the inner rectangle = 19 ã — 12 = 228 m 2 required area = ( 368 â € “ 228 ) = 140 m 2 answer b"
Answer: b