regisss/math_qa huggingface dataset:
Problem: from the digits 2 , 3 , 4 , 5 , 6 and 7 , how many 5 - digit numbers can be formed that have distinct digits and are multiples of 12 ?
Options: a ) 36 , b ) 60 , c ) 84 , d ) 72 , e ) 86
Rationale: detailed solution any multiple of 12 should be a multiple of 4 and 3 . first , let us look at the constraint for a number being a multiple of 3 . sum of the digits should be a multiple of 3 . sum of all numbers from 2 to 7 is 27 . so , if we have to drop a digit and still retain a multiple of 3 , we should drop either 3 or 6 . so , the possible 5 digits are 2 , 4 , 5 , 6 , 7 or 2 , 3 , 4 , 5 , 7 . when the digits are 2 , 4 , 5 , 6 , 7 . the last two digits possible for the number to be a multiple of 4 are 24 , 64 , 52 , 72 , 56 , 76 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 36 different numbers . when the digits are 2 , 3 , 4 , 5 , 7 . the last two digits possible for the number to be a multiple of 4 are 32 , 52 , 72 , 24 . for each of these combinations , there are 6 different numbers possible . so , with this set of 5 digits we can have 24 different numbers . overall , there are 60 different 5 - digit numbers possible . correct answer : b
Answer: b
Problem: what is the least common multiple of 8,12 , 32,14
Options: a ) 672 , b ) 682 , c ) 328 , d ) 964 , e ) 285
Rationale: "the given numbers are 8,12 , 32,14 thus the l . c . m is 2 * 2 * 2 * 1 * 3 * 4 * 7 = 672 the answer is a"
Answer: a
Problem: the difference between the local value and the face value of 8 in the numeral 96348621 is
Options: a ) 6992 , b ) 6982 , c ) 7982 , d ) 7972 , e ) 7992
Rationale: "explanation : ( local value of 8 ) - ( face value of 8 ) = ( 8000 - 8 ) = 7992 e )"
Answer: e
Problem: find the ratio in which rice at rs . 7.20 a kg be mixed with rice at rs . 5.80 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 5 : 9 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 50 : 90 = 5 : 9 answer a"
Answer: a
Problem: three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 4 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 12 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 12 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 720 min = 12 hours answer : b
Answer: b
Problem: when positive integer x is divided by 8 , the quotient is y and the remainder is 2 . when 2 x is divided by 7 , the quotient is 2 y and the remainder is 4 . what is the value of 6 y – x ?
Options: a ) - 1 , b ) 1 , c ) - 2 , d ) 2 , e ) - 3
Rationale: "( 1 ) x = 8 y + 2 ( 2 ) 2 x = 14 y + 4 ( 2 ) - ( 1 ) : x = 6 y + 2 6 y - x = - 2 the answer is c ."
Answer: c
Problem: if n = 2 ^ 0.15 and n ^ b = 32 , b must equal
Options: a ) 3 / 80 , b ) 3 / 5 , c ) 4 , d ) 100 / 3 , e ) 80 / 3
Rationale: "15 / 100 = 3 / 20 n = 2 ^ 3 / 20 n ^ b = 2 ^ 5 ( 2 ^ 3 / 20 ) ^ b = 2 ^ 5 b = 100 / 3 answer : d"
Answer: d
Problem: a man is 25 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is
Options: a ) 21 , b ) 22 , c ) 20 , d ) 18 , e ) 23
Rationale: "explanation : let the son ' s present age be x years . then , man ' s present age = ( x + 25 ) years = > ( x + 25 ) + 2 = 2 ( x + 2 ) = > x + 27 = 2 x + 4 so , x = 23 . answer : e"
Answer: e
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 5 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 107 % , c ) 116.7 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 5 + 0.9 * 15 = 18.5 gallons , so the overall discount she got was 1.5 / 20 = 7.5 % . isabella purchased 25 gallons of gas . she paid for 5 + 0.9 * 20 = 23 gallons , so the overall discount she got was . 5 / 25 = 8 % . 8 is 8 / 7.5 * 100 = 107 % of 7.5 . answer : b ."
Answer: b
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 2000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 2000 ) solving for x , we get the shares as 12000 . ans : ( option c )
Answer: c
Problem: if m is a positive integer and m ^ 2 is divisible by 54 , then the largest positive integer that must divide m is ?
Options: a ) 3 , b ) 6 , c ) 18 , d ) 12 , e ) 16
Rationale: m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 18 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is c but if m = 54 then answer should be 16 . is the question right ? or am i missing some thing ? c
Answer: c
Problem: if 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 24 lines is 24 c 2 = 276 the answer is a ."
Answer: a
Problem: a marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each . there can be no less than 8 musicians per row and no more than 30 musicians per row . how many different rectangular formations p are possible ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) p = 8
Rationale: "the combinations could be p { ( 1,240 ) , ( 2,120 ) , ( 3,80 ) , ( 4,60 ) , ( 5,48 ) , ( 6,40 ) , ( 8,30 ) , ( 10,24 ) , ( 12,20 ) , ) 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) , ( 40,6 ) , ( 48,5 ) , ( 60,4 ) , ( 80,3 ) , ( 120,2 ) , ( 240,1 ) } of these we are told 8 < = t < = 30 so we can remove these pairs , and we are left only with . { ( 8,30 , ( 10,24 ) , ( 12,20 ) , ( 15,16 ) , ( 16,15 ) , ( 20,12 ) , ( 24,10 ) , ( 30,8 ) } hence 8 . e"
Answer: e
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 9,4 ) , and ( 9,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 5 , b ) 3 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 2 / 9
Rationale: "the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 36 . p ( x + y < 4 ) = 8 / 36 = 2 / 9 the answer is e ."
Answer: e
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.2 = 6 * 0 + 2 * 7.2 + 8 - 6.2 = 0 + 14.4 + 1.8 16.2 answer d"
Answer: d
Problem: machine a takes 100 hours to complete a certain job and starts that job at 6 am . after ten hour of working alone , machine a is joined by machine b and together they complete the job at 6 pm . how long would it have taken machine b to complete the job if it had worked alone for the entire job ?
Options: a ) 24.65 , b ) 22.27 , c ) 2.273 , d ) 11.62 , e ) 21.13
Rationale: "let us assume total job = 100 units a finishes 100 units in 100 hrs ( given ) hence a ( working rate ) = 1 units / hr now given that a works for 10 hr ( so 10 units done ) then a and b finish total work in 12 hours . hence a and b finish 90 units in 2 hours . of these 1 x 2 = 2 units were done by a . hence b did 88 units in 2 hours . hence b ( working rate ) = 44 units / hr hence b takes 100 / 44 = 2.273 hours to complete the job . answer c ."
Answer: c
Problem: efrida and frazer who live 12 miles apart , meet at a restaurant that is directly north of efrida ' s home and directly east of frazer ' s home . if the restaurant is two miles closer to efrida ' s home , than to frazer ' s home , how many miles is the restaurant from frazer ' s home ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 11
Rationale: "it ' s a simple geometry problem . look at the diagram below : answer : d ."
Answer: d
Problem: a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 7 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 0.07 , b ) 0.049 , c ) 0.7 , d ) 0.49 , e ) 4.9
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 49 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 490 / 10,000 = 49 / 1000 = 0.049 ft the answer is b ."
Answer: b
Problem: at the end of the first quarter , the share price of a certain mutual fund was 25 percent higher than it was at the beginning of the year . at the end of the second quarter , the share price was 80 percent higher than it was at the beginning of the year . what was the percent increase in the share price from the end of the first quarter to the end of the second quarter ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 33 % , e ) 44 %
Rationale: "another method is to use the formula for 2 successive percentage changes : total = a + b + ab / 100 80 = 25 + b + 25 b / 100 b = 44 answer ( e )"
Answer: e
Problem: an article is bought for rs . 1200 and sold for rs . 1300 , find the loss percent ?
Options: a ) 8.33 % , b ) 9.33 % , c ) 10.00 % , d ) 11.11 % , e ) 7.56 %
Rationale: "1200 - - - - 100 100 - - - - ? = > 16 2 / 3 % answer : a"
Answer: a
Problem: by selling an article for $ 100 a man gains $ 20 then his gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 100 gain = $ 20 c . p . = 100 - 20 = 80 gain % = 20 / 80 * 100 = 25 % answer is a"
Answer: a
Problem: john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 50 miles per hour , what is v in miles per hour ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 50 = > v = 20 ( option a ) .
Answer: a
Problem: john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 5 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 50 , e ) s . 290
Rationale: let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 5 / 100 ) = 15000 - 750 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 750 + 800 = rs . 50 as this is positive , an overall profit of rs . 50 was made . d
Answer: d
Problem: the manufacturing cost of a shoe is rs . 230 and the transportation lost is rs . 500 for 100 shoes . what will be the selling price if it is sold at 20 % gains
Options: a ) s 282 , b ) s 216 , c ) s 220 , d ) s 210 , e ) s 217
Rationale: "explanation : total cost of a watch = 230 + ( 500 / 100 ) = 235 . gain = 20 % = > sp = 1.2 cp = 1.2 x 235 = 282 answer : a"
Answer: a
Problem: we have boxes colored either red or blue . in each blue box there is a fixed number of blueberries . in each red box there is a fixed number of strawberries . if we dispose of one blue box for one additional red box , the total number of berries would increase by 15 , and the difference between the total number of strawberries and the total number of blueberries would increase by 87 . each blue box contains how many blueberries ?
Options: a ) 28 , b ) 30 , c ) 32 , d ) 34 , e ) 36
Rationale: "let x be the number of blueberries in each blue box . then there are x + 15 strawberries in each red box . x + ( x + 15 ) = 87 x = 36 the answer is e ."
Answer: e
Problem: suppose you work for a manufacturing plant that pays you $ 12.50 an hour plus $ 0.16 for each widget you make . how many widgets must you produce in a 40 hour week to earn $ 700 ( before payroll deductions ) ?
Options: a ) 1220 , b ) 1250 , c ) 1280 , d ) 1310 , e ) 1340
Rationale: "total pay = 40 * $ 12.50 + $ 0.16 * x = 700 x = 200 / 0.16 = 1250 the answer is b ."
Answer: b
Problem: how many positive integers less than 500 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 68 , e ) 84
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : d"
Answer: d
Problem: a rope of which a calf is tied is increased from 12 m to 25 m , how much additional grassy ground shall it graze ?
Options: a ) 1400 , b ) 141.71 , c ) 1210 , d ) 1511.71 , e ) 1500
Rationale: "π ( 252 – 122 ) = 1511.71 answer : d"
Answer: d
Problem: two pipes a and b can fill a tank in 30 and 60 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 24 , e ) 25
Rationale: "part filled by a in 1 min . = 1 / 30 part filled by b in 1 min . = 1 / 60 part filled by ( a + b ) in 1 min . = 1 / 30 + 1 / 60 = 1 / 20 . both the pipes can fill the tank in 20 minutes . answer : b"
Answer: b
Problem: by selling 22 pencils for a rupee a man loses 40 % . how many for a rupee should he sell in order to gain 40 % ?
Options: a ) 8.56 , b ) 9.35 , c ) 9.43 , d ) 6.56 , e ) 5.5
Rationale: "60 % - - - 22 140 % - - - ? 60 / 140 * 22 = 9.43 answer : c"
Answer: c
Problem: the difference between the place values of two threes in the numerical 40378273 is
Options: a ) 29997 , b ) 299997 , c ) 297 , d ) 0 , e ) none of them
Rationale: "required difference = ( 300000 - 3 ) = 299997 . answer is b"
Answer: b
Problem: if m = 3 ^ n , what is the greatest value of n for which m is a factor of 22 !
Options: a ) 8 , b ) 10 , c ) 9 , d ) 14 , e ) 16
Rationale: "solution - consider multiples of 25 ! = > 3 , 6,9 , 12,15 , 18,21 count no . of 3 in each multiple . 3 = 3 x 1 - > 1 6 = 3 x 2 - > 1 9 = 3 x 3 - > 2 12 = 3 x 4 - > 1 15 = 3 x 5 - > 1 18 = 3 x 3 x 2 - > 2 21 = 3 x 7 - > 1 - - - - count 3 ' s = 9 so answer is 9 answer : c"
Answer: c
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 14 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 114 let marked price be $ x . then , 95 / 100 x = 114 x = 114 / 95 = $ 120 now , s . p . = $ 120 , c . p . = $ 100 profit % = 20 % . b"
Answer: b
Problem: three table runners have a combined area of 212 square inches . by overlapping the runners to cover 80 % of a table of area 175 square inches , the area that is covered by exactly two layers of runner is 24 square inches . what is the area of the table that is covered with three layers of runner ?
Options: a ) 18 square inches , b ) 20 square inches , c ) 24 square inches , d ) 28 square inches , e ) 30 square inches
Rationale: "total = a + b + c - ( sum of exactly 2 - group overlaps ) - 2 * ( all three ) + neither 80 % * 175 = 212 - 24 - 2 * ( all three ) + 0 2 * ( all three ) = 212 - 24 - 140 all three = 24 answer : c"
Answer: c
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 75 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 30 , c ) 26 , d ) 23 , e ) 12
Rationale: "relative speed = 45 + 75 = 120 km / hr . 120 * 5 / 18 = 100 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 100 = 30 sec . answer : b"
Answer: b
Problem: patty ran a marathon at an average speed of 3 mph for some time and then at an average speed of 6 mph for the rest of the marathon . if she made no stops during the run and her average speed for the entire marathon was 5 mph , for what fraction of the total time did she run at 3 mph ?
Options: a ) 1 / 5 , b ) 2 / 3 , c ) 2 / 5 , d ) 3 / 5 , e ) 1 / 3
Rationale: we do n ' t need to get into calculations for solving this question . we can use the concept of weighted averages . we know that if the average speed for the entire marathon was 5 mph , she ran at 6 mph for a longer duration . 2 1 3 - - 5 - - - - 6 this shows that you can divide the entire journey in 3 equal parts . thus , 2 / 3 part she ran at 6 mph and 1 / 3 part she ran at 3 mph . answer : e
Answer: e
Problem: kamal obtained 66 , 65 , 77 , 62 and 75 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: sol . average = 66 + 65 + 77 + 62 + 75 / 5 ) = ( 345 / 5 ) = 69 . answer b
Answer: b
Problem: a furniture store owner decided to drop the price of her recliners by 20 % to spur business . by the end of the week she had sold 25 % more recliners . what is the percentage increase of the gross ?
Options: a ) 00 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: "say a recliner is actually worth $ 100 if she sells 100 recliners then she earns $ 10000 after the discount of 20 % , she will earn $ 80 per recliner and she sells 25 % more ie . , 125 recliners hence her sales tields 125 * 80 = $ 10000 increase in sales = 10000 - 10000 = $ 0 so % increase = 0 * 100 / 10000 = 0 % a is the answer"
Answer: a
Problem: a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 750 more than that by the previous schema , his sales were worth ?
Options: a ) s . 4,000 , b ) s . 6,000 , c ) s . 30,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 750 x = 6000 answer : b"
Answer: b
Problem: what ratio must a shopkeepermix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 22 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 1 : 2 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3 : 6 = 1 : 2"
Answer: c
Problem: calculate how long it will take a swimmer to swim a distance of 7 km against the current of a river which flows at 2.5 km / hr , given that he can swim in still water at 4.4 km / h
Options: a ) 6.67 , b ) 1.67 , c ) 2.67 , d ) 3.67 , e ) 4.67
Rationale: "swim in still water at = 4.4 speed of river = 2.5 us = 4.4 - 2.5 = 1.9 distance = 7 t = 7 / 1.9 = 3.67 answer : d"
Answer: d
Problem: a sporting good store sells one type of baseball bat and one type of baseball . the cost for 2 bats and 4 balls is $ 200 . the cost for 1 bat and 6 balls is $ 220 , as well . if someone were to buy an equal number of bats and balls , at most how many bats can he purchase if he has a budget of $ 210 for the purchase ?
Options: a ) 1
b ) 2
c ) 3
d ) 4
e ) 5
Rationale: imo it should be c that is 3 reason : formed an equation . . . bat = b ball = c 2 b + 4 c = 200 1 b + 6 c = 220 solving both we get b that is bat = 40 and c that is ball = 30 new equation 210 to be divided in equal 3 b + 3 c = 210 3 * 40 + 3 * 30 = 210 120 + 90 = 210
Answer: c
Problem: if the product of the integers from 1 to n is divisible by 686 , what is the least possible value of n ?
Options: a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
Rationale: "686 = 7 x 7 x 7 x 2 n must include at least 7 , 2 * 7 , and 3 * 7 . the answer is c ."
Answer: c
Problem: find the area of a parallelogram with base 12 cm and height 18 cm .
Options: a ) 200 , b ) 216 , c ) 345 , d ) 244 , e ) 242
Rationale: "area of a parallelogram = base * height = 12 * 18 = 216 cm 2 answer : option b"
Answer: b
Problem: if a number p is prime , and 2 p + 4 = q , where q is also prime , then the decimal expansion of 1 / q will produce a decimal with q - 1 digits . if this method produces a decimal with 166 digits , what is the units digit of the product of p and q ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "1 / 6 = 0.1666666 . . . ( a repeating pattern one digit long ) a"
Answer: a
Problem: a train 110 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 82 kmph
Rationale: speed of train relative to man : 110 / 6 * 18 / 5 km / hr = 66 km / hr let speed of train = x therefore x + 6 = 66 x = 66 - 6 x = 60 km / hr answer : b
Answer: b
Problem: a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 32 , the how old is b ?
Options: a ) 10 years , b ) 12 years , c ) 14 years , d ) 15 years , e ) 16 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 32 5 x = 30 x = 6 . hence , b ' s age = 2 x = 12 years . b )"
Answer: b
Problem: a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 45000 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 90000 , c ) 85000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 45000 - > x = 150000 answer : b"
Answer: b
Problem: in a certain company , the formula for maximizing profits is p = - 25 x ^ 2 + 7500 x , , where p is profit and x is the number of machines the company operates in its factory . what value for x will maximize p ? this one is from integratedlearning . here ' s what i did : the oa states : to find a maximum or minimum value of an equation with an exponent in it , you take the derivative of the equation , set it to zero , and solve . i dont really get what that means . so whoever solves it , could you plz post explanation of what the above sentence mean as well ?
Options: a ) 10 , b ) 50 , c ) 150 , d ) 200 , e ) 300
Rationale: recognize that 25 is a factor of 7500 . if we take this out , we have two parts to the equation : - x ^ 2300 x one part of the equation brings our value down , whereas the other part brings our value up . at this point , we can test the numbers in the answer choice . notice that they are very straight forward to square , and multiplication by 300 is very easy . a ) 10 - 3000 - 100 = 2900 b ) 50 - 15000 - 2500 = 12500 c ) 150 - 45000 - 22500 = 22500 d ) 200 - 60000 - 40000 = 20000 e ) 300 - recognize that this is zero therefore , answer is 150 . hope this helps those - like myself - who have n ' t thought about calculus for over half a decade . c
Answer: c
Problem: in the coordinate plane , one of the vertices of a square is the point ( - 5 , - 4 ) . if the diagonals of that square intersect at point ( 3 , 2 ) , what is the area of that square ?
Options: a ) 100 , b ) 225 , c ) 169 , d ) 256 , e ) 324
Rationale: "one point ( - 5 - 4 ) , intersection ( 3,2 ) so the distance from the first point - 5 - 3 = - 8 is the midpoint of the square - - > whole side 16 , 16 * 16 = 256 d"
Answer: d
Problem: the cost of the paint is rs . 30 per kg . if 1 kg of paint covers 18 sq . ft , how much will it cost to paint outside of a cube having 6 feet each side
Options: a ) rs . 962 , b ) rs . 672 , c ) rs . 540 , d ) rs . 876 , e ) none of these
Rationale: "explanation : surface area of a cube = 6 x 6 ^ 2 = 216 sq . ft quantity of paint required = ( 216 / 18 ) = 12 kg cost of painting = 30 x 18 = rs . 540 answer : c"
Answer: c
Problem: what is the smallest number which when diminished by 18 , is divisible 8 , 14 , 26 and 28 ?
Options: a ) 746 , b ) 750 , c ) 789 , d ) 678 , e ) 897
Rationale: "required number = ( lcm of 8 , 14 , 26 and 28 ) + 18 = 728 + 18 = 746 option a"
Answer: a
Problem: in a mixture of 45 litres the ratio of milk to water is 4 : 1 . additional 11 litres of water is added to the mixture . find the ratio of milk to water in the resulting mixture .
Options: a ) 2 / 1 , b ) 4 / 1 , c ) 2 / 3 , d ) 9 / 5 , e ) 3 / 2
Rationale: "given that milk / water = 4 x / x and 4 x + x = 45 - - > x = 9 . thus milk = 4 x = 36 liters and water = x = 9 liters . new ratio = 36 / ( 9 + 11 ) = 36 / 20 = 9 / 5 . answer : d ."
Answer: d
Problem: two men started from the same place walk at the rate of 5 kmph and 5.5 kmph respectively . what time will they take to be 8.5 km apart , if they walk in the same direction ?
Options: a ) 10 hours , b ) 12 hours , c ) 17 hours , d ) 15 hours , e ) 20 hours
Rationale: "to be 0.5 km apart they take 1 hour to be 8.5 km apart they take = 1 / 0.5 * 8.5 = 17 hours answer is c"
Answer: c
Problem: ? % of 360 = 162
Options: a ) 277 , b ) 36 , c ) 45 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 162 or , ? = 162 × 100 / 360 = 45 answer c"
Answer: c
Problem: how many factors does 35 ^ 2 have ?
Options: a ) 2 , b ) 8 , c ) 24 , d ) 25 , e ) 26
Rationale: "36 ^ 2 = 6 * 6 * 6 * 6 = 2 ^ 4 * 3 ^ 4 total factors = ( 4 + 1 ) * ( 4 + 1 ) = 6 * 4 = 24 answer c ."
Answer: c
Problem: at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the men are married ?
Options: a ) 3 / 4 , b ) 2 / 5 , c ) 4 / 5 , d ) 2 / 3 , e ) 1 / 4
Rationale: - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married man / total man , so 10 / 40 = 1 / 4 e
Answer: e
Problem: p , q , r enter into a partnership & their share are in the ratio 1 / 2 : 1 / 3 : 1 / 4 , after two months , p withdraws half of the capitals & after 10 months , a profit of rs 378 is divided among them . what is r ' s share ?
Options: a ) 108 , b ) 120 , c ) 134 , d ) 144 , e ) none of these
Rationale: explanation : the ratio of their initial investment = 1 / 2 : 1 / 3 : 1 / 4 = 6 : 4 : 3 let ' s take the initial investment of p , q and r as 6 x , 4 x and 3 x respectively a : b : c = ( 6 x * 2 + 3 x * 10 ) : 4 x * 12 : 3 x * 12 = ( 12 + 30 ) : 4 * 12 : 3 * 12 = ( 4 + 10 ) : 4 * 4 : 12 = 14 : 16 : 12 = 7 : 8 : 6 r ' s share = 378 * ( 6 / 21 ) = 108 . answer : option a
Answer: a
Problem: light glows for every 18 seconds . how many times did it between 1 : 57 : 58 and 3 : 20 : 47 am
Options: a ) 281 , b ) 277 , c ) 283 , d ) 384 , e ) 385
Rationale: "the diff in sec between 1 : 57 : 58 and 3 : 20 : 47 is 4969 sec , 4969 / 18 = 276 . so total 277 times light ll glow answer : b"
Answer: b
Problem: find the smallest number which leaves 2235 , 48 and 61 as remainders when divided by 26 , 39 , 52 and 65 respectively .
Options: a ) 67 , b ) 26 , c ) 99 , d ) 26 , e ) 91
Rationale: answer : d
Answer: d
Problem: if k ^ 3 is divisible by 168 , what is the least possible value of integer k ?
Options: a ) 36 , b ) 42 , c ) 48 , d ) 54 , e ) 60
Rationale: k ^ 3 = 168 * x = 2 ^ 3 * 3 * 7 * x the factors of k must at minimum include 2 * 3 * 7 = 42 . the answer is b .
Answer: b
Problem: a and b can do a work in 20 days , b and c in 25 days , c and a in 30 days . if a , b and c work together , they will complete the work in ?
Options: a ) 10 days , b ) 12 days , c ) 16 days , d ) 20 days , e ) 25 days
Rationale: "a + b 1 day work = 1 / 20 b + c 1 day work = 1 / 25 c + a 1 day work = 1 / 30 adding we get 2 ( a + b + c ) = 1 / 20 + 1 / 25 + 1 / 30 = 37 / 300 a + b + c 1 day work = 37 / 600 a , b , c can finish the work in 600 / 37 days = 16 days approximately answer is c"
Answer: c
Problem: in what time will a train 100 m long cross an electric pole , it its speed be 136 km / hr ?
Options: a ) 2.6 sec , b ) 1.9 sec , c ) 8.9 sec , d ) 6.9 sec , e ) 2.9 sec
Rationale: "speed = 136 * 5 / 18 = 37.8 m / sec time taken = 100 / 37.8 = 2.6 sec . answer : a"
Answer: a
Problem: 5220 / ? * 15 = 2175
Options: a ) 34 , b ) 36 , c ) 33 , d ) 42 , e ) 24
Rationale: "b ( 5220 / ? ) * 15 = 2175 ? = ( 5220 * 15 ) / 2175 = > ? = 36"
Answer: b
Problem: the megatek corporation is displaying its distribution of employees by department in a circle graph . the size of each sector of the graph representing a department is proportional to the percentage of total employees in that department . if the section of the circle graph representing the manufacturing department takes up 126 ° of the circle , what percentage of megatek employees are in manufacturing ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 70 %
Rationale: answer : d 126 ° divided by 360 ° equals 0.35 , therefore the sector is equal to 35 % of the total
Answer: d
Problem: what is the unit digit in 14 ^ 100 ?
Options: a ) 0 , b ) 5 , c ) 2 , d ) 3 , e ) 6
Rationale: unit digit in 14 ^ 100 = unit digit in [ ( 14 ^ 4 ) ^ 25 ] but unit digit in 14 ^ 4 = 6 unit digit 14 ^ 100 = 6 answer is e
Answer: e
Problem: if n is the smallest integer such that 864 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "865 can written as = 2 * 2 * 2 * 2 * 2 * 3 * 3 * 3 - - > 2 ^ 5 * 3 ^ 3 - - - ( 1 ) so for 864 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 3 to make the power of 3 in ( 1 ) even option b is correct"
Answer: b
Problem: tim came second in math . when his mother asked him how much he had scored , he answered that he got the sum of the first 5 even numbers . his mother immediately worked out the answer . how much had he scored in math ?
Options: a ) 80 , b ) 30 , c ) 40 , d ) 70 , e ) 60
Rationale: "b 30 sum = ( n x n ) + n hence , 5 x 5 = 25 + 5 = 30"
Answer: b
Problem: what is the sum of all digits for the number 10 ^ 25 - 58 ?
Options: a ) 197 , b ) 201 , c ) 205 , d ) 209 , e ) 213
Rationale: "10 ^ 25 is a 26 - digit number : 1 followed by 25 zeros . 10 ^ 25 - 58 is a 25 - digit number : 23 9 ' s and 42 at the end . the sum of the digits is 23 * 9 + 4 + 2 = 213 . the answer is e ."
Answer: e
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 24 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 p w = 24 = 6 k + 4 p = > k = 2 , p = 3 total red ' s in bag a will be 2 k = 4 c"
Answer: c
Problem: a can do a piece of work in 40 days ; b can do the same in 30 days . a started alone but left the work after 10 days , then b worked at it for 10 days . c finished the remaining work in 10 days . c alone can do the whole work in ?
Options: a ) 24 days , b ) 65 days , c ) 86 days , d ) 45 days , e ) 17 days
Rationale: "10 / 40 + 10 / 30 + 10 / x = 1 x = 24 days answer : a"
Answer: a
Problem: what least value should be replaced by * in 2631 * 4 so the number become divisible by 3
Options: a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7
Rationale: "explanation : trick : number is divisible by 3 , if sum of all digits is divisible by 3 , so ( 2 + 6 + 3 + 1 + * + 4 ) = 16 + * should be divisible by 9 , 16 + 2 will be divisible by 2 , so that least number is 2 . answer : option d"
Answer: d
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 735 , krishan has ?
Options: a ) s . 4335 , b ) s . 2330 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
Rationale: ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 735 : n & there n = 289 x 735 / 49 = rs . 4335 answer : a
Answer: a
Problem: a train 146 m long is running at a speed of 98 kmph . how long does it take to pass a man who is running at 12 kmph in the same direction as the train ?
Options: a ) 6 sec , b ) 9 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : a . speed of the train relative to man = ( 98 - 12 ) kmph = ( 86 * 5 / 18 ) m / sec = ( 215 / 9 ) m / sec time taken by the train to cross the man = time taken by it to cover 146 m at 219 / 9 m / sec = 146 * 9 / 219 sec = 6 sec"
Answer: a
Problem: nails and screws are manufactured at a uniform weight per nail and a uniform weight per screw . if the total weight of one screw and one nail is half that of 6 screws and one nail , then the total weight of 3 screws , and 3 nails is how many times that of 5 screws and 1 nails ?
Options: a ) a . 4 , b ) b . 5 / 2 , c ) c . 2 , d ) d . 3 / 2 , e ) e . 5 / 4
Rationale: let the weight of nail be n and that of screw be s . . so s + w = 1 / 2 * ( 6 s + 1 n ) . . . or 1 n = 4 s . . lets see the weight of 3 s and 3 n = 3 s + 3 * 4 s = 15 s . . and weight of 5 s and 1 n = 5 s + 1 * 5 s = 10 s . . ratio = 15 s / 10 s = 15 / 10 = 3 / 2 d
Answer: d
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 5 , and the ratio of soap to salt is four times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 9 : 100 , b ) 100 : 9 , c ) 12 : 100 , d ) 12 : 20 , e ) 13 : 100
Rationale: "water : soap = 3 : 5 soap : salt = 12 : 20 = > for 12 soap , salt = 20 = > for 5 soap , salt = ( 20 / 12 ) * 5 = 100 / 12 = 25 / 3 so , water : soap : salt = 3 : 5 : 25 / 3 = 9 : 15 : 25 after open container , water : soap : salt = 2.25 : 15 : 25 so , water : salt = 2.25 : 25 = 9 : 100 answer : a"
Answer: a
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 94 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 94 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 94 * 7 ) = 1350 - ( 609 + 658 ) = 1350 - 1267 = 83 answer a"
Answer: a
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 1200 in 5 years ?
Options: a ) 12 , b ) 3 , c ) 14 , d ) 5 , e ) 6
Rationale: "450 = ( 750 * 5 * r ) / 100 r = 12 % . answer : a"
Answer: a
Problem: the difference between simple and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is ?
Options: a ) rs . 7 , b ) rs . 3 , c ) rs . 8 , d ) rs . 1 , e ) rs . 4
Rationale: "s . i . = ( 1200 * 10 * 1 ) / 100 = rs . 120 c . i . = [ 1200 * ( 1 + 5 / 100 ) 2 - 1200 ] = rs . 123 difference = ( 123 - 120 ) = rs . 3 . answer : b"
Answer: b
Problem: stacy and heather are 25 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour fast than heather ' s constant rate of 5 miles / hour . if heather starts her journey 24 minutes after stacy , how far from the original destination has heather walked when the two meet ? .
Options: a ) 9.0 mile , b ) 13.0 mile , c ) 11.0 mile , d ) 10.2 mile , e ) 12 mile
Rationale: ss - stacy ' s speed = 6 m / hr sh - heather ' s speed = 5 m / hr in 24 minutes stacy will cover = ( 24 / 60 ) * 6 = 2.4 miles now since both are walking in opposite directions , add their speeds - 6 + 5 = 11 m / hr and distance to cover is 25 - 2.4 = 22.6 time taken = distance / speed = 22.6 / 11 = 2.05 hrs heather will cover = 5 * 2.4 = 10.2 miles . answer d
Answer: d
Problem: ganesh , ram and sohan together can do a work in 16 days . if ganesh and ram together can do a the same work in 24 days then , how long will take sohan to do the same work ?
Options: a ) 48 , b ) 58 , c ) 68 , d ) 78 , e ) 100
Rationale: solution : work done by three of them together in 1 day = 1 / 16 . . . . . . . . . . . . ( 1 ) work done by ganesh and ram together in 1 day = 1 / 24 . . . . . ( 2 ) so , work done by sohan in one day = ( 1 ) - ( 2 ) = ( 1 / 16 ) - ( 1 / 24 ) = 1 / 48 = > total days taken by sohan to complete the work alone = 48 days . answer a
Answer: a
Problem: one fourth of one third of two fifth of a number is 25 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 200 , e ) e ) 300
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 25 then x = 25 * 30 = 750 40 % of 750 = 300 answer : option e"
Answer: e
Problem: the cost price of an article is 56 % of the marked price . calculate the gain percent after allowing a discount of 13 % .
Options: a ) 23.4 % , b ) 44.5 % , c ) 55.3 % , d ) 57.4 % , e ) none
Rationale: "sol . let marked price = rs . 100 . then , c . p . = rs . 56 . s . p = rs . 87 . â ˆ ´ gain % = [ 31 / 56 * 100 ] % = 55.3 % . answer c"
Answer: c
Problem: two trains each 260 m in length are running on the same parallel lines in opposite directions with the speed of 80 kmph and 70 kmph respectively . in what time will they cross each other completely ?
Options: a ) 15 sec , b ) 19 sec , c ) 12.48 sec , d ) 10 sec , e ) 11 sec
Rationale: "explanation : d = 260 m + 260 m = 520 m rs = 80 + 70 = 150 * 5 / 18 = 125 / 3 t = 520 * 3 / 125 = 12.48 sec answer : option c"
Answer: c
Problem: 1024 people in village 720 speak tamil , 562 speak english while 346 speak both . person who don not speack english or tamil speak hindi . what is probibility that person speak hindi
Options: a ) 13 / 128 , b ) 12 / 128 , c ) 11 / 126 , d ) 11 / 127 , e ) 11 / 128
Rationale: n ( t ) = 720 n ( e ) = 562 n ( t ^ e ) = 346 n ( tue ) = 720 + 562 - 346 = 936 now , n ( h ) = 1024 - 936 = 88 p ( h ) = 88 / 1024 = 11 / 128 = 0.085 answer : e
Answer: e
Problem: a train 140 m long passes a man , running at 6 kmph in the direction opposite to that of the train , in 6 seconds . the speed of the train is
Options: a ) 54 kmph , b ) 60 kmph , c ) 66 kmph , d ) 72 kmph , e ) 78 kmph
Rationale: "speed of train relative to man : 140 / 6 * 18 / 5 km / hr = 84 km / hr let speed of train = x therefore x + 6 = 84 x = 84 - 6 x = 78 km / hr answer : e"
Answer: e
Problem: the speed of a train is 120 kmph . what is the distance covered by it in 8 minutes ?
Options: a ) 15 kmph , b ) 11 kmph , c ) 16 kmph , d ) 18 kmph , e ) 12 kmph
Rationale: "120 * 8 / 60 = 16 kmph answer : c"
Answer: c
Problem: a goods train runs at the speed of 72 kmph and crosses a 260 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 260 m , b ) 270 m , c ) 643 m , d ) 832 m , e ) 270 m
Rationale: "speed = ( 72 x 5 / 18 ) m / sec = 20 m / sec . time = 26 sec . let the length of the train be x metres . then , x + 260 / 26 = 20 x + 260 = 520 x = 260 . answer : a"
Answer: a
Problem: if albert ’ s monthly earnings rise by 14 % , he would earn $ 678 . if , instead , his earnings rise by only 15 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 689 , c ) 683 , d ) 690 , e ) 693
Rationale: "= 678 / 1.14 ∗ 1.15 = 683 = 683 answer is c"
Answer: c
Problem: a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 45 minutes . the total distance is ?
Options: a ) 1 km , b ) 2.87 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "b 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 45 / 60 47 x / 60 = 45 / 60 = > x = 0.95 . total distance = 3 * 0.95 = 2.87 km ."
Answer: b
Problem: a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container .
Options: a ) 26.34 litres , b ) 27.36 liters , c ) 28 litres , d ) 29.16 litres , e ) can not be determined
Rationale: solution amount of milk left after 3 operations [ 40 ( 1 - 4 / 40 ) 3 ] litres = ( 40 x 9 / 10 x 9 / 10 x 9 / 10 ) = 29.16 litres answer d
Answer: d
Problem: if grapes are 90 % water and raisins are 17 % water , then how many kilograms did a quantity of raisins , which currently weighs 14 kilograms , weigh when all the raisins were grapes ? ( assume that the only difference between their raisin - weight and their grape - weight is water that evaporated during their transformation . )
Options: a ) 108.6 , b ) 110.4 , c ) 112.6 , d ) 114.8 , e ) 116.2
Rationale: "let x be the original weight of the grapes . the weight of the grape pulp was 0.1 x . since the grape pulp is 83 % of the raisins , 0.1 x = 0.83 ( 14 kg ) . then x = 8.3 * 14 = 116.2 kg . the answer is e ."
Answer: e
Problem: on multiplying a number f by 153 , the result obtained was 102325 . however , it is found that both the 2 ' s are wrong . find the correct result .
Options: a ) 104345 , b ) 107375 , c ) 108385 , d ) 109395 , e ) 105355
Rationale: the only thing you actually know about the correct number f is that it is divisible by 153 and has 5 as a factor . you should immediately try to find the factors of 153 and look for them in the options . 153 = 9 * 17 divisibility by 9 is easy to check . only ( d ) satisfies .
Answer: d
Problem: at an election 2 candidates are participated a candidate got 30 % of votes and defeated by 5000 votes . 100 votes are invalid . find the total polled votes ?
Options: a ) 11520 , b ) 12600 , c ) 15000 , d ) 13560 , e ) 12560
Rationale: winners votes = 100 - 30 = 70 % invalid votes = 100 polled votes = [ ( 100 * 5000 ) / ( 2 * 70 - 100 ) ] + 100 = 12600 answer is b
Answer: b
Problem: the marks obtained by vijay and amith are in the ratio 4 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 6 : 2 , c ) 6 : 5 , d ) 6 : 4 , e ) 6 : 2
Rationale: "4 : 5 3 : 2 - - - - - - - 12 : 15 : 10 12 : 10 6 : 5 answer : c"
Answer: c
Problem: if a large pizza has a radius that is 10 % larger that that of a medium pizza , what is the percent increase in area between a medium and a large pizza ?
Options: a ) 15 % , b ) 21 % , c ) 25 % , d ) 30 % , e ) 36 %
Rationale: "let the radius of medium pizza be r . then the radius of large pizza is 1.1 r . the area of the medium pizza is pi * r ^ 2 the area of the large pizza is pi * ( 1.1 * r ) ^ 2 = 1.21 * pi * r ^ 2 , an increase of 21 % . the answer is b ."
Answer: b
Problem: if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 5 times , what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips ?
Options: a ) 3 / 5 , b ) 1 / 32 , c ) 1 / 5 , d ) 1 / 4 , e ) 1 / 2
Rationale: ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 32 answer : b
Answer: b
Problem: 60 kg of an alloy a is mixed with 100 kg of alloy b . if alloy a has lead and tin in the ratio 3 : 2 and alloy b has tin and copper in the ratio 1 : 4 , then the amount of tin in the new alloy is ?
Options: a ) 24 kg , b ) 44 kg , c ) 20 kg , d ) 30 kg , e ) 52 kg
Rationale: quantity of tin in 60 kg of a = 60 * 2 / 5 = 24 kg quantity of tin in 100 kg of b = 100 * 1 / 5 = 20 kg quantity of tin in the new alloy = 24 + 20 = 44 kg answer is b
Answer: b
Problem: what is the sum of all possible solutions to the equation √ 2 x ^ 2 − x − 9 = x + 1 ?
Options: a ) - 2 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "first of all notice that since lhs is the square root of a number , it must be non - negative ( the square root function can not give negative result ) , then the rhs must also be non - negative : x + 1 ≥ 0 - - > x ≥ − 1 square the equation : 2 x ^ 2 − x − 9 = x ^ 2 + 2 x + 1 - - > x ^ 2 − 3 x − 10 = 0 - - > x = - 2 or x = 5 . discard x = - 2 because it ' s not > = - 1 . we are left with only one root : 5 . answer : d"
Answer: d
Problem: pipe a can fill a tank in 10 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
Options: a ) 18 , b ) 27 , c ) 98 , d ) 27 , e ) 48
Rationale: "let the pipe b be closed after x minutes . 30 / 10 - x / 24 = 1 = > x / 24 = 30 / 10 - 1 = 2 = > x = 2 * 24 = 48 . answer : e"
Answer: e
Problem: if price of t . v set is reduced by 18 % , then its sale increases by 88 % , find net effect on sale value
Options: a ) 44 , b ) 54 , c ) 46 , d ) 47 , e ) 48
Rationale: "- a + b + ( ( - a ) ( b ) / 100 ) = - 18 + 88 + ( - 18 * 88 ) / 100 = - 18 + 88 - 16 = 54 answer : b"
Answer: b
Problem: a father said his son , ` ` i was as old as you are at present at the time of your birth . ` ` if the father age is 38 now , the son age 5 years back was :
Options: a ) 14 , b ) 19 , c ) 33 , d ) 38 , e ) 56
Rationale: "explanation : let the son ' s present age be x years . then , ( 38 - x ) = x x = 19 . son ' s age 5 years back = ( 19 - 5 ) = 14 years . answer : a"
Answer: a
Problem: 20 machines can do a work in 5 days . how many machines are needed to complete the work in 10 days ?
Options: a ) 10 , b ) 15 , c ) 8 , d ) 12 , e ) 20
Rationale: "required number of machines = 20 * 5 / 10 = 10 answer is a"
Answer: a
Problem: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 225 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 180 , c ) 24 , d ) 28 , e ) 40
Rationale: "slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 225 ^ 2 16 x ^ 2 + 9 x ^ 2 = 225 ^ 2 25 x ^ 2 = 225 ^ 2 x ^ 2 = 25 * 9 ^ 2 x = 45 therefore ab = 45 * 4 = 180 answer : b"
Answer: b
Problem: at company x , senior sales representatives visit the home office once every 18 days , and junior sales representatives visit the home office once every 12 days . the number of visits that a junior sales representative makes in a 2 - year period is approximately what percent greater than the number of visits that a senior representative makes in the same period ?
Options: a ) 10 % , b ) 25 % , c ) 33 % , d ) 50 % , e ) 67 %
Rationale: "each 36 - day period , senior representatives visit the home office 2 times while junior representatives visit 3 times , thus 50 % more . the answer is d ."
Answer: d
Problem: set a of 8 positive integers may have the same element and have 36 . and set b of 8 positive integers must have different elements and have 36 . when m and n are the greatest possible differences between 36 and other elements ’ sums in set a and set b , respectively , m - n = ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: this is maximum - minimum . hence , 36 - ( 1 + 1 + 1 + 1 + 1 + 1 + 1 ) = 29 and 36 - ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) = 8 . so , 29 - 8 = 21 . the correct answer is b .
Answer: b