Cheukting/mathqa huggingface dataset:
Question (general): before 5 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 58 , d ) 60 , e ) 64
Rationale: "a - 5 = 4 ( b - 5 ) - - > a - 4 b = - 15 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 23 - - > a = 3 ( 27 ) = 81 a - b = 81 - 23 = 58 answer : c"
Answer: c
Question (other): the number of people who purchased book a is twice the number of people who purchased book b . the number of people who purchased both books a and b is 500 , which is twice the number of people who purchased only book b . what is the number of people b who purchased only book a ?
Options: a ) 250 , b ) 500 , c ) 750 , d ) 1000 , e ) 1500
Rationale: this is best solved using overlapping sets or a venn diagram . we know that a = 2 b , and that 500 people purchased both a and b . further , those purchasing both was double those purchasing b only . this gives us 250 people purchasing b only . with the 500 that pruchased both , we have a total of 750 that purchased b and this is 1 / 2 of those that purchased a . so , 1500 purchased a . less the 500 that purchased both , b = 1000 purchased a only . ( this is much simpler to solve using the venn diagram ) . correct answer is d . 1000
Answer: d
Question (general): of 70 players on a football team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 59 , c ) 63 , d ) 71 , e ) 92
Rationale: "37 are throwers and right handed 1 / 3 of remaining 33 , i . e 11 are left handed and remaining are right handed . basically , out of 70 , only 11 are left handed and remaining 70 - 11 = 59 are right handed . b is the answer"
Answer: b
Question (geometry): the perimeter of a rhombus is 120 feet and one of its diagonal has a length of 40 feet . find the area of the rhombus .
Options: a ) 100 sqrt ( 5 ) ft . sq
b ) 400 sqrt ( 5 ) ft . sq
c ) 500 sqrt ( 5 ) ft . sq
d ) 200 sqrt ( 5 ) ft . sq
e ) 150 sqrt ( 5 ) ft . sq
Rationale: a perimeter of 120 when divided by 4 gives the side of the rhombus 30 feet . the length of the side oc of the right triangle is equal to half the diagonal : 20 feet . let us now consider the right triangle boc and apply pythagora ' s theorem to find the length of side bo . 30 ^ 2 = bo ^ 2 + 20 ^ 2 bo = 10 sqrt ( 5 ) feet we now calculate the area of the right triangle boc and multiply it by 4 to obtain the area of the rhombus . area = 4 ( 1 / 2 ) bo * oc = 4 ( 1 / 2 ) 10 sqrt ( 5 ) * 20 = 400 sqrt ( 5 ) ft . sq answer is b
Answer: b
Question (general): paul ' s income is 40 % less than rex ' s income , quentin ' s income is 20 % less than paul ' s income , and sam ' s income is 40 % less than paul ' s income . if rex gave 60 % of his income to sam and 40 % of his income to quentin , sam ' s new income would be what fraction of quentin ' s new income ?
Options: a ) 11 / 12 , b ) 12 / 11 , c ) 13 / 19 , d ) 12 / 19 , e ) 11 / 19
Rationale: "make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get s = 9.6 and q 8.8 so 9.6 / 8.8 = 1.2 / 1.1 ans : b"
Answer: b
Question (general): how many integers k greater than 100 and less than 900 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 7 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . . . . 6 . . . . 7 . 708 | 807 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 7 sets with 10 such number in each set will give 7 x 10 = 70 integers . c"
Answer: c
Question (general): there are 200 female managers in a certain company . find the total number of female employees q in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) q = 300 , b ) q = 400 , c ) q = 500 , d ) q = 600 , e ) none of these
Rationale: { managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c .
Answer: c
Question (gain): john invests $ x at the semi - annual constant compounded rate of 2 percent and also does $ 8,000 at the quarterly constant compounded rate of 4 percent . if the interests are the same after 1 year , what is the value of x ? ?
Options: a ) 10000 , b ) 12000 , c ) 16160.8 , d ) 14000 , e ) 15000
Rationale: "a = p ( 1 + r / n ) ^ nt a = total amount accrued p = principal deposited r = rate of interest in decimal form n = number of times per year , interest compounded t = time in number of years . . x ( 1 + 0.02 / 2 ) ^ 2 - x = 8,000 ( 1 + 0.04 / 4 ) ^ 4 - 8,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal ) = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 4 - 1 ] = > x [ ( 1.01 ) ^ 2 - 1 ] = 8,000 [ ( 1.01 ) ^ 2 + 1 ] [ ( 1.01 ) ^ 2 - 1 ] - - > using a ^ 2 - b ^ 2 = a + b x a - b formula and cancel common expression on both sides = > x = 8,000 ( 1.0201 + 1 ) = 16160.8 hence answer is c ."
Answer: c
Question (general): if the sum of two numbers is 24 and the sum of their squares is 404 , then the product of the numbers is
Options: a ) 40 , b ) 44 , c ) 80 , d ) 86 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 24 and x 2 + y 2 = 404 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 24 ) 2 - 404 = 576 - 404 = 172 xy = 86 . answer d"
Answer: d
Question (general): product of two natural numbers is 3 . then , the sum of reciprocals of their squares is
Options: a ) 10 / 9 , b ) 1 / 289 , c ) 290 / 90 , d ) 290 / 19 , e ) none of these
Rationale: "explanation : if the numbers are a , b , then ab = 3 , as 3 is a prime number , so a = 1 , b = 3 . 1 / a 2 + 1 / b 2 = 1 / 1 ( 2 ) + 1 / 3 ( 2 ) = 10 / 9 option a"
Answer: a
Question (general): if the least common multiple of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
Rationale: lcm of two prime numbers will basically be multiple of those numbers . lcm = 10 = 2 * 5 , both of which are prime . now we know x > y , so x = 5 and y = 2 . 2 x + y = 2 * 5 + 2 = 10 + 2 = 12 . answer : d
Answer: d
Question (gain): if the cost price is 96 % of selling price then what is the profit percentage .
Options: a ) 7.14 , b ) 7.41 , c ) 4.71 , d ) 4.17 , e ) none of them
Rationale: "selling price = rs 100 : then cost price = rs 96 : profit = rs 4 . profit = { ( 4 / 96 ) * 100 } % = 4.17 % answer is d ."
Answer: d
Question (other): ratio between rahul and deepak is 4 : 3 , after 6 years rahul age will be 50 years . what is deepak present age
Options: a ) 14 , b ) 15 , c ) 33 , d ) 22 , e ) 23
Rationale: "explanation : present age is 4 x and 3 x , = > 4 x + 6 = 50 = > x = 11 so deepak age is = 3 ( 11 ) = 33 answer : option c"
Answer: c
Question (general): if x ^ 3 is divisible by 240 what is the least possible value of integer x ?
Options: a ) 12 , b ) 30 , c ) 60 , d ) 90 , e ) 120
Rationale: "240 can be written as ( 2 ^ 4 ) * 3 * 5 . for k ^ 3 to be divisible by 240 it should contain atleast 2 ^ 4 and 3 and 5 in its factors . we can leave out option a because 12 doesnt have 5 as one of its factor . now if we check for option b , 30 can be written as 2 * 3 * 5 , hence 30 ^ 3 will have 3 as the maximum power of 2 , so we can leave out this option too . option c is the right answer if we follow the same method as we followed for other two previous options . 60 = ( 2 ^ 2 ) * 3 * 5 ; 60 ^ 3 = ( 2 ^ 6 ) * ( 3 ^ 3 ) * ( 5 ^ 3 ) . so it shows that 60 ^ 3 is divisible by 240 and hence the answer . answer : c"
Answer: c
Question (gain): a man buys a cycle for rs . 1750 and sells it at a loss of 8 % . what is the selling price of the cycle ?
Options: a ) s . 1090 , b ) s . 1610 , c ) s . 1190 , d ) s . 1202 , e ) s . 1092
Rationale: "s . p . = 92 % of rs . 1750 = rs . 92 x 1750 / 100 = rs . 1610 answer : option b"
Answer: b
Question (general): in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 12 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 40 , b ) 44 , c ) 66 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 12 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 12 = 4 / 9 ( t - 12 ) 10 t = 1188 - 528 = > t = 66 . answer : c"
Answer: c
Question (geometry): a metallic sheet is of rectangular shape with dimensions 100 m x 50 m . from each of its corners , a square is cut off so as to make an open box . if the length of the square is 10 m , the volume of the box ( in m cube ) is :
Options: a ) 42500 m cube , b ) 20000 m cube , c ) 44140 m cube , d ) 24000 m cube , e ) none of these
Rationale: "explanation : l = ( 100 - 20 ) m = 80 m , [ because 10 + 10 = 20 ] b = ( 50 - 20 ) m = 30 m , h = 10 m . volume of the box = ( 80 x 30 x 8 ) m cube = 24000 m cube . option d"
Answer: d
Question (general): a rope of which a calf is tied is increased from 5 m to 9 m , how much additional grassy ground shall it graze ?
Options: a ) 1218 , b ) 180 , c ) 176 , d ) 200 , e ) 291
Rationale: "π ( 92 – 52 ) = 176 answer : c"
Answer: c
Question (general): if the number of white balls in a box are 6 times the black balls , which of the below is the total number of balls , if there are 8 black balls in the box ?
Options: a ) a - 56 , b ) b - 57 , c ) c - 58 , d ) d - 59 , e ) e - 60
Rationale: let the number of black balls = x and the number of white balls = 6 x then , total number of balls in the box = x + 6 x = 7 x i . e . , the total number of balls must be a multiple of 7 from the given choices , only 56 is the multiple of 7 . hence , 56 are the number of balls in the box . answer is a .
Answer: a
Question (gain): a trader marked the selling price of an article at 50 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 7.3 % , b ) 10.5 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 150 * 100 ] % = 7.3 % answer a"
Answer: a
Question (general): 45 % of 750 - 25 % of 480 = ?
Options: a ) 216 , b ) 217.5 , c ) 236.5 , d ) 245 , e ) 250
Rationale: "explanation : given expression = ( 45 / 100 * 750 ) - ( 25 / 100 * 480 ) = ( 337.50 - 120 ) = 217.50 answer is b"
Answer: b
Question (general): among all sales staff at listco corporation , college graduates and those without college degrees are equally represented . each sales staff member is either a level - 1 or level - 2 employee . level - 1 college graduates account for 15 % of listco ' s sales staff . listco employs 90 level - 1 employees , 30 of whom are college graduates . how many sales staff members without college degrees are level - 2 employees ?
Options: a ) 46 , b ) 42 , c ) 56 , d ) 32 , e ) 40
Rationale: "i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 90 and that c and l 1 = 0.15 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.15 x = 30 , therefore the grand total is 200 . now we know that l 2 is 200 - 90 = 110 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 60 = 40 . thus e is the correct answer choice"
Answer: e
Question (physics): 72 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) a ) 77 , b ) b ) 99 , c ) c ) 66 , d ) d ) 55 , e ) e ) 88
Rationale: "( 72 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 160 160 – 72 = 88 answer : e"
Answer: e
Question (general): how many of the positive divisors of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: given to find the positive divisors of 120 and condition is that divisors have to be multiple of 4 but not including 120 . consider factors of 120 4 * 30 6 * 20 15 * 8 24 * 5 60 * 2 total we get 5 different ways and all are part of 4 . answer : c is correct option .
Answer: c
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 15 % and 5 % is ?
Options: a ) 297 , b ) 879 , c ) 323 , d ) 762 , e ) 269
Rationale: "400 * ( 85 / 100 ) * ( 95 / 100 ) = 323 answer : c"
Answer: c
Question (physics): efrida and frazer who live 15 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 ) 13
Rationale: it ' s a simple geometry problem . look at the diagram below : answer : e .
Answer: e
Question (physics): the sum of two consecutive integers is 15 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 15 2 n + 1 = 15 2 n = 14 n = 7 answer : b"
Answer: b
Question (general): a and b are two partially filled buckets of water . if 3 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 5 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 11 , b ) 13 , c ) 39 / 5 , d ) 21 , e ) 23
Rationale: "let a contains a , b contains b liters so , ( a - 3 ) / ( b + 3 ) = 1 / 3 . . . . . . . ( 1 ) again , ( b - 5 ) / ( a + 5 ) = 1 / 2 . . . . . . . . . . ( 2 ) from ( 1 ) ( 2 ) we find a = 39 / 5 ans : ( c )"
Answer: c
Question (physics): a space shuttle orbits the earth at about 2 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 7,200 , b ) 8,880 , c ) 10,800 , d ) 28,800 , e ) 48,000
Rationale: "seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 2 * 3600 = 28,800 answer : a"
Answer: a
Question (physics): a train 220 m long is running with a speed of 59 kmph . . in what will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going
Options: a ) 8 sec , b ) 10 sec , c ) 12 sec , d ) 14 sec , e ) 15 sec
Rationale: "explanation : speed of the train relative to man = ( 59 + 7 ) kmph = 66 × 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 × 3 / 55 ) sec = 12 sec answer : option c"
Answer: c
Question (general): each week , harry is paid x dollars per hour for the first 35 hours and 1.5 x dollars for each additional hour worked that week . each week , james is paid x dollars per per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week james worked a total of 41 hours if harry and james were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 35 , b ) 36 , c ) 34 , d ) 38 , e ) 39
Rationale: "james worked for 41 hours hence he earned 40 * x + 1 * 2 x = 42 x dollars ; we know that harry also earned the same 42 x dollars , out of which he earned 35 x dollars for thefirst 35 hoursplus 7 x additional dollars . since for each additional hour he gets 1.5 x dollars then he worked for 7 x / 1.5 x = 4 additional hours , so harry worked for total of 30 + 4 = 34 hours . answer : c ."
Answer: c
Question (physics): in what time will a railway train 80 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 4 sec , b ) 7 sec , c ) 2 sec , d ) 6 sec , e ) 8 sec
Rationale: "t = 80 / 36 * 18 / 5 = 8 sec answer : e"
Answer: e
Question (geometry): two equilateral triangles of side 12 cm are placed one on top of another , such that a 6 pointed star is formed . if the six verticals lie on a circle what is the area of the circle not enclosed by the star ?
Options: a ) 68
b ) 83
c ) 57
d ) 61
e ) 62
Rationale: area of star = √ 3 / 4 * ( 12 ) ^ 2 + 3 * √ 3 / 4 * ( 12 / 3 ) ^ 2 = 48 √ 3 if r be radius of circle then r = 6 / cos 30 = > r = 12 / √ 3 = > r ^ 2 = 48 area of circle = pi * 48 area of the circle not enclosed by the star = 48 * pi - 48 √ 3 = 48 ( 3.14 - 1.732 ) = 68 ( approax ) answer : a
Answer: a
Question (gain): jaclyn buys $ 30 000 worth of debentures in a company . she earns 9.5 % p . a . simple interest , paid to her quarterly ( that is , every 3 months ) . if the agreed period of the debenture was 18 months : calculate the amount of interest jaclyn will earn for each quarter
Options: a ) 712.5 , b ) 1234 , c ) 1289 , d ) 1345 , e ) none of these
Rationale: "explanation : i = ( p x r x t ) / 100 = 30000 * 9.5 / 100 * ( 18 / 12 ) ^ 1 / 6 = 712.50 answer : a"
Answer: a
Question (general): the average of 6 observations is 12 . a new seventh observation is included and the new average is decreased by 1 . the seventh observation is :
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "explanation : seventh observation = ( 7 × × 11 - 6 × × 12 ) = 5 correct option : c"
Answer: c
Question (general): for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 5 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28350 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 5 : 55 in the afternoon , inclusive there are 9 * 12 = 108 five - minute intervals , thus total of 108 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 108 * 30 - - > x = 27 * 30 and 3 x = 3 * ( 27 * 30 ) = 27 * 90 . therefore , the total revenue from ticket sales that day was 27 * 30 * 5 + 27 * 90 * 10 = $ 28,350 . answer : d ."
Answer: d
Question (other): how many factors of 880 are odd numbers greater than 1 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: when factorized , 880 has 6 prime factors . of these prime factors 2 are odd and 4 are even . hence total number of odd factors is 2 * 2 ( 4 ) , which includes 4 . the total number of odd factors greater than 1 are 3 . ( option a )
Answer: a
Question (general): how many multiples of 9 are there between 18 and 270 ?
Options: a ) 12 , b ) 27 , c ) 42 , d ) 61 , e ) 60
Rationale: "it should be mentioned whether 18 and 270 are inclusive . if 18 and 270 are inclusive , then the answer is ( 270 - 18 ) / 9 + 1 = 29 . if 18 and 270 are not inclusive , then the answer is ( 261 - 27 ) / 9 + 1 = 27 . since oa is b , then we have not inclusive case ."
Answer: b
Question (physics): if it takes 30 construction workers 70 days to build a skyscraper , how long would it take 50 workers ?
Options: a ) 52 days , b ) 47 days , c ) 42 days , d ) 37 days , e ) 32 days
Rationale: 30 * 70 = 50 * x x = 42 answer : c
Answer: c
Question (geometry): there are thirty - 4 lines that are tangent to a circle , and these lines create regions in the plane . can you tell how many of these regions are not enclosed ?
Options: a ) 50 , b ) 74 , c ) 37 , d ) 77 , e ) 68
Rationale: e 68 68 regions . each new tangent increases the non - enclosed areas by two
Answer: e
Question (general): 2 cow ’ s and 8 goats are brought for rs . 1400 . if the average price of a goat be rs . 60 . what is the average price of a cow .
Options: a ) rs . 480 , b ) rs . 960 , c ) rs . 960 , d ) rs . 460 , e ) rs . 560
Rationale: explanation : average price of a goat = rs . 60 total price of 8 goats = 8 * 60 = rs . 480 but total price of 2 cows and 8 goats = rs . 1400 total price of 2 cows is = 1400 - 480 = 980 average price of a cow = 980 / 2 = rs . 460 answer : option d
Answer: d
Question (general): 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ?
Options: a ) 1 , b ) 2 , c ) 345 , d ) 445 , e ) 235
Rationale: 1 = 6,2 = 36,3 = 363,4 = 364,5 = 365 , then 36 = ? 36 = 2 check the second eqn . answer : b
Answer: b
Question (physics): p alone can complete a job in 6 days . the work done by q alone in one day is equal to one - fifth of the work done by p alone in one day . in how many days can the work be completed if p and q work together ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "p ' s rate is 1 / 6 q ' s rate is 1 / 30 the combined rate is 1 / 6 + 1 / 30 = 1 / 5 if they work together , the job will take 5 days . the answer is e ."
Answer: e
Question (gain): 60 % of a number is added to 150 , the result is the same number . find the number ?
Options: a ) 375 , b ) 277 , c ) 266 , d ) 99 , e ) 121
Rationale: ": ( 60 / 100 ) * x + 150 = x 2 x = 750 x = 375 answer : a"
Answer: a
Question (general): x , y , and z are different prime numbers . the product x ^ 3 * y ^ 2 * z ^ 2 is divisible by how many different positive numbers ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 60 , e ) 72
Rationale: "the exponents of x ^ 3 * y ^ 2 * z ^ 2 are 3 , 2 , and 2 . the number of factors is ( 3 + 1 ) ( 2 + 1 ) ( 2 + 1 ) = 36 the answer is b ."
Answer: b
Question (general): what is the smallest integer that is multiple of 87 and 20
Options: a ) 141 , b ) 180 , c ) 130 , d ) 122 , e ) 280
Rationale: correct answer : e it is the lcm of 8,7 and 20 which is 280
Answer: e
Question (general): two employees x and y are paid a total of rs . 600 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 200.72 , b ) s . 250.72 , c ) s . 272.72 , d ) s . 300.72 , e ) s . 310.72
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 600 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 600 ⇒ y [ 12 / 10 + 1 ] = 600 ⇒ 22 y / 10 = 600 ⇒ 22 y = 6000 ⇒ y = 6000 / 22 = rs . 272.72 c"
Answer: c
Question (gain): a reduction of 20 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 41 , e ) s . 32
Rationale: "800 * ( 20 / 100 ) = 160 - - - - 5 ? - - - - 1 = > rs . 32 answer : e"
Answer: e
Question (general): mary ' s income is 40 percent more than tim ' s income , and tim ' s income is 40 percent less than juan ' s income . what percent of juan ' s income is mary ' s income ?
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 84 %
Rationale: "juan ' s income = 100 ( assume ) ; tim ' s income = 60 ( 40 percent less than juan ' s income ) ; mary ' s income = 84 ( 40 percent more than tim ' s income ) . thus , mary ' s income ( 84 ) is 84 % of juan ' s income ( 100 ) . answer : e ."
Answer: e
Question (general): kim has 40 percent more money than sal and sal has 20 percent less money than phil . if sal and phil have a combined total of $ 1.80 , how much money does kim have ?
Options: a ) $ 1.00 , b ) $ 1.12 , c ) $ 1.20 , d ) $ 1.32 , e ) $ 1.40
Rationale: phil = x sal = 0.8 x kim = ( 1.4 ) * 0.8 x = 1.12 x x + 0.8 x = 1.8 - - > x = 1 kim = 1.12 answer : b
Answer: b