Cheukting/mathqa huggingface dataset:
Question (physics): if in a race of 110 m , a covers the distance in 20 seconds and b in 25 seconds , then a beats b by :
Options: a ) 20 m , b ) 16 m , c ) 11 m , d ) 22 m , e ) 15 m
Rationale: "explanation : the difference in the timing of a and b is 5 seconds . hence , a beats b by 5 seconds . the distance covered by b in 5 seconds = ( 110 * 5 ) / 25 = 22 m hence , a beats b by 22 m . answer d"
Answer: d
Question (gain): a small company reduced its faculty by approximately 20 percent to 195 employees . what was the original number of employees ?
Options: a ) a ) 182 , b ) b ) 208 , c ) c ) 220 , d ) d ) 224 , e ) e ) 244
Rationale: "if x is the original number of employees , then after 20 % reduction in employees number is . 80 x but we are given . 80 x = 195 x = 244 so the original number of employees is 244 correct answer - e"
Answer: e
Question (gain): a part of certain sum of money is invested at 9 % per annum and the rest at 15 % per annum , if the interest earned in each case for the same period is equal , then ratio of the sums invested is ?
Options: a ) 4 : 6 , b ) 4 : 9 , c ) 5 : 3 , d ) 4 : 1 , e ) 4 : 2
Rationale: "15 : 9 = 5 : 3 answer : c"
Answer: c
Question (physics): if 3 men or 4 women can reap a field in 43 days how long will 7 men and 5 women take to reap it ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 18 , e ) 19
Rationale: "explanation : 3 men reap 1 / 43 field in 1 day 1 man reap 1 / ( 3 x 43 ) 4 women reap 1 / 43 field in 1 day 1 woman reap 1 / ( 43 x 4 ) 7 men and 5 women reap ( 7 / ( 3 x 43 ) + 5 / ( 4 x 43 ) ) = 1 / 12 in 1 day 7 men and 5 women will reap the field in 12 days answer : option b"
Answer: b
Question (general): the smallest number when increased by ` ` 3 ` ` is exactly divisible by 510 , 4590 , and 105 is :
Options: a ) 630 , b ) 633 , c ) 150 , d ) 140 , e ) 627
Rationale: lcm = 630 630 - 3 = 627 answer : e
Answer: e
Question (geometry): if the perimeter of square region d and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of d
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pd ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pd = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Question (general): a waiter ' s salary consists of his salary and tips . during one week his tips were 5 / 3 of his salary . what fraction of his income came from tips ?
Options: a ) 4 / 9 , b ) 5 / 4 , c ) 5 / 8 , d ) 5 / 9 , e ) 6 / 9
Rationale: "income = salary ( s ) + tips = s + s * 5 / 3 = s * 8 / 3 tips = s * 8 / 3 fraction of his income came from tips = ( s * 5 / 3 ) / ( s * 8 / 3 ) = 5 / 8 answer : c"
Answer: c
Question (general): if ( c - a ) / ( c - b ) = 3 , then ( 5 b - 5 a ) / ( c - a ) =
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 3.33 , e ) 2.5
Rationale: "let ' s say c = 7 , b = 5 , a = 1 so that our 1 st expression holds true . now , ibsert those numbers in the second expression and we ' ll get 3.33 answer d ( hopefully ) ) )"
Answer: d
Question (general): rachel and sarah spent $ 8 for gasoline , $ 15.65 for their lunch , and $ 5 apiece for gifts for grandma . grandma gave each of them $ 10 . if the girls left home with a total of $ 50 , how much do they have for the return trip ?
Options: a ) $ 36.35 , b ) $ 26.35 , c ) $ 16.35 , d ) $ 46.35 , e ) $ 56.35
Rationale: $ 50 + $ 20 = $ 70 what they left with plus $ 10 to each $ 8 + $ 15.65 + $ 10 = $ 33.65 what they spent ( gifts are $ 5 + $ 5 ) $ 70 - $ 33.65 = $ 36.35 left correct answer a
Answer: a
Question (gain): in the fifth grade at parkway elementary school there are 420 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 69 . , b ) 73 . , c ) 81 , d ) 65 , e ) 108
Rationale: "total students = 420 boys = 320 , girls = 100 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 100 - 35 = 65 . correct option : d"
Answer: d
Question (gain): p and q invested in a shop . the profits were divided in the ratio of 2 : 4 respectively . if p invested rs . 500000 , the amount invested by q is :
Options: a ) 5000000 , b ) 4000000 , c ) 1000000 , d ) 6000000 , e ) none
Rationale: "suppose q invested rs . y . then , 500000 / y = 2 / 4 or y = [ 500000 x 4 / 2 ] = 1000000 . answer c"
Answer: c
Question (general): 1939392 * 625
Options: a ) 1212120010 , b ) 1212120000 , c ) 1212120011 , d ) 1212121010 , e ) 1212121000
Rationale: "explanation : trick : when multiplying with 5 n 5 n then put n zeros to the right of multiplicand and divide the number with 2 n 2 n so using this we can solve this question in much less time . 1939392 × 5 ( 4 ) = 1939392000016 = 1212120000 option b"
Answer: b
Question (general): if ( m - 8 ) is a factor of m ^ 2 - qm - 24 , then q =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: "( m - 8 ) ( m - a ) = m ^ 2 - qm - 24 a = - 3 q = 8 + a = 5 = b"
Answer: b
Question (gain): peter invests a sum of money and gets back an amount of $ 815 in 3 years . david invests an equal amount of money and gets an amount of $ 870 in 4 years . if both amounts were invested at the same rate ( simple interest ) what was the sum of money invested ?
Options: a ) 670 , b ) 650 , c ) 698 , d ) 744 , e ) 700
Rationale: "since both peter and david invested the same amount of money at the same rate , they would earn same interest per year . david invested for one year more than peter and hence he got interest amount for one more year . interest earned per year = amount received by david - amount received by peter = 870 - 815 = 55 interest earned for 3 years = 55 * 3 = 165 amount invested = 815 - 165 = 650 answer : b"
Answer: b
Question (other): the ratio of the adjacent angles of a parallelogram is 5 : 13 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
Options: a ) 168 ° , b ) 134 ° , c ) 156 ° , d ) 224 ° , e ) none of these
Rationale: "the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 5 x + 13 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 50 ° and 130 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 50 ° + 84 ° = 134 ° answer : b"
Answer: b
Question (probability): in a bag containing 3 balls , a white ball was placed and then 1 ball was taken out at random . what is the probability that the extracted ball would turn on to be white , if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ?
Options: a ) 2 / 3 , b ) 5 / 8 , c ) 5 / 9 , d ) 3 / 7 , e ) 4 / 7
Rationale: "since , all possible hypothesis regarding the colour of the balls are equally likely , therefore these could be 3 white balls , initially in the bag . ∴ required probability = 1 / 4 [ 1 + 3 / 4 + 1 / 2 + 1 / 4 ] = 1 / 4 [ ( 4 + 3 + 2 + 1 ) / 4 ] = 5 / 8 b"
Answer: b
Question (general): half a number plus 5 is 13 . what is the number ?
Options: a ) 8 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 5 = 13 ( 1 / 2 ) x = 13 - 5 ( 1 / 2 ) x = 8 x = 16 correct answer is b"
Answer: b
Question (other): a hare and a jackal are running a race . 3 leaps of the hare are equal to 4 leaps of the jackal . for every 6 leaps of the hare , the jackal takes 7 leaps . find the ratio of the speed of the hare to the speed of the jackal .
Options: a ) 64 : 25 , b ) 8 : 7 , c ) 5 : 8 , d ) 25 : 64 , e ) 6 : 7
Rationale: the hare takes 6 leaps and the jackal takes 7 leaps . 1 hare leap = 4 / 3 jackal leaps thus the hare ' s 6 leaps = 6 * ( 4 / 3 ) = 8 jackal leaps . the ratio of their speeds is 8 : 7 . the answer is b .
Answer: b
Question (general): on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 15
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 c"
Answer: c
Question (gain): a , b and c enter into a partnership by investing $ 15000 , $ 21000 and $ 27000 respectively . at the end of 8 months , b receives $ 1540 as his share . find the share of a .
Options: a ) $ 800 , b ) $ 900 , c ) $ 1000 , d ) $ 1100 , e ) $ 1200
Rationale: "the ratio of capital of a , b and c = 15000 : 21000 : 27000 = 5 : 7 : 9 a ' s share = ( 5 / 7 ) * 1540 = $ 1100 the answer is d ."
Answer: d
Question (physics): a is twice as good as workman as b and together they finish a piece of work in 18 days . in how many days will a alone finish the work ?
Options: a ) 27 , b ) 26 , c ) 29 , d ) 25 , e ) 24
Rationale: "a : b = 2 : 1 ab ' s together wrk in 18 days a ; s alone is 1 / 18 * 2 / 3 = 27 days answer : a"
Answer: a
Question (general): when a number is divided by 6 & then multiply by 12 the answer is 15 what is the no . ?
Options: a ) 4.5 , b ) 5 , c ) 5.6 , d ) 7.5 , e ) 6.5
Rationale: "if $ x $ is the number , x / 6 * 12 = 15 = > 2 x = 15 = > x = 7.5 d"
Answer: d
Question (gain): by selling 15 pens for a rupee a woman loses 25 % . how many for a rupee should he sell in order to gain 25 % ?
Options: a ) 12 , b ) 14 , c ) 45 , d ) 10 , e ) 65
Rationale: "d 85 % - - - 15 125 % - - - ? 85 / 125 * 15 = 10"
Answer: d
Question (geometry): if the perimeter of square region z and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of z
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pz ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pz = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 9 years hence ?
Options: a ) 22 , b ) 77 , c ) 78 , d ) 98 , e ) 71
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 9 years , their ages will be 49 and 29 . sum of their ages = 49 + 29 = 78 . answer : c"
Answer: c
Question (physics): a , band c can do a piece of work in 35 days , 20 days and 55 days respectively , working alone . how soon can the work be done if a is assisted by band c on alternate days ?
Options: a ) 7 days , b ) 8 days , c ) 9 days , d ) 10 days , e ) 16 days
Rationale: "( a + b ) ' s 1 day ' s work = 1 / 35 + 1 / 20 = 11 / 140 ( a + c ) ' s 1 day ' s work = 1 / 35 + 1 / 55 = 18 / 385 work done in 2 day ' s = 11 / 140 + 18 / 385 = 48 / 383 48 / 383 th work done in 2 days work done = 383 / 48 * 2 = 16 days ( approx ) answer : e"
Answer: e
Question (general): aram ’ s car was fined when he gave joe and peter a ride , so they decided to help aram pay the fine . joe paid $ 3 more than 1 / 4 of the fine and peter paid $ 3 less than 1 / 3 of the fine , leaving pay $ 4 less than 1 / 2 the fine to complete the payment . what fraction of the fine did aram pay ?
Options: a ) $ 13 , b ) $ 15 , c ) $ 20 , d ) $ 28 , e ) $ 48
Rationale: as given aram ' payment is [ 1 ] [ / 2 ] * fine - 4 i . e total fine = 2 * ( sam ' s payment + 4 ) now , as everything looks integer , fine should be able to divide by 4 and 3 . because joe ' s contribution has 1 / 4 of the fine and peter ' s contribution has 1 / 3 of the fine so , that leads me to following : options , aram ' s pay , total fine ( f ) , f / 4 , f / 3 a ) , 13 , 34 , no i . e 34 / 4 , no i . e 34 / 3 b ) , 14 , 38 , no , no c ) , 20 , 48 , yes yes , no need to further go on as we have got f / 4 and f / 3 correct , just for confirmation we go further d ) , 28 , 64 , yes , no e ) , 48 , 104 , yes , no correct answer is c
Answer: c
Question (general): what is 992 * 992 ?
Options: a ) 974,169 , b ) 974,219 , c ) 984,064 , d ) 985,219 , e ) 985,369
Rationale: "if you take a base of 1000 then 992 is 8 less than 1000 to get the product of 992 x 992 write like this 992 - 8 ( as 8 less than base 1000 ) 992 - 8 now 8 x 8 = 64 and 992 - 8 = 984 so 992 x 992 = 984064 . . . ( bingo the answer is c . you can even have a shortcut . . . . . . 8 x 8 = 64 . . . only answer choice has last three digits as 64 . . so no need to calculate 992 - 8 . after you get 8 x 8 you can straight way pick answer choice c ."
Answer: c
Question (general): the mean of 50 observations was 36 . it was found later that an observation 43 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.2 , b ) 36.1 , c ) 36.2 , d ) 36.4 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 43 - 23 ) = 1820 . â ˆ ´ correct mean = 1820 / 50 = 36.4 . answer d"
Answer: d
Question (physics): due to construction , the speed limit along an 5 - mile section of highway is reduced from 52 miles per hour to 36 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) a ) 3.12 , b ) b ) 8 , c ) c ) 10 , d ) d ) 2.57 , e ) e ) 24
Rationale: "old time in minutes to cross 5 miles stretch = 5 * 60 / 52 = 5 * 15 / 13 = 5.76 new time in minutes to cross 5 miles stretch = 5 * 60 / 36 = 5 * 5 / 3 = 8.33 time difference = 2.57 ans : d"
Answer: d
Question (physics): it is currently 7 : 16 pm . at what time in the morning was it exactly 19,443 minutes earlier ?
Options: a ) 7 : 11 , b ) 7 : 13 , c ) 7 : 17 , d ) 7 : 19 , e ) 7 : 21
Rationale: converting 19,443 minutes to hours , we get 19,443 / 60 = 324 r 3 ; that is 324 hours and 3 minutes . all of the answers are during the same hour of the morning , thus the hours can be assumed to bring us into the 7 am hour evenly from 7 : 16 pm . thus 324 hours ago was 7 : 16 am . take an extra 3 minutes off , and it was 7 : 13 am . b
Answer: b
Question (general): 52 is to be divided into two parts such that the sum of 10 times the first and 22 times the second is 780 . the bigger part is :
Options: a ) 30.33 , b ) 34.44 , c ) 26.1 , d ) 28.0 , e ) 21.0
Rationale: "explanation : let the two parts be ( 52 - x ) and x . then , 10 ( 52 - x ) + 22 x = 780 = > 12 x = 260 = > x = 21.66 . bigger part = ( 52 - x ) = 30.33 . answer : a ) 30.33"
Answer: a
Question (general): the price of 2 sarees and 4 shirts is $ 1600 . with the same money one can buy 1 saree and 6 shirts . if one wants to buy 12 shirts , how much shall he have to pay ?
Options: a ) 3800 , b ) 3300 , c ) 2400 , d ) 4200 , e ) 1400
Rationale: c $ 2400 let the price of a saree and a shirt be $ x and $ y respectively . then , 2 x + 4 y = 1600 . . . . ( i ) and x + 6 y = 1600 . . . . ( ii ) divide equation ( i ) by 2 , we get the below equation . = > x + 2 y = 800 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 6 y = 1600 ( - ) x + 2 y = 800 - - - - - - - - - - - - - - - - 4 y = 800 - - - - - - - - - - - - - - - - therefore , y = 200 . now apply value of y in ( iii ) = > x + 2 x 200 = 800 = > x + 400 = 800 therefore x = 400 solving ( i ) and ( ii ) we get x = 400 , y = 200 . cost of 12 shirts = $ ( 12 x 200 ) = $ 2400 .
Answer: c
Question (general): on dividing 271 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) a ) 12 , b ) b ) 15 , c ) c ) 16 , d ) d ) 17 , e ) e ) 30
Rationale: "d = ( d - r ) / q = ( 271 - 1 ) / 9 = 270 / 9 = 30 e )"
Answer: e
Question (physics): working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 12 days . if b starts , they take half a day more . how long does it take to complete the task if they both work together ?
Options: a ) 4 , b ) 4.5 , c ) 6 , d ) 8 , e ) 6.5
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 6 no . of days when b works = 6 → 6 x + 6 y = 1 when b starts : no . of days when a works = 6.5 no . of days when b works = 5.5 → 6.5 x + 5.5 y = 1 solving the above two equations for xy x = 1 / 12 y = 1 / 12 → total work done by ab in a day = 1 / 12 + 1 / 12 = 2 / 12 = 1 / 6 → no . of days to complete the work when both work together = 6 answer : c"
Answer: c
Question (geometry): on dividing a number by 5 , we get 3 as remainder . what will the remainder when the square of the this number is divided by 5 ?
Options: a ) 0 , b ) 5 , c ) 8 , d ) 9 , e ) 4
Rationale: "explanation : let the number be x and on dividing x by 5 , we get k as quotient and 3 as remainder . x = 5 k + 3 x ^ 2 = ( 5 k + 3 ) ^ 2 = ( 25 k ^ 2 + 30 k + 9 ) = 5 ( 5 k ^ 2 + 6 k + 1 ) + 4 on dividing x 2 by 5 , we get 4 as remainder . e )"
Answer: e
Question (geometry): find the area of a rhombus one side of which measures 20 cm and one diagonal is 24 cm .
Options: a ) 370 cm 2 , b ) 365 cm 2 , c ) 380 cm 2 , d ) 384 cm 2 , e ) 394 cm 2
Rationale: "explanation : let other diagonal = 2 x cm . since diagonals of a rhombus bisect each other at right angles , we have : ( 20 ) 2 = ( 12 ) 2 + ( x ) 2 = > x = √ ( 20 ) 2 – ( 12 ) 2 = √ 256 = 16 cm . _ i so , other diagonal = 32 cm . area of rhombus = ( 1 / 2 ) x ( product of diagonals ) = ( 1 / 2 × 24 x 32 ) cm 2 = 384 cm 2 answer : option d"
Answer: d
Question (physics): a taxi leaves point a 4 hours after a bus left the same spot . the bus is traveling 30 mph slower than the taxi . find the speed of the taxi , if it overtakes the bus in two hours .
Options: a ) 40 , b ) 42 , c ) 45 , d ) 48 , e ) 49
Rationale: "let the speed of bus be v - 30 , speed of taxi be v the bus travelled a total of 6 hrs and taxi a total of 2 hrs . hence 6 * ( v - 30 ) = 2 v 6 v - 180 = 2 v 4 v = 180 v = 45 mph c"
Answer: c
Question (general): m and n are the x and y coordinates , respectively , of a point in the coordinate plane . if the points ( m , n ) and ( m + p , n + 15 ) both lie on the line defined by the equation x = ( y / 5 ) - ( 2 / 5 ) , what is the value of p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "x = ( y / 5 ) - ( 2 / 5 ) , and so y = 5 x + 2 . the slope is 5 . ( n + 15 - n ) / ( m + p - m ) = 5 p = 3 the answer is c ."
Answer: c
Question (other): in a certain pet shop , the ratio of dogs to cats to bunnies in stock is 7 : 7 : 8 . if the shop carries 330 dogs and bunnies total in stock , how many dogs are there ?
Options: a ) 42 , b ) 66 , c ) 98 , d ) 112 , e ) 154
Rationale: "let us assume the number of dogs , cats and bunnies to be 7 x , 7 x and 8 x total dogs and bunnies = 15 x . and we are given that 15 x = 330 . hence x = 22 . dogs = 7 x = 7 * 22 = 154 ( option e )"
Answer: e
Question (general): of the 150 employees at company x , 80 are full - time , and 100 have worked at company x for at least a year . there are 10 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ?
Options: a ) 10 , b ) 30 , c ) 50 , d ) 80 , e ) 100
Rationale: "full time employee who have not worked for at least one year = a full time employee who have worked for at least one year = b non full time employee who have worked for at least one year = c non full time employee who have not worked for at least one year = d a + b + c + d = 150 a + b = 80 i . e . c + d = 70 b + c = 100 i . e . a + d = 50 d = 20 i . e . c = 70 - 20 = 50 i . e . b = 100 - 50 = 50 i . e . a = 80 - 50 = 30 b = 10 answer : option a"
Answer: a
Question (geometry): if y is the smallest positive integer such that 7,700 multiplied by y is the square of an integer , then y must be
Options: a ) 29 , b ) 58 , c ) 63 , d ) 74 , e ) 77
Rationale: "7700 = 5 * 5 * 2 * 2 * 7 * 11 , so we need one 7 and one 11 to make it a square of a number . so 7 * 11 = 77 ans : e"
Answer: e
Question (gain): a bookstore has a shelf that contains biographies which normally sell for $ 20 each and mysteries that normally sell for $ 12 each . during a sale , the biographies and mysteries are discounted at different rates so that a customer saves a total of $ 19 from the normal price by buying 5 discounted biographies and 3 discounted mysteries . if the sum of the discount rates for the two types of books is 38 percent , what is the discount rate on mysteries ?
Options: a ) 18 % , b ) 29.68 % , c ) 19.68 % , d ) 29 % , e ) 68 %
Rationale: "let b be the discount on biographies and m be the discount on mysteries so . , b + m = 0.38 - - - - - ( 1 ) and ( 20 * 5 + 12 * 3 ) - ( 20 * 5 * ( 1 - b ) + 12 * 3 * ( 1 - m ) ) = 19 - - > 100 ( 1 - ( 1 - b ) ) + 36 ( 1 - ( 1 - m ) = 19 100 b + 36 m = 19 - - - - - - ( 2 ) solving 12 . , we get m = 0.2968 = 29.68 % b"
Answer: b
Question (general): find the ones digit of 73 ^ 320
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 320 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer d ."
Answer: d
Question (general): the ratio of ducks and frogs in a pond is 37 : 39 respectively . the average number of ducks and frogs in the pond is 152 . what is the number of frogs in the pond ?
Options: a ) 148 , b ) 152 , c ) 156 , d ) 144 , e ) none
Rationale: "solution : ratio of ducks and frogs in pond , = 37 : 39 . average of ducks and frogs in pond , = 152 . so , total number of ducks and frogs in the pond , = 2 * 152 = 304 . therefore , number of frogs , = ( 304 * 39 ) / 76 = 156 . answer : option c"
Answer: c
Question (geometry): the side of a square is increased by 30 % then how much % does its area increases ?
Options: a ) 52.65 , b ) 69 , c ) 50.75 , d ) 42.75 , e ) 52.75
Rationale: "a = 100 a 2 = 10000 a = 130 a 2 = 16900 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 6900 100 - - - - - - - ? = > 69 % answer : b"
Answer: b