Cheukting/mathqa huggingface dataset:
Question (general): evaluate : 1182 - 12 * 3 * 2 = ?
Options: a ) 674 , b ) 574 , c ) 174 , d ) 274 , e ) 374
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 1182 - 12 * 3 * 2 = 1182 - 8 = 174 correct answer c"
Answer: c
Question (general): if a ( a - 4 ) = 5 and b ( b - 4 ) = 5 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 4 , c ) 4 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 5 or if a = 5 then b = - 1 but in each case a + b = - 1 + 5 = 4 answer : option c"
Answer: c
Question (general): in a software company 4 / 10 of people know c + + , 2 / 4 of them know java , 2 / 8 of them know neither , find the total possibility to know c + + ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: assume 100 persons in a company person knows c + + = 4 / 10 = 100 * 4 / 100 = 20 persons person knows java = 2 / 4 = 100 * 2 / 4 = 50 persons neither = 2 / 8 = 100 * 2 / 8 = 25 persons according to our assumption 100 person = 20 + 50 + 25 = 95 person covered ( 5 remaining ) so , total possibility = 20 person ( c + + ) + 5 ( remaining ) = 25 persons which is 25 / 100 = 1 / 4 answer : a
Answer: a
Question (general): the average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 10 years . find the average age of the women ?
Options: a ) 87 , b ) 98 , c ) 30 , d ) 28 , e ) 23
Rationale: "20 + 10 + 8 * 2 = 46 / 2 = 23 answer : e"
Answer: e
Question (general): the number 0.8 is how much greater than 1 / 2 ?
Options: a ) ½ , b ) 3 / 10 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 8 - 1 / 2 = x 8 / 10 - 1 / 2 = x x = 3 / 10 ans b"
Answer: b
Question (physics): two trains running in opposite directions cross a man standing on the platform in 20 seconds and 18 seconds respectively and they cross each other in 19 seconds . the ratio of their speeds is :
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 3 : 8 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 20 x meters , and length of the second train = 18 y meters . ( 20 x + 15 y ) / ( x + y ) = 19 = = > 20 x + 18 y = 19 x + 19 y = = > x = y = = > x / y = 1 / 1 answer : option a"
Answer: a
Question (general): cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 68 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
Options: a ) $ 0.00 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.00 , e ) $ 6.80
Rationale: 0.85 * { original price } = $ 68 - - > { original price } = $ 80 . { final price } = $ 68 * 1.25 = $ 85 . the difference = $ 85 - $ 85 = $ 5 . answer : d .
Answer: d
Question (general): the cost per pound of milk powder and coffee were the same in june . in july , the price of coffee shot up by 200 % and that of milk powder dropped by 60 % . if in july , a mixture containing equal quantities of milk powder and coffee costs $ 5.10 for 3 lbs , how much did a pound of milk powder cost in july ?
Options: a ) $ 4 , b ) $ 0.4 , c ) $ 1 , d ) $ 3 , e ) $ 1.65
Rationale: "lets assume price of coffee in june = 100 x price of tea in june = 100 x price of coffee in july = 300 x ( because of 200 % increase in price ) price of tea in july = 40 x ( because of 60 % decrease in price ) price of 1.5 pound of coffee 1.5 pound of tea in july will be = 450 x + 60 x = 510 x as per question 510 x = 5.10 $ x = 0.01 s so the price of tea in july = 40 x = 40 x 0.01 = 0.4 $ / pound answer b"
Answer: b
Question (geometry): each of the 55 points is placed either inside or on the surface of a perfect sphere . if 60 % or fewer of the points touch the surface , what is the maximum number of segments which , if connected from those points to form chords , could be the diameter of the sphere ?
Options: a ) 7
b ) 11
c ) 13
d ) 16
e ) 38
Rationale: maximum number of points on the surface is 60 % * 55 = 33 now note that if two points form a diameter , they can not be part of any other diameter . so in the best case we can pair up the points we have 33 points , so at best we can form 16 pairs ( 32 ) . so , answer is ( d )
Answer: d
Question (general): on the richter scale , which measures the total amount of energy released during an earthquake , a reading of x - 1 indicates one - tenth the released energy as is indicated by a reading of x . on that scale , the frequency corresponding to a reading of 2 is how many times as great as the frequency corresponding to a reading of 8 ?
Options: a ) 40 , b ) 50 , c ) 10 ^ 4 , d ) 10 ^ 5 , e ) 10 ^ 6
Rationale: "if richter scale reading goes from x - 1 to x it will be 10 if richter scale reading goes from 2 to 3 it will be 10 if richter scale reading goes from 3 to 4 it will be 10 if richter scale reading goes from 4 to 5 it will be 10 if richter scale reading goes from 5 to 6 it will be 10 similarly if richter scale reading goes from 6 to 7 it will be 10 and if richter scale reading goes from 7 to 8 it will be 10 so it will from 2 to 8 i . e 3,4 , 5,6 , 7,8 = 10 * 10 * 10 * 10 * 10 * 10 = 10 ^ 6 answer is e"
Answer: e
Question (physics): a train leaves mumabai at 9 am at a speed of 40 kmph . after one hour , another train leaves mumbai in the same direction as that of the first train at a speed of 60 kmph . when and at what distance from mumbai do the two trains meet ?
Options: a ) 187 , b ) 279 , c ) 120 , d ) 278 , e ) 379
Rationale: "when the second train leaves mumbai the first train covers 40 * 1 = 40 km so , the distance between first train and second train is 40 km at 10.00 am time taken by the trains to meet = distance / relative speed = 40 / ( 60 - 40 ) = 2 hours so , the two trains meet at 12 a . m . the two trains meet 2 * 60 = 120 km away from mumbai . answer : c"
Answer: c
Question (general): for any number z , z * is defined as the greatest positive even integer less than or equal to y . what is the value of 6.30 – 6.30 * ?
Options: a ) 1.5 , b ) 0.5 , c ) 6.25 , d ) 0.25 , e ) 0.3
Rationale: "since z * is defined as the greatest positive even integer less than or equal to z , then 6.30 * = 6 ( the greatest positive even integer less than or equal to 6.30 is 6 ) . hence , 6.30 – 6.30 * = 6.30 - 6 = 0.30 answer : e ."
Answer: e
Question (general): the guests at a football banquet consumed a total of 406 pounds of food . if no individual guest consumed more than 2.5 pounds of food , what is the minimum number of guests that could have attended the banquet ?
Options: a ) 160 , b ) 161 , c ) 162 , d ) 163 , e ) 164
Rationale: "to minimize one quantity maximize other . 162 * 2.5 ( max possible amount of food a guest could consume ) = 405 pounds , so there must be more than 162 guests , next integer is 163 . answer : d ."
Answer: d
Question (other): in a group of 600 readers who read science fiction or literacy works or both , 200 read science fiction and 230 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 30 , c ) 25 , d ) 100 , e ) 110
Rationale: "consider total number of reader n ( s u l ) = 600 people who read science fiction n ( s ) = 400 people who read literacy works n ( l ) = 230 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 600 = 400 + 230 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 630 - 600 n ( s â ˆ © l ) = 30 so people read both science fiction and literacy works are 30 answer : b"
Answer: b
Question (general): if x : y = 3 : 5 , find the value of ( 2 x + 4 y ) : ( 3 x – y )
Options: a ) 13 : 2 , b ) 11 : 2 , c ) 13 : 3 , d ) 13 : 4 , e ) 13 : 5
Rationale: "explanation : given : x / y = 3 / 5 ( 2 x + 4 y ) / ( 3 x – y ) = ( 2 * 3 + 4 * 5 ) : ( 3 * 3 – 5 ) = 26 : 4 = 13 : 2 answer : a"
Answer: a
Question (physics): if daily wages of a man is double to that of a woman , how many men should work for 20 days to earn rs . 14400 ? given that wages for 40 women for 30 days are rs . 21600 .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 2 / 40 ã — 30 wages of 1 man for 20 days = 21600 ã — 2 ã — 20 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 2 ã — 20 / 40 ã — 30 ) = 144 / ( 216 ã — 40 / 40 ã — 30 ) = 20 answer : option e"
Answer: e
Question (probability): persons a and b . person a picks a random no . from 1 to 1000 . then person b picks a random no . from 1 to 1000 . what is the probability of b getting no . greater then what a has picked .
Options: a ) 0.3995 , b ) 0.4995 , c ) 0.5995 , d ) 0.6995 , e ) 0.7995
Rationale: probability of a choosing 1 and b greater = ( 1 / 1000 ) * ( 999 / 1000 ) ; probability of a choosing 2 and b greater = ( 1 / 1000 ) * ( 998 / 1000 ) ; probability of a choosing 3 and b greater = ( 1 / 1000 ) * ( 997 / 1000 ) ; . . . ; probability of a choosing 998 and b greater = ( 1 / 1000 ) * ( 2 / 1000 ) ; probability of a choosing 999 and b greater = ( 1 / 1000 ) * ( 1 / 1000 ) ; total = ( 1 / 1000 ) * ( 1 / 1000 ) * ( 999 + 998 + 997 + . . . + 2 + 1 ) = ( 1 / 1000 ) * ( 1 / 1000 ) * ( 999 * 1000 / 2 ) = 0.4995 answer : b
Answer: b
Question (physics): cole drove from home to work at an average speed of 50 kmh . he then returned home at an average speed of 110 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66.5 , b ) 70.5 , c ) 72.5 , d ) 75.5 , e ) 82.5
Rationale: "let the distance one way be x time from home to work = x / 50 time from work to home = x / 110 total time = 2 hrs ( x / 50 ) + ( x / 110 ) = 2 solving for x , we get x = 275 / 4 time from home to work in minutes = ( 275 / 4 ) * 60 / 50 = 82.5 minutes ans = e"
Answer: e
Question (other): john distributes his pencil among his 4 friends rose , mary , ranjan , and rohit in the ratio 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5 . what is the minimum no . of pencils that the person should have ?
Options: a ) 59 , b ) 65 , c ) 70 , d ) 77 , e ) 98
Rationale: "rakesh : rahul : ranjan : rohit = 1 / 5 : 1 / 3 : 1 / 4 : 1 / 5 step 1 : at first we need to do is lcm of 2 , 3,4 and 5 is 60 . step 2 : then pencil are distributed in ratio among friends , rakesh = ( 1 / 5 x 60 ) = 12 rahul = ( 1 / 3 x 60 ) = 20 . ranjan = ( 1 / 4 x 60 ) = 15 . rohit = ( 1 / 5 x 60 ) = 12 . step 3 : total number of pencils are ( 12 x + 20 x + 15 x + 12 x ) = 59 x . for minimum number of pencils x = 1 . the person should have at least 59 pencils . a )"
Answer: a
Question (general): an equal number of desks and bookcases are to be placed along a library wall that is 15 meters long . each desk is 2 meters long , and each bookshelf is 1.5 meters long . if the maximum possible number of desks and bookcases are to be placed along the wall , then the space along the wall that is left over will be how many g meters long ?
Options: a ) 0.5 , b ) 1 , c ) 1.5 , d ) 2 , e ) 3
Rationale: "let x be the number of desks and bookcases that are placed along the library wall . 2 x + 1.5 x < 15 3.5 x < 15 since x is a non negative integer , the largest number x can be is 4 . when x is 4 , the desks and bookcases take up 3.5 * 4 = 14 m , leaving 1 m of empty space . thus , i believe the answer is b ) 1"
Answer: b
Question (general): - 88 × 39 + 312 = ?
Options: a ) - 3200 , b ) 3120 , c ) - 3120 , d ) 3200 , e ) 3208
Rationale: - 88 × 39 + 312 = - 88 × ( 40 - 1 ) + 312 = - 88 × 40 + 88 + 312 = - 3520 + 88 + 312 = - 3120 answer is c
Answer: c
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 25 sq ft , if the price per foot of building the fence is rs . 58 ?
Options: a ) 1160 , b ) 1251 , c ) 1102 , d ) 1352 , e ) 1450
Rationale: "let the side of the square plot be a ft . a 2 = 25 = > a = 5 length of the fence = perimeter of the plot = 4 a = 20 ft . cost of building the fence = 20 * 58 = rs . 1160 . answer : a"
Answer: a
Question (physics): a train 280 m long , running with a speed of 63 km / hr will pass a tree in
Options: a ) 15 sec . , b ) 16 sec . , c ) 18 sec . , d ) 20 sec . , e ) none
Rationale: "solution speed = ( 63 x 5 / 18 ) m / sec = 35 / 2 msec time taken = ( 280 x 2 / 35 ) m / sec = 16 sec . answer b"
Answer: b
Question (gain): a shop owner sells 15 mtr of cloth and gains sp of 10 mtrs . find the gain % ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 100 % , e ) 200 %
Rationale: "here , selling price of 10 m cloth is obtained as profit . profit of 10 m cloth = ( s . p . of 15 m cloth ) – ( c . p . of 15 m cloth ) selling price of 5 m cloth = selling price of 15 m of cloth let cost of each metre be rs . 100 . therefore , cost price of 5 m cloth = rs . 500 and s . p . of 5 m cloth = rs . rs . 1500 profit % = 1000 / 500 × 100 = 200 % profit of 200 % was made by the merchant . e"
Answer: e
Question (general): if f ( x ) = 12 - x ^ 2 / 2 and f ( 2 k ) = 7 k , what is one possible value for k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
Rationale: "first of all , see thisgmat blog postand check the related lesson linked below for some background on function notation . we can plug anything in for x and get a result . you can find f ( 1 ) , for example , by plugging in 1 where x is , and you would get 12 - 1 / 2 = 11.5 . or we could find f ( 2 ) , which would be 12 - 4 / 2 = 10 . so the notation f ( 2 k ) means that we are going to plug a 2 k in for x everywhere in the formula for f ( x ) . that would be : f ( 2 k ) = 12 - ( 2 k ) ^ 2 / 2 = 12 - 2 k ^ 2 . remember that we have to square both the 2 and the k , to get 4 k 2 . now , this expression , the output , we will set equal to 2 k . 12 - 2 k ^ 2 = 2 k - - > k = - 3 or k = 7 . all the answers are positive , so we choose k = 2 . answer = e"
Answer: e
Question (gain): there were two candidates in an election . winner candidate received 62 % of votes and won the election by 348 votes . find the number of votes casted to the winning candidate ?
Options: a ) 456 , b ) 744 , c ) 899 , d ) 1200 , e ) 1400
Rationale: "w = 62 % l = 38 % 62 % - 38 % = 24 % 24 % - - - - - - - - 348 62 % - - - - - - - - ? = > 899 answer : c"
Answer: c
Question (other): what is the greatest positive integer t such that 3 ^ t is a factor of 9 ^ 10 ?
Options: a ) 5 , b ) t = 9 , c ) t = 10 , d ) t = 20 , e ) 30
Rationale: "what is the greatest positive integer t such that 3 ^ t is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Question (other): in a ratio which is equal to 3 : 4 , if the antecedent is 12 , then the consequent is ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 22 , e ) 25
Rationale: "we have 3 / 4 = 12 / x 3 x = 48 x = 16 consequent = 16 answer is b"
Answer: b
Question (gain): what is the rate percent when the simple interest on rs . 4000 amount to rs . 640 in 2 years ?
Options: a ) 8.2 % , b ) 8 % , c ) 8.5 % , d ) 9 % , e ) 9.5 %
Rationale: "interest for 1 year = 640 / 2 = 320 interest on rs 4000 p / a = 320 interest rate = 320 / 4000 * 100 = 8 % answer : b"
Answer: b
Question (general): if 2 x + y = 7 and x + 2 y = 8 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 5 / 3
Rationale: "we have two equations : 2 x + y = 7 x + 2 y = 8 notice that something nice happens when we add them . we get : 3 x + 3 y = 15 divide both sides by 3 to get : x + y = 5 so , ( x + y ) / 3 = 5 / 3 answer : e"
Answer: e
Question (general): farm tax is levied on the 90 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 0.125 % , d ) 13.88 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 90 ) = 13.88 % the correct answer is ( d ) ."
Answer: d
Question (general): the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8500 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 2981 , e ) 2711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8500 = 34000 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 2000 salary of may is rs . 6500 salary of january = rs . 4500 . answer : c"
Answer: c
Question (gain): don and his wife each receive an 8 percent annual raise . if don receives a raise rs . 800 and his wife receives a raise of rs . 840 , what is the difference between their annual income after their raises ?
Options: a ) 40 , b ) 460 , c ) 500 , d ) 540 , e ) 150
Rationale: don salary 8 % = 800 ; therefore , 100 % = 10000 his wife salary 8 % = 840 ; therefore , 100 % = 10500 after raise 8 % , don salary = 10000 + 800 = 10800 and his wife salary = 10500 + 840 = 11340 difference = 11340 - 10800 = 540 answer : d
Answer: d
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what will be the compound interest on same values
Options: a ) rs . 51.75 , b ) rs 51.50 , c ) rs 51.25 , d ) rs 51 , e ) none of these
Rationale: "explanation : s . i . = p ∗ r ∗ t / 100 p = 50 ∗ 100 / 5 ∗ 2 = 500 amount = 500 ( 1 + 5100 ) 2 500 ( 21 / 20 ∗ 21 / 20 ) = 551.25 c . i . = 551.25 − 500 = 51.25 option c"
Answer: c
Question (general): if x + y = 300 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 250 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 300 x - y = 200 2 x = 100 x = 50 y = 250 answer is b"
Answer: b
Question (gain): ramu bought an old car for rs . 42000 . he spent rs . 13000 on repairs and sold it for rs . 66900 . what is his profit percent ?
Options: a ) 22 , b ) 77 , c ) 18 , d ) 21.6 , e ) 88
Rationale: "total cp = rs . 42000 + rs . 13000 = rs . 55000 and sp = rs . 66900 profit ( % ) = ( 66900 - 55000 ) / 55000 * 100 = 21.6 % answer : d"
Answer: d
Question (physics): a can do a work in 8 days . b can do the same work in 16 days . if both a & b are working together in how many days they will finish the work ?
Options: a ) 3 days , b ) 16 / 3 days , c ) 3 / 4 days , d ) 9 / 12 days , e ) 5 / 7 days
Rationale: "a rate = 1 / 8 b rate = 1 / 16 ( a + b ) rate = ( 1 / 8 ) + ( 1 / 16 ) = 3 / 16 a & b finish the work in 16 / 3 days correct option is b"
Answer: b
Question (physics): tom , working alone , can paint a room in 6 hours . peter and john , working independently , can paint the same room in 3 hours and 6 hours , respectively . tom starts painting the room and works on his own for one hour . he is then joined by peter and they work together for an hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 3 , e ) 2 / 5
Rationale: "tom paints 1 / 6 of the room in the first hour . tom and peter paint 1 / 6 + 1 / 3 = 1 / 2 of the room in the next hour for a total of 4 / 6 . the three people then paint the remaining 2 / 6 in a time of ( 2 / 6 ) / ( 4 / 6 ) = 1 / 2 hours peter worked for 3 / 2 hours so he painted 3 / 2 * 1 / 3 = 1 / 2 of the room . the answer is a ."
Answer: a
Question (general): if ( 1 – 1.25 ) n = 5 , then n =
Options: a ) − 20 , b ) − 140 , c ) − 4 , d ) 4 , e ) 400
Rationale: "( 1 – 1.25 ) n = 5 simplify to get : - 0.25 n = 5 rewrite as ( - 1 / 4 ) n = 5 multiply both sides by - 4 to get : n = - 20 answer : a"
Answer: a
Question (physics): if in a race of 70 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 ) 14 m , d ) 10 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 = ( 70 * 5 ) / 25 = 14 m hence , a beats b by 14 m . answer c"
Answer: c
Question (general): a certain social security recipient will receive an annual benefit of $ 12000 provided he has annual earnings of $ 9360 or less , but the benefit will be reduced by $ 1 for every $ 3 of annual earnings over $ 9360 . what amount of total annual earnings would result in a 65 percent reduction in the recipient ' s annual social security benefit ? ( assume social security benefits are not counted as part of annual earnings . )
Options: a ) $ 15,360 , b ) $ 17,360 , c ) $ 18,000 , d ) $ 21,960 , e ) $ 27,360
Rationale: for every $ 3 earn above $ 9360 , the recipient loses $ 1 of benefit . or for every $ 1 loss in the benefit , the recipient earns $ 3 above $ 9360 if earning is ; 9360 + 3 x benefit = 12000 - x or the vice versa if benefit is 12000 - x , the earning becomes 9360 + 3 x he lost 50 % of the benefit ; benefit received = 12000 - 0.65 * 12000 = 12000 - 7800 x = 4200 earning becomes 9360 + 3 x = 9360 + 3 * 4200 = 21960 ans : d
Answer: d
Question (physics): a bus covered a distance of 250 km , partly at an average speed of 40 kmph and partly at 60 kmph . if the total time taken is 5.2 hours , then the distance covered at 40 kmph is
Options: a ) 130 km , b ) 120 km , c ) 100 km , d ) 124 km , e ) none of these
Rationale: "let the partial distance covered at 40 kmph be x let the another partial distance covered at 60 kmph be ( 250 - x ) thus , x / 40 - ( 250 - x ) / 60 = 5.2 or , x / 40 + ( 250 - x ) / 60 = 5.2 or , ( 3 x + 500 - 2 x ) / / 120 = 5.2 or 500 + x = 624 x = 124 answer : d"
Answer: d
Question (physics): jane and ashley take 13 1 / 3 days and 40 days respectively to complete a project when they work on it alone . they thought if they worked on the project together , they would take fewer days to complete it . during the period that they were working together , jane took an 8 day leave from work . this led to jane ' s working for 4 extra days on her own to complete the project . how long did it take to finish the project ?
Options: a ) 10 days , b ) 15 days , c ) 16 days , d ) 17 days , e ) 20 days
Rationale: let us assume that the work is laying 40 bricks . jane = 3 bricks per day ashley = 1 brick per day together = 4 bricks per day let ' s say first 8 days ashley works alone , no of bricks = 8 last 4 days jane works alone , no . of bricks = 12 remaining bricks = 40 - 20 = 20 so together , they would take 20 / 4 = 5 total no . of days = 8 + 4 + 5 = 17 answer is d
Answer: d
Question (general): the average ( arithmetic mean ) of all scores on a certain algebra test was 90 . if the average of the 8 male students ’ grades was 82 , and the average of the female students ’ grades was 92 , how many female students took the test ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 21 , e ) 32
Rationale: "total marks of male = m total marks of female = f number of males = 8 number of females = f given : ( m + f ) / ( 8 + f ) = 90 - - - - - - - - - - - - - 1 also given , m / 8 = 82 thus m = 656 - - - - - - - - - 2 also , f / f = 92 thus f = 92 f - - - - - - - - - 3 put 2 and 3 in 1 : we get ( 656 + 92 f ) / ( 8 + f ) = 90 solving this we get f = 32 ans : e"
Answer: e
Question (geometry): if the length of the longest chord of a certain circle is 24 , what is the radius of that certain circle ?
Options: a ) 12 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "longest chord of a circle is the diameter of the circle diameter = 2 * radius if diameter of the circle is given as 24 = 2 * 12 so radius of the circle = 12 correct answer - a"
Answer: a