Cheukting/mathqa huggingface dataset:
Question (general): if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 3 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 3 people . so $ 75 . but , he also has to put in the average for himself ( the fourth person ) , so add $ 75 . so $ 150 is your answer . answer b"
Answer: b
Question (other): in a class of 40 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 14
Rationale: 26 + 20 - 17 = 29 40 - 29 = 11 play neither answer is d
Answer: d
Question (general): seller selling an apple for rs . 18 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 19 , d ) 18 , e ) 20
Rationale: "sp = 18 loss = cp 19 loss = cp − sp = cp − 18 ⇒ cp 19 = cp − 18 ⇒ 18 cp 19 = 18 ⇒ cp 19 = 1 ⇒ cp = 19 c"
Answer: c
Question (general): if n is a positive integer and the product of all the integers from 1 to n , inclusive , is a multiple of 8 , what is the least possible value of n ?
Options: a ) 7 , b ) 4 , c ) 5 , d ) 3 , e ) 6
Rationale: we need 3 factors of 2 , so n must be at least 4 . therefore , the answer is b .
Answer: b
Question (general): 1.5 , 2.5 , 4.5 , 7.5 , 11.5 , ( . . . . )
Options: a ) 16.5 , b ) 15.5 , c ) 14.5 , d ) 17.5 , e ) 17
Rationale: "explanation : 1 , 2 , 3 , 4 , 5 , etc . hence 5 = 16.5 answer : a"
Answer: a
Question (physics): a train covers a distance of 12 km in 10 minutes . if it takes 4 seconds to pass a telegraph post , then the length of the train is
Options: a ) 80 m , b ) 120 m , c ) 140 m , d ) 160 m , e ) 170 cm
Rationale: "explanation : speed = 12 / 10 x 60 km / hr = 72 x 5 / 18 m / sec = 20 m / sec . length of the train = ( speed x time ) = ( 20 x 4 ) m = 80 m answer : option a"
Answer: a
Question (geometry): what positive number , when squared , is equal to the cube of the positive square root of 14 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 4 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 16 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 4 = > x = 4 answer d"
Answer: d
Question (general): a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 250 per month . what is his monthly salary ?
Options: a ) 5000 , b ) 2999 , c ) 2878 , d ) 6250 , e ) 2771
Rationale: "income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 250 = > 6250 answer : d"
Answer: d
Question (general): if 15 students in a class average 75 % on an exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 80 % , b ) 81 % , c ) 82 % , d ) 83 % , e ) 84 %
Rationale: "( 15 * 75 + 10 * 90 ) / 25 = 81 % the answer is b ."
Answer: b
Question (physics): in a 100 m race a beats b by 25 m b beats c by 4 then a beats c by
Options: a ) 24 m , b ) 25 m , c ) 26 m , d ) 27 m , e ) 28 m
Rationale: a : b = 100 : 75 b : c = 100 : 96 . a : c = ( a / b x b / c ) = ( 100 / 75 x 100 / 96 ) = 100 / 72 = 100 : 72 . a beats c by ( 100 - 72 ) m = 28 m . answer : e
Answer: e
Question (general): for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 50 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 27 % , e ) 31 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 50 / 100 ) * 300 = 100 + 150 = 250 % comission = ( 250 / 800 ) * 100 = 31.3 ~ 31 % answer is e"
Answer: e
Question (general): the number of singles that a baseball player hit increased 10 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 1 percent . if the total number of singles and doubles that she hit increased 3 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 2 : 3 , b ) 3 : 5 , c ) 4 : 7 , d ) 5 : 8 , e ) 7 : 9
Rationale: "soln : - 1.10 s + 0.99 d = 1.03 [ s + d ] 0.07 s = 0.04 d s / d = 4 / 7 answer : c"
Answer: c
Question (physics): a man swims downstream 60 km and upstream 100 km taking 10 hours each time , what is the speed of the man in still water ?
Options: a ) 24 , b ) 42 , c ) 6 , d ) 8 , e ) 12
Rationale: "60 - - - 10 ds = 6 ? - - - - 1 100 - - - - 10 us = 10 ? - - - - 1 m = ? m = ( 10 + 6 ) / 2 = 8 answer : d"
Answer: d
Question (physics): a light flashes every 30 seconds , how many times will it flash in ? of an hour ?
Options: a ) 550 , b ) 600 , c ) 650 , d ) 700 , e ) 120
Rationale: 1 flash = 30 sec for 1 min = 2 flashes so for 1 hour = 2 * 60 = 120 flashes . answer : e
Answer: e
Question (general): the difference between the place values of two sixes in the numerical 81369206 is
Options: a ) 0 , b ) 599 , c ) 5994 , d ) 59994 , e ) none of them
Rationale: "required difference = ( 60000 - 6 ) = 59994 . answer is d"
Answer: d
Question (geometry): if the area of a circle is 81 pi square feet , find its circumference .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "the area is given by pi * r * r . hence pi * r * r = 81 pi r * r = 81 * hence r = 81 feet the circumference is given by 2 * pi * r = 2 * pi * 9 = 18 pi feet correct answer d"
Answer: d
Question (general): tourist purchased a total of 30 travelers checks in $ 50 and $ 100 denominations . the total worth of the travelers checks is $ 1800 . how many checks of $ 50 denominations can he spend so that average amount ( arithmetic mean ) of the remaining travelers checks is $ 100 ?
Options: a ) 4 , b ) 12 , c ) 15 , d ) 20 , e ) 24
Rationale: "you could set - up a quick table and brute force the answer . a 4 * 50 200 1800 - 200 1600 26 61.54 b 12 * 50 600 1800 - 600 1200 18 66.67 c 15 * 50 750 1800 - 750 1050 15 70.00 d 20 * 50 1000 1800 - 1000 800 10 80.00 e 24 * 50 1200 1800 - 1200 600 6 100.00 answer is e"
Answer: e
Question (gain): at an election 2 candidates are participated and a candidate got 20 % of votes and defeated by 500 . and 10 votes are invalid . find the total polled votes ?
Options: a ) 843 , b ) 1023 , c ) 965 , d ) 413 , e ) 1245
Rationale: "winner votes = 100 - 20 = 80 polled votes = [ ( 100 * 500 ) / 2 * 80 - 100 ] + 10 = 843 ( approximately ) answer is a"
Answer: a
Question (physics): a cat chases a rat 6 hours after the rat runs . cat takes 4 hours to reach the rat . if the average speed of the cat is 90 kmph , what s the average speed of the rat ?
Options: a ) 32 kmph , b ) 26 kmph , c ) 35 kmph , d ) 36 kmph , e ) 32 kmph
Rationale: cat take 10 hours and rat take 4 hours . . . then distance chased by them is 90 * 4 . so speed of rat is ( 90 * 4 ) / 10 = 36 kmph . answer is d
Answer: d
Question (general): average of 5 consecutive even numbers is 35 . find the greatest number in these 5 numbers ?
Options: a ) 26 , b ) 29 , c ) 39 , d ) 42 , e ) 43
Rationale: 39 option ' c '
Answer: c
Question (geometry): a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . what is the area of the wall photo , in square inches ?
Options: a ) 96
b ) 86
c ) 108
d ) 144
e ) 118
Rationale: this question is an example of a ' punch out ' question - we have to find the area of everything , then ' punch out ' the part that we do n ' t want . we ' re told that a wall photo 2 inches wide is placed around a rectangular paper with dimensions 8 inches by 12 inches . we ' re asked for the area of the wall photo , in square inches . area of a rectangle = ( length ) ( width ) so the area of the wall photo is . . . ( 8 ) ( 12 ) = 96 the wall photo ' adds ' 2 inches to the top , bottom , left and right ' sides ' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we ' punch out ' the area of the paper , we ' ll be left with the area of the wall photo : 192 - 96 = 96 final answer : a
Answer: a
Question (geometry): the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle
Options: a ) a ) 72 , b ) b ) 45 , c ) c ) 729 , d ) d ) 34 , e ) e ) 35
Rationale: "explanation : area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : option b"
Answer: b
Question (general): john found that the average of 15 no . ' s is 40 . if 10 is added to each number then the mean of number is ?
Options: a ) 50 , b ) 55 , c ) 65 , d ) 72 , e ) 78
Rationale: ( x + x 1 + . . . x 14 ) / 15 = 40 50 option a
Answer: a
Question (general): a car salesman earns a base salary of $ 1000 per month plus a commission of $ 200 for each car he sells . if the car salesman earned $ 2000 in march , how many cars does he need to sell in april in order to double his march earnings ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: 1000 + 200 x = 4000 x = 15 cars . the answer is b .
Answer: b
Question (general): barbata invests $ 2200 in the national bank at 5 % . how much additional money must she invest at 8 % so that the total annual income will be equal to 6 % of her entire investment ?
Options: a ) 1100 , b ) 3000 , c ) 1000 , d ) 3600 , e ) 2400
Rationale: "let the additional invested amount for 8 % interest be x ; equation will be ; 2200 + 0.05 * 2200 + x + 0.08 x = 2200 + x + 0.06 ( 2200 + x ) 0.05 * 2200 + 0.08 x = 0.06 x + 0.06 * 2200 0.02 x = 2200 ( 0.06 - 0.05 ) x = 2200 * 0.01 / 0.02 = 1100 ans : ` ` a ' '"
Answer: a
Question (general): 24 lbs of coffee p and 25 lbs of coffee v are mixed to make coffee x and y . the ratio of p to v in coffee x is 4 to 1 , in y is 1 to 5 . how much of p is contained in the mixture x ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: let there be 4 x lbs of p in x and x lbs of v in x let there be y lbs of p in y and 5 y lbs of v in y now total p is 4 x + y = 24 and total q is x + 5 y = 25 solving the two equations , we get x = 5 and y = 4 mixture x has 4 x lbs of p = 4 x = 4 * 5 = 20 lbs answer : b
Answer: b
Question (general): the average of 10 numbers is 0 . in those 10 , at the least , how many may be greater than or equal to zero ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: explanation : average of 10 numbers = 0 sum of 10 numbers = ( 0 x 10 ) = 0 . it is quite possible that 9 of these numbers may be negative and if there sum is - a , then 10 th number is ( a ) . answer : b
Answer: b
Question (other): a movie buff buys movies on dvd and on blu - ray in a ratio of 13 : 4 . if she returns 2 blu - ray movies , that ratio would change to 7 : 2 . if she buys movies on no other medium , what was the original number of movies purchased ?
Options: a ) 22 , b ) 28 , c ) 77 , d ) 99 , e ) 119
Rationale: "now coming to the process m ( d ) = 13 x and b ( d ) = 4 x now from the next line the new eqn becomes 13 x / ( 4 x - 2 ) = 7 / 2 solving it 26 x = 28 x - 14 x = 7 which means m ( d ) = 91 and b ( d ) = 28 so total initially is m ( d ) + b ( d ) = 119 e"
Answer: e
Question (general): arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 80 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 9 , c ) 5 , d ) 6 , e ) 7
Rationale: "suppose anoop joined after 3 months . then , 20000 * 12 = 80000 * ( 12 – x ) = > x = 9 . answer : b"
Answer: b
Question (general): if x + y = 260 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 230 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 260 x - y = 200 2 x = 60 x = 30 y = 230 answer is b"
Answer: b
Question (gain): a man can row 24 kmph in still water . it takes him thrice as long to row up as to row down the river . find the rate of the stream ?
Options: a ) 6 , b ) 12 , c ) 18 , d ) 15 , e ) 20
Rationale: "let man ' s rate upsteam be x kmph then his rate of downstream = 3 x kmph rate still water = 1 / 2 ( 3 x + x ) = 2 x 2 x = 24 x = 12 rate of upstream = 12 rate of downstream = 36 rate of stream 1 / 2 ( 36 - 12 ) = 12 kmph answer is b ."
Answer: b
Question (gain): a bookseller sells his books at a 20 % markup in price . if he sells a book for $ 36.00 , how much did he pay for it ?
Options: a ) $ 34.40 , b ) $ 34.00 , c ) $ 32.00 , d ) $ 30.00 , e ) $ 35.00
Rationale: "let the cost price of book = x selling price of book = 36 $ markup % = 20 ( 120 / 100 ) x = 36 = > x = 30 answer d"
Answer: d
Question (other): the hcf of two numbers is 42 and the other two factors of their lcm are 10 and 20 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 840 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 10 & 20 then the numbers are ( 42 * 10 ) and ( 42 x 20 ) = 420 and 840 answer : option c"
Answer: c
Question (general): suraj has a certain average of runs for 16 innings . in the 17 th innings he scores 92 runs thereby increasing his average by 4 runs . what is his average after the 17 th innings ?
Options: a ) 48 , b ) 64 , c ) 28 , d ) 72 , e ) 27
Rationale: to improve his average by 4 runs per innings he has to contribute 16 x 4 = 64 runs for the previous 16 innings . thus , the average after the 17 th innings = 92 - 64 = 28 . answer : c
Answer: c
Question (general): the wages earned by robin is 38 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 23 % , b ) 27.53 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 138 and $ 160 respectively . charles earns $ 38 more than robin who earns $ 138 . therefore , charles ' wage is 38 / 138 * 100 = 27.53 % . the correct choice is ( b )"
Answer: b
Question (other): a dog have birth to 12 puppies , 2 female and 10 male . what is the ratio of the female puppies to the male ?
Options: a ) 1 / 5 , b ) 1 / 6 , c ) 1 / 10 , d ) 2 / 12 , e ) 1 / 8
Rationale: if female is 2 and male is 10 , then 1 / 5 . so ratio of female to male is = 2 / 10 = 1 / 5 answer : a
Answer: a
Question (other): a box contains 6 black , 8 red and 4 green marbles . 2 marbles are drawn from the box at random . what is the probability that both the marbles are of the same color ?
Options: a ) 49 / 153 , b ) 18 / 153 , c ) 49 / 153 , d ) 40 / 153 , e ) 24 / 72
Rationale: "explanation : total marbles in a box = 6 black + 8 red + 4 green marbles = 18 marbles 2 marbles are drawn from 18 marbles at random . therefore , n ( s ) = 18 c 2 = 153 ways let a be the event that 2 marbles drawn at random are of the same color . number of cases favorable to the event a is n ( a ) = 6 c 2 + 8 c 2 + 4 c 2 = 15 + 28 + 6 = 49 therefore , by definition of probability of event a , p ( a ) = n ( a ) / n ( s ) = 49 / 153 answer : a"
Answer: a
Question (general): if x / 2 = y / 5 = z / 6 , then ( x + y + z ) / x is equal to :
Options: a ) 13 , b ) 12 , c ) 15 / 2 , d ) 13 / 2 , e ) none of these
Rationale: "explanation : solution : let x / 2 = y / 5 = z / 6 = k = > x = 2 k , y = 5 k , z = 6 k . . ' . ( x + y + z ) / x = ( 2 k + 5 k + 6 k ) / 2 k = > 13 k / 2 k = 13 / 2 answer : d"
Answer: d
Question (general): a man has some hens and cows . if the number of heads be 48 and the number of feet equals 136 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 48 = > h + c = 48 - - - ( equation 1 ) number of feet = 136 = > 2 h + 4 c = 136 = > h + 2 c = 68 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 68 - 48 = > c = 20 substituting the value of c in equation 1 , we get h + 20 = 48 = > h = 48 - 20 = 28 i . e . , number of hens = 28 answer : e"
Answer: e
Question (physics): a train covers a distance of 100 km in 1 hour . if its speed is decreased by 12 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 8 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 12 = 88 km / hr time taken = 100 / 88 = 1 hr 8 min answer is b"
Answer: b
Question (general): the average of 25 results is 20 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 128 , b ) 75 , c ) 69 , d ) 78 , e ) 45
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 20 or , x = 128 . answer : option a"
Answer: a
Question (geometry): if d is the smallest positive integer such that 3,150 multiplied by d is the square of an integer , then d must be
Options: a ) 2
b ) 5
c ) 6
d ) 7
e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3,150 . 3,150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3,150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3,150 itself is not a perfect square . ) we also are given that 3,150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .
Answer: e
Question (gain): x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 14190 ?
Options: a ) 3200 , b ) 4000 , c ) 3250 , d ) 4128 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 14190 ã — 16 / 55 = rs . 4128 . share of z in the profit is rs . 4128 . option d"
Answer: d
Question (other): there are 250 doctors and nurses at a hospital . if the ratio of doctors to nurses is 2 to 3 , how many nurses are at the hospital ?
Options: a ) 134 , b ) 138 , c ) 142 , d ) 146 , e ) 150
Rationale: "the number of nurses at the hospital is ( 3 / 5 ) * 250 = 150 . the answer is e ."
Answer: e
Question (general): in an examination , 300 students appeared . out of these students ; 26 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 60 , e ) 01
Rationale: "the number of students with first division = 26 % of 300 = 26 / 100 × 300 = 7800 / 100 = 78 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 78 + 162 ) = 60 answer : d"
Answer: d
Question (gain): on a certain transatlantic crossing , 30 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 75 %
Rationale: "0.30 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.30 p = 0.40 ( rt ) rt / p = 3 / 4 = 75 % answer - e"
Answer: e
Question (gain): p and q invested in a shop . the profits were divided in the ratio of 4 : 6 respectively . if p invested rs . 55,000 , the amount invested by q is :
Options: a ) 48000 , b ) 40000 , c ) 35000 , d ) 60000 , e ) none
Rationale: "suppose q invested rs . y . then , 50000 / y = 4 / 6 or y = [ 50000 x 6 / 4 ] = 75000 . answer e"
Answer: e
Question (general): evaluate ( 12 + 22 + 32 + . . . + 102 )
Options: a ) 430 , b ) 720 , c ) 385 , d ) 265 , e ) 295
Rationale: "we know that ( 12 + 22 + 32 + . . . + n 2 ) = 1 / 6 n ( n + 1 ) ( 2 n + 1 ) putting n = 10 , required sum = 1 / 6 x 10 x 11 x 21 = 385 option c"
Answer: c
Question (other): divide rs . 32000 in the ratio 3 : 3 ?
Options: a ) 12000 , 20000 , b ) 12000 , 200098 , c ) 16000 , 16000 , d ) 12000 , 20006 , e ) 12000 , 20001
Rationale: "3 / 6 * 32000 = 16000 5 / 6 * 32000 = 16000 answer : c"
Answer: c
Question (general): find value for x from below equation ? x + 1 = - 4
Options: a ) - 5 , b ) - 4 , c ) 4 , d ) 3 , e ) 2
Rationale: "1 . subtract 1 from both sides : x + 1 - 1 = - 4 - 1 2 . simplify both sides : x = - 5 a"
Answer: a
Question (general): what is the remainder when 1201 × 1202 × 1204 × 1205 is divided by 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the remainders when dividing each number by six are : 1 , 2 , 4 , and 5 . the product is 1 * 2 * 4 * 5 = 40 the remainder when dividing 40 by 6 is 4 . the answer is d ."
Answer: d
Question (general): students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio d of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) d = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Question (gain): at what rate of compound interest per annum will a sum of $ 1200 becomes 1348.32 in 2 years ?
Options: a ) 5 % , b ) 6 % , c ) 7 % , d ) 8 % , e ) 10 %
Rationale: "let the rate be r % p . a . 1200 * ( 1 + r / 100 ) ^ 2 = 1348.32 ( 1 + r / 100 ) ^ 2 = 134832 / 120000 = 11236 / 10000 ( 1 + r / 100 ) ^ 2 = ( 106 / 100 ) ^ 2 1 + r / 100 = 106 / 100 r = 6 % answer is b"
Answer: b
Question (general): the average weight of a group of boys is 30 kg . after a boy of weight 45 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 45 kg joins the group , total weight of boys = 30 x + 45 so 30 x + 45 = 31 ( x + 1 ) = > x = 14 . answer : a"
Answer: a
Question (physics): the food in a camp lasts for 10 men for 50 days . if 10 more men join , how many days will the food last ?
Options: a ) 22 days , b ) 25 days , c ) 50 days , d ) 16 days , e ) 17 days
Rationale: "one man can consume the same food in 10 * 50 = 500 days . 10 more men join , the total number of men = 20 the number of days the food will last = 500 / 20 = 25 days . answer : b"
Answer: b
Question (physics): a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 6 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "on the way down , the rate is 1.5 * 6 = 9 miles per day . the distance of the route down the mountain is 2 * 9 = 18 miles . the answer is c ."
Answer: c