Cheukting/mathqa huggingface dataset:
Question (general): ? x 120 = 173 x 240
Options: a ) 545 , b ) 685 , c ) 865 , d ) 495 , e ) 346
Rationale: let y x 120 = 173 x 240 then y = ( 173 x 240 ) / 120 = 346 . answer : e
Answer: e
Question (physics): in a soap company a soap is manufactured with 11 parts . for making one soap you will get 1 part as scrap . at the end of the day you have 251 such scraps . from that how many soaps can be manufactured ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: using 251 scraps we make = 22 soaps . ( i . e . , 11 * 22 = 242 ) remaining scraps = 9 . again , 22 soaps produce = 22 scraps . so , now we have 22 + 9 = 31 scraps remaining . using 31 scraps we make 2 soaps and 2 scraps remaining . ( i . e . , 2 * 11 = 22 ) again , that 2 soaps produce = 2 scraps . and already we have 9 scraps . total 9 + 2 = 11 sscraps . by using 11 scraps , we make 1 soap . so , total = 22 + 2 + 1 = 25 soaps we produce . answer : b
Answer: b
Question (gain): a sum of rs . 2665 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1888 , b ) 1640 , c ) 2768 , d ) 2976 , e ) 2691
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2665 - x ) * 3 * 5 ) / 100 24 x / 100 = 39975 / 100 - 15 x / 100 39 x = 39975 = > x = 1025 second sum = 2665 – 1025 = 1640 answer : b"
Answer: b
Question (general): in a survey of parents , exactly 3 / 4 of the mothers and 9 / 10 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 27 % , b ) 21 % , c ) 19 % , d ) 18 % , e ) 16 %
Rationale: "let the total number of parents = 100 number of women = 40 number of men = 60 number of mothers who held full time jobs = 3 / 4 * 40 = 30 number of fathers who held full time jobs = 9 / 10 * 60 = 54 total number of parents who held full time jobs = 84 total number of parents who did not hold jobs = 100 - 84 = 16 alternatively , percentage of women = 40 % percentage of women who did not hold full time jobs = ( 1 - 3 / 4 ) * 100 % = 25 % of all mothers did not have full time jobs 25 % of 40 % - - > 10 % of the total parents percentage of men = 60 % percentage of men who held full time jobs = ( 1 - 9 / 10 ) * 100 % = 10 % of all fathers did not have full time jobs 10 % of 60 % - - > 6 % of the total parents therefore , percentage of parents who did not hold full time jobs = 10 + 6 = 16 % answer e - 16 %"
Answer: e
Question (physics): a garrison of 1850 men has provisions for 28 days . at the end of 12 days , a reinforcement arrives , and it is now found that the provisions will last only for 10 days more . what is the reinforcement ?
Options: a ) 1850 , b ) 2960 , c ) 3000 , d ) 1110 , e ) 1712
Rationale: "1850 - - - - 28 1850 - - - - 16 x - - - - - 10 x * 10 = 1850 * 16 x = 2960 1850 - - - - - - - 1110 answer : d"
Answer: d
Question (gain): a certain sum is invested at simple interest at 18 % p . a . for two years instead of investing at 12 % p . a . for the same time period . therefore the interest received is more by rs . 240 . find the sum ?
Options: a ) 7000 , b ) 7029 , c ) 2778 , d ) 2800 , e ) 2000
Rationale: "let the sum be rs . x . ( x * 18 * 2 ) / 100 - ( x * 12 * 2 ) / 100 = 240 = > 36 x / 100 - 24 x / 100 = 240 = > 12 x / 100 = 240 = > x = 2000 . answer : e"
Answer: e
Question (physics): a train 150 m long is running at a speed of 62 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 5 sec , b ) 10 sec , c ) 12 sec , d ) 18 sec , e ) 15 sec
Rationale: "answer : b . speed of the train relative to man = ( 62 - 8 ) kmph = ( 54 * 5 / 18 ) m / sec = 15 m / sec time taken by the train to cross the man = time taken by it to cover 150 m at 15 m / sec = 150 * 1 / 15 sec = 10 sec"
Answer: b
Question (geometry): the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 588 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "area = l * w = 3 w ^ 2 = 588 w ^ 2 = 196 w = 14 the answer is a ."
Answer: a
Question (geometry): the radius of a cone is 10 m , height 21 m . the volume of the cone is :
Options: a ) 2200
b ) 1100
c ) 5500
d ) 3300
e ) 1050
Rationale: 1 / 3 π rh = 1 / 3 × 22 / 7 × 100 × 21 = 2200 m ( power 3 ) answer is a .
Answer: a
Question (physics): jamshid can paint a fence in 50 percent less time than taimour can when each works alone . when they work together , they can paint the fence in 5 hours . how long would it take taimour to paint the fence alone ?
Options: a ) 6 hours , b ) 8 hours , c ) 15 hours , d ) 24 hours , e ) 32 hours
Rationale: "i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 5 = > 1 / 15 working alone taimour can do the job in 1 = 1 / 15 * hours = > 15 answer c"
Answer: c
Question (gain): a group of boy scouts and girls scouts is going on a rafting trip . 45 % of the scouts arrived with signed permission slips . if 60 % of the scouts were boy scouts and 25 % of the boy scouts arrived with signed permission slips , then what percentage of the scouts were girl scouts who arrived with signed permission slips ?
Options: a ) 20 , b ) 21 , c ) 25 , d ) 28 , e ) 30
Rationale: "we do n ' t know how many scouts went on the trip , so let ' s assume 100 scouts went on the trip 60 % were boy scouts so 60 % of 100 = 60 were boy scouts 25 % of the boy scouts brought their permission slips signed , so . 25 * 60 = 15 boy scouts had signed slips 60 - 15 = 45 boy scouts did not 45 % of all the scouts had signed slips , so . 45 * 100 = 45 in total had signed slips thus 45 - 15 = 30 girl scouts had signed slips thus the percentage of scouts who were girl scouts arriving with signed permission slips is 30 / 100 = . 30 = 30 % e"
Answer: e
Question (probability): two dice are thrown simultaneously . what is the probability of getting two numbers whose product is even ?
Options: a ) 1 / 2 , b ) 3 / 8 , c ) 3 / 4 , d ) 5 / 16 , e ) 9 / 16
Rationale: "in a simultaneous throw of two dice , we have n ( s ) = ( 6 x 6 ) = 36 . then , e = { ( 1 , 2 ) , ( 1 , 4 ) , ( 1 , 6 ) , ( 2 , 1 ) , ( 2 , 2 ) , ( 2 , 3 ) , ( 2 , 4 ) , ( 2 , 5 ) , ( 2 , 6 ) , ( 3 , 2 ) , ( 3 , 4 ) , ( 3 , 6 ) , ( 4 , 1 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 4 ) , ( 4 , 5 ) , ( 4 , 6 ) , ( 5 , 2 ) , ( 5 , 4 ) , ( 5 , 6 ) , ( 6 , 1 ) , ( 6 , 2 ) , ( 6 , 3 ) , ( 6 , 4 ) , ( 6 , 5 ) , ( 6 , 6 ) } n ( e ) = 27 . p ( e ) = n ( e ) / n ( s ) = 27 / 36 = 3 / 4 . answer : c ."
Answer: c
Question (gain): when sold at a 40 % discount , a sweater nets the merchant a 20 % profit on the wholesale cost at which he initially purchased the item . by what % is the sweater marked up from wholesale at its normal retail price ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 80 % , e ) 100 %
Rationale: "et the marked up price = 100 . . selling price = 100 - 40 % of 100 = 60 . . profit = 20 % . . therefore the wholesale purchase cost = x . . . . 1.2 x = 60 or x = 50 . . . marked price was 100 so 50 over 50 . . . so answer is 100 % . . answer : e"
Answer: e
Question (physics): a man can row upstream at 15 kmph and downstream at 25 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 29 , c ) 30 , d ) 20 , e ) 24
Rationale: "us = 15 ds = 25 m = ( 15 + 25 ) / 2 = 20 answer : d"
Answer: d
Question (general): workers decided to raise rs . 3 lacs by equal contribution from each . had they contributed rs . 50 eachextra , the contribution would have been rs . 3.60 lacs . how many workers were they ?
Options: a ) 220 , b ) 230 , c ) 1200 , d ) 560 , e ) 590
Rationale: "n * 50 = ( 360000 - 300000 ) = 60000 n = 60000 / 50 = 1200 c"
Answer: c
Question (general): evaluate : 983 x 207 - 983 x 107
Options: a ) 93700 , b ) 97300 , c ) 93800 , d ) 98300 , e ) none of them
Rationale: "983 x 207 - 983 x 107 = 983 x ( 207 - 107 ) = 983 x 100 = 98300 . answer is d ."
Answer: d
Question (general): find value of x : 3 x ^ 2 + 5 x + 2 = 0
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "a = 3 , b = 5 , c = 2 x 1,2 = ( - 5 ± √ ( 52 - 4 × 3 × 2 ) ) / ( 2 × 3 ) = ( - 5 ± √ ( 25 - 24 ) ) / 6 = ( - 5 ± 1 ) / 6 x 1 = ( - 5 + 1 ) / 6 = - 4 / 6 = - 2 / 3 x 2 = ( - 5 - 1 ) / 6 = - 6 / 6 = - 1 a"
Answer: a
Question (other): the probability that a computer company will get a computer hardware contract is 3 / 4 and the probability that it will not get a software contract is 3 / 5 . if the probability of getting at least one contract is 4 / 5 , what is the probability that it will get both the contracts ?
Options: a ) 4 / 11 , b ) 5 / 12 , c ) 6 / 17 , d ) 7 / 20 , e ) 11 / 30
Rationale: "let , a ≡ event of getting hardware contract b ≡ event of getting software contract ab ≡ event of getting both hardware and software contract . p ( a ) = 3 / 4 , p ( ~ b ) = 5 / 9 = > p ( b ) = 1 - ( 3 / 5 ) = 2 / 5 . a and b are not mutually exclusive events but independent events . so , p ( at least one of a and b ) = p ( a ) + p ( b ) - p ( ab ) . = > 4 / 5 = ( 3 / 4 ) + ( 2 / 5 ) - p ( ab ) . = > p ( ab ) = 7 / 20 . hence , the required probability is 7 / 20 . the answer is d ."
Answer: d
Question (general): if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exectly twice in 3 consecutive flips ?
Options: a ) 0.375 , b ) 0.25 , c ) 0.325 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : a"
Answer: a
Question (general): if the average ( arithmetic mean ) of 10 consecutive odd integers is 154 , then the least of these integers is
Options: a ) a ) 51 , b ) b ) 58 , c ) c ) 145 , d ) d ) 190 , e ) e ) 210
Rationale: "a very helpful rule to know in arithmetic is the rule that in evenly spaced sets , average = median . because the average will equal the median in these sets , then we quickly know that the median of this set of consecutive odd integer numbers is 154 . there are 10 numbers in the set , and in a set with an even number of terms the median is just the average of the two most median terms ( here the 5 th and 6 th numbers in the set ) . this means that numbers 5 and 6 in this set are 153 and 155 . because we know that number 5 is 153 , we know that the smallest number is 4 odd numbers below this , which means that it is 4 * 2 = 8 below this ( every odd number is every other number ) . therefore 153 - 8 = 145 , answer choice c"
Answer: c
Question (general): the average weight of a class is x pounds . when a new student weighing 100 pounds joins the class , the average decreases by 1 pound . in a few months the student ’ s weight increases to 110 pounds and the average weight of the class becomes x + 4 pounds . none of the other students ’ weights changed . what is the value of x ?
Options: a ) 85 , b ) 86 , c ) 88 , d ) 90 , e ) 92
Rationale: "when the student weighs 80 pounds the average weight is x - 1 pounds ; when the student weighs 110 pounds the average weight is x + 4 pounds . so , the increase in total weight of 110 - 80 = 30 pounds corresponds to the increase in average weight of ( x + 4 ) - ( x - 1 ) = 5 pounds , which means that there are 30 / 5 = 6 students ( including the new one ) . so , initially there were 5 student . total weight = 5 x + 80 = 6 ( x - 1 ) - - > x = 92 pounds . answer : e ."
Answer: e
Question (general): each of 3 investments has a 20 % of becoming worthless within a year of purchase , independently of what happens to the other two investments . if simone invests an equal sum v in each of these 3 investments on january 1 , the approximate chance that by the end of the year , she loses no more than 1 / 3 of her original investment is
Options: a ) 90 % , b ) 80 % , c ) 70 % , d ) 60 % , e ) 40 %
Rationale: the problem asks for the approximate chance that no more than 1 / 3 of the original investment is lost . we can apply the “ 1 – x ” technique : what ’ s the chance that more than 1 / 3 of the original investment is lost ? there are two outcomes we have to separately measure : ( a ) all 3 investments become worthless . ( b ) 2 of the 3 investments become worthless , while 1 doesn ’ t . outcome ( a ) : the probability is ( 0.2 ) ( 0.2 ) ( 0.2 ) = 0.008 , or a little less than 1 % . outcome ( b ) : call the investments x , y , and z . the probability that x retains value , while y and z become worthless , is ( 0.8 ) ( 0.2 ) ( 0.2 ) = 0.032 . now , we have to do the same thing for the specific scenarios in which y retains value ( while x and z don ’ t ) and in which z retains value ( while x and y don ’ t ) . each of those scenarios results in the same math : 0.032 . thus , we can simply multiply 0.032 by 3 to get 0.096 , or a little less than 10 % . the sum of these two probabilities is 0.008 + 0.096 = 0.104 , or a little more than 10 % . finally , subtracting from 100 % and rounding , we find that the probability we were looking for is approximately 90 % . the correct answer is a . this problem illustrates the power of diversification in financial investments . all else being equal , it ’ s less risky to hold a third of your money in three uncorrelated ( independent ) but otherwise equivalent investments than to put all your eggs in one of the baskets . that said , be wary of historical correlations ! housing price changes in different us cities were not so correlated — and then they became highly correlated during the recent housing crisis ( they all fell together ) , fatally undermining spreadsheet models that assumed that these price changes were independent .
Answer: a
Question (general): a man owns 2 / 3 of market reserch beauro buzness , and sells 3 / 4 of his shares for 75000 rs , what is the value of buzness ?
Options: a ) 150000 , b ) 160000 , c ) 170000 , d ) 190000 , e ) 250000
Rationale: "if value of business = x total sell ( 2 x / 3 ) ( 3 / 4 ) = 75000 - > x = 150000 answer : a"
Answer: a
Question (general): on a certain day , joey , the ice - cream seller sold his ice creams to 4 different kids in a manner that each of the kids purchased half of the remaining ice creams and half ice - cream more . if we tell you that the fourth kid bought just a single ice cream , can you find out how many ice creams were sold by joey that day ?
Options: a ) 15 , b ) 20 , c ) 22 , d ) 12 , e ) 8
Rationale: a joey sold 15 ice creams that day . the fourth kid bought a single ice cream . therefore , we have the following equation : total - ( total / 2 + 1 / 2 ) = 1 solving it , we get the total as 3 . let ' s work this method till we reach the first kid . the first kid bought 15 / 2 + 1 / 2 = 8 ( leaving 7 ) the second kid bought 7 / 2 + 1 / 2 = 4 ( leaving 3 ) the third kid bought 3 / 2 + 1 / 2 = 2 ( leaving 1 ) the fourth kid bought 1 / 2 + 1 / 2 = 1 adding all of them together , we get 8 + 4 + 2 + 1 = 15 .
Answer: a
Question (gain): the population of a town is 7900 . it decreases annually at the rate of 10 % p . a . what was its population 2 years ago ?
Options: a ) 9750 , b ) 8000 , c ) 8500 , d ) 9500 , e ) 10000
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 7900 ã — 100 / 90 ã — 100 / 90 = 9753 a )"
Answer: a
Question (physics): a 160 meter long train crosses a man standing on the platform in 12 sec . what is the speed of the train ?
Options: a ) 48 kmph , b ) 54 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 12 * 18 / 5 = 48 kmph answer : a"
Answer: a
Question (other): 9 log 9 ( 5 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: "exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 5 ) = 5 correct answer d"
Answer: d
Question (general): the unit digit in the product ( 124 * 812 * 816 * 467 ) is :
Options: a ) 2 , b ) 7 , c ) 6 , d ) 8 , e ) 1
Rationale: "explanation : unit digit in the given product = unit digit in ( 4 * 2 * 6 * 7 ) = 6 answer : c"
Answer: c
Question (physics): if a truck is traveling at a constant rate of 72 kilometers per hour , how many seconds will it take the truck to travel a distance of 600 meters ? ( 1 kilometer = 1000 meters )
Options: a ) 18 , b ) 24 , c ) 30 , d ) 36 , e ) 48
Rationale: "speed = 72 km / hr = > 72,000 m / hr in one minute = > 72000 / 60 = 1200 meters in one sec = > 1200 / 60 = 20 meters time = total distance need to be covered / avg . speed = > 600 / 20 = 30 and hence the answer : c"
Answer: c
Question (general): the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 4 people , the cost per person would have been $ 40 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 300 , c ) $ 480 , d ) $ 500 , e ) $ 600
Rationale: "c for cost . p price per person . c = 3 * p c = 4 * p - 160 substituting the value of p from the first equation onto the second we get p = 160 . plugging in the value of p in the first equation , we get c = 480 . which leads us to answer choice c"
Answer: c
Question (general): a certain mixture of nuts consists of 5 parts almonds to 2 parts walnuts , by weight . what is the number of pounds of almonds in 150 pounds of the mixture ?
Options: a ) 107 , b ) 84 , c ) 40 , d ) 28 , e ) 20
Rationale: "almonds : walnuts = 5 : 2 total mixture has 7 parts in a 150 pound mixture , almonds are 5 / 7 ( total mixture ) = 5 / 7 * 150 = 107 pounds answer ( a )"
Answer: a
Question (physics): a , b and c , each working alone can complete a job in 6 , 8 and 12 days respectively . if all three of them work together to complete a job and earn $ 2340 , what will be c ' s share of the earnings ?
Options: a ) $ 1100 , b ) $ 520 , c ) $ 1080 , d ) $ 1170 , e ) $ 630
Rationale: "explanatory answer a , b and c will share the amount of $ 2340 in the ratio of the amounts of work done by them . as a takes 6 days to complete the job , if a works alone , a will be able to complete 1 / 6 th of the work in a day . similarly , b will complete 1 / 8 th and c will complete 1 / 12 th of the work . so , the ratio of the work done by a : b : c when they work together will be equal to 1 / 6 : 1 / 8 : 1 / 12 multiplying the numerator of all 3 fractions by 24 , the lcm of 6 , 8 and 12 will not change the relative values of the three values . we get 24 / 6 : 24 / 8 : 24 / 12 = 4 : 3 : 2 . i . e . , the ratio in which a : b : c will share $ 2340 will be 4 : 3 : 2 . hence , c ' s share will be 2 * 2340 / 9 = 520 . correct choice is ( b )"
Answer: b
Question (general): in the coordinate plane , points ( x , 1 ) and ( 5 , y ) are on line k . if line k passes through the origin and has slope 1 / 5 , then what are the values of x and y respectively ?
Options: a ) 4 and 1 , b ) 1 and 5 , c ) 5 and 1 , d ) 3 and 5 , e ) 5 and 3
Rationale: "line k passes through the origin and has slope 1 / 5 means that its equation is y = 1 / 5 * x . thus : ( x , 1 ) = ( 5 , 1 ) and ( 5 , y ) = ( 5,1 ) - - > x = 5 and y = 1 answer : c"
Answer: c
Question (gain): one fourth of a solution that was 13 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 25 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.13 + 25 * x = 100 * 0.16 - - > x = 0.25 . 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 25 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 × 30 wages of 1 man for 1 day = 21600 × 2 / 40 × 30 wages of 1 man for 25 days = 21600 × 2 × 25 / 40 × 30 number of men = 14400 / ( 21600 × 2 × 25 / 40 × 30 ) = 144 / ( 216 × 50 / 40 × 30 ) = 144 / 9 = 16 answer : option c
Answer: c
Question (probability): what is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 7 / 9
Rationale: "it has two vertices on sides , which do not make a diagonal but a side . . so remaining 3 vertices make diagonals . . . only the opposite vertex will make largest diagonal and other two smaller ones . . so prob = 2 / ( 2 + 1 ) = 2 / 3 answer : d"
Answer: d
Question (gain): what is the compound interest on rs : 30,000 for 4 months at the rate of 5 % per annum
Options: a ) 501.13 , b ) 502.13 , c ) 503.13 , d ) 504.13 , e ) 505.13
Rationale: it is monthly compound rate = 5 / 12 % per month 30000 * ( 1 + 5 / 1200 ) ^ 4 - 30000 = 503.13 answer : c
Answer: c
Question (physics): the speed of a car is 90 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 65 , e ) 15
Rationale: "s = ( 90 + 40 ) / 2 = 65 kmph answer : d"
Answer: d
Question (other): how many trailing zeroes does 53 ! + 54 ! have ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: 53 ! + 54 ! = 53 ! + 54 * 53 ! = 53 ! ( 1 + 54 ) = 53 ! * 55 number of trailing 0 s in 53 ! = number of 5 s in the expansion of 53 ! = 10 + 2 = 12 there is 1 more 5 in 55 . hence , total number of trailing 0 s = 12 + 1 = 13 answer ( b ) . in most cases , when we are adding multiple terms , all of which have trailing 0 s , the sum will have as many trailing 0 s as that in the lowest term . example : 20 + 2300 + 34210000 = 34212320 - > one 0 because lowest term 20 has one 0 . this case has an exception because of an additional 5 in 55 . answer is b
Answer: b
Question (gain): an empty fuel tank with a capacity of 208 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 82 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 208 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 208 - a gallons of fuel b is 0.16 ( 208 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 208 - a ) = 30 - - > a = 82 . answer : c ."
Answer: c
Question (general): 5020 − ( 502 ÷ 100.4 ) = ?
Options: a ) 15 , b ) 20 , c ) 5015 , d ) 25 , e ) 35
Rationale: "explanation : = 5020 − ( 502 / 1004 × 10 ) = 5020 − 5 = 5015 option c"
Answer: c
Question (general): the average of 10 numbers is calculated as 46 . it is discovered later on that while calculating the average , the number 65 was incorrectly read as 25 , and this incorrect number was used in the calculation . what is the correct average ?
Options: a ) 48 , b ) 50 , c ) 54 , d ) 66 , e ) 86
Rationale: "the total sum of the numbers should be increased by 40 . then the average will increase by 40 / 10 = 4 . the correct average is 50 . the answer is b ."
Answer: b
Question (general): a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent w should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "correct answer : c solution : c . we can set up equations for income before and after the wage reduction . initially , the employee earns w wage and works h hours per week . after the reduction , the employee earns . 8 w wage and works x hours . by setting these equations equal to each other , we can determine the increase in hours worked : wh = . 8 wx ( divide both sides by . 8 w ) 1.25 h = x we know that the new number of hours worked w will be 25 % greater than the original number . the answer is c ."
Answer: c