Cheukting/mathqa huggingface dataset:
Question (physics): p can lay railway track between two stations in 16 days . q can do the same job in 12 days . with the help of r , they completes the job in 4 days . how much days does it take for r alone to complete the work ?
Options: a ) 9 days , b ) 9 ( 3 / 5 ) days , c ) 11 1 / 5 days , d ) 13 days , e ) 13 1 / 7
Rationale: amount of work p can do in 1 day = 1 / 16 amount of work q can do in 1 day = 1 / 12 amount of work p , q and r can together do in 1 day = 1 / 4 amount of work r can do in 1 day = 1 / 4 - ( 1 / 16 + 1 / 12 ) = 3 / 16 – 1 / 12 = 5 / 48 = > hence r can do the job on 48 / 5 days = 9 ( 3 / 5 ) days b )
Answer: b
Question (gain): two men started from the same place walk at the rate of 10 kmph and 12 kmph respectively . what time will they take to be 20 km apart , if they walk in the same direction ?
Options: a ) 5 hours , b ) 10 hours , c ) 8 hours , d ) 10 hours , e ) 12 hours
Rationale: "to be 2 km apart they take 1 hour to be 10 km apart they take = 1 / 2 * 20 = 10 hours answer is b"
Answer: b
Question (physics): in a games hour 4 different types of players came to the ground ? cricket 16 , hokey 12 , football 18 , softball 13 . how many players are present in the ground ?
Options: a ) 70 , b ) 52 , c ) 62 , d ) 59 , e ) 50
Rationale: "total number of players = 16 + 12 + 18 + 13 = 59 answer is d"
Answer: d
Question (other): in a class of 69 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 54
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 69 54 + not = 69 not = 69 - 54 = 15 so answer is b"
Answer: b
Question (gain): the charge for a single room at hotel p is 50 percent less than the charge for a single room at hotel r and 20 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 50 % , b ) 60 % , c ) 75 % , d ) 80 % , e ) 90 %
Rationale: "p = 0.5 r = 0.8 g r = 0.8 g / 0.5 = 1.6 * g thus r is 60 % greater than g . the answer is b ."
Answer: b
Question (physics): laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 18 kmph and prasanna moves southward at a speed of 27 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 11 , b ) 50 , c ) 28 , d ) 45 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 18 kmph x 1 hr = 18 km total southward prasanna ' s distance = 27 kmph x 1 hr = 27 km total distance between prasanna and laxmi is = 18 + 27 = 45 km . answer : d"
Answer: d
Question (gain): a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 894 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 578
Rationale: "s . i . for 1 year = rs . ( 894 - 815 ) = rs . 79 . s . i . for 3 years = rs . ( 79 x 3 ) = rs . 237 . principal = rs . ( 815 - 237 ) = rs . 578 . answer : option e"
Answer: e
Question (physics): tom traveled the entire 80 miles trip . if he did the first 30 miles of at a constant rate 30 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 55 mph , b ) 50 mph , c ) 40 mph , d ) 60 mph , e ) 70 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 30 + 50 ) / ( ( 30 / 30 ) + ( 50 / 50 ) ) = 80 / 2 = 40 mph c"
Answer: c
Question (physics): there are 24 students in a seventh grade class . they decided to plant birches and roses at the school ' s backyard . while each girl planted 3 roses , every three boys planted 1 birch . by the end of the day they planted 2424 plants . how many birches and roses were planted ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 2 , e ) 9
Rationale: let xx be the number of roses . then the number of birches is 24 − x 24 − x , and the number of boys is 3 × ( 24 − x ) 3 × ( 24 − x ) . if each girl planted 3 roses , there are x 3 x 3 girls in the class . we know that there are 24 students in the class . therefore x 3 + 3 ( 24 − x ) = 24 x 3 + 3 ( 24 − x ) = 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 9 ( 24 − x ) = 3 ⋅ 24 x + 216 − 9 x = 72 x + 216 − 9 x = 72 216 − 72 = 8 x 216 − 72 = 8 x 1448 = x 1448 = x x = 18 x = 18 so , students planted 18 roses and 24 - x = 24 - 18 = 6 birches . answer : a
Answer: a
Question (general): having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 1.20 , b ) $ 1.50 , c ) $ 1.80 , d ) $ 2.00 , e ) $ 2.50
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 40 cents ( 4 / 15 ) x = 40 x = $ 1.50 the answer is b ."
Answer: b
Question (general): 3 / 4 of 5 / 7 of a number is greater than 2 / 3 of 4 / 7 of the same number by 26 . what is half of that number ?
Options: a ) 32 , b ) 78 , c ) 92 , d ) 84 , e ) 96
Rationale: "let no . be x 3 / 4 * 5 / 7 * x - 2 / 3 * 4 / 7 * x = 26 by further solving 15 x / 28 - 8 x / 21 = 26 13 x / 84 = 26 x = 168 we have to find x / 2 = 168 / 2 = 84 answer : d"
Answer: d
Question (general): robert left from a pvt company . management hold his salary rs . 15000 / - for one month . earlier robert earned a performance incentive rs . 7280 / - from company . but robert forgot that . after one month robert asked his salary and accountant gives rs . 18500 / - to him . what is the bonus amount given to robert ?
Options: a ) a ) 9500 , b ) b ) 12500 , c ) c ) 10780 , d ) d ) 10500 , e ) e ) 8600
Rationale: total salary = rs . 15000 / - incentive earned earlier = 7280 / - balance salary = 15000 - 7280 = 7720 paid amount = 18500 / - bonus = 18500 - 7720 = 10780 / - answer is c
Answer: c
Question (physics): if a and b run on a circular path in opposite directions of constant speeds with different velocities from p and q . first time they meet 800 mts away from p and second time they meet 700 mts away from p , what is the lenght of the circular path .
Options: a ) 2300 mtrs , b ) 2400 mtrs , c ) 2500 mtrs , d ) 2600 mtrs , e ) 2700 mtrs
Rationale: 800 + 800 + 700 = 2300 mtrs answer : a
Answer: a
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 11 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.8 %
Rationale: "let us suppose the interest rate last year is x , this year the interest rate is increased by 10 % . hence this year interest rate would be 1.1 * x . setting up the equation - - - - - > 11 = 1.1 * x x = 10 % answer : d"
Answer: d
Question (geometry): the cost of the paint is rs . 36.50 per kg . if 1 kg of paint covers 16 squares feet , how much will it cost to paint outside of a cube having 8 feet each side ?
Options: a ) rs . 692 , b ) rs . 768 , c ) rs . 876 , d ) rs . 972 , e ) none
Rationale: "solution surface area of the cube = ( 6 × 82 ) sq . ft = 384 sq . ft . quantity of paint required = ( 384 / 16 ) kg ‹ = › 24 kg . cost of painting = rs . ( 36.50 × 24 ) = rs . 876 . answer c"
Answer: c
Question (physics): express a speed of 84 kmph in meters per second ?
Options: a ) 13.33 mps , b ) 23.33 mps , c ) 33.33 mps , d ) 25.33 mps , e ) 43.33 mps
Rationale: "84 * 5 / 18 = 23.33 mps answer : b"
Answer: b
Question (gain): a shopkeeper sells 300 metres of cloth for rs . 9000 at a loss of rs . 6 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 58 , c ) s . 36 , d ) s . 46 , e ) s . 13
Rationale: "sp per metre = 9000 / 300 = rs . 30 loss per metre = rs . 6 cp per metre = 30 + 6 = rs . 36 answer : c"
Answer: c
Question (other): the h . c . f . of two numbers is 42 and the other two factors of their l . c . m . are 12 and 14 . the larger of the two numbers is :
Options: a ) 588 , b ) 642 , c ) 567 , d ) 344 , e ) 789
Rationale: "explanation : clearly , the numbers are ( 42 x 12 ) and ( 42 x 14 ) . { \ color { blue } \ therefore } larger number = ( 42 x 14 ) = 588 . answer : a ) 588"
Answer: a
Question (general): jack , jill , and sandy each have one try to make a basket from half court . if their individual probabilities of making the basket are 1 / 6 , 1 / 7 , and 1 / 8 respectively , what is the probability that all three will make a basket ?
Options: a ) 1 / 336 , b ) 5 / 336 , c ) 11 / 336 , d ) 1 / 168 , e ) 1 / 84
Rationale: "the probability that all three will make a basket is 1 / 6 * 1 / 7 * 1 / 8 = 1 / 336 . the answer is a ."
Answer: a
Question (general): how much is 75 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 67 , c ) 10 , d ) 12 , e ) 66
Rationale: "( 75 / 100 ) * 40 – ( 4 / 5 ) * 25 = 10 answer : c"
Answer: c
Question (general): a number is doubled and 5 is added . if the resultant is trebled , it becomes 105 . what is that number ?
Options: a ) 12 , b ) 29 , c ) 27 , d ) 15 , e ) 99
Rationale: "explanation : let the number be x . therefore , 3 ( 2 x + 5 ) = 105 6 x + 15 = 105 6 x = 90 x = 15 answer : d"
Answer: d
Question (general): 10 play kabadi , 35 play kho kho only , 5 play both gmaes . then how many in total ?
Options: a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
Rationale: "10 play kabadi = > n ( a ) = 10 , 5 play both gmaes . = > n ( anb ) = 5 35 play kho kho only , = > n ( b ) = n ( b only ) + n ( anb ) = 35 + 5 = 40 total = > n ( aub ) = n ( a ) + n ( b ) - n ( anb ) = 10 + 40 - 5 = 45 answer : e"
Answer: e
Question (general): if the average of 12 x and 8 y is greater than 200 , and x is twice y , what is the least integer value of x ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 25 , e ) 35
Rationale: substitution can be used in the following way : always start with the equation : x = 2 y . it is more straight forward to manage as compared to the inequality . substitute y = x / 2 , not the other way because you need to find the minimum value of x . so you can get rid of y . now go on to the inequality . so 8 y = 8 x / 2 = 4 x now average of 12 x and 4 x is greater than 200 . average of 12 x and 4 x is 8 x . so , 8 x > 200 x > 25 answer : d
Answer: d
Question (gain): i sold a book at a profit of 10 % . had i sold it for $ 150 more , 15 % would have been gained . find the cost price ?
Options: a ) $ 2000 , b ) $ 2500 , c ) $ 3000 , d ) $ 3120 , e ) $ 1540
Rationale: "115 % of cost - 110 % of cost = $ 150 5 % of cost = $ 150 cost = 150 * 100 / 5 = $ 3000 answer is c"
Answer: c
Question (general): in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 7 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: 8 / 7 * 24 = 27.4 the answer is b .
Answer: b
Question (gain): add 8 % of 24 and 10 % of 40 .
Options: a ) 9.5 , b ) 10.5 , c ) 5.5 , d ) 5.9 , e ) 8.5
Rationale: "8 % of 24 + 10 % of 40 24 * 8 / 100 + 40 * 10 / 100 1.9 + 4 = 5.9 answer d"
Answer: d
Question (gain): in a certificate by mistake a candidate gave his height as 20 % more than actual height . in the interview panel , he clarified that his height was 5 feet 5 nches . find the % correction made by the candidate from his stated height to his actual height ?
Options: a ) 13 , b ) 20 , c ) 30 , d ) 43 , e ) 50
Rationale: "his height was = 5 feet 5 inch = 5 + 60 = 65 inch . required % correction = 65 * ( 1.20 - 1 ) = 13 a"
Answer: a
Question (physics): if 2 men or 3 women can reap a field in 12 days how long will 4 men and 5 women take to reap it ?
Options: a ) 12 / 16 , b ) 11 / 36 , c ) 14 / 24 , d ) 18 / 36 , e ) 2 / 24
Rationale: "explanation : 2 men reap 1 / 12 field in 1 day 1 man reap 1 / ( 2 x 12 ) 3 women reap 1 / 12 field in 1 day 1 woman reap 1 / ( 12 x 3 ) 4 men and 5 women reap ( 4 / ( 2 x 12 ) + 5 / ( 3 x 12 ) = 11 / 36 in 1 day 4 men and 5 women will reap the field in 11 / 36 days answer : option b"
Answer: b
Question (general): one pack of cake mix is being stirred before being poured into two separate baking trays . the first tray can hold a certain amount of cups of the mix while the other holds 20 cups less than the first . if the total number of cups poured is 500 , how many cups of batter does the second tray hold ?
Options: a ) 250 , b ) 260 , c ) 500 , d ) 280 , e ) 240
Rationale: tray one as t 1 and tray two as t 2 . t 2 = t 1 - 20 cups as equation a . t 1 + t 2 = 500 cups in total as equation b . substitute equation a into equation b , resulting in t 1 + ( t 1 - 20 ) = 500 transpose like terms , 2 * t 1 = 500 + 20 ( 2 * t 1 ) / 2 = 520 / 2 t 1 = 260 , thus t 2 is t 1 less 20 cups , which is 240 cups . answer is e .
Answer: e
Question (physics): a , b and c can do a work in 7 , 14 and 21 days respectively . they completed the work and got $ 242 . what is the share of c ?
Options: a ) $ 25 , b ) $ 48 , c ) $ 44 , d ) $ 49 , e ) $ 40
Rationale: "c $ 44 the ratio of their working rates = 1 / 7 : 1 / 14 : 1 / 21 = 6 : 3 : 2 . since , they work together , the share of c = 2 / 11 * 242 = $ 44"
Answer: c
Question (general): a certain no . when divided by 95 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 95 + 25 = 120 / 15 = 8 ( remainder ) d"
Answer: d
Question (gain): during a sale of 20 % on everything in a store , a kid is successful in convincing the store manager to give him 20 candies for the discounted price of 14 candies . the store still makes a profit of 10 % on this sale . what is the mark up percentage on each candy ?
Options: a ) 100 % , b ) 80 % , c ) 75 % , d ) 66 + 2 / 3 % , e ) 55 %
Rationale: "hi akhil , i can share the way i solved it . . let ' s say marked price = m so , there ' s a discount of 20 % on m so , new s . p . = 80 % of m now , the child convinces the owner to sell 20 candies for the price of 14 candies . let ' s say each candy after discount is 1 $ . so , s . p . of 20 candies = 20 $ . the child bought it for 14 $ so , he got a discount of 6 / 20 * 100 = 30 % so , the latest s . p . = 70 % of 80 % of m = 0.7 * 0.8 m now , we are given that the shopkeeper still makes a profit of 12 % . so we have , 0.7 * 0.8 * m = 1.12 c . p so , we get , m = 2 c . p . i . e . marked price was kept 100 % above c . p . c"
Answer: c
Question (physics): a and b are two multiples of 14 , and q is the set of consecutive integers between a and b , inclusive . if q contains 14 multiples of 14 , how many multiples of 7 are there in q ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "halfway between the multiples of 14 , there will be another multiple of 7 . the total number of multiples of 7 is 14 + 13 = 27 . the answer is b ."
Answer: b
Question (physics): the length of a train and that of a platform are equal . if with a speed of 180 k / hr , the train crosses the platform in one minute , then the length of the train ( in meters ) is ?
Options: a ) 1500 , b ) 266 , c ) 299 , d ) 750 , e ) 261
Rationale: "speed = [ 180 * 5 / 18 ] m / sec = 50 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x meters . then , 2 x / 60 = 50 = > x = 50 * 60 / 2 = 1500 answer : a"
Answer: a
Question (gain): running at the same constant rate , 8 identical machines can produce a total of 240 pens per minute . at this rate , how many pens could 5 such machines produce in 5 minutes ?
Options: a ) 114 , b ) 108 , c ) 192 , d ) 750 , e ) 777
Rationale: "let ' s take the approach that uses the answer choices to eliminate wasted time . 240 / 8 = 30 pens per minute per machine . 5 machines = 150 per minute . 5 minutes worth = 750 pens . looking at the answers it is clear . . . we can only choose ( d ) . the correct answer is d ."
Answer: d
Question (geometry): the product of the squares of two positive integers is 81 . how many pairs of positive integers satisfy this condition ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "ans : c - 2 pairs ( x ˆ 2 ) ( y ˆ 2 ) = 81 [ square root both sides ] xy = 9 9 = 1 x 9 , 9 x 1 , 3 x 3 cancel the repeats this leaves us with exactly 2 options . hence , c"
Answer: c
Question (general): before 2 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 64
Rationale: a - 2 = 4 ( b - 2 ) - - > a - 4 b = - 6 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 14 - - > a = 3 ( 18 ) = 50 a - b = 50 - 14 = 36 answer : a
Answer: a
Question (general): how many integers between 500 and 1000 are there such that their unit digit is even ?
Options: a ) 250 , b ) 150 , c ) 500 , d ) 100 , e ) 200
Rationale: 500 numbers between - 500 and 1000 out of which half would be even , half odd . number of even unit digit number = 250 . correct option is a
Answer: a
Question (general): a man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses . next year his income increases by 50 % but his savings increase by 100 % . if his total expenditure in 2 years is double his expenditure in 1 st year , what % age of his income in the first year did he save ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "1 st year income = i 1 st year savings = s 1 st year expense = e 1 2 nd year income = 1.5 i 2 nd year savings = 2 s ( 100 % increase ) 2 nd year expense = e 2 e 1 + e 2 = 2 e 1 e 2 = e 1 that means expenses are same during both years . with increase of 50 % income the savings increased by 100 % . or s = . 5 i or s = 50 % of income c is the answer"
Answer: c
Question (gain): the cost price of 24 articles is the same as the selling price of x articles . if the profit is 20 % , what is x ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "let the cost price = y the cost price of 24 articles = 24 y the selling price of x articles = 1.20 y * x 1.20 y * x = 24 y x = 24 / 1.2 = 20 the answer is d ."
Answer: d
Question (general): on increasing the number of lines in a page by 110 , they become 240 . what is the % of increase in the no . of lines in the page ?
Options: a ) 20 % , b ) 305 , c ) 50 % , d ) 55 % , e ) 84.6 %
Rationale: "explanation : number of pages increased = 110 now , the number of pages of book = 240 number of pages of the books before increase = 240 – 110 = 130 % increase in the number of pages in the book = 110 / 130 x 100 % = 84.6 % e"
Answer: e
Question (gain): an empty fuel tank with a capacity of 200 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 18 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 350
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 18 gallons then 0.12 a + 0.16 ( 200 - a ) = 18 - - > a = 350 . answer : e ."
Answer: e
Question (gain): a discount electronics store normally sells all merchandise at a discount of 10 percent to 40 percent off the suggested retail price . if , during a special sale , an additional 5 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 500 before any discount ?
Options: a ) $ 130.00 , b ) $ 285.00 , c ) $ 200.00 , d ) $ 258.00 , e ) $ 210.00
Rationale: "original price : 500 $ max first discount = - 40 % thus : 500 â ˆ — ( 1 â ˆ ’ 40 / 100 ) = 300 second discount on the discounted price = - 20 % thus : 300 â ˆ — ( 1 â ˆ ’ 5 / 100 ) = 285 answer b ."
Answer: b
Question (general): what is the total number of d integers between 100 and 200 that are divisible by 3 ?
Options: a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29
Rationale: yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33
Answer: a
Question (physics): 10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 6 days , b ) 7 days , c ) 8 days , d ) 9 days , e ) none of these
Rationale: explanation : 1 woman ' s 1 day ' s work = 1 / 70 1 child ' s 1 day ' s work = 1 / 140 5 women and 10 children 1 day work = ( 570 + 10140 ) = 17 so 5 women and 10 children will finish the work in 7 days answer : b
Answer: b
Question (general): the average weight of a group of boys is 30 kg . after a boy of weight 38 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 ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 7
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 38 kg joins the group , total weight of boys = 30 x + 38 so 30 x + 38 = 31 ( x + 1 ) = > x = 7 . answer : e"
Answer: e
Question (general): the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 20 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "let the output of a factory is 100 first , increased by 10 % = 110 due to holiday rush , it increase by 20 % = 110 + 22 = 132 132 - ( x / 100 * 132 ) = 100 24.24 answer : b"
Answer: b
Question (physics): maria sold 10 kg of apples in her first hour at the market , but only 2 kg of apples in the second hour . on average , how many kg of apples did she sell in two hours at the market ?
Options: a ) 6 kg , b ) 5 kg , c ) 12 kg , d ) 24 kg , e ) 20 kg
Rationale: ( 10 kg + 2 kg ) / 2 = 6 kg correct answer is : a
Answer: a
Question (physics): a can finish a piece of work in 15 days . b can do it in 30 days . they work together for 6 days and then a goes away . in how many days will b finish the work ?
Options: a ) 11 days , b ) 12 days , c ) 14 days , d ) 10 days , e ) 15 days
Rationale: "6 / 15 + ( 6 + x ) / 30 = 1 = > x = 12 days answer : b"
Answer: b
Question (general): find the largest 5 digit number which is exactly divisible by 88 ?
Options: a ) 98765 , b ) 98907 , c ) 99944 , d ) 99954 , e ) 99968
Rationale: "largest 5 digit number is 99999 after doing 99999 ÷ 88 we get remainder 31 hence largest 5 digit number exactly divisible by 88 = 99999 - 31 = 99968 e"
Answer: e
Question (general): a club wants to mix 15 pounds of candy worth $ 8.00 per pound with candy worth $ 5.00 per pound to reduce the cost of the mixture to $ 6.00 per pound . how many pounds of the $ 5.00 per pound candy should be used ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "let number of pounds of 5 $ candy to be used be w 6 = ( 15 * 8 + 5 * w ) / ( 15 + w ) = > 90 + 6 w = 120 + 5 w = > w = 30 answer b"
Answer: b
Question (general): 300 + 5 × 8 = ?
Options: a ) 820 , b ) 340 , c ) 420 , d ) 209 , e ) none of these
Rationale: 300 + 5 × 8 = ? or , ? = 300 + 40 = 340 answer b
Answer: b