regisss/math_qa huggingface dataset:
Problem: p and q are the only two applicants qualified for a short - term research project that pays 480 dollars in total . candidate p has more experience and , if hired , would be paid 50 percent more per hour than candidate q would be paid . candidate q , if hired , would require 10 hours more than candidate p to do the job . candidate p ’ s hourly wage is how many dollars greater than candidate q ’ s hourly wage ?
Options: a ) $ 5 , b ) $ 8 , c ) $ 11 , d ) $ 14 , e ) $ 17
Rationale: "let q ' s hourly wage be x , then p ' s hourly wage is 1.5 x let t be the number of hours that q needs , then p needs t - 10 hours to do the job . since they both are paid an equal total amount of $ 480 : x * t = 1.5 x * ( t - 10 ) t = 30 hours and q ' s hourly wage is 480 / 30 = $ 16 p ' s hourly wage is 480 / ( t - 10 ) = $ 24 which is $ 8 per hour more . the answer is b ."
Answer: b
Problem: the area of the largest circle that can be drawn inside a rectangle with sides 18 cm by 14 cm is
Options: a ) 237
b ) 154
c ) 2376
d ) 198
e ) 171
Rationale: explanation : the diameter is equal to the shortest side of the rectangle . so radius = 14 / 2 = 7 cm . answer : b ) 154
Answer: b
Problem: what profit percent is made by selling an article at a certain price , if by selling at 1 / 3 rd of that price , there would be a loss of 20 % ?
Options: a ) 140 % , b ) 29 % , c ) 70 % , d ) 27 % , e ) 28 %
Rationale: "sp 2 = 1 / 3 sp 1 cp = 100 sp 2 = 80 1 / 3 sp 1 = 80 sp 1 = 240 100 - - - 240 = > 140 % answer : a"
Answer: a
Problem: a certain company had a total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries last year . if the company employed 420 people , what was the average employee salary ?
Options: a ) $ 20,000 , b ) $ 25,000 , c ) $ 35,000 , d ) $ 40,000 , e ) $ 45,000
Rationale: "given : total annual expenditure of 1.89 ∗ 10 ^ 7 on employee salaries total employees = 420 observe that 420 * 4 = 1890 therefore try to bring the numerator in terms of 1890 average salary = ( 1890 * 10 ^ 4 ) / 420 = 4.5 * 10 ^ 4 = 45,000 option e"
Answer: e
Problem: the timing of a college is from 12 p . m to 4.00 p . m . five lectures are held in the given duration and a break of 5 minutes after each lecture is given to the students . find the duration of each lecture .
Options: a ) 52 minutes , b ) 45 minutes , c ) 30 minutes , d ) 48 minutes , e ) 44 minutes
Rationale: "explanation : total time a student spends in college = 4 hours 00 minutes = 240 minutes as there are 5 lectures , the number of breaks between lectures is 4 . total time of the break = 20 minutes hence , the duration of each lecture is = ( 240 â € “ 20 ) / 5 = 44 minutes answer e"
Answer: e
Problem: a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 4 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 15 , d ) 18 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 4 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 4 ) = 0.08 t - - > 60 + 6 ( t - 4 ) = 8 t - - > t = 18 . answer : d ."
Answer: d
Problem: three solid cubes of sides 1 cm , 6 cm and 8 cm are melted to form a new cube . find the surface area of the cube so formed
Options: a ) 486
b ) 366
c ) 299
d ) 278
e ) 1888
Rationale: explanation : volume of new cube = = edge of new cube = = 9 cm surface area of the new cube = ( 6 x 9 x 9 ) = 486 answer : a ) 486
Answer: a
Problem: a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 12 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 21 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "there is a one step calculation method too . it requires more thought but is faster . the man takes 10 % more than what he pays for . so if he claims to take 100 pounds , he pays $ 100 but he actually takes 110 pounds for which he will take from the customer $ 110 . hence , in effect , there is a 10 % mark up . while selling , he sells 20 % less . this means , he claims to sell 100 pounds and gets $ 100 but actually sells only 80 pounds and should have got only $ 80 for it . so this is again a mark up of $ 20 on $ 80 which is 25 % . but he also sells at 12 % less ( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 22 / 25 = ( 1 + p % ) profit % = 21 % b"
Answer: b
Problem: in a recent head - to - head run - off election , 12,000 absentee ballets were cast . 1 / 2 of the absentee ballets were thrown out and 1 / 2 of the remaining absentee ballets were cast for candidate a . how many absentee votes did candidate b receive ?
Options: a ) 2,000 , b ) 3,000 , c ) 6,000 , d ) 8,000 , e ) 9,000
Rationale: "1 / 2 * 1 / 2 ( total absentee votes ) = 1 / 4 ( total votes ) = 1 / 4 * 12000 = 3000 answer is b"
Answer: b
Problem: the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is
Options: a ) rs . 500 , b ) rs . 515 , c ) rs . 550 , d ) rs . 600 , e ) none
Rationale: "solution 110 % of s . p . = 616 ‹ = › s . p . = ( 616 x 100 / 110 ) . ‹ = › rs . 560 . c . p . ‹ = › rs . ( 100 / 112 x 560 ) ‹ = › rs . 500 . answer a"
Answer: a
Problem: a man swims downstream 45 km and upstream 25 km taking 5 hours each time , what is the speed of the man in still water ?
Options: a ) 17 , b ) 24 , c ) 7 , d ) 24 , e ) 20
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - 5 us = 5 ? - - - - 1 m = ? m = ( 9 + 5 ) / 2 = 14 / 2 = 7 answer : c"
Answer: c
Problem: the length of a bridge in meters , which a train 90 - meters long and traveling at 45 km / hr can cross in 30 seconds is ?
Options: a ) 145 , b ) 215 , c ) 265 , d ) 285 , e ) 375
Rationale: 45 km / h = 45000 m / 3600 s = 12.5 m / s in 30 seconds , the train can go 30 ( 12.5 ) = 375 meters let x be the length of the bridge . x + 90 = 375 meters x = 285 meters the answer is d .
Answer: d
Problem: if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b .
Answer: b
Problem: a couple decides to have 4 children . if they succeed in having 4 children and each child is equally likely to be a boy or a girl , what is the probability that they will have exactly 2 girls and 2 boys ?
Options: a ) 3 / 8 , b ) 1 / 4 , c ) 3 / 16 , d ) 1 / 8 , e ) 1 / 16
Rationale: "no of ways of getting p ( ggbb ) is 4 ! / 2 ! * 2 ! ; total no of ways is 2 ^ n = 2 ^ 4 = 16 ; 6 / 16 = 3 / 8 ; we can consider this question to a coin that is flipped for 4 times . what is the probability of getting exactly two heads . p ( all out comes ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 ; p ( favorable outcomes ) = 4 ! / ( 2 ! * 2 ! ) = 6 / 16 = 3 / 8 ; answer : a"
Answer: a
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 3 x km .
Options: a ) 18 kmph , b ) 17 kmph , c ) 24 kmph , d ) 19 kmph , e ) 12 kmph
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 3 x / ( x / 8 ) = 24 kmph answer : c"
Answer: c
Problem: the avg weight of a , b & c is 70 kg . if d joins the group , the avg weight of the group becomes 70 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 68 kg . what is the weight of a ?
Options: a ) 81 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 70 = 210 a + b + c + d = 4 * 70 = 280 - - - - ( i ) so , d = 70 & e = 70 + 3 = 73 b + c + d + e = 68 * 4 = 272 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 280 – 272 = 8 a = e + 8 = 73 + 8 = 81 answer : a"
Answer: a
Problem: john paid a sum of money for purchasing 30 pens , which he recovered in full when he sold 20 of them . what was his percentage of profit or loss per pen ?
Options: a ) 50 % , b ) 60 % , c ) 40 % , d ) 30 % , e ) 45 %
Rationale: "a 50 % if the sum he paid whilst purchasing 30 pens = a , then the cost price of each pen = a / 30 . since the amount he got whilst selling 20 pens is also = a then the selling price of each pen = a / 20 . since selling price > cost price , he made a profit . profit per pen = selling price - cost price = a / 20 - a / 30 = a / 60 . profit percentage per pen = profit per pen / cost per pen x 100 = ( a / 60 ) / ( a / 30 ) x 100 = 50 %"
Answer: a
Problem: 1 / 0.025 is equal to
Options: a ) 25.5 , b ) 2.5 , c ) 40 , d ) . 25 , e ) none of these
Rationale: "explanation : 1 / 0.025 = ( 1 * 1000 ) / 25 = 1000 / 25 = 40 option c"
Answer: c
Problem: find the circumference and area of radius 4 cm .
Options: a ) 24 cm ² , b ) 44 cm ² , c ) 50 cm ² , d ) 84 cm ² , e ) 94 cm ²
Rationale: "area of circle = π r ² = 22 / 7 × 4 × 4 cm ² = 50 cm ² answer : c"
Answer: c
Problem: a train covers a distance of 18 km in 3 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 370 , b ) 380 , c ) 390 , d ) 400 , e ) 410
Rationale: "speed = ( 18 / 3 * 60 ) km / hr = ( 360 * 5 / 18 ) m / sec = 100 m / sec . length of the train = 100 * 4 = 400 m . answer : option d"
Answer: d
Problem: a merchant sells an item at a 20 % discount , but still makes a gross profit of 25 percent of the cost . what percent of the cost would the gross profit on the item have been if it had been sold without the discount ?
Options: a ) 20 % , b ) 40 % , c ) 56.25 % , d ) 60 % , e ) 75 %
Rationale: "original sp = x cost = c current selling price = . 8 x ( 20 % discount ) . 8 x = 1.5 c ( 25 % profit ) x = 1.25 / . 8 * c x = 12.5 / 8 c original selling price is 1.5625 c which is 56.25 % profit answer c"
Answer: c
Problem: evaluate : | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | =
Options: a ) 49 , b ) 55 , c ) 69 , d ) 70 , e ) 82
Rationale: "according to order of operations , inner brackets first . hence | 4 - 8 ( 3 - 12 ) | - | 5 - 11 | = | 4 - 8 * ( - 9 ) | - | 5 - 11 | according to order of operations , multiplication within absolute value signs ( which may be considered as brackets when it comes to order of operations ) next . hence = | 4 + 72 | - | 5 - 11 | = | 76 | - | - 6 | = 76 - 6 = 70 correct answer d ) 70"
Answer: d
Problem: how much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 50 sec , b ) 26 sec , c ) 80 sec , d ) 82 sec , e ) 81 sec
Rationale: the distance to be covered = sum of their lengths = 200 + 300 = 500 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 500 / 10 = 50 sec . answer : a
Answer: a
Problem: a train covers a distance of 36 km in 12 min . if it takes 7 sec to pass a telegraph post , then the length of the train is ?
Options: a ) 330 , b ) 340 , c ) 350 , d ) 360 , e ) 370
Rationale: "speed = ( 36 / 12 * 60 ) km / hr = ( 180 * 5 / 18 ) m / sec = 50 m / sec . length of the train = 50 * 7 = 350 m . answer : option c"
Answer: c
Problem: a sum of money deposited at c . i . amounts to rs . 2420 in 2 years and to rs . 3146 in 3 years . find the rate percent ?
Options: a ) 11 , b ) 30 , c ) 28 , d ) 24 , e ) 82
Rationale: "explanation : 2420 - - - 726 100 - - - ? = > 30 % answer : option b"
Answer: b
Problem: the rate of spin of a certain gyroscope doubled every 10 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 800 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 3 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 9 times . 2 ^ 9 * x = 800 x = ( 2 ^ 5 * 25 ) / 2 ^ 9 = 25 / 16 the answer is d .
Answer: d
Problem: if i equals the sum of the even integers from 2 to 224 , inclusive , and k equals the sum of the even integers from 8 to 80 , inclusive , what is the value of i - k ?
Options: a ) 11028 , b ) 14172 , c ) 14284 , d ) 14015 , e ) 14397
Rationale: use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 224 - 2 ) / 2 ] + 1 = 112 and [ ( 80 - 8 ) / 2 ] + 1 = 37 mean of integers = ( 224 + 2 ) / 2 = 113 and ( 80 + 8 ) / 2 = 44 sum of integers = ( 112 * 113 ) = 12656 and ( 37 * 44 ) = 1628 thus their difference ( i - k ) = 12656 - 1628 = 11028 answer : a
Answer: a
Problem: if 25 % of x is 15 less than 12 % of 1500 , then x is ?
Options: a ) 660 , b ) 738 , c ) 837 , d ) 840 , e ) 83
Rationale: "25 % of x = x / 4 ; 12 % of 1500 = 12 / 100 * 1500 = 180 given that , x / 4 = 180 - 15 = > x / 4 = 165 = > x = 660 . answer : a"
Answer: a
Problem: evaluate : 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = . . . .
Options: a ) 3 , b ) 33 , c ) 43 , d ) 23 , e ) 13
Rationale: according to order of operations , inner brackets first where 6 × 4 ÷ 3 is first calculated since it has a multiplication and a division . 6 × 4 ÷ 3 = 24 ÷ 3 = 8 hence 11 + sqrt ( - 4 + 6 × 4 ÷ 3 ) = 11 + sqrt ( - 4 + 8 ) = 11 + sqrt ( 4 ) = 11 + 2 = 13 correct answer is e ) 13
Answer: e
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 800,000 ?
Options: a ) 60 , b ) 100 , c ) 160 , d ) 240 , e ) 300
Rationale: "the first digit and last digit are the same so the only possibility is 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 1 * 10 * 10 = 100 the answer is b ."
Answer: b
Problem: a trader sold an item at a loss of 18 % . if he had increased the price by $ 25 he would have made a gain of 5 % . what is the cost price of the item ?
Options: a ) $ 414.78 , b ) $ 424.78 , c ) $ 534.78 , d ) $ 434.78 , e ) $ 435.78
Rationale: let c . p . be $ x then 105 % of x - 82 % of x = 100 23 % of x = 100 23 / 100 * x = 100 23 x = 10000 x = 434.78 answer is d
Answer: d
Problem: if 3 women can color 180 m long cloth in 2 days , then 5 women can color 300 m long cloth in ?
Options: a ) 2 days , b ) 3 days , c ) 5 days , d ) 1 day , e ) 4 days
Rationale: "the length of cloth painted by one woman in one day = 180 / 3 × 2 = 30 m no . of days required to paint 300 m cloth by 5 women = 300 / 5 × 30 = 2 days answer : a"
Answer: a
Problem: if $ 5,000 is invested in an account that earns 6 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 6 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "ans a solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.06 / 2 ) ^ 2 = 5406 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5406 - 5400 = 6 $ a"
Answer: a
Problem: a train with 1200 m crosses a tree in 120 sec , how much time will i take to pass a platform 700 m long ?
Options: a ) 150 sec , b ) 130 sec , c ) 190 sec , d ) 200 sec , e ) 100 sec
Rationale: s = 1200 / 120 s - 10 m / sec total length = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer c
Answer: c
Problem: the area of a circle is added to its diameter , and the circumference is then subtracted from this total , the result is 10 . what is the radius of the circle ?
Options: a ) 2 * pi
b ) pi
c ) 2
d ) 4 * pi
e ) 4
Rationale: the equation is ; diameter + area - circumference = d + a - c = d + pi * r ^ 2 - 2 * pi * r = 2 r + pi * r ( r - 2 ) . by plugging in the answers we can test the answers quickly ; then , 4 is the only possible answer . answer : e
Answer: e
Problem: a circular well with a diameter of 2 metres , is dug to a depth of 8 metres . what is the volume of the earth dug out ?
Options: a ) 32 m 3 , b ) 25.1 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) none
Rationale: "solution volume = π r 2 h ‹ = › ( 22 / 7 × 1 × 1 × 8 ) m 3 ‹ = › 25.1 m 3 . answer b"
Answer: b
Problem: a man can row upstream at 5 kmph and downstream at 25 kmph , and then find the speed of the man in still water ?
Options: a ) 15 , b ) 77 , c ) 30 , d ) 88 , e ) 34
Rationale: "us = 5 ds = 25 m = ( 5 + 25 ) / 2 = 15 answer : a"
Answer: a
Problem: sum of 49 odd numbers is ?
Options: a ) 2398 , b ) 2399 , c ) 2400 , d ) 2401 , e ) 2402
Rationale: sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 49 odd numbers = 49 ^ 2 = 2401 answer : d
Answer: d
Problem: a walks at 30 kmph and 30 hours after his start , b cycles after him at 40 kmph . how far from the start does b catch up with a ?
Options: a ) 1200 km , b ) 1500 km , c ) 2000 km , d ) 2500 km , e ) 3600 km
Rationale: "suppose after x km from the start b catches up with a . then , the difference in the time taken by a to cover x km and that taken by b to cover x km is 30 hours . x / 30 - x / 40 = 30 x = 3600 km answer is d"
Answer: d
Problem: one side of a rectangular field is 16 m and one of its diagonal is 18 m . find the area of the field .
Options: a ) 100 , b ) 120 , c ) 150 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 18 ) 2 - ( 16 ) 2 = √ 324 - 256 = √ 68 = 8.2 m . ∴ area = ( 16 x 8.2 ) m 2 = 131.2 m 2 . answer e"
Answer: e
Problem: the product of x and y is a constant . if the value of x is increased by 20 % , by what percentage must the value of y be decreased ?
Options: a ) 16.66 % , b ) 33.33 % , c ) 44.44 % , d ) 55.55 % , e ) 19.92 %
Rationale: "x * y = constt . let x = y = 100 in beginning i . e . x * y = 100 * 100 = 10000 x ( 100 ) - - - becomes - - - > 1.2 x ( 120 ) i . e . 120 * new ' y ' = 10000 i . e . new ' y ' = 10000 / 120 = 83.33 i . e . y decreases from 100 to 83.33 i . e . decrease of 16.66 % answer : option a"
Answer: a
Problem: if 12 men or 20 women can do a piece of work in 27 days , then in how many days can 9 men and 12 women together do the work ?
Options: a ) 10 days , b ) 30 days , c ) 20 days , d ) 80 days , e ) 40 days
Rationale: "c 20 days given that 12 m = 20 w = > 3 m = 5 w 9 men + 12 women = 15 women + 12 women = 27 women 20 women can do the work in 27 days . so , 27 women can do it in ( 20 * 27 ) / 27 = 20 days ."
Answer: c
Problem: how many trucks are there if each truck carrying 70 packages and total of 490 packages ?
Options: a ) a ) 7 , b ) b ) 6 , c ) c ) 9 , d ) d ) 11 , e ) e ) none of the above
Rationale: sol . total packages 490 each truck carries 70 packages = 490 / 70 = 7 answer : a
Answer: a
Problem: calculate 42120 ÷ ? = 195
Options: a ) 212 , b ) 219 , c ) 217 , d ) 213 , e ) 216
Rationale: "answer let 42120 / x = 195 then x = 42120 / 195 = 216 option : e"
Answer: e
Problem: the average of 6 observations is 14 . a new observation is included and the new average is decreased by 1 . the seventh observation is ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 7
Rationale: "let seventh observation = x . then , according to the question we have = > ( 84 + x ) / 7 = 13 = > x = 7 . hence , the seventh observation is 7 . answer : e"
Answer: e
Problem: find the value of ( 50 + 20 / 90 ) × 90
Options: a ) 2520 , b ) 3520 , c ) 4520 , d ) 1520 , e ) 1750
Rationale: "( 4500 + 20 ) / 90 * 90 = 4520 answer : c"
Answer: c
Problem: if a and b are positive real numbers , and a ^ 3 + b ^ 3 = 20 , then the greatest possible value of a is between :
Options: a ) 0 and 3 , b ) 3 and 4 , c ) 4 and 5 , d ) 5 and 7 , e ) 7 and 9
Rationale: "if a > 3 , then a ^ 3 + b ^ 3 > 20 . the answer is a ."
Answer: a
Problem: the ages of 2 persons differ by 32 years . if 9 years ago the elder one be 5 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 42.5 , c ) 45 , d ) 49 , e ) 47.9
Rationale: "age of the younger person = x age of the elder person = x + 32 5 ( x - 9 ) = x + 32 - 9 x = 17 age of elder person = 17 + 32 = 49 answer is d"
Answer: d
Problem: what is the greatest possible length which can be used to measure exactly the lengths 18 m , 40 m and 6 m 50 cm ?
Options: a ) 20 cm , b ) 23 cm , c ) 25 cm , d ) 10 cm , e ) 28 cm
Rationale: "required length = hcf of 1800 cm , 4000 cm , 650 cm = 50 cm answer is d"
Answer: d
Problem: from january 1 , 2015 , to january 1 , 2017 , the number of people enrolled in health maintenance organizations increased by 5 percent . the enrollment on january 1 , 2017 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 2015 ?
Options: a ) 38 , b ) 39 , c ) 40 , d ) 41 , e ) 43
Rationale: "soln : - 5 x = 45 - - > 21 / 20 * x = 45 - - > x = 45 * 20 / 21 = 300 / 7 = ~ 43 . answer : e ."
Answer: e
Problem: the number which exceeds 16 % of it by 42 is :
Options: a ) 50 , b ) 52 , c ) 58 , d ) 60 , e ) 62
Rationale: "solution solution let the number be x . x - 16 % of x = 42 x - 16 / 100 x = 42 x - 4 / 25 x = 42 21 / 25 x = 42 x = ( 42 x 25 / 21 ) = 50 answer a"
Answer: a
Problem: in assembling a bluetooth device , a factory uses one of two kinds of modules . one module costs $ 10 and the other one , that is cheaper , costs $ 2.5 . the factory holds a $ 62.50 worth stock of 22 modules . how many of the modules in the stock are of the cheaper kind ?
Options: a ) 31 , b ) 35 , c ) 21 , d ) 40 , e ) 45
Rationale: "so the number of $ 2.50 modules must be 21 so that the leftover 1 modules are of $ 10 which will give a total value $ 62.50 . 21 * 2.50 + 1 * 10 = 52.50 + 10 = 62.50 answer : c"
Answer: c
Problem: mary goes into labor at her local grocery store and is rushed to a hospital in an ambulance traveling 60 mph . her husband don drives after the ambulance at an average speed of 30 mph . mary reaches the hospital fifteen minutes later . how long does it take don to get there from the store ?
Options: a ) 25 minutes , b ) 30 minutes , c ) 10 minutes , d ) 15 minutes , e ) 7 minutes
Rationale: distance covered by the ambulance in 15 minutes = 15 miles 60 mph is one mile per minute , therefore 30 mph will be 1 / 2 a mile per minute . so , he reaches the hospital half an hour after leaving the store . correct answer : b
Answer: b
Problem: what is the ratio between perimeters of two squares one having 7 times the diagonal then the other ?
Options: a ) 3 : 7 , b ) 3 : 5 , c ) 3 : 8 , d ) 7 : 1 , e ) 3 : 5
Rationale: "d = 7 d d = d a √ 2 = 7 d a √ 2 = d a = 7 d / √ 2 a = d / √ 2 = > 7 : 1 answer : d"
Answer: d
Problem: square a has an area of 65 square centimeters . square b has a perimeter of 16 centimeters . if square b is placed within square a and a random point is chosen within square a , what is the probability the point is not within square b ?
Options: a ) 0.25 , b ) 0.5 , c ) 0.75 , d ) 0.1 , e ) 0.3
Rationale: "i guess it ' s mean that square b is placed within square aentirely . since , the perimeter of b is 16 , then its side is 16 / 4 = 4 and the area is 4 ^ 2 = 16 ; empty space between the squares is 65 - 16 = 48 square centimeters , so if a random point is in this area then it wo n ' t be within square b : p = favorable / total = 48 / 64 = 0.75 . answer : c"
Answer: c
Problem: in an election , candidate a got 80 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate .
Options: a ) 330000 , b ) 340000 , c ) 380800 , d ) 356000 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 80 % therefore , the number of valid votes polled in favour of candidate a = 80 % of 476000 = 80 / 100 × 476000 = 38080000 / 100 = 380800 c )"
Answer: c
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 560 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 76 , e ) 92
Rationale: "given that length and area , so we can find the breadth . length x breadth = area 20 x breadth = 560 breadth = 28 feet area to be fenced = 2 b + l = 2 ( 28 ) + 20 = 76 feet answer : d"
Answer: d