regisss/math_qa huggingface dataset:
Problem: a can do a work in 7 days b in 12 days and c in 5 days . if they work on it together then in how many days required to complete the work ?
Options: a ) 420 / 177 , b ) 420 / 179 , c ) 410 / 87 , d ) 90 / 14 , e ) 77 / 56
Rationale: "person ( a ) ( b ) ( c ) ( a + b + c ) time - ( 7 ) ( 12 ) ( 5 ) rate - ( 60 ) ( 35 ) ( 84 ) ( 179 ) work - ( 420 ) ( 420 ) ( 420 ) ( 420 ) therefore a + b + c requires ( 420 / 179 ) days to complete entire work = 420 / 179 answer is b"
Answer: b
Problem: find a sum for 1 st 5 prime number ' s ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 ) = 28 note : 1 is not a prime number option b"
Answer: b
Problem: a hiker walking at a constant rate of 5 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 25 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 25 = 25 / 12 km . the time it takes the hiker to complete this distance is ( 25 / 12 ) / 5 = 5 / 12 hours = 25 minutes the cyclist needs to wait 25 - 5 = 20 minutes the answer is c ."
Answer: c
Problem: each employee of company x is a member of precisely 1 of 3 shifts of employees . among the 60 members of the first shift , 20 percent participate in the pension program ; among the 50 members of the second shift , 40 percent participate in the pension program ; and among the 40 members of the third shift , 10 percent participate in the pension program . what percent of the workers at company x participate in the pension program ?
Options: a ) 20 % , b ) 24 % , c ) 36 % , d ) 37.5 % , e ) 70 %
Rationale: 60 members & 20 percent = 12 50 members & 40 percent = 20 40 members & 10 percent = 4 = > 36 / 150 ∗ 100 = 24 % answer b
Answer: b
Problem: a farmer spent $ 35 on feed for chickens and goats . he spent 40 % money on chicken feed , which he bought at a 60 % discount off the full price , and spent the rest on goat feed , which he bought at full price . if the farmer had paid full price for both the chicken feed and the goat feed , what amount would he have spent on the chicken feed and goat feed combined ?
Options: a ) $ 37.80 , b ) $ 38.50 , c ) $ 39.20 , d ) $ 39.50 , e ) $ 51
Rationale: "a farmer spent 40 % money on chicken feed , so he spent 0.4 * $ 35 = $ 14 on chicken feed , thus he spent the remaining 35 - 14 = $ 21 on goat feed . now , since he bought chicken feed at a 20 % discount then the original price of it was x * 0.4 = $ 14 - - > x = $ 35 . therefore if the farmer had paid full price for both the chicken feed and the goat feed , then he would he have spent 35 + 21 = $ 51 . answer : e ."
Answer: e
Problem: the ratio of the amount of the oil bill for the month of february to the amount of the oil bill for the month of january was 5 : 4 . if the oil bill for february had been $ 30 more , the corresponding ratio would have been 3 : 2 . how much was the oil bill for january ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 100 , d ) $ 120 , e ) $ 140
Rationale: "5 : 4 = 15 : 12 and 3 : 2 = 18 : 12 . an increase in $ 30 increases the ratio by 3 : 12 . therefore an increase in $ 10 increases the ratio by 1 : 12 . therefore , january ' s bill was 12 ( $ 10 ) = $ 120 . the answer is d ."
Answer: d
Problem: a driver goes on a trip of 50 kilometers , the first 25 kilometers at 66 kilometers per hour and the remaining distance at 33 kilometers per hour . what is the average speed of the entire trip in kilometers per hour ?
Options: a ) 38 , b ) 40 , c ) 44 , d ) 45 , e ) 48
Rationale: the time for the first part of the trip was 25 / 66 hours . the time for the second part of the trip was 25 / 33 hours . the total time fro the trip was 25 / 66 + 25 / 33 = 75 / 66 = 25 / 22 hours . the average speed for the trip was 50 / ( 25 / 22 ) = 44 kph the answer is c .
Answer: c
Problem: a hollow spherical metallic ball has an external diameter 6 cm and is 1 / 2 cm thick . the volume of metal used in the metal is :
Options: a ) 47 1 / 5 cm 3
b ) 47 3 / 5 cm 3
c ) 47 7 / 5 cm 3
d ) 47 9 / 5 cm 3
e ) none of these
Rationale: explanation : please note we are talking about ` ` hollow ' ' ball . do not ignore this word in this type of question in a hurry to solve this question . if we are given with external radius and thickness , we can get the internal radius by subtracting them . then the volume of metal can be obtained by its formula as , external radius = 3 cm , internal radius = ( 3 - 0.5 ) cm = 2.5 cm volume of sphere = 4 / 3 π r 3 = 4 / 3 ∗ 22 / 7 ∗ [ 3 ( 2 ) − 2.52 ] cm 3 = 4 / 3 ∗ 22 / 7 ∗ 91 / 8 cm 3 = 143 / 3 cm 3 = 47 2 / 3 cm 3 option b
Answer: b
Problem: if a book is sold at 6 % profit instead of 6 % loss , it would have brought rs 15 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 60 , d ) 70 , e ) 125
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.06 x - 0.94 x = 15 = > 0.12 x = 15 = 15 / 0.12 = rs 125 answer : e"
Answer: e
Problem: at what rate percent per annum will a sum of money double in 10 years ?
Options: a ) 10 % , b ) 15 % , c ) 18 % , d ) 20 % , e ) 25 %
Rationale: "let principle = p s . i . = p t = 10 yrs rate = 100 * p / p * 10 = 10 % answer is a"
Answer: a
Problem: the average of 9 observations was 5 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 45 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 5 = 45 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 45 = 45 option a"
Answer: a
Problem: a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.10 of per share earnings . if quarterly earnings are $ 1.10 per share , what will be the dividend paid to a person who owns 600 shares of the company ' s stock ?
Options: a ) $ 92 , b ) $ 312 , c ) $ 104 , d ) $ 120 , e ) $ 240
Rationale: eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 600 - - > $ 312 answer is b
Answer: b
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 10 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,10 = 10 / 100 x = 80 * 10 / 100 x = 8 8 / 10 = 0.8 = 800 % , answer a"
Answer: a
Problem: bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 60 white marbles . how many red marbles could be in bag a ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 12 , e ) 8
Rationale: "6 is the answer . bag a - r : w : b = 2 : 6 : 9 let w in bag a be 6 k bab b - r : w = 1 : 4 let w in bag b be 4 k w = 60 = 6 k + 4 k = > k = 6 total red ' s in bag a will be 2 k = 12 d"
Answer: d
Problem: if the areas of the three adjacent faces of a cuboidal box are 120 cm ² , 72 cm ² and 60 cm ² respectively , then find the volume of the box .
Options: a ) 120 m ³
b ) 400 m ³
c ) 660 m ³
d ) 720 cm m ³
e ) none
Rationale: sol . let the length , breadth and height of the box be , l , b , and h respectively , then , volume = lbh = √ ( lbh ) ² = √ lb * bh * lh = √ 120 * 72 * 60 = 720 cm ³ answer d
Answer: d
Problem: solution a is 20 % barium and solution b is 80 % barium . if you have 30 ounces of solution a and 60 ounces of solution b , in what ratio could you mix solution a with solution b to produce 50 ounces of a 50 % barium solution ?
Options: a ) 6 : 4 , b ) 6 : 14 , c ) 4 : 4 , d ) 4 : 6 , e ) 3 : 7
Rationale: forget the volumes for the time being . you have to mix 20 % and 80 % solutions to get 50 % . this is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities . if this does n ' t strike , use w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) w 1 / w 2 = ( 80 - 50 ) / ( 50 - 20 ) = 1 / 1 so the volume of the two solutions will be equal . answer has to be 4 : 4 = c
Answer: c
Problem: a cyclist bikes x distance at 12 miles per hour and returns over the same path at 8 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.3 , c ) 9.6 , d ) 8.9 , e ) 9.0
Rationale: "distance = d 1 = x miles speed = s 1 = 12 miles per hour time = t 1 = distance / speed = x / 12 2 . going from b to a distance = d 2 = x miles speed = s 2 = 8 miles per hour time = t 2 = distance / speed = x / 8 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 12 + x / 8 = x ( 1 / 12 + 1 / 8 ) = = 5 x / 24 speed = 2 x / ( 5 x / 24 ) = 48 / 5 = 9.6 answer : c"
Answer: c
Problem: in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 85 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 59 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: "say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.85 = 51 democrats are expected to vote for candidate a ; 40 * 0.20 = 8 republicans are expected to vote for candidate a . thus total of 51 + 8 = 59 registered voters are expected to vote for candidate a , which is 59 % of the total number of registered voters . answer : b ."
Answer: b
Problem: while driving from a - ville to b - town , harriet drove at a constant speed of 100 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 150 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 180
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 180 min * leg a - b - - - > d = 100.180 / 60 = 18000 / 60 * leg b - a - - - - > d = 150 * 120 / 60 = 18000 / 60 so the correct ans . ise"
Answer: e
Problem: find the value for x from below equation : x / 3 = - 7 ?
Options: a ) - 6 , b ) - 21 , c ) - 2 , d ) - 3 , e ) 4
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 7 / 3 simplify both sides : x = - 21 b"
Answer: b
Problem: at a speed of 50 miles per hour , a certain car uses 1 gallon of gasoline every 30 miles . if the car starts with a full 15 gallon tank of gasoline and travels for 5 hours at 50 miles per hour , the amount of gasoline used would be what fraction of a full tank ?
Options: a ) 3 / 25 , b ) 11 / 36 , c ) 5 / 9 , d ) 2 / 3 , e ) 25 / 36
Rationale: gas used = ( 5 hours ) * ( 50 miles / hour ) * ( 1 gallon / 30 miles ) = 8 + 1 / 3 gallons portion used = ( 8 + 1 / 3 ) / 15 = 5 / 9 ans c
Answer: c
Problem: robert ate 13 chocolates , nickel ate 4 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 13 - 4 = 9 . answer is c
Answer: c
Problem: by selling an article at rs . 150 , a profit of 25 % is made . find its cost price ?
Options: a ) s . 486 , b ) s . 455 , c ) s . 487 , d ) s . 120 , e ) s . 489
Rationale: "sp = 150 cp = ( sp ) * [ 100 / ( 100 + p ) ] = 150 * [ 100 / ( 100 + 25 ) ] = 150 * [ 100 / 125 ] = rs . 120 answer : d"
Answer: d
Problem: eddy and freddy start simultaneously from city a and they travel to city b and city c respectively . eddy takes 3 hours and freddy takes 4 hours to complete the journey . if the distance between city a and city b is 600 kms and city a and city c is 360 kms . what is the ratio of their average speed of travel ? ( eddy : freddy )
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 8 / 5 , d ) 5 / 8 , e ) 20 / 9
Rationale: "distance traveled by eddy = 600 km time taken by eddy = 3 hours average speed of eddy = 600 / 3 = 200 km / hour distance traveled by freddy = 360 km time taken by freddy = 4 hours average speed of freddy = 360 / 4 = 90 km / hour ratio of average speed of eddy to freddy = 200 / 90 = 20 / 9 answer e"
Answer: e
Problem: a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 120,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 45,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: "the 15 managers have an average salary of $ 120,000 . the sum of their salaries is : sum = ( average ) * ( number of salaries ) = $ 120,000 * 15 = $ 1 , 800,000 the 75 associates have an average salary of $ 30,000 . the sum of their salaries is : sum = ( average ) * ( number of salaries ) = $ 30,000 * 75 = $ 2 , 250,000 when we add those two sums , we get the total payroll of all 90 employees . $ 1 , 800,000 + $ 2 , 250,000 = $ 4 , 050,000 so , we have 90 employees , and together they earn $ 4 , 050,000 , so the average is average = $ 4 , 050,000 ÷ 90 = $ 45,000 answer : b ."
Answer: b
Problem: excluding stoppages , the speed of a bus is 5454 kmph and including stoppages , it is 4545 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 12 , b ) 11 , c ) 10 , d ) 9 , e ) 8
Rationale: "explanation : speed of the bus excluding stoppages = 54 = 54 kmph speed of the bus including stoppages = 45 = 45 kmph loss in speed when including stoppages = 54 â ˆ ’ 45 = 9 kmph = 54 â ˆ ’ 45 = 9 kmph â ‡ ’ â ‡ ’ in 11 hour , bus covers 99 km less due to stoppages . hence , time in which the bus stops per hour = time taken to cover 99 km = distancespeed = 954 hour = 16 hour = distancespeed = 954 hour = 16 hour = 606 min = 10 min answer is c"
Answer: c
Problem: sheela deposits rs . 2500 in bank savings account . if this is 25 % of her monthly income . what is her monthly income in ?
Options: a ) 10000 , b ) 20000 , c ) 25000 , d ) 22235 , e ) none of these
Rationale: explanation : 25 % of income = rs . 2500 100 % of income = 2500 x 100 / 25 = rs . 10000 answer : a
Answer: a
Problem: in one hour , a boat goes 15 km along the stream and 5 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 15 + 5 ) km / hr = 10 kmph . answer e"
Answer: e
Problem: what percent of 9.6 kg is 28 gms ?
Options: a ) 25 , b ) 66 , c ) 288 , d ) 29 , e ) 17
Rationale: "explanation : required percentage = ( 28 / 9600 * 100 ) % = 29 / 100 % = 0.29 % answer : d ) . 29 %"
Answer: d
Problem: a palindrome is a number that reads the same front - to - back as it does back - to - front ( e . g . 202 , 575 , 1991 , etc . ) p is the smallest integer greater than 400 that is both a prime and a palindrome . what is the sum of the digits of p ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "given that p is smallest integer greater than 400 - assume there is a 3 - digit that satisfies the above conditions . let the number be xyx ; question asks us the values of 2 x + y we can straight away cross out options a ) and d ) - sum of digits 3 or 6 implies it is divisible by 3 - - - > we know that p is a prime number coming to option b ) 2 x + y = 4 - - > only x = 2 and y = 0 satisfy this equation ( x > 2 will never give sum of digits = 4 ) ; but 202 is divisible by 2 ; we know that p is a prime number similarly option c ) 2 x + y = 5 - - > only x = 2 and y = 1 satisfy this equation ( x > 2 will never give sum of digits = 5 ) ; but 212 is divisible by 2 ; we know that p is a prime number therefore answer option should be e - - - > can be verified by taking 2 x + y = 7 - - - > x = 3 and y = 1 ; gives 313 a"
Answer: a
Problem: the difference between simple and compound interests on a certain sum for 2 years at 4 % per annum is rs . 50 . the sum is
Options: a ) rs . 20,400 , b ) rs . 25,000 , c ) rs . 31,250 , d ) rs . 38,000 , e ) rs . 48,000
Rationale: "difference between 2 yr ci and si is given by pr ^ 2 . . pr ^ 2 = 50 p * r / 100 * r / 100 = 50 p * 4 / 100 * 4 / 100 = 50 p = ( 50 * 100 * 100 ) / 4 * 4 p = 31,250 answer : c"
Answer: c
Problem: if a certain number is divided by 3 , the quotient , dividend , and divisor , added together , will amount to 63 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 45 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 3 + x + 3 = 63 . and x = 45 . c"
Answer: c
Problem: an electric pump can fill a tank in 7 hours . because of a leak in the tank , it took 14 hours to fill the tank . if the tank is full , how much time will the leak take to empty it ?
Options: a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 14 hours
Rationale: "work done by the leak in 1 hour = 1 / 7 - 1 / 14 = 1 / 14 the leak will empty the tank in 14 hours answer is e"
Answer: e
Problem: a vendor sells 30 percent of the apples he had and throws away 20 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: let x be the original number of apples . on day one , the vendor throws away ( 0.2 ) ( 0.7 ) x = 0.14 x . the remaining apples are ( 0.8 ) ( 0.7 ) x = 0.56 x . on day two , the vendor throws away ( 0.5 ) ( 0.56 ) x = 0.28 x . the vendor throws away a total of 0.14 x + 0.28 x = 0.42 x . the vendor throws away 42 percent of the apples . the answer is b .
Answer: b
Problem: if log 2 = 0.3010 and log 3 = 0.4771 , the values of log 5 512 is
Options: a ) 3.879 , b ) 3.875 , c ) 3.872 , d ) 3.828 , e ) 3.192
Rationale: "ans : log 5512 = { \ color { black } \ frac { \ log 512 } { \ log 5 } } = { \ color { black } \ frac { \ log 2 ^ { 9 } } { \ log ( \ frac { 10 } { 2 } ) } } = { \ color { black } \ frac { 9 \ log 2 } { \ log 10 - \ log 2 } } = { \ color { black } \ frac { ( 9 \ times 0.3010 ) } { 1 - 0.3010 } } = { \ color { black } \ frac { 2.709 } { 0.699 } } = { \ color { black } \ frac { 2709 } { 699 } } = 3.876 answer : b ) 3.875"
Answer: b
Problem: 79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,071 bacteria each . how many bacteria are there approximately ?
Options: a ) 10 ^ 7 , b ) 10 ^ 11 , c ) 10 ^ 9 , d ) 10 ^ 10 , e ) 10 ^ 8
Rationale: "79 laboratories raise the bacterium , the laboratory have 48 culture dishes on average , which has about 25,071 bacteria each . how many bacteria are there approximately ? a . 10 ^ 7 b . 10 ^ 8 c . 10 ^ 9 d . 10 ^ 10 e . 10 ^ 11 - > due to approximately , 79 = 80 , 48 = 50 , 25,071 = 25,000 are derived , which makes ( 79 ) ( 48 ) ( 25,075 ) = ( 80 ) ( 50 ) ( 25,000 ) = 10 ^ 8 . the answer is e ."
Answer: e
Problem: there is a train and car . the ratio btw the speed of a train & a car is 16 : 15 respectively . also , a bus covered a distance of 480 km in 8 h . the speed of the bus is 3 / 4 th of the speed of the train . how much distance will the car cover in 6 h ?
Options: a ) 300 km , b ) 320 km , c ) 370 km , d ) 430 km , e ) 450 km
Rationale: sol . speed of bus = 480 / 8 = 60 km / h speed of train = ( 60 * 4 ) / 3 = 80 km / h speed of train : speed of car = 16 : 15 speed of car = 80 / 16 * 15 = 75 km / h distance covered by car in 6 hr = 75 × 6 = 450 km e
Answer: e
Problem: how many different pairs of positive integers ( a , b ) satisfy the equation 1 / a + 1 / b = 34 / 41 ?
Options: a ) 6 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "there is no certain way to solve 2 unknown with 1 equation . the best way is to look at the question and retrospect the most efficient way . in this question , a and b are only positive integers . so that is a big relief . now , we can start with putting a = 1,2 , . . and so on till the time we are confident about one of the options . so , we start with a = 1 , we get b as - ve . out a = 2 , we get b as 6 . yes ( now ( a , b ) = ( 2,6 ) . we can directly see that ( a , b ) = ( 6,2 ) will also satisfy . so we have 2 possible solutions ) a = 3 , we get b as 3 . yes ( now we have 3 possible solutions ) a = 4 , we get b as fraction . out a = 5 , we get b again as some fraction . out a = 6 already taken . we have a , b options left . c , d , e are out . a is 6 . to have 6 as the answer , we will need one more pair like 2,6 and one more solution where a = b . when a = b , we have only 1 solution = 1 . so , one more solution , where a = b is not possible . so , answer will be d ."
Answer: d
Problem: if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same at the same rate and for the same time ?
Options: a ) rs . 52 , b ) rs . 51.25 , c ) rs . 54.25 , d ) rs . 60 , e ) rs . 70
Rationale: "simple interest for 2 years = rs . 50 ie . for 1 years rs . 25 . . in the first year the s . i and c . i are same ie . rs . 25 . so in the 2 nd year in c . i calculated for 1 years interest also . so in second years for rs . 25 interest is 25 * 5 / 100 = 1.25 . so total c . p = 51.25 . answer : b"
Answer: b
Problem: of 61 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 53 , b ) 55 , c ) 59 , d ) 71 , e ) 92
Rationale: "total = 61 thrower = 37 rest = 61 - 37 = 24 left handed = 24 / 3 = 8 right handed = 16 if all thrower are right handed then total right handed is 37 + 16 = 53 so a . 53 is the right answer"
Answer: a
Problem: what is the remainder when 7 ^ 498 is divided by 5 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "7 ^ 0 = 1 7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = . . . 1 7 ^ 5 = . . . . 7 7 ^ 6 = . . . . . . 9 and so on in a recurring pattern of 1,7 , 9,3 , 1,7 , 9,3 . . . . 498 / 4 = 124 ( with a remainder 2 ) so the last number is a 9 . so when 7 ^ 498 is divided by 5 the remainder is 4 , ans = a"
Answer: a
Problem: a person bought 118 glass bowls at a rate of rs . 12 per bowl . he sold 102 of them at rs . 15 and the remaining broke . what is the percentage gain for a ?
Options: a ) 40 , b ) 300 / 11 , c ) 243 / 7 , d ) 475 / 59 , e ) 279 / 8
Rationale: cp = 118 * 12 = 1416 and sp = 102 * 15 = 1530 gain % = 100 * ( 1530 - 1416 ) / 1100 = 11400 / 1416 = 475 / 59 answer : d
Answer: d
Problem: an engineering student has to secure 36 % marks to pass . he gets 130 marks and fails by 14 marks . the maximum no . of marks obtained by him is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: "130 14 - - - - - - - 361 - - - - - - 144 100 % - - - - - - ? = > 400 answer : b"
Answer: b
Problem: he ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 . answer : e"
Answer: e
Problem: what is the cp of rs 100 stock at 2 discount , with 1 / 5 % brokerage ?
Options: a ) 99.6 , b ) 96.2 , c ) 97.5 , d ) 98.2 , e ) none of these
Rationale: "explanation : use the formula , cp = 100 â € “ discount + brokerage % cp = 100 - 2 + 1 / 5 98.2 thus the cp is rs 98.2 . answer d"
Answer: d
Problem: two trains of length 100 meters and 200 meters are 840 meters apart . they are moving towards each other on parallel tracks , at speeds of 54 km / h and 72 km / h . after how many seconds will the trains meet ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "the speeds are 54000 / 3600 = 15 m / s and 72000 / 3600 = 20 m / s the relative speed is 35 m / s . time = 840 / 35 = 24 seconds the answer is c ."
Answer: c
Problem: if a man walks to his office at ¾ of his usual rate , he reaches office 1 / 3 of an hour late than usual . what is his usual time to reach office ?
Options: a ) 2 hour , b ) 5 hour , c ) 1 hour , d ) 3 hour , e ) 2 hour
Rationale: c 1 hour speed ratio = 1 : 3 / 4 = 4 : 3 time ratio = 3 : 4 1 - - - - - - - - 1 / 3 3 - - - - - - - - - ? 1 hour
Answer: c
Problem: a batsman in his 15 th innings makes a score of 85 , and thereby increases his average by 3 . what is his average after the 15 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 15 th innings = 85 - 3 × 15 = 40 average score after 15 th innings = > 40 + 3 = 43 answer : d"
Answer: d
Problem: a candidate appearing for an examination has to secure 40 % marks to pass paper i . but he secured only 40 marks and failed by 20 marks . what is the maximum mark for paper i ?
Options: a ) 110 , b ) 120 , c ) 130 , d ) 140 , e ) 150
Rationale: "he secured 40 marks nd fail by 20 marks so total marks for pass the examinatn = 60 let toal marks x x * 40 / 100 = 60 x = 150 answer : e"
Answer: e
Problem: two - third of a positive number and 49 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 7 / 12 , c ) 25 / 144 , d ) 144 / 25 , e ) 146 / 25
Rationale: "let the number be x . then , 2 / 3 x = 49 / 216 * 1 / x x 2 = 49 / 216 * 3 / 2 = 49 / 144 x = 7 / 12 answer : b"
Answer: b
Problem: a 160 meter long train crosses a man standing on the platform in 16 sec . what is the speed of the train ?
Options: a ) 36 kmph , b ) 54 kmph , c ) 92 kmph , d ) 86 kmph , e ) 76 kmph
Rationale: "s = 160 / 16 * 18 / 5 = 36 kmph answer : a"
Answer: a
Problem: a race course is 400 m long . aa and bb run a race and aa wins by 5 m . bb and cc run over the same course and bb win by 4 m . cc and dd run over it and dd wins by 16 m . if aa and dd run over it , then who would win and by how much ?
Options: a ) 7.1 m , b ) 7.2 m , c ) 8 m , d ) 9 m , e ) 11 m
Rationale: if aa covers 400 m , bb covers 395 m if bb covers 400 m , cc covers 396 m if dd covers 400 m , cc covers 384 m now if bb covers 395 m , then cc will cover 396400 × 395 = 391.05396400 × 395 = 391.05 m if cc covers 391.05 m , then dd will cover 400384 × 391.05 = 407.24400384 × 391.05 = 407.24 if aa and dd run over 400 m , then dd win by 7.2 m option b
Answer: b
Problem: a boat takes 19 hours for travelling downstream from point a to point b and coming back to a point c midway between a and b . if the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph , what is the distance between a and b ?
Options: a ) 160 km , b ) 180 km , c ) 200 km , d ) 220 km , e ) 240 km
Rationale: down stream speed : ( 14 + 4 ) km / hr = 18 km / hr up stream speed : ( 14 - 4 ) km / hr = 10 km / hr ( x / 18 ) + ( x / 2 / 20 ) = 19 x = 180 km answer : b
Answer: b
Problem: 12.5 * 4.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 462 , d ) 646 , e ) 742
Rationale: "c 462 ? = 12.5 * 4.2 * 8.8 = 462"
Answer: c
Problem: sonika bought a v . c . r . at the list price of 18,900 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,412 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,900 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,900 = 8 ⁄ 100 × 18500 = 1512 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,900 + 1512 = 20,412 . answer a"
Answer: a
Problem: you collect baseball cards . suppose you start out with 21 . maria takes half of one more than the number of baseball cards you have . since you ' re nice , you give peter 1 baseball card . since his father makes baseball cards , paul decides to triple your baseball cards . how many baseball cards do you have at the end ?
Options: a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 27
Rationale: "solution start with 21 baseball cards . maria takes half of one more than the number of baseball cards you have . so maria takes half of 21 + 1 which is 11 , so you ' re left with 21 - 11 = 10 . peter takes 1 baseball card from you : 10 - 1 = 9 baseball cards . paul triples the number of baseball cards you have : 9 ã — 3 = 27 baseball cards . so you have 27 at the end . correct answer : e"
Answer: e
Problem: a man ' s speed with the current is 18 km / hr and the speed of the current is 3.4 km / hr . the man ' s speed against the current is
Options: a ) 9 , b ) 10.4 , c ) 11.2 , d ) 12.5 , e ) 13
Rationale: "man ' s rate in still water = ( 18 - 3.4 ) km / hr = 14.6 km / hr . man ' s rate against the current = ( 14.6 - 3.4 ) km / hr = 11.2 km / hr . answer : c"
Answer: c
Problem: in town p , 60 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 20 % , b ) 25 % , c ) 30 % , d ) 35 % , e ) 40 %
Rationale: "the percent of the population who are employed females is 60 - 48 = 12 % the percent of employed people who are female is 12 % / 60 % = 20 % . the answer is a ."
Answer: a
Problem: average monthly income of a family of 4 earning members was rs . 782 . one of the earning members died and therefore , the average income came down to rs 650 . the income of the deceased was ?
Options: a ) rs . 1178 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 782 x 4 - 650 x 3 rs . = 1178 rs . correct option : a"
Answer: a
Problem: how many words , with or without meaning , can be formed using all letters of the word equation using each letter exactly once ?
Options: a ) 38,320 , b ) 39,320 , c ) 40,320 , d ) 38,400 , e ) 39,400
Rationale: "the word equation has exactly 8 letters which are all different . therefore the number of words that can be formed = number of permutations of 8 letters taken all at a time . = p ( 8 , 8 ) = 8 ! = 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1 = 40,320 answer : c"
Answer: c
Problem: a train 350 m long is running at a speed of 68 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 ) 9 sec , c ) 12 sec , d ) 21 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 350 m at 50 / 3 m / sec = 350 * 3 / 50 sec = 21 sec answer : d"
Answer: d
Problem: what is remainder of the division ( 1125 * 1127 * 1129 ) / 12 ?
Options: a ) 0 , b ) 3 , c ) 1 , d ) 2 , e ) 4
Rationale: "remainder will be number / 100 here as the divisor is two digit number = 12 . hence checking for the last two digits = 5 * 7 * 9 = 15 thus remainder = 3 . answer : b"
Answer: b
Problem: the average salary of all the workers in a workshop is rs . 8000 . the average salary of 7 technicians is rs . 8000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is
Options: a ) 20 , b ) 21 , c ) 22 , d ) 7 , e ) 24
Rationale: "solution let the toatl number of workers be x . then 8000 x = ( 8000 x 7 ) + 6000 ( x - 7 ) x = 7 . answer d"
Answer: d
Problem: 0.0005 ? = 0.01
Options: a ) 5 , b ) 0.05 , c ) 0.5 , d ) 50 , e ) none of these
Rationale: "explanation : required answer = 0.0005 / 0.01 = 0.05 / 1 = 0.05 . answer : option b"
Answer: b
Problem: a library has an average of 140 visitors on sundays and 80 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
Options: a ) 90 , b ) 100 , c ) 105 , d ) 110 , e ) 125
Rationale: "explanation : since the month begins with a sunday , so there will be five sundays in the month , required average = ( 140 * 5 + 80 * 25 ) / 30 = 2700 / 30 = 90 answer : a ) 90"
Answer: a
Problem: the diagonal of a rhombus are 62 m and 80 m . its area is :
Options: a ) 1940 , b ) 2480 , c ) 2460 , d ) 2500 , e ) 1980
Rationale: "area of the rhombus = 1 / 2 d 1 d 2 = ( 1 / 2 ã — 62 ã — 80 ) cm ( power ) 2 = 62 ã — 40 = 2480 cm ( power ) 2 answer is b ."
Answer: b
Problem: the distance from city a to city b is 180 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 54
Rationale: "the time it takes bob to drive to city b is 180 / 40 = 4.5 hours . alice needs to take less than 4 hours for the trip . alice needs to exceed a constant speed of 180 / 4 = 45 miles per hour . the answer is a ."
Answer: a
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer"
Answer: d
Problem: find the least number must be added to 228712 so that remaining no . is divisible by 9 ?
Options: a ) 5 , b ) 3 , c ) 1 , d ) 6 , e ) 2
Rationale: on dividing 228712 by 9 we get the remainder 4 , so 5 should be subtracted a
Answer: a
Problem: how many revolutions will a circular wheel make to travel a distance of 3 km , given that the radius is 2.4 m ?
Options: a ) 11085.7 , b ) 15085.7 , c ) 35085.7 , d ) 15015.7 , e ) 15083.7
Rationale: 2 * 22 / 7 * 2.4 * x = 15085.7 x = 1000 answer : a
Answer: a
Problem: if 4 gallons of gasoline are added to a tank that is already filled to 3 / 4 of its capacity , the tank is then filled to 9 / 10 of its capacity . how many gallons does the tank hold ?
Options: a ) 20 , b ) 24 , c ) 36 , d ) 40 , e ) 60
Rationale: "let the capacity of the tank = c ( 3 / 4 ) c + 4 = ( 9 / 10 ) c = > ( 9 / 10 ) c - ( 3 / 4 ) c = 4 = > ( 3 / 20 ) c = 4 = > c = ( 4 * 20 ) / 3 = 26.66 number of gallons of gasoline that the tank currently holds = 3 / 4 * c + 4 = 19.99 + 4 = 23.99 = 24 answer b"
Answer: b
Problem: a drink vendor has 50 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
Options: a ) 135 , b ) 237 , c ) 281 , d ) 300 , e ) 380
Rationale: "the number of liters in each can = hcf of 50 , 144 and 368 = 2 liters . number of cans of maaza = 50 / 2 = 25 number of cans of pepsi = 144 / 2 = 72 number of cans of sprite = 368 / 2 = 184 the total number of cans required = 25 + 72 + 184 = 281 cans . answer : c"
Answer: c
Problem: express a speed of 36 kmph in meters per second ?
Options: a ) 10 mps , b ) 76 mps , c ) 26 mps , d ) 97 mps , e ) 16 mps
Rationale: "36 * 5 / 18 = 10 mps answer : a"
Answer: a
Problem: lily shop runs a sale on goldfish and platys . if one customer buys 13 goldfish and 12 platys for $ 5.60 , and another buys 14 goldfish and 21 platys for $ 8.05 , what is the ratio of the price of goldfish to platys ?
Options: a ) 0.8 , b ) 0.75 , c ) c ) 8 / 9 , d ) 5 / 7 , e ) 6 / 8
Rationale: the approach of plugging in the numbers is a fine approach . but , in this case , the answer was the first option and thus , by plugging in a number in the ration given , we arrived at the answer quickly ! however , what if the correct ratio was option d or c ? in any case , the algebraic solution is n ' t that complex if you realize a key concept : the number 7 can be factored out of the second equation ! here ' s the working : lily shop runs a sale on goldfish and platys . 13 x + 12 y = 5.60 < < < < < equation 1 14 x + 21 y = 8.05 < < < < < equation 2 2 x + 3 y = 1.15 [ factor out 7 from equation 2 ] < < < < < equation 3 8 x + 12 y = 4.6 [ multiply equation 3 with 4 ] 5 x = 1.0 [ equation 1 - equation 2 ] x = 0.2 3 y = 1.15 - 0.4 = 0.75 [ substitute for x in equation 1 ] y = 0.25 x / y = 0.2 / 0.25 = 20 / 25 = 4 / 5 = 0.8 [ answer a ] the whole thing must have taken me about 45 s : d
Answer: d
Problem: a woman invested $ 1,000 , part at 5 % and the rest at 6 % . her total investment with interest at the end of the year was $ 1,051 . how much did she invest at 5 % ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 900 , e ) $ 950
Rationale: "et x be the portion invested at 5 % and let ( 1 - x ) be the rest which is invested at 6 % the question states that the return after 1 year is ( 1051 / 1000 ) - 1 = 0.051 = 5.1 % we want to find the dollar amount invested in x using our defined variables , put together the equation and solve for x ( the percentage of 1000 invested at 5 % ) 0.05 x + 0.06 ( 1 - x ) = 0.051 ( 0.05 ) x + 0.06 - ( 0.06 ) x = 0.051 - 0.01 x = - 0.009 x = - 0.009 / - 0.01 = 9 / 10 = 90 % so x = 90 % of the 1000 which is 900 answer : d"
Answer: d
Problem: in a class , 9 students like to play basketball and 8 like to play cricket . 6 students like to play on both basketball and cricket . how many students like to play basketball or cricket or both ?
Options: a ) 12 , b ) 11 , c ) 16 , d ) 18 , e ) 22
Rationale: "draw a venn diagram yourself ! b + c - bc = number of students that play either basketball or cricket 9 + 8 - 6 = 11 b )"
Answer: b
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 7000 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2900 , d ) 2200 , e ) 2520
Rationale: "e number of valid votes = 80 % of 7000 = 5600 . valid votes polled by other candidate = 45 % of 6000 = ( 45 / 100 x 5600 ) = 2520 ."
Answer: e
Problem: if daily wages of a man is double to that of a woman , how many men should work for 10 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 ) 20 , e ) 40
Rationale: "explanation : wages of 1 woman for 1 day = 21600 / 40 ã — 30 wages of 1 man for 1 day = 21600 ã — 2 / 40 ã — 30 wages of 1 man for 10 days = 21600 ã — 2 ã — 10 / 40 ã — 30 number of men = 14400 / ( 21600 ã — 2 ã — 10 / 40 ã — 30 ) = 144 / ( 216 ã — 20 / 40 ã — 30 ) = 40 answer : option e"
Answer: e
Problem: two assembly line inspectors , lauren and steven , inspect widgets as they come off the assembly line . if lauren inspects every fifth widget , starting with the fifth , and steven inspects every third , starting with the third , how many of the 98 widgets produced in the first hour of operation are not inspected by either inspector ?
Options: a ) 91 , b ) 59 , c ) 53 , d ) 47 , e ) 45
Rationale: "widgets inspected by lauren : ( ( 95 - 5 ) / 5 ) + 1 = 18 + 1 = 19 widgets inspected by steven : ( ( 96 - 3 ) / 3 ) + 1 = 31 + 1 = 32 widgets inspected by both : ( ( 90 - 15 ) + 1 = 6 total : 19 + 32 - 6 = 45 hence , widgets not inspected : 98 - 45 = 53 answer : c"
Answer: c
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 1600 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 = 1600 x = ( 2 ^ 6 * 25 ) / 2 ^ 9 = 25 / 8 the answer is c ."
Answer: c
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 40 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 781 , b ) $ 755 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 790 * 20 ) / 26 = 781 answer is a . posted from my mobile device"
Answer: a
Problem: if two different solutions of alcohol with a respective proportion of water to alcohol of 3 : 1 and 2 : 3 were combined , what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts ?
Options: a ) 30.0 % , b ) 36.6 % , c ) 42.5 % , d ) 44.4 % , e ) 60.0 %
Rationale: alcohol : water first mixture - - 3 : 1 - - 15 : 5 second mixture - - 2 : 3 - - 8 : 12 equal amounts of the mixture were combined , hence the final mixture will be in the ratio - - ( 15 + 8 ) : ( 5 + 12 ) - - 23 : 17 % of alcohol - - 17 / ( 23 + 17 ) * 100 = ( 17 / 40 ) * 100 = 42.5 answer : c
Answer: c
Problem: if the sum of 3 consecutive even numbers is 44 more than the average of these numbers , then the largest of these numbers is ?
Options: a ) 24 , b ) 66 , c ) 9 , d ) 7 , e ) 01
Rationale: answer : 24 explanation : let the smallest of these number be x . the other two numbers are ( x + 2 ) and ( x + 4 ) . x + ( x + 2 ) + ( x + 4 ) = ( x + ( x + 2 ) + ( x + 4 ) ) / 3 + 44 3 x + 3 * ( x + 2 ) + 3 * ( x + 4 ) = x + ( x + 2 ) + ( x + 4 ) + 132 9 x + 18 = 3 x + 138 6 x = 120 x = 20 therefore , the largest number is 24 . answer : a
Answer: a
Problem: a man swims downstream 72 km and upstream 45 km taking 9 hours each time ; what is the speed of the current ?
Options: a ) 3 kmph , b ) 1.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 72 - - - 9 ds = 8 ? - - - - 1 45 - - - - 9 us = 5 ? - - - - 1 s = ? s = ( 8 - 5 ) / 2 = 1.5 answer : option b"
Answer: b
Problem: solution y is 30 percent liquid x and 70 percent water . if 4 kilograms of water evaporate from 8 kilograms of solution y and 4 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 40 % , b ) 41 1 / 2 % , c ) 44 % , d ) 45 % , e ) 46 %
Rationale: "in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 4 kilograms of water are replaced by 4 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 4 = 1.2 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 1.2 = 3.6 kilograms of solution x , which is 3.6 / 8 * 100 = 45 % of this new solution . answer : d ."
Answer: d
Problem: a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6600 ?
Options: a ) s . 4991 , b ) s . 5591 , c ) s . 6001 , d ) s . 6991 , e ) s . 7991
Rationale: "total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6600 * 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 . answer : b"
Answer: b
Problem: a can run 3 kms in 3 min 18 sec and b can run same distance in 3 min 40 sec , then by how much distance a can beat b ?
Options: a ) 300 m , b ) 220 m , c ) 280 m , d ) 195 m , e ) 295 m
Rationale: distance travelled = 3000 m time taken by a = 3 m 18 s time taken by b = 3 m 40 sec = 220 sec speed of b = 3000 m / 220 s = 150 / 11 m / s difference between time of a and b = 22 sec when time will be 3 m 18 s a will have travelled 3000 m but b need 22 sec more to finish . distance travelled by b in 22 sec = ( 150 / 11 ) * 22 = 300 m hence , a beat b by 300 m answer : a
Answer: a
Problem: 22 cubic centimetres of silver is drawn into a wire 1 mm in diameter . the length of the wire in metres will be :
Options: a ) 84 m , b ) 28 m , c ) 120 m , d ) 137 m , e ) none
Rationale: "sol . let the length of the wire b h . radius = 1 / 2 mm = 1 / 20 cm . then , 22 / 7 * 1 / 20 * 1 / 20 * h = 22 ⇔ = [ 22 * 20 * 20 * 7 / 22 ] = 2800 cm = 28 m . answer b"
Answer: b
Problem: two cyclists are moving towards each other at 10 miles / hour . they are now 50 miles apart . at this instance a fly starts from one cyclist and move towards other and moves to and fro till the two cyclist meet each other . if the fly is moving at 15 miles / hour , what is the total distance covered by the fly ?
Options: a ) 37.5 miles , b ) 38.5 miles , c ) 39.5 miles , d ) 36.5 miles , e ) 35.5 miles
Rationale: time taken by cyclists to meet = 50 / 20 2.5 hrs distance covered by fly during 2.5 hrs = 15 * 2.5 = 37.5 miles answer : a
Answer: a
Problem: students at a school were on average 180 cm tall . the average female height was 170 cm , and the average male height was 184 cms . what was the ratio s of men to women ?
Options: a ) 5 : 2 , b ) 5 : 1 , c ) 4 : 3 , d ) 4 : 1 , e ) 3 : 1
Rationale: ( a ) s = 184 x 5 + 170 x 2 = 1260 . a
Answer: a
Problem: the maximum numbers of students among them 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
Options: a ) 91 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
Rationale: "olution required number of students . = h . c . f of 1001 and 910 . ‹ = › 91 . answer a"
Answer: a
Problem: when a train travels at a speed of 100 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 15 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: let x be the time reached with the speed 100 km / h 50 km / h - - - - > x + 15 distance is equal so 100 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 100 x = 50 x + 750 so the would be in km and x = 15 answer : a
Answer: a
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 10 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 10 ° , c ) 18 ° , d ) 36 ° , e ) 50 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 10 + 24 + 15 + 29 + 8 = 86 % . so remaining 14 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 14 % will be 50 degrees . . imo option e ."
Answer: e
Problem: a train running at the speed of 60 km / hr crosses a pole in 3 sec . what is the length of the train ?
Options: a ) 50 , b ) 75 , c ) 100 , d ) 120 , e ) 25
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 3 = 50 m answer : a"
Answer: a
Problem: if the compound interest on a certain sum of money for 3 years at 10 % per annum be rs . 993 , what would be the simple interest ?
Options: a ) rs . 880 , b ) rs . 890 , c ) rs . 895 , d ) rs . 900 , e ) none
Rationale: let p = principal a - amount we have a = p ( 1 + r / 100 ) 3 and ci = a - p atq 993 = p ( 1 + r / 100 ) 3 - p ? p = 3000 / - now si @ 10 % on 3000 / - for 3 yrs = ( 3000 x 10 x 3 ) / 100 = 900 / - answer : d .
Answer: d
Problem: what least number must be subtracted from 427398 so that remaining no . is divisible by 13
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 10
Rationale: "explanation : on dividing 427398 by 13 we get the remainder 10 , so 10 should be subtracted answer : option e"
Answer: e
Problem: if k is the greatest positive integer such that 3 ^ k is a divisor of 24 ! then k =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 10
Rationale: "24 / 3 = 8 24 / 9 = 2 8 + 2 = 10 k = 10 answer : e"
Answer: e