regisss/math_qa huggingface dataset:
Problem: it is currently 7 : 05 pm . what time was it in the morning exactly 51,132 minutes ago ?
Options: a ) 6 : 53 , b ) 6 : 55 , c ) 6 : 59 , d ) 7 : 03 , e ) 7 : 09
Rationale: convert 51,132 minutes to hours by dividing by 60 : 51,132 / 60 = 852 r 12 . that is 852 hours , 12 minutes . convert 852 hours to days by dividing by 24 : 852 / 24 = 35 r 12 . that is 35 days , 12 hours . thus 852 hours before 7 : 05 pm is 12 hours before 7 : 05 pm which is 7 : 05 am . 12 minutes before that is 6 : 53 am . a
Answer: a
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 60 kmph , find the speed of the stream ?
Options: a ) 18 kmph , b ) 19 kmph , c ) 21 kmph , d ) 22 kmph , e ) 20 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 60 / 3 = 20 kmph . answer : e"
Answer: e
Problem: a contractor undertook to do a piece of work in 18 days . he employed certain number of laboures but 9 of them were absent from the very first day and the rest could finish the work in only 6 days . find the number of men originally employed ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 4.2 , e ) 4.3
Rationale: "let the number of men originally employed be x . 18 x = 6 ( x â € “ 9 ) or x = 4.5 answer c"
Answer: c
Problem: the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 432 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: area = l * w = 3 w ^ 2 = 432 w ^ 2 = 144 w = 12 the answer is c .
Answer: c
Problem: a certain car uses 12 gallons of gasoline in traveling 120 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 120 / 10 = 12 . the difference is 12 - 10 = 2 . answer a
Answer: a
Problem: the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . find out the average age of the team .
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25
Rationale: "number of members in the team = 11 let the average age of of the team = x = > ( sum of ages of all 11 members ) / 11 = x = > sum of the ages of all 11 members = 11 x age of the captain = 26 age of the wicket keeper = 26 + 3 = 29 sum of the ages of 9 members of the team excluding captain and wicket keeper = 11 x − 26 − 29 = 11 x − 55 average age of 9 members of the team excluding captain and wicket keeper = ( 11 x − 55 ) / 9 given that ( 11 x − 55 ) / 9 = ( x − 1 ) ⇒ 11 x − 55 = 9 ( x − 1 ) ⇒ 11 x − 55 = 9 x − 9 ⇒ 2 x = 46 ⇒ x = 46 / 2 = 23 years answer is d ."
Answer: d
Problem: a box contains 7 pairs of shoes ( 14 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 13 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 14 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 13 ( as after taking one at random there are 13 shoes left and only one is the pair of the first one ) = 1 / 13 answer : d ."
Answer: d
Problem: a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 2 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 4.8 km , c ) 3.4 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the required distance be x km total time taken = 2 hour â ‡ ’ x / 6 + x / 4 = 2 â ‡ ’ 2 x + 3 x = 24 â ‡ ’ 5 x = 24 â ‡ ’ x = 4.8 km answer : option b"
Answer: b
Problem: when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 3 - - > x = qy + 3 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 3 - - > y = 25 . answer : d ."
Answer: d
Problem: twelve machines , each working at the same constant rate , together can complete a certain job in 6 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 3 days ?
Options: a ) 14 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "rate of one machine = 1 job / ( 12 * 6 ) days let x = number of machines needed to complete the job in 3 days 1 / ( 12 * 6 ) * 3 * x = 1 job x = 24 24 - 12 = 12 answer : b"
Answer: b
Problem: if 2 + 3 = 13 ; 3 + 5 = 31 ; 5 + 7 = 59 , then 7 + 9 = ?
Options: a ) 95 , b ) 86 , c ) 67 , d ) 98 , e ) 89
Rationale: "2 x 2 + 3 ^ 2 = 4 + 9 = 13 3 x 2 + 5 ^ 2 = 6 + 25 = 31 5 x 2 + 7 ^ 2 = 10 + 49 = 59 and 7 x 2 + 9 ^ 2 = 14 + 81 = 95 answer : a"
Answer: a
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 1 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 1 people . so $ 25 . but , he also has to put in the average for himself ( the twoth person ) , so add $ 75 . so $ 100 is your answer . answer a"
Answer: a
Problem: 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days . how many days will 10 men and 10 boys together take to complete the same work
Options: a ) 9 days , b ) 10 days , c ) 11 days , d ) 12 days , e ) 13 days
Rationale: solution : work done by one man in one day = 1 / ( 15 * 10 ) work done by one boy in one day = 1 / ( 20 * 15 ) work done by 10 men and 10 boys in one day = 10 [ 1 / ( 15 * 10 ) + 1 / ( 20 * 15 ) ] days taken = 1 / work done by 10 men and 10 boys in one day answer b
Answer: b
Problem: a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 96 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 96 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 96 ( 2 r - 4 ) * r = 96 2 r ^ 2 - 4 r - 96 = 0 r can not be negative so r = 8 and c = 12 so , answer will be c"
Answer: c
Problem: what is 78 % of 4 / 5 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.624 , e ) 0.69
Rationale: "78 % * ( 4 / 5 ) = 0.78 * 0.8 = 0.624 answer : d"
Answer: d
Problem: find the area of a parallelogram with base 12 cm and height 48 cm ?
Options: a ) 122 cm 2 , b ) 576 cm 2 , c ) 246 cm 2 , d ) 42 cm 2 , e ) 39 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 48 = 576 cm 2 answer : b"
Answer: b
Problem: of the diplomats attending a summit conference , 25 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 70 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 25 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 70 . answer : b ."
Answer: b
Problem: a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price q per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average q = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Problem: excluding the stoppages , the speed of a bus is 48 km / hr and including the stoppages the speed of the bus is 12 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 45 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 48 km / hr speed of the bus with stoppage = 12 km / hr difference in speed = 36 km / hr so , the time taken in the stoppages = time taken to cover 36 km = ( 36 / 48 ) hr = 3 / 4 hr = 45 min answer : a"
Answer: a
Problem: a furniture dealer purchased a desk for $ 120 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 120 selling price = x 120 + 0.4 * x = x 0.6 * x = 120 x = 200 profit = 200 - 150 = 50 answer : a"
Answer: a
Problem: there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
Options: a ) 100 , b ) 105 , c ) 115 , d ) 120 , e ) 125
Rationale: "n ( s ) = sample space = 25 c 3 = 2300 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 15 or 1 girl from 10 = 15 c 2 + 10 c 1 = 115 ans - c"
Answer: c
Problem: the area of the square formed on the diagonal of a rectangle as its side is 108 1 / 3 % more than the area of the rectangle . if the perimeter of the rectangle is 28 units , find the difference between the sides of the rectangle ?
Options: a ) 5
b ) 4
c ) 7
d ) 2
e ) 1
Rationale: let the sides of the rectangle be l and b respectively . from the given data , ( √ l 2 + b 2 ) = ( 1 + 108 1 / 3 % ) lb = > l 2 + b 2 = ( 1 + 325 / 3 * 1 / 100 ) lb = ( 1 + 13 / 12 ) lb = 25 / 12 lb = > ( l 2 + b 2 ) / lb = 25 / 12 12 ( l 2 + b 2 ) = 25 lb adding 24 lb on both sides 12 l 2 + 12 b 2 + 24 lb = 49 lb 12 ( l 2 + b 2 + 2 lb ) = 49 lb but 2 ( l + b ) = 28 = > l + b = 14 12 ( l + b ) 2 = 49 lb = > 12 ( 14 ) 2 = 49 lb = > lb = 48 since l + b = 14 , l = 8 and b = 6 l - b = 8 - 6 = 2 m . answer : d
Answer: d
Problem: for what value of x between − 9 and 9 , inclusive , is the value of x ^ 2 − 10 x + 16 the greatest ?
Options: a ) − 9 , b ) − 2 , c ) 0 , d ) 2 , e ) 9
Rationale: "we can see from the statement that two terms containing x , x ^ 2 will always be positive and - 10 x will be positive if x is - ive . . so the equation will have greatest value if x is - ive , and lower the value of x , greater is the equation . so - 9 will give the greatest value . . ans a"
Answer: a
Problem: the owner of a furniture shop charges his customer 10 % more than the cost price . if a customer paid rs . 8800 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 6725 , b ) rs . 6727 , c ) rs . 8000 , d ) rs . 6725 , e ) rs . 6728
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 8800 ( 100 / 110 ) = rs . 8000 . answer : c"
Answer: c
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 348 per week . if instead , her weekly salary were to increase by 15 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 345 , d ) $ 392 , e ) $ 399
Rationale: "( 348 / 116 ) 115 = 345 in this case long division does not take much time . ( 348 / 116 ) = 3 3 * 115 = 345 ( 300 + 45 ) answer c"
Answer: c
Problem: the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 440 per month . the salary of the new supervisor is :
Options: a ) 233 , b ) 960 , c ) 287 , d ) 771 , e ) 191
Rationale: explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 440 = 3960 salary of the new supervisor = 3960 â ˆ ’ 3000 = 960 answer : b
Answer: b
Problem: if ( m - 8 ) is a factor of m ^ 2 - hm - 24 , then h =
Options: a ) 3 , b ) 5 , c ) 6 , d ) 11 , e ) 16
Rationale: ( m - 8 ) ( m - a ) = m ^ 2 - hm - 24 a = - 3 h = 8 + a = 5 = b
Answer: b
Problem: if the average of 5 x and 8 y is greater than 90 , and x is twice y , what is the least integer value of x ?
Options: a ) 4 , b ) 5 , c ) 20 , d ) 21 , e ) 23
Rationale: "if y is greater than 110 percent of x , is y greater than 75 ? ( 1 ) x > 75 x > 75 ( 2 ) y − x = 10 y − x = 10 pls verify . 1 ) sufficient . y > 1.1 x and x > 75 . min ( x ) = 75 y > 1.1 * 75 y > 82.5 2 ) insufficient . substituting ( x = y - 10 ) in y > 1.1 x y > 1.1 ( y - 10 ) y < 110 hence a ."
Answer: a
Problem: how many three - element subsets of { 1,2 , 3,4 } are there that do not contain the pair of elements 2 and 4 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "required subsets are = { 1 , 2,3 } , { 1 , 3,4 } = 2 answer : b"
Answer: b
Problem: the length of the bridge , which a train 500 metres long and travelling at 42 km / hr can cross in 60 seconds , is ?
Options: a ) 100 m , b ) 200 m , c ) 300 m , d ) 250 m , e ) 350 m
Rationale: "speed = [ 42 x 5 / 18 ] m / sec = [ 35 / 3 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 60 35 / 3 = ( 130 + x ) / 60 500 + x = 700 = > x = 200 m answer : b"
Answer: b
Problem: a bowl contains equal numbers of red , orange , green , blue , and yellow candies . kaz eats all of the green candies and half of the orange ones . next , he eats half of the remaining pieces of each color . finally , he eats red and yellow candies in equal proportions until the total number of remaining candies of all colors equals 20 % of the original number . what percent of the red candies remain ?
Options: a ) 5 % , b ) 7.5 % , c ) 10 % , d ) 12.5 % , e ) 15 %
Rationale: "let x be the original number of each color . kaz eats all of the green candies and half of the orange ones . there are 0 green candies and 0.5 x orange candies remaining . he eats half of the remaining pieces of each color . there are 0.25 x orange candies , and 0.5 x each of red , yellow , and blue candies . he eats red and yellow candies in equal proportions . orange + blue + red + yellow = 0.75 x + red + yellow = x red + yellow = 0.25 x red = 0.125 x , since red = yellow . the answer is d ."
Answer: d
Problem: there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 2343 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 12000 . t = 3 years and r = 10 % p . a . c . i . = rs . 12000 x 1 + 10 3 - 1 100 = rs . 12000 x 331 1000 = 3972 . e"
Answer: e
Problem: a man bought 40 shares of rs . 80 at 5 discount , the rate of dividend being 12 1 / 2 % the rate of interest obtained is
Options: a ) 13.33 % , b ) 15.5 % , c ) 14 % , d ) 14.25 % , e ) 14.95 %
Rationale: "explanation : face value of a share = rs . 80 he bought each share at rs . 80 - rs . 5 = rs . 75 number of shares = 40 dividend = 12 1 / 2 % = 25 / 2 % dividend per share = 80 × 25 / 2 / 100 = rs . 10 total dividend = ( 40 × 10 ) ie , he got a dividend of ( 40 × 10 ) for an investment of rs . ( 40 × 75 ) interest obtained = 40 × 10 × 100 / 40 × 75 = 13.33 % answer : option a"
Answer: a
Problem: the average of 2 , 76 and x is 5 . find the value of x ?
Options: a ) 10 , b ) 8 , c ) 12 , d ) 15 , e ) 5
Rationale: average = ( 2 + 7 + 6 + x ) / 4 = 5 x = 5 answer is e
Answer: e
Problem: a car averages 65 mph for the first 5 hours of a trip and averages 75 mph for each additional hour . the average speed for the entire trip was 60 mph . how many hours long is the trip ?
Options: a ) 9 , b ) 8 , c ) 7 , d ) 6 , e ) 5
Rationale: "let the time for which car averages 75 mph = t 60 * ( t + 5 ) = 65 * 4 + 70 t = > 10 t = 40 = > t = 4 total duration of the trip = 5 + 4 = 9 answer a"
Answer: a
Problem: if y > 0 , ( 6 y ) / 20 + ( 3 y ) / 10 is what percent of y ?
Options: a ) 40 % , b ) 50 % , c ) 60 % , d ) 70 % , e ) 80 %
Rationale: "can be reduced to 3 y / 10 + 3 y / 10 = 3 y / 5 = 60 % c"
Answer: c
Problem: if the number is divided by 3 , it reduced by 36 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 54 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 36 = > 2 x / 3 = 36 = > x = 54 answer : option d"
Answer: d
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 4 women and 30 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 4 women ’ s 1 day ’ s work = 1 / 192 × 4 = 1 / 48 1 child ’ s 1 day ’ s work = 1 / 240 30 children ’ s 1 day ’ s work = 1 / 8 therefore , ( 10 men + 4 women + 30 children ) ’ s 1 day ’ s work = 5 / 48 + 1 / 48 + 1 / 8 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Problem: in a group of 150 readers who read science fiction or literacy works or both , 120 read science fiction and 90 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 70 , b ) 60 , c ) 90 , d ) 100 , e ) 110
Rationale: consider total number of reader n ( s u l ) = 150 people who read science fiction n ( s ) = 120 people who read literacy works n ( l ) = 90 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 150 = 120 + 90 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 210 - 150 n ( s â ˆ © l ) = 60 so people read both science fiction and literacy works are 160 answer : b
Answer: b
Problem: the speed of a boat in still water in 30 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 36 minutes is :
Options: a ) 18.4 km , b ) 20.6 km , c ) 21.4 km , d ) 1111 km , e ) 22.2 km
Rationale: "explanation : speed downstream = ( 30 + 7 ) = 37 kmph time = 36 minutes = 36 / 60 hour = 3 / 5 hour distance travelled = time × speed = ( 3 / 5 ) × 37 = 22.2 km answer : option e"
Answer: e
Problem: 39 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 3 hours a day , complete the work ?
Options: a ) 10 , b ) 26 , c ) 14 , d ) 15 , e ) 16
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 3 : 5 30 x 3 x x = 39 x 5 x 12 x = ( 39 x 5 x 12 ) / ( 30 x 3 ) x = 26 . answer : b"
Answer: b
Problem: in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 90 kmph being 160 m and 140 m in length respectively ?
Options: a ) 5.6 sec , b ) 6.2 sec , c ) 6.0 sec , d ) 7.2 sec , e ) 6.8 sec
Rationale: "d = 160 m + 140 m = 300 m * 1 / 1000 = 0.3 kms rs = 90 + 90 = 180 kmph t = ( 0.3 / 180 ) * 3600 = 6.0 sec answer : c"
Answer: c
Problem: cole drove from home to work at an average speed of 80 kmh . he then returned home at an average speed of 120 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "first round distance travelled ( say ) = d speed = 80 k / h time taken , t 2 = d / 80 hr second round distance traveled = d ( same distance ) speed = 120 k / h time taken , t 2 = d / 120 hr total time taken = 2 hrs therefore , 2 = d / 80 + d / 120 lcm of 80 and 120 = 240 2 = d / 80 + d / 120 = > 2 = 3 d / 240 + 2 d / 240 = > d = 240 * 2 / 5 km therefore , t 1 = d / 80 = > t 1 = ( 240 * 2 ) / ( 5 x 80 ) = > t 1 = ( 6 x 60 ) / 5 - - in minutes = > t 1 = 72 minutes . c"
Answer: c
Problem: the total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year , less the age of the tree in years ( rounded down to the nearest integer ) . during its 2 nd year , the plum tree grew 50 plums . if this trend continues , how many plums will it grow during its 6 th year ?
Options: a ) 36 , b ) 38 , c ) 40 , d ) 42 , e ) 48
Rationale: "1 st year : 0 - 1 ( age ) , we take age = 0 ( as the question says that we have to ( rounded down to the nearest integer ) ) 2 ndyear : 1 - 2 ( age ) , we take age = 1 3 rd year : 2 - 3 ( age ) , we take age = 2 4 th year : 3 - 4 ( age ) , we take age = 3 5 th year : 4 - 5 ( age ) , we take age = 4 6 th year : 5 - 6 ( age ) , we take age = 5 thus for the 2 nd year = 50 , 3 rd year = 50 - 2 = 48 4 th year = 48 - 3 = 45 5 th year = 45 - 4 = 41 . 6 th year = 41 - 5 = 36 the correct answer is a ."
Answer: a
Problem: a trader mixes 80 kg of tea at 15 per kg with 20 kg of tea at cost price of 20 per kg . in order to earn a profit of 25 % , what should be the sale price of the mixed tea ?
Options: a ) 23.75 , b ) 22 , c ) 20 , d ) 19.20 , e ) none of these
Rationale: "c . p . of mixture = 80 × 15 + 20 × 20 / 80 + 20 = 16 ∴ s . p . = ( 100 + 25 ) / 100 × 16 = 20 answer c"
Answer: c
Problem: pipe a fills a tank of capacity 800 liters at the rate of 40 liters a minute . another pipe b fills the same tank at the rate of 30 liters a minute . a pipe at the bottom of the tank drains the tank at the rate of 20 liters a minute . if pipe a is kept open for a minute and then closed and pipe b is open for a minute and then closed and then pipe c is open for a minute and then closed and the cycle is repeated , when will the tank be full ?
Options: a ) 48 minutes , b ) 14 minutes , c ) 39 minutes , d ) 40 minutes 20 seconds , e ) none of these
Rationale: "in one cycle they fill 40 + 30 - 20 = 50 liters 800 = 50 * n = > n = 16 here n = number of cycles . total time = 16 * 3 = 48 as in one cycle there are 3 minutes . thus 48 minutes answer : a"
Answer: a
Problem: in a dairy farm , 20 cows eat 10 bags of husk in 40 days . in how many days one cow will eat one bag of husk ?
Options: a ) 20 , b ) 40 , c ) 80 , d ) 30 , e ) 60
Rationale: "one cow eats 10 / 20 = 0.5 bags of husk in 40 days . then , it eats 1 bag in 40 / 0.5 = 80 days answer : c"
Answer: c
Problem: if w / x = 1 / 3 and w / y = 3 / 4 , then ( x + y ) / y =
Options: a ) 13 / 4 , b ) 6 / 5 , c ) 7 / 5 , d ) 8 / 5 , e ) 9 / 5
Rationale: "w / x = 1 / 3 = > x = 3 w and w / y = 3 / 4 = > y = ( 4 / 3 ) w ( x + y ) / y = ( 3 w + 4 / 3 w ) / ( 4 / 3 w ) = ( 13 / 3 w ) / ( 4 / 3 w ) = 13 / 4 correct option : a"
Answer: a
Problem: the speed of a boat in still water is 15 km / hr and the rate of current is 3 km / hr . the distance travelled downstream in 24 minutes is
Options: a ) 17.2 km , b ) 7.2 km , c ) 7.6 km , d ) 17.6 km , e ) 27.2 km
Rationale: "speed of a boat in still water = 15 km / hr speed of the current = 3 km / hr speed downstream = ( 15 + 3 ) = 18 km / hr distance travelled downstream in 24 minutes = ( 24 / 60 ) × 18 = ( 2 × 18 ) / 5 = 7.2 km answer is b"
Answer: b
Problem: a man is 20 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 11 , b ) 25 , c ) 27 , d ) 18 , e ) 91
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 20 ) years . ( x + 20 ) + 2 = 2 ( x + 2 ) x + 22 = 2 x + 4 = > x = 18 . answer : d"
Answer: d
Problem: a gardener grows cabbages in her garden that is in the shape of a square . each cabbage takes 1 square feet of area in her garden . this year , she has increased her output by 193 cabbages as compared to last year . the shape of the area used for growing the cabbages has remained a square in both these years . how many cabbages did she produce this year ?
Options: a ) 8,208 , b ) 9,409 , c ) 11,424 , d ) 12,586 , e ) can not be determined
Rationale: "let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 193 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 193 ( x + y ) ( x - y ) = 193 193 is a prime number and thus it will be ( 97 + 96 ) * ( 97 - 96 ) . thus x = 97 and y = 96 x ^ 2 = 97 ^ 2 = 9409 the answer is b ."
Answer: b
Problem: a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2400
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 164.36 * 100 / 2400 ) = 6.84 % = 7 % approx option d"
Answer: d
Problem: if d is the smallest positive integer such that 3150 multiplied by d is the square of an integer , then d must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 14
Rationale: solution : this problem is testing us on the rule that when we express a perfect square by its unique prime factors , every prime factor ' s exponent is an even number . let ’ s start by prime factorizing 3150 . 3150 = 315 x 10 = 5 x 63 x 10 = 5 x 7 x 3 x 3 x 5 x 2 3150 = 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 ( notice that the exponents of both 2 and 7 are not even numbers . this tells us that 3150 itself is not a perfect square . ) we also are given that 3150 multiplied by d is the square of an integer . we can write this as : 2 ^ 1 x 3 ^ 2 x 5 ^ 2 x 7 ^ 1 x d = square of an integer according to our rule , we need all unique prime factors ' exponents to be even numbers . thus , we need one more 2 and one more 7 . therefore , d = 7 x 2 = 14 answer is e .
Answer: e
Problem: at garage sale , all of the prices of the items sold were different . if the price of a radio sold at the garage sale was both the 9 th highest price and the 35 th lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 43 , b ) 28 , c ) 44 , d ) 49 , e ) 46
Rationale: 8 + 34 + 1 = 43 answer : a
Answer: a
Problem: excluding the stoppages , the speed of a bus is 12 km / hr and including the stoppages the speed of the bus is 6 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 30 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 12 km / hr speed of the bus with stoppage = 6 km / hr difference in speed = 6 km / hr so , the time taken in the stoppages = time taken to cover 6 km = ( 6 / 12 ) hr = 1 / 2 hr = 30 min answer : b"
Answer: b
Problem: the diameter of the driving wheel of a bus in 140 cm . how many revolutions per minute must the wheel make in order to keep a speed of 14 kmph ?
Options: a ) 53.03 , b ) 50.01 , c ) 23.23 , d ) 24.23 , e ) 41.23
Rationale: "distance covered in 1 min = ( 14 * 1000 ) / 60 = 233.33 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 233.33 / 4.4 = 53.03 answer : a"
Answer: a
Problem: in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 45 ducks and in the larger pond there are 55 ducks . if 20 % of the ducks in the smaller pond are green and 40 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
Options: a ) 25 % , b ) 27 % , c ) 29 % , d ) 31 % , e ) 33 %
Rationale: "number of ducks in small pond = 45 green ducks in small pond = 20 % of 45 = 9 ducks number of ducks in large pond = 55 green ducks in large pond = 40 % of 55 = 22 ducks total number of ducks = 45 + 55 = 100 total number of green ducks = 9 + 22 = 31 ducks percentage of green ducks = 31 / 100 * 100 = 31 % answer : d"
Answer: d
Problem: rice weighing 35 / 2 pounds was divided equally and placed in 4 containers . how many ounces of rice were in each container ? ( note that 1 pound = 16 ounces )
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: 35 / 2 ÷ 4 = 35 / 8 pounds in each container 35 / 8 pounds * 16 ounces / pound = 70 ounces in each container the answer is d .
Answer: d
Problem: what is the sum of the greatest common factor and the lowest common multiple of 12 and 48 ?
Options: a ) 20 , b ) 60 , c ) 40 , d ) 56 , e ) 20
Rationale: "prime factorization of 12 = 2 x 2 x 3 prime factorization of 48 = 2 x 2 x 2 x 2 x 3 gcf = 12 lcm = 48 sum = 60 ans : b"
Answer: b
Problem: a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 10 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 3000 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,050 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 10 $ then total value is 300 * 10 = 3000 . imo option a is correct answer . ."
Answer: a
Problem: ashok secured average of 74 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 66 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 74 therefore total marks in 6 subjects = 74 * 6 = 444 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 444 – 370 = 74 answer b"
Answer: b
Problem: susan made a block with small cubes of 5 cubic cm volume to make a block 7 small cubes long , 7 small cubes wide and 6 small cubes deep . she realise that she has used more small cubes than she really needed . she realised that she could have glued a fewer number of cubes together ot look like a block with same dimensions , if it were made
Options: a ) 194
b ) 195
c ) 196
d ) 197
e ) 198
Rationale: volume of cube of dimensions 7 7 6 is 7 * 7 * 6 = 294 if it were to look hollow the imaginary inside cube volume is to be deducted which is ( 7 - 2 ) * ( 7 - 2 ) * ( 6 - 2 ) = 100 ( here 2 is deducted because the inside cube which has to be hollow is 2 cubes more on every dimension ) so minimum number of cubes required to make hollow cube is 294 - 100 = 194 cubes answer : a
Answer: a
Problem: in a dairy farm , 55 cows eat 55 bags of husk in 55 days . in how many days one cow will eat one bag of husk ?
Options: a ) 34 days , b ) 40 days , c ) 46 days , d ) 50 days , e ) 55 days
Rationale: "explanation : less cows , more days ( indirect proportion ) less bags , less days ( direct proportion ) [ cows 1 55 bags 55 1 ] : : 55 : x = > x ∗ 55 ∗ 1 = 55 ∗ 1 ∗ 55 = > x = 55 option e"
Answer: e
Problem: today joelle opened an interest - bearing savings account and deposited $ 10,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
Options: a ) $ 12025 , b ) $ 11075 , c ) $ 11025 , d ) $ 11095 , e ) $ 11015
Rationale: "interest for 1 st year = 10000 * 5 / 100 = 500 interest for 2 nd year = 10500 * 5 / 100 = 525 total = 10000 + 500 + 525 = 11025 answer : c"
Answer: c
Problem: what is the prime factors ’ number of 18 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "prime factors ’ number , as i assume , for a number x = a ^ n * b ^ m * c ^ o * d ^ p . . . is = n + m + o + p . . . so , 24 = 2 ^ 1 * 3 ^ 2 prime factors ’ number will be 1 + 2 = 3 . hence , answer is b ."
Answer: b
Problem: a sum of money at simple interest amounts to $ 645 in 3 years and to $ 690 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 510 , c ) $ 598 , d ) $ 549 , e ) $ 675
Rationale: "b $ 510 s . i . for 1 year = $ ( 690 - 645 ) = $ 45 . s . i . for 3 years = $ ( 45 x 3 ) = $ 135 . principal = $ ( 645 - 135 ) = $ 510 ."
Answer: b
Problem: john and david can finish a job together in 4 hours . if john can do the job by himself in 5 hours , what percent of the job does david do ?
Options: a ) 20 % , b ) 25 % , c ) 24 % , d ) 23 % , e ) 22 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 20 donuts which is the job ( i picked this as a smart number ) . john on his own works 20 / 5 = 4 donuts per hour . john and david work 20 / 4 = 5 donuts per hour so david works 1 donuts / hour to find out the percentage , david works 1 donuts / hr x 4 hours = 4 donuts per hour . therefore 4 donuts / 20 donuts = 1 / 5 = 20 % answer : a"
Answer: a
Problem: a tank is filled in 10 hours by 3 pipes a , b and c . the pipe c is twice as fast as b and b is twice as fast as a . how much time will pipe a alone take to fill the tank ?
Options: a ) 70 hours , b ) 30 hours , c ) 35 hours , d ) 50 hours , e ) 60 hours
Rationale: 1 / a + 1 / b + 1 / c = 1 / 10 ( a , b and c 1 hour work ) given . . 1 / b = 2 / a and 1 / c = 2 / b = 4 / a hence 1 / a + 2 / a + 4 / a = 1 / 10 on solving . . . . we get 1 / a = 1 / 70 ( work done by a in 1 hour ) therefore time taken by a is 70 hours to finish the whole work answer : a
Answer: a
Problem: in a certain production lot , 40 percent of the toys are red and the remaining toys are green . half of toys are small and half are large . if 10 percent of the toys are red and small , and 40 toys are green and large . how many of the toys are red and large ?
Options: a ) 40 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: 40 % toys are red . 50 % toys are small - 50 % are large red and small - 10 % red and large must be 30 % ( since there are total 40 % red toys ) but 50 % toys are large . if 30 % are red and large , the rest 20 % large toys must be green . so large and green toys are 20 % . these 20 % large and green toys are actually 40 so total number of toys must be 200 . since red and large toys are 30 % , they must be 60 . answer : b
Answer: b
Problem: if 4 ( p ' s capital ) = 6 ( q ' s capital ) = 10 ( r ' s capital ) , then out of the total profit of rs 4030 , r will receive
Options: a ) 600 , b ) 780 , c ) 800 , d ) 900 , e ) none of these
Rationale: "explanation : let p ' s capital = p , q ' s capital = q and r ' s capital = r then 4 p = 6 q = 10 r = > 2 p = 3 q = 5 r = > q = 2 p / 3 r = 2 p / 5 p : q : r = p : 2 p / 3 : 2 p / 5 = 15 : 10 : 6 r ' s share = 4030 * ( 6 / 31 ) = 130 * 6 = 780 . answer : option b"
Answer: b
Problem: a train 150 m long is running with a speed of 68 kmph . in what time will it pass a man who is running at 8 kmph in the same direction in which the train is going ?
Options: a ) 5 seconds , b ) 6 seconds , c ) 9 seconds , d ) 8 seconds , e ) 7 seconds
Rationale: "relative speed of train and man = 60 kmph or 300 / 18 m / s time taken by the train to pass the man : length of the train / relative speed 150 / 300 / 18 = 9 seconds . answer : c"
Answer: c
Problem: mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 11 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: if n = 12 mark sold 1 box and ann sold 10 boxes total 11 < 12 answer : c
Answer: c
Problem: in a forest 10 rabbits were caught , tagged with electronic markers , then released . a month later , 10 rabbits were captured in the same forest . of these 10 rabbits , it was found that 2 had been tagged with the electronic markers . if the percentage of tagged rabbits in the second sample approximates the percentage of tagged rabbits in the forest , and if no rabbits had either left or entered the forest over the preceding month , what is the approximate number of rabbits in the forest ?
Options: a ) 150 , b ) 70 , c ) 50 , d ) 1500 , e ) 500
Rationale: given that 10 rabbits were caught and tagged in the first sample , and 10 were caught in the second sample of which 2 had tags , then 2 / 10 approximates the fraction of the population of tagged rabbits in the forest . proportion : a / x = c / d a = rabbits tagged first sample c / d = the fraction of the population of tagged rabbits in the forest x = the population of rabbits in the forest proportion : 10 / x = 1 / 5 x = ( 1 ) ( 10 ) ( 5 ) = 50 . there are approximately 50 rabbits in the forest . answer is c
Answer: c
Problem: a man ' s speed with the current is 18 km / hr and the speed of the current is 2.5 km / hr . the man ' s speed against the current is ?
Options: a ) 10 , b ) 18 , c ) 50 , d ) 30 , e ) 40
Rationale: "man ' s speed with the current = 18 km / hr = > speed of the man + speed of the current = 18 km / hr speed of the current is 2.5 km / hr hence , speed of the man = 18 - 2.5 = 20.5 km / hr man ' s speed against the current = speed of the man - speed of the current = 20.5 - 2.5 = 18 km / hr answer is b ."
Answer: b
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 45 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 160 , e ) 180
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 15 miles per hour . the time to catch up is 60 / 15 = 4 hours . in 4 hours , train a travels another 30 * 4 = 120 miles for a total of 180 miles . the answer is e ."
Answer: e
Problem: if a is a positive integer , and if the units digit of a ^ 2 is 9 and the units digit of ( a + 1 ) ^ 2 is 4 , what is the units g digit of ( a + 2 ) ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) c . 14
Rationale: "i also got a . by punching in numers : g . . . 7 ^ 2 = . . . 9 . . . 8 ^ 2 = . . . 4 . . . 9 ^ 2 = . . . 1 . a"
Answer: a
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 30 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 25.7 , e ) 27
Rationale: "producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 30 % of the final price - - > ( final price ) * 0.7 = $ 18 - - > ( final price ) = $ 25.7 . answer : d ."
Answer: d
Problem: micheal and adam can do together a piece of work in 20 days . after they have worked together for 15 days micheal stops and adam completes the remaining work in 10 days . in how many days micheal complete the work separately .
Options: a ) 40 days , b ) 100 days , c ) 120 days , d ) 110 days , e ) 90 days
Rationale: "rate of both = 1 / 20 together they do = 1 / 20 * 15 = 3 / 4 left work = 1 - 3 / 4 = 1 / 4 adam completes 1 / 4 work in 10 day so he took 10 * 4 = 40 days to complete the left work alone . thus the rate of adam is 40 / 1 rate of micheal = 1 / 20 - 1 / 40 = 1 / 40 thus micheal takes 40 days to complete the whole work . ans . a ."
Answer: a
Problem: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 10 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 17 , c ) 15 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 10 = > 1 / x = 1 / 6 - 1 / 10 = ( 5 - 3 ) / 30 = 2 / 30 = 1 / 15 = > x = 15 . answer : c"
Answer: c
Problem: rs . 1581 is divided among a , b and c in the ratio 10 : 15 : 6 . what is the share of b ?
Options: a ) 306 , b ) 765 , c ) 700 , d ) 510 , e ) 520
Rationale: "10 + 15 + 6 = 31 1581 / 31 = 51 so b ' s share = 15 * 51 = 765 a ' s share = 10 * 51 = 510 c ' s share = 6 * 51 = 306 answer : a"
Answer: a
Problem: employees of a certain company are each to receive a unique 10 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 9 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 145,660 , b ) 149,720 , c ) 155,420 , d ) 161,280 , e ) 167,480
Rationale: "there are 8 ! ways to make codes starting with 12 . there are 8 ! ways to make codes starting with 24 . there are 8 ! ways to make codes starting with 36 . there are 8 ! ways to make codes starting with 48 . the number of codes is 4 * 8 ! = 161,280 . the answer is d ."
Answer: d
Problem: how many terminating zeroes w does 200 ! have ?
Options: a ) 40 , b ) 48 , c ) 49 , d ) 55 , e ) 64
Rationale: you have 40 multiples of 5 , 8 of 25 and 1 of 125 . this will give 49 zeros . c
Answer: c
Problem: two trains 500 m and 750 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.6 , b ) 45 , c ) 10.4 , d ) 10.8 , e ) 10.1
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 500 + 750 = 1250 m . required time = 1250 * 9 / 250 = 45 sec . answer : b"
Answer: b
Problem: a train 110 m long is running with a speed of 36 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 9 , e ) 5
Rationale: "speed of train relative to man = 36 + 6 = 42 km / hr . = 42 * 5 / 18 = 35 / 3 m / sec . time taken to pass the men = 110 * 3 / 35 = 9 sec . answer : d"
Answer: d
Problem: if x + y = 3 and y / x = 2 then y = ?
Options: a ) 0 , b ) 1 / 2 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "from the given data : y / ( 3 - y ) = 2 = > y = 6 - 2 y = > y = 2 answer : e"
Answer: e
Problem: tough and tricky questions : remainders . 1 ^ 1 + 2 ^ 2 + 3 ^ 3 + . . . + 7 ^ 7 is divided by 7 . what is the remainder ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: a number is divisible by 5 , if its last digit is divisible by 5 let ' s look into the sum of last digits of each term of the given expression 1 ^ 1 = 1 2 ^ 2 = 4 3 ^ 3 = 7 4 ^ 4 = 6 5 ^ 5 = 5 6 ^ 6 = 6 7 ^ 7 = 3 adding all these numbers we get 32 which gives a remainder of 4 when divided by 7 . so answer must be 4 . bunuel , can you please confirm the answer of this question . yes , the oa is c . clicked the wrong button when posting . edited . thank you . e
Answer: e
Problem: a sells a bicycle to b and makes a profit of 50 % . b sells the same bicycle to c at a profit of 25 % . if the final s . p . of the bicycle was rs . 225 , find out the cost price of the bicycle for a .
Options: a ) 237 , b ) 126 , c ) 971 , d ) 611 , e ) 120
Rationale: "explanation : let cp be 100 a sells at 50 % profit so sp = 150 b sells at 25 % profit = 150 x ( 1 + 25 / 100 ) = 187.50 cp - - - sp 100 - - - 187.50 x - - - 225 cp = 225 x 100 / 187.50 = 120 answer : e"
Answer: e
Problem: what is the units digit of ( 147 ^ 17 ) ^ 47 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 17 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 47 has the form 4 n + 3 , so the units digit is 3 . the answer is b .
Answer: b
Problem: how many times digit 5 is used while writing numbers from 100 to 1000 ?
Options: a ) 648 , b ) 300 , c ) 252 , d ) 225 , e ) 290
Rationale: "there are 100 numbers which begin with 600 next , in every 10 numbers such as 100 to 110 , 110 to 120 , 120 to 130 5 comes at least once . number of such intervals = end limit - first no . / interval . our range of numbers is 100 - 1000 1000 - 100 = 900 / 10 = 90 number of 10 s interval in this is 90 . so 90 ' 6 s ' so far we have calculated 190 . the total now comes to 280 . the nearest to which is 290 . hence e ."
Answer: e
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 90,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 76000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 190000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 190000 - x ) = x / 3 + x / 2 = 95000 = 5 x / 6 = 95000 = x = 95000 x 6 / 5 = 114000 savings in public provident fund = rs . ( 190000 - 114000 ) = rs . 76000 answer is d"
Answer: d
Problem: average marks of a , b , c is 48 . when d joins average becomes 47 . e has 3 more marks than d . average marks of b , c , d , e is 48 . what is the marks of a ?
Options: a ) 43 , b ) 44 , c ) 45 , d ) 46 , e ) 47
Rationale: a + b + c = 144 a + b + c + d = 188 d = 44 e = 47 b + c + d + e = 192 b + c = 101 a = 43 answer : a
Answer: a
Problem: a sum of money at simple interest amounts to rs . 720 after 2 years and to rs . 1020 after a further period of 5 years . the sum is :
Options: a ) 400 , b ) 500 , c ) 600 , d ) 700 , e ) 800
Rationale: "si of 5 year = ( 1020 - 720 ) = 300 so , si of 1 year = 300 / 5 = 60 so , si of 2 year = 60 * 2 = 120 so , sum is = ( 720 - 120 ) = 600 answer : c"
Answer: c
Problem: 3 candidates in an election and received 3136 , 7636 and 11628 votes respectively . what % of the total votes did the winning candidate got in that election ?
Options: a ) 45 % , b ) 49 % , c ) 52 % , d ) 59 % , e ) 61 %
Rationale: "total number of votes polled = ( 3136 + 7636 + 11628 ) = 22400 so , required percentage = 11628 / 22400 * 100 = 52 % c"
Answer: c
Problem: two pipes p and q can fill a cistern in 12 and 15 minutes respectively . both are opened together , but at the end of 2 minutes the first is turned off . how many more minutes will it take for the cistern to fill after the first pipe is turned off ?
Options: a ) 8.5 , b ) 9.5 , c ) 10.5 , d ) 11.5 , e ) 12.5
Rationale: "let x be the total time it takes for the cistern to fill . 2 / 12 + x / 15 = 1 x / 15 = 5 / 6 x = 12.5 after the first pipe is turned off , it takes 10.5 more minutes to fill the cistern . the answer is c ."
Answer: c
Problem: 864.942 - ? + 45.76 = 547.905
Options: a ) a ) 899.015 , b ) b ) 752.804 , c ) c ) 714.642 , d ) d ) 362.797 , e ) of these
Rationale: "explanation : 362.797 answer : option d"
Answer: d
Problem: the l . c . m . of 2 numbers is 66 . the numbers are in the ratio 2 : 3 . find their sum ?
Options: a ) 36 , b ) 40 , c ) 48 , d ) 32 , e ) 55
Rationale: "let the numbers be 2 x and 3 x l . c . m . = 6 x 6 x = 66 x = 11 the numbers are = 22 and 33 required sum = 22 + 33 = 55 answer is e"
Answer: e