regisss/math_qa huggingface dataset:
Problem: the dimensions of a rectangular solid are 6 inches , 5 inches , and 8 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17
b ) 2 : 5
c ) 5 : 16
d ) 10 : 19
e ) 32 : 25
Rationale: answer : d .
Answer: d
Problem: john purchased some shirts and trousers for $ 1300 . he paid $ 500 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "given that the total purchase of two items cost 1300 so the average purchase of one item will cost 1300 / 2 = 650 . its given as total shirt cost 500 $ less . hence total shirt cost = 650 - 250 and total trouser cost = 650 + 250 5 shirts = 400 $ = = > one shirt = 80 $ one trouser = 80 + 20 = 100 $ total trousers = 900 / 100 = 9 . e"
Answer: e
Problem: a contractor undertakes to complete the construction of a tunnel 720 meters long in 240 days and employs 50 men for the purpose . after 120 days , he finds that only 240 meters of the tunnel is complete . how many more men should be employ in order to complete the work in time ?
Options: a ) 75 men , b ) 80 men , c ) 70 men , d ) 60 men , e ) 50 men
Rationale: "in 120 days , only 240 m of the tunnel is constructed by 50 men . the remaining 120 days , 480 m of the tunnel can be constructed by 120 men . additional number of men required = 120 - 50 = 70 men . answer : c"
Answer: c
Problem: for all integers x > 1 . < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 . what is the value of < 2 > * < 4 > ?
Options: a ) 60 , b ) 116 , c ) 210 , d ) 263 , e ) 360
Rationale: since < x > = 2 x + ( 2 x - 1 ) + ( 2 x - 2 ) + . . . . . . 2 + 1 = 1 + 2 + . . + ( 2 x - 2 ) + ( 2 x - 1 ) + 2 x then < x > is basically the sum of all integers from 1 to 2 x , inclusive . hence < 2 > is the sum of all integers from 1 to 2 * 2 = 4 and < 4 > is the sum of all integers from 1 to 2 * 4 = 8 - > < 4 > = 36 and < 2 > = 10 - - > < 3 > * < 2 > = 21 * 10 = 360 answer : e
Answer: e
Problem: two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm . what is the area of the region where the two circles intersect ?
Options: a ) 16 - 4 pi
b ) 4 - pi
c ) 2 pi - 4
d ) 8 pi - 16
e ) pi ^ 2 - 4
Rationale: drawing a diagram , we see that the radius of the circle equals the side of the square . the area of intersection is : pi * r ^ 2 / 4 - ( r ^ 2 - pi * r ^ 2 / 4 ) = pi * r ^ 2 / 2 - r ^ 2 = 8 pi - 16 the answer is d .
Answer: d
Problem: pradeep has to obtain 35 % of the total marks to pass . he got 150 marks and failed by 25 marks . the maximum marks are
Options: a ) 300 , b ) 600 , c ) 800 , d ) 500 , e ) 900
Rationale: "explanation : let their maximum marks be x . then , 35 % of x = 150 + 25 = > 35 / 100 x = 175 x = ( 17500 / 35 ) x = 500 . answer : d"
Answer: d
Problem: if 4 people are selected from a group of 6 married couples , what is the probability that none of them would be married to each other ?
Options: a ) 1 / 33 , b ) 2 / 33 , c ) 1 / 3 , d ) 16 / 33 , e ) 11 / 12
Rationale: "each couple can send only one ` ` representative ' ' to the committee . we can choose 4 couples ( as there should be 4 members ) to send only one ` ` representatives ' ' to the committee in c 46 c 64 # of ways . but these 4 chosen couples can send two persons ( either husband or wife ) : 2 ∗ 2 ∗ 2 ∗ 2 = 242 ∗ 2 ∗ 2 ∗ 2 = 24 . so # of ways to choose 4 people out 6 married couples so that none of them would be married to each other is : c 46 ∗ 24 c 64 ∗ 24 . total # of ways to choose 4 people out of 12 is c 412 c 124 . p = c 46 ∗ 24 c 412 = 1633 p = c 64 ∗ 24 c 124 = 1633 answer : d ."
Answer: d
Problem: if the length of a rectangle is increased by 20 % and the breadth is reduced by 20 % , what will be the effect on its area ?
Options: a ) 4 % increase
b ) 6 % increase
c ) 5 % decrease
d ) 4 % decrease
e ) none of these
Rationale: percentage change = x - y - xy ⁄ 100 = 20 – 20 – 20 × 20 / 100 = − 4 % = 4 % decrease answer d
Answer: d
Problem: each light bulb at a hotel is either incandescent or fluorescent . at a certain moment , forty percent of the incandescent bulbs are switched on , and eighty percent of the fluorescent bulbs are switched on . if 75 percent of all the bulbs are switched on at this moment , what percent of the bulbs that are switched on are incandescent ?
Options: a ) 6.7 % , b ) 10.3 % , c ) 14.5 % , d ) 18.2 % , e ) 23.6 %
Rationale: "let i be the number of incandescent bulbs . let f be the number of fluorescent bulbs . 0.4 i + 0.8 f = 0.75 ( i + f ) 0.05 f = 0.35 i f = 7 i this means that for every 1 incandescent bulb , there are 7 fluorescent bulbs . the percent of bulbs that are switched on which are incandescent is : 0.4 i / ( 0.4 i + 0.8 f ) = 0.4 i / ( 0.4 i + 0.8 * 7 i ) = 0.4 i / 6 i = 1 / 15 which is about 6.7 % . the answer is a ."
Answer: a
Problem: a and b can do a piece of work in 2 days and 6 days respectively . both work for 1 days and then a goes away . find how long will b take to complete the remaining work ?
Options: a ) 1 days , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
Rationale: 1 / 2 + ( 1 + x ) / 6 = 1 x = 2 days answer : b
Answer: b
Problem: karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many h miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: "let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him h : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer ."
Answer: d
Problem: rs . 1210 were divided among 3 person p , q , r so that p : q = 5 : 4 and q : r = 9 : 10 . then r gets the amount .
Options: a ) rs . 300 , b ) rs . 400 , c ) rs . 480 , d ) rs . 490 , e ) rs . 500
Rationale: "p : q = 5 : 4 , q : r = 9 : 10 = ( 9 x 4 / 9 ) : ( 10 x 4 / 9 ) = 4 : 40 / 9 . so , p : q : r = 5 : 4 : 40 / 9 = 45 : 36 : 40 sum of ratio terms is = ( 45 + 36 + 40 ) = 121 . r share of amount is rs ( 1210 x 40 / 121 ) = rs . 400 . b"
Answer: b
Problem: in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 14.50 per kg to obtain a mixture costing rs . 9.75 per kg ?
Options: a ) 19 : 10 , b ) 19 : 11 , c ) 11 : 19 , d ) 12 : 18 , e ) 11 : 20
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 14.50 - 9.75 ) / ( 9.75 - 7 ) = 31 / 15 answer : b"
Answer: b
Problem: if 10 is added to thrice a number and this sum is multiplied by 5 , the result is the same as if the number is multiplied by 5 and 13 is added to the product . what is the number ?
Options: a ) - 3.5 , b ) - 3.7 , c ) - 5 , d ) - 9 , e ) 11
Rationale: "let the number be x ; 5 ( 10 + 3 x ) = 5 x + 13 ; x = - 3.7 answer : b"
Answer: b
Problem: if a 2 + b 2 + c 2 = 390 and ab + bc + ca = 5 , then a + b + c is
Options: a ) 19 , b ) 20 , c ) 25 , d ) 30 , e ) 64
Rationale: by formula , ( a + b + c ) ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 + 2 ( ab + bc + ca ) , since , a ^ 2 + b ^ 2 + c ^ 2 = 390 and ab + bc + ca = 5 , ( a + b + c ) ^ 2 = 390 + 2 ( 5 ) = 400 = 20 ^ 2 therefore : a + b + c = 20 answer : b
Answer: b
Problem: in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1500 employees , then the no . of female employees who are computer literate ?
Options: a ) 630 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1500 female employees , 60 % of 1500 . = ( 60 * 1500 ) / 100 = 900 . then male employees , = 600 50 % of male are computer literate , = 300 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1500 ) / 100 = 930 computer literate . thus , female computer literate = 930 - 300 = 630 answer : option a"
Answer: a
Problem: what will be the remainder when ( 27 ^ 27 ) + 27 is divided by 28 ?
Options: a ) 22 , b ) 20 , c ) 24 , d ) 26 , e ) 28
Rationale: "x ^ n + 1 will be divisible by x + 1 only when n is odd 27 ^ 27 + 1 will be divisible by 27 + 1 ( 27 ^ 27 + 1 ) + 26 , when divided by 28 will give 26 as remainder answer is d"
Answer: d
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 140 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 18
Rationale: let number of hens = h number of cows = c number of heads = 48 ⇒ h + c = 48 ⋯ ( 1 ) number of feet = 140 ⇒ 2 h + 4 c = 140 ⇒ h + 2 c = 70 ⋯ ( 2 ) ( 2 ) − ( 1 ) gives 2 c − c = 70 − 48 ⇒ c = 22 substituting the value of c in ( 1 ) , we get h + 22 = 48 ⇒ h = 48 − 22 = 26 h + 22 = 48 ⇒ h = 48 − 22 = 26 i . e . , number of hens = 26 answer : c
Answer: c
Problem: the cash realised on selling a 14 % stock is rs . 120.50 , brokerage being 1 / 4 % is
Options: a ) 120.25 , b ) 120.35 , c ) 106.5 , d ) 156 , e ) 240
Rationale: "explanation : cash realised = rs . ( 120.50 - 0.25 ) = rs . 120.25 . answer : a"
Answer: a
Problem: a and b are two partially filled buckets of water . if 7 liters are transferred from a to b , then a would contain one - third of the amount of water in b . alternatively , if 7 liters are transferred from b to a , b would contain one - half of the amount of water in a . bucket a contains how many liters of water ?
Options: a ) 77 / 5 , b ) 13 , c ) 17 , d ) 21 , e ) 23
Rationale: "let bucket a be a and bucket b be b scenario 1 a - 7 = 1 / 3 ( b + 7 ) - - - - > 3 a - 21 = b + 7 scenario 2 b - 7 = 1 / 2 ( a + 7 ) - - - - - > 2 b - 14 = a + 7 from scenario 1 , b = 3 a - 28 substitute b with this information in stmt 2 2 ( 3 a - 28 ) - 14 = a + 7 - - - - - - > 6 a - 56 - 14 = a + 7 - - - - - - > 6 a - a = 70 + 7 - - - > 5 a = 77 a = 77 / 5 , answer choice a"
Answer: a
Problem: how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 5 percent sugar solution ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 32 , e ) 35
Rationale: "let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.05 ( 50 - x ) 0.05 x = 2.5 - 1 x = 1.5 / 0.05 = 30 liters the answer is c ."
Answer: c
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 50 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 50 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues . so we have 50,25 , 12.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 50 / 1 - ( 1 / 2 ) = 100 equilateral triangle perimeter is 3 a = 3 * 100 = 300 . so option e ."
Answer: e
Problem: three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 40 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 5 square meters , b ) 36 square meters , c ) 40 square meters , d ) 83.3 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 40 = 80 sq m of the wallpaper overlaps in three layers . 80 sq m makes two extra layers hence the area over which it makes two extra layers is 40 sq m . answer ( c ) ."
Answer: c
Problem: a trained covered x km at 40 kmph and another 2 x km at 20 kmph . find the average speed of the train in covering the entire 4 x km .
Options: a ) 16 , b ) 18 , c ) 32 , d ) 19 , e ) 12
Rationale: "total time taken = x / 40 + 2 x / 20 hours = 5 x / 40 = x / 8 hours average speed = 4 x / ( x / 8 ) = 32 kmph answer : c"
Answer: c
Problem: if n = 2.0254 and n * is the decimal obtained by rounding n to the nearest hundredth , what is the value of n * – n ?
Options: a ) - 0.0053 , b ) - 0.0003 , c ) 0.0007 , d ) 0.0046 , e ) 0.0153
Rationale: "n * = 2.03 n * - n = 2.03 - 2.0254 0.0046 answer : d"
Answer: d
Problem: find the sum lend at c . i . at 5 p . c per annum will amount to rs . 240 in 2 years ?
Options: a ) 217 , b ) 287 , c ) 400 , d ) 288 , e ) 171
Rationale: "explanation : 240 = p ( 21 / 20 ) 2 p = 217 answer : a"
Answer: a
Problem: a bag contains 7 green balls and 7 white balls . if two balls are drawn simultaneously , what is the probability that both balls are the same colour ?
Options: a ) 4 / 13 , b ) 6 / 13 , c ) 8 / 21 , d ) 11 / 21 , e ) 17 / 42
Rationale: "the total number of ways to draw two balls is 14 c 2 = 91 the number of ways to draw two green balls is 7 c 2 = 21 the number of ways to draw two white balls is 7 c 2 = 21 p ( two balls of the same colour ) = 42 / 91 = 6 / 13 the answer is b ."
Answer: b
Problem: a vendor sells 60 percent of apples he had and throws away 15 percent of the remainder . next day he sells 50 percent of the remainder and throws away the rest . what percent of his apples does the vendor throw ?
Options: a ) 17 , b ) 23 , c ) 77 , d ) 26 , e ) 30
Rationale: explanation : let , the number of apples be 100 . on the first day he sells 60 % apples i . e . , 60 apples . remaining apples = 40 . he throws 15 % of the remaining i . e . , 15 % of 40 = 6 . now he has 40 − 6 = 34 apples the next day he throws 50 % of the remaining 34 apples i . e . , 17 . therefore , in total he throws 6 + 17 = 23 apples . answer : b
Answer: b
Problem: the radius of a cylinder is 8 m , height 14 m . the volume of the cylinder is :
Options: a ) 2816 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = ï € r ( power 2 ) h = 22 / 7 ã — 8 ã — 8 ã — 14 = 2816 m ( power 3 ) answer is a ."
Answer: a
Problem: average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 880 . what was original rent of friend whose rent is increased ?
Options: a ) 800 , b ) 900 , c ) 1600 , d ) 1100 , e ) 1200
Rationale: 0.2 x = 4 ( 880 - 800 ) 0.2 x = 320 x = 1600 answer c
Answer: c
Problem: when a student joe , weighing 43 kg , joins a group of students whose average weight is 30 kg , the average weight goes up by 1 kg . subsequently , if two students , excluding joe , leave the group the average weight comes back to 30 kg . what is the difference between the average weight of the two students who left and the weight of joe ?
Options: a ) 5.5 kg , b ) 11 kg , c ) 30 kg , d ) 6.5 kg , e ) 71 kg
Rationale: "after two persons leave the group the average remains the same . that means the weight of the two persons = 43 + 30 = 73 so , the average the two persons = 36.5 that gives the answer 43 - 36.5 = 6.5 answer d"
Answer: d
Problem: while working alone at their respective constant rates , server p uploads 480 files in 4 hours and server y uploads 480 files in 8 hours . if all files uploaded by these servers are the same size , how long would it take the two servers , working at the same time and at their respective constant rates , to process a total of 480 files ?
Options: a ) 2 hr , b ) 2 hr 20 min , c ) 2 hr 40 min , d ) 5 hr 40 min , e ) 6 hr
Rationale: server p processes 480 / 4 files per hour = 120 per hour server y processes 180 / 8 files per hour = 60 per hour total files processed per hour when p and y work together = 120 + 60 per hour = 180 files per hour 480 / 180 = 2 2 / 3 hours = c
Answer: c
Problem: 0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = ?
Options: a ) 0.7 , b ) 0 , c ) 0.8 , d ) 8 , e ) 7
Rationale: "= 0.0203 x 2.92 / 0.0073 x 14.5 x 0.7 = 203 x 292 / 73 x 145 x 7 = 4 / 5 = 0.8 answer is c ."
Answer: c
Problem: the speed of a train is 90 kmph . what is the distance covered by it in 30 minutes ?
Options: a ) 15 , b ) 66 , c ) 77 , d ) 52 , e ) 45
Rationale: "90 * 30 / 60 = 45 kmph answer : e"
Answer: e
Problem: what is the smallest positive integer x such that 280 - x is the cube of a positive integer
Options: a ) 5 , b ) 64 , c ) 62 , d ) 60 , e ) 12
Rationale: "given 280 - x is a perfect cube so we will take 216 = 6 * 6 * 6 280 - x = 216 x = 280 - 216 = 64 correct option is b"
Answer: b
Problem: in a kilometer race , a beats b by 60 meters or 15 seconds . what time does a take to complete the race ?
Options: a ) 221 , b ) 235 , c ) 245 , d ) 289 , e ) 260
Rationale: "time taken by b run 1000 meters = ( 1000 * 15 ) / 60 = 250 sec . time taken by a = 250 - 15 = 235 sec . answer : b"
Answer: b
Problem: in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.3 , 9.0 , 6.0 , and 8.6 , what was the point value of the dive ?
Options: a ) 78.08 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 81.6
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.0 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.3 + 8.6 ) = 24 point of value of the dive = 24.4 * 3.2 = 78.08 answer a"
Answer: a
Problem: train starts from amritsar to bombay at 9 am . it reaches destination after 3 days at 9 : 30 am . every day a train starts . how many trains does it come across on the way ?
Options: a ) 5 th , b ) 4 th , c ) 6 th , d ) 7 th , e ) 8 th
Rationale: because one train taking 3 days so 1 train first day another at second day and 3 rd one at third day but as given train reaches at 9.30 am insted of 9 . oo am so d same day train already left that train will be 4 th train . answer : b
Answer: b
Problem: if a ( a - 9 ) = 10 and b ( b - 9 ) = 10 , where a ≠ b , then a + b =
Options: a ) − 48 , b ) − 2 , c ) 2 , d ) 9 , e ) 48
Rationale: "i . e . if a = - 1 then b = 10 or if a = 10 then b = - 1 but in each case a + b = - 1 + 10 = 9 answer : option d"
Answer: d
Problem: there are 12 teams in a certain league and each team plays each of the other teams exactly twice . if each game is played by 2 teams , what is the total number of games played ?
Options: a ) 15 , b ) 16 , c ) 28 , d ) 56 , e ) 132
Rationale: "every team plays with 11 teams . . . so total no of matches = 12 x 11 = 132 . now , each match is played twice = > 132 x 2 but 2 teams play a match = > 132 x 2 / 2 = 132 . answer : e"
Answer: e
Problem: at what rate percent per annum will the simple interest on a sum of money be 1 / 5 of the amount in 10 years ?
Options: a ) 2 % , b ) 7 % , c ) 9 % , d ) 3 % , e ) 1 %
Rationale: "let sum = x . then , s . i . = x / 5 , time = 10 years . rate = ( 100 * x ) / ( x * 5 * 10 ) = 2 % answer : a"
Answer: a
Problem: a man can do a job in 15 days . his father takes 10 days and his son finishes it in 25 days . how long will they take to complete the job if they all work together ?
Options: a ) 6.3 , b ) 6.9 , c ) 7.1 , d ) 6.1 , e ) 6.2
Rationale: "1 day work of the three persons = ( 1 / 15 + 1 / 10 + 1 / 25 ) = 21 / 150 so , all three together will complete the work in 150 / 21 = 7.1 days . answer : c"
Answer: c
Problem: in a neighborhood having 90 households , 11 did not have either a car or a bike . if 22 households had a both a car and a bike and 44 had a car , how many had bike only ?
Options: a ) 30 , b ) 35 , c ) 20 , d ) 18 , e ) 10
Rationale: { total } = { car } + { bike } - { both } + { neither } - - > 90 = 44 + { bike } - 22 + 11 - - > { bike } = 57 - - > # those who have bike only is { bike } - { both } = 57 - 22 = 35 . answer : b .
Answer: b
Problem: the 3 digits of a number add up to 11 . the number is divisible by 5 . the leftmost digit is double the middle digit . what is the product of the 3 digits ?
Options: a ) 38 , b ) 40 , c ) 78 , d ) 88 , e ) 125
Rationale: xyz is a 3 digit integer divisible by 5 . so z can take only 0 or 5 . we are also given that x = 2 y this means x + y ( 2 y + y ) must be a multiple of 3 xy 5 or xy 0 case 1 x + y + 0 = 11 x + y = 11 this ca n ' t be the case because 11 is not a multiple of 3 case 2 x + y + 5 = 11 x + y = 6 solving we get , x = 4 y = 2 so the 3 digit number is 425 thus the product of the digits will be = 4 x 2 x 5 = 40 answer b
Answer: b
Problem: if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability t that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability t = 1 / 24 . answer c ."
Answer: c
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 8 : 2 . if 80 % of the toyota bought and 20 % of the honda bought were suv â € ™ s . how many suv â € ™ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 69 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 80 and honda 20 , so total number of suv ' s bought for toyota and honda respectively 80 * 80 / 100 = 64 and 20 * 20 / 100 = 4 so total 68 suv ' s were bought out of 100 vehicles bought . . so required % is 68 % answer : c"
Answer: c
Problem: 10 ^ ( 655 ) ã · 10 ^ ( 650 ) = ?
Options: a ) 100 , b ) 10 , c ) 10000 , d ) 100000 , e ) 1000000
Rationale: "10 ^ ( 655 ) ã · 10 ^ ( 651 ) = 10 ^ ( 655 - 651 ) = 10 ^ 5 = 100000 answer : d"
Answer: d
Problem: a corporation that had $ 115.19 billion in profits for the year paid out $ 250.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.22 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 250.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 250.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2.2 / 1000 ) * 100 = 0.22 % so answer is ( e )"
Answer: e
Problem: a reduction of 10 % in the price of salt enables a lady to obtain 10 kgs more for rs . 100 , find the original price per kg ?
Options: a ) 1.1 , b ) 2.2 , c ) 2.5 , d ) 2.1 , e ) 2.9
Rationale: "100 * ( 10 / 100 ) = 10 - - - 10 ? - - - 1 = > rs . 1 100 - - - 90 ? - - - 1 = > rs . 1.1 answer : a"
Answer: a
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 62.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 62 = 930 so , the score of the person who left is 70 ( 1000 - 930 ) answer will be ( e )"
Answer: e
Problem: the triplicate ratio of 2 : 3 is ?
Options: a ) 1 : 64 , b ) 1 : 62 , c ) 1 : 34 , d ) 8 : 27 , e ) 5 : 64
Rationale: 2 ^ 3 : 3 ^ 3 = 8 : 27 answer : d
Answer: d
Problem: if 15 lions can kill 15 deers in 15 minutes how long will it take 100 lions to kill 100 deers ?
Options: a ) 1 minutes , b ) 15 minute , c ) 100 minutes , d ) 10000 minutes , e ) 1000 minutes
Rationale: we can try the logic of time and work , our work is to kill the deers so 15 ( lions ) * 15 ( min ) / 15 ( deers ) = 100 ( lions ) * x ( min ) / 100 ( deers ) hence answer is x = 15 answer : b
Answer: b
Problem: what is the least number that should be added to 1076 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: ( 1076 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e .
Answer: e
Problem: the sum of two numbers is 40 and their product is 375 . what will be the sum of their reciprocals ?
Options: a ) 1 / 40 , b ) 8 / 75 , c ) 75 / 4 , d ) 75 / 8 , e ) 75 / 6
Rationale: ( 1 / a ) + ( 1 / b ) = ( a + b ) / ab = 40 / 375 = 8 / 75 answer : b
Answer: b
Problem: in a throw of a coin find the probability of getting a tail ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 2 / 5 , e ) 2 / 7
Rationale: "s = { h , t } e = { t } p ( e ) = 1 / 2 answer is a"
Answer: a
Problem: on her annual road trip to visit her family in seal beach , california , traci stopped to rest after she traveled 1 ⁄ 3 of the total distance and again after she traveled 1 ⁄ 2 of the distance remaining between her first stop and her destination . she then drove the remaining 100 miles and arrived safely at her destination . what was the total distance , in miles , from traci ’ s starting point to seal beach ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 550
Rationale: "let d = total distance traci traveled 1 / 3 = d / 3 i . e . remaining distance = 2 d / 3 she traveled 1 / 2 th of 2 d / 3 = d / 3 thus : d = ( d / 3 ) + ( d / 3 ) + 100 d = 300 answer : b"
Answer: b
Problem: pavan travelled for 15 hours . he covered the first half of the distance at 30 kmph and remaining half of the distance at 25 kmph . find the distance travelled by pavan .
Options: a ) 408 km , b ) 409 km , c ) 410 km , d ) 412 km , e ) 419 km
Rationale: let the distance travelled be x km . total time = ( x / 2 ) / 30 + ( x / 2 ) / 25 = 15 = > x / 60 + x / 50 = 15 = > ( 5 x + 6 x ) / 300 = 15 = > x = 409 km answer : b
Answer: b
Problem: how many quarters are equal to 5 dollars ?
Options: a ) 1 , b ) 8 , c ) 12 , d ) 20 , e ) 7
Rationale: "5 * 4 = 20 quarters answer : d"
Answer: d
Problem: when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 204.06 , what is value of j ?
Options: a ) 100 , b ) 500 , c ) 600 , d ) 800 , e ) 200
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.06 here 204 is the quotient . given that remainder = 12 so , 204.06 = 204 + 12 / j so , j = 200 answer : e"
Answer: e
Problem: if taxi fares were $ 1.00 for the first 1 / 5 mile and $ 0.25 for each 1 / 5 mile there after , then the taxi fare for a 3 - mile ride was
Options: a ) $ 1.56 , b ) $ 2.40 , c ) $ 3.80 , d ) $ 4.50 , e ) $ 2.80
Rationale: "in 3 miles , initial 1 / 5 mile charge is $ 1 rest of the distance = 3 - ( 1 / 5 ) = 14 / 5 rest of the distance charge = 14 ( 0.25 ) = $ 3.5 ( as the charge is 0.25 for every 1 / 5 mile ) = > total charge for 3 miles = 1 + 3.5 = 4.5 answer is d ."
Answer: d
Problem: during a particular baseball game , the probability of a team ' s pitcher throwing a strike on each throw is 2 / 5 . what is the least number of times that the pitcher should pitch the ball that will increase the probability of getting a strike at least once to more than 50 % .
Options: a ) 3 , b ) 2 , c ) 1 , d ) 4 , e ) 5
Rationale: rule of subtraction : p ( a ) = 1 - p ( a ' ) rule of multiplication : p ( a ∩ b ) = p ( a ) p ( b ) the probability that the pitcher throws a strike at least once in 2 guesses is 1 - ( 3 / 5 ) ^ 2 = 1 - 9 / 25 = 16 / 25 > 50 % . answer : b
Answer: b
Problem: y = x ^ 2 + bx + 64 cuts the x axis at ( h , 0 ) and ( k , 0 ) . if h and k are integers , what is the least value of b ?
Options: a ) - 65 , b ) - 64 , c ) - 32 , d ) 32 , e ) 64
Rationale: "as the curve cuts the x - axis at ( h , 0 ) and ( k , 0 ) . therefore h , k are the roots of the quadratic equation . for the quadratic equation is in the form ofax ^ 2 + bx + c = 0 , the product of the roots = c / a = 64 / 1 = 256 and the sum of the roots = - b / a = - b 64 can be expressed as product of two numbers in the following ways : 1 * 64 2 * 32 4 * 16 the sum of the roots is maximum when the roots are 1 and 64 and the maximum sum is 1 + 64 = 65 . the least value possible for b is therefore - 65 . b"
Answer: b
Problem: a merchant marks his goods up by 20 % and then offers a discount of 5 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 6 % , c ) 21 % , d ) 14 % , e ) 17 %
Rationale: "let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 5 % on 120 . profit = 114 - 100 14 % answer d"
Answer: d
Problem: a fruit seller sells mangoes at the rate of rs . 16 per kg and thereby loses 12 % . at what price per kg , he should have sold them to make a profit of 20 % ?
Options: a ) rs . 21.81 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 88 : 16 = 120 : x x = ( 16 ã — 120 / 88 ) = rs . 21.81 hence , s . p per kg = rs . 21.81 answer a"
Answer: a
Problem: a batsman scored 120 runs which included 5 boundaries and 5 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 , b ) 58.33 % , c ) 600 / 11 , d ) 55 , e ) 35
Rationale: "explanation : number of runs made by running , = > 120 − ( 5 × 4 + 5 × 6 ) . = > 120 − ( 50 ) . = > 70 . hence , the required percentage is : - = > 70 / 120 * 100 = > 58.33 % answer : b"
Answer: b
Problem: right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 30 years . what is molly ' s age right now ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "now , sandy is 30 - 6 = 24 molly ' s age is ( 3 / 4 ) * 24 = 18 the answer is d ."
Answer: d
Problem: a goods train runs at a speed of 72 kmph and crosses a 290 m long platform in 26 seconds . what is the length of the goods train ?
Options: a ) 230 m , b ) 240 m , c ) 260 m , d ) 270 m , e ) 250 m
Rationale: "s = 290 + x / t 72 * 5 / 18 = 290 + x / 26 x = 230 answer : a"
Answer: a
Problem: two years ago , ram put $ 1000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1000 ?
Options: a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
Rationale: investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %
Answer: e
Problem: in a certain egg - processing plant , every egg must be inspected , and is either accepted for processing or rejected . for every 96 eggs accepted for processing , 4 eggs are rejected . if , on a particular day , 12 additional eggs were accepted , but the overall number of eggs inspected remained the same , the ratio of those accepted to those rejected would be 99 to 1 . how many r eggs does the plant process per day ?
Options: a ) 100 , b ) 300 , c ) 400 , d ) 3,000 , e ) 4,000
Rationale: "straight pluggin in for me . as usual , i started with c and got the answer . lets ' back calculate and see what we get let us consider eggs processed each day to be 400 so initial ratio of eggs processed and rejected is 96 : 4 or 24 : 1 so out of 400 eggs , there will be 384 eggs processed and 16 rejected . now if the no . of eggs inspected remain and 12 more eggs get accepted that means there r = 384 + 12 = 396 eggs accepted and 4 rejected . . . and the ratio will be 99 : 1 bingo . . . this is what the questions says . . . . its always a good idea to start with c ."
Answer: c
Problem: an empty fuel tank with a capacity of 200 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 160 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 200 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 200 - a gallons of fuel b is 0.16 ( 200 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 200 - a ) = 30 - - > a = 50 . answer : e ."
Answer: e
Problem: what quantity of water should taken out to concentrate 24 liters of 40 % acidic liquid to 60 % acidic liquid ?
Options: a ) 5 liters , b ) 10 liters , c ) 15 liters , d ) 8 liters , e ) 6 liters
Rationale: "required answer is = 24 ( 60 - 40 ) / 60 = 8 liters answer is d"
Answer: d
Problem: if 2 x + y = 7 and x + 2 y = 5 , then 2 xy / 3 = ?
Options: a ) 1 , b ) 2 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 ( 2 * 3 * 1 ) / 3 = 6 / 3 = 2 b"
Answer: b
Problem: in a colony of 50 residents , the ratio of the number of men and women is 3 : 2 . among the women , the ratio of the educated to the uneducated is 1 : 3 . if the ratio of the number of education to uneducated persons is 4 : 6 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 1 , b ) 3 : 2 , c ) 1 : 3 , d ) 2 : 5 , e ) 5 : 7
Rationale: "number of men in the colony = 3 / 5 ( 50 ) = 30 number of women in the colony = 2 / 5 ( 50 ) = 20 number of educated women in the colony = 1 / 4 ( 20 ) = 5 number of uneducated women in the colony = 3 / 4 ( 20 ) = 15 number of educated persons in the colony = 4 / 10 ( 50 ) = 20 as 5 females are educated , remaining 15 educated persons must be men . number of uneducated men in the colony = 30 - 15 = 15 number of educated men and uneducated men are in the ratio 15 : 15 = > 1 : 1 answer : a"
Answer: a
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 14.8 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 135 ( multiplying factor is 9 : ( 135 / 15 ) ) then typical dosage would be 2 * 9 = 18 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 18 ) * 100 = 11.11 % c is the answer ."
Answer: c
Problem: a train running at the speed of 72 km / hr crosses a pole in 8 seconds . find the length of the train .
Options: a ) 150 meter , b ) 145 meter , c ) 160 meter , d ) 135 meter , e ) none of these
Rationale: "explanation : speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time = 20 * 8 = 160 meter option c"
Answer: c
Problem: 1,000 ^ 2 + 1,001 ^ 2 =
Options: a ) 6 , 030,053 , b ) 6 , 002,001 , c ) 6 , 030,055 , d ) 6 , 030,056 , e ) 6 , 030,057
Rationale: "interesting problem . i think key is to notice that all the given answer choices differs in last two digits . therefore , our entire focus should be to figure out how the given terms contribute to last two digits of total . 1000 ^ 2 - > 00 1001 ^ 1 - > 01 total - > * 1 answer b ."
Answer: b
Problem: a container contains 40 litres of milk . from this container 4 litres of milk was taken out and replaced by water . this process was repeated further two times . how much milk is now contained by the container ?
Options: a ) 26.34 litres , b ) 27.36 litres , c ) 28 litres , d ) 29.16 litres , e ) 30 litres
Rationale: "amount of milk left after 3 operations = [ 40 ( 1 - 4 / 40 ) ^ 3 ] litres = 40 x 9 / 10 x 9 / 10 x 9 / 10 = 29.16 litres answer : d"
Answer: d
Problem: a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 3000 more than d , what is b ' s share ?
Options: a ) a ) 8239 , b ) b ) 2900 , c ) c ) 6000 , d ) d ) 2393 , e ) e ) 2009
Rationale: "let the shares of a , b , c and d be 5 x , 2 x , 4 x and 3 x rs . respectively . then , 4 x - 3 x = 3000 = > x = 3000 . b ' s share = rs . 2 x = 2 * 3000 = rs . 6000 . answer : c"
Answer: c
Problem: last year a certain bond price with a face value of 5000 yielded 5 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 3846 , c ) 5351 , d ) 6000 , e ) 6154
Rationale: "interest = 0.05 * 5000 = 0.065 * selling price - - > selling price = 0.05 * 5000 / 0.065 - - > selling price = ~ 3,846 answer : b ."
Answer: b
Problem: in how many ways can 5 people be arranged in a circle ?
Options: a ) 2 ! , b ) 5 ! , c ) 4 ! , d ) 3 ! , e ) 6 !
Rationale: "( 5 − 1 ) ! = 4 ! = 24 ways ans - c"
Answer: c
Problem: if 3 a – 2 b – 2 c = 30 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . c"
Answer: c
Problem: a man can row his boat with the stream at 8 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 2 kmph , c ) 8 kmph , d ) 7 kmph , e ) 5 kmph
Rationale: "ds = 8 us = 4 s = ? s = ( 8 - 4 ) / 2 = 2 kmph answer : b"
Answer: b
Problem: in a class of 30 students in an examination in maths 3 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
Options: a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48.5 , e ) e ) 49
Rationale: "explanation : total marks obtained by a class of 25 students = 3 * 95 + 3 * 0 + 26 * 45 = 1455 average marks of whole class = 1455 / 30 = 48.5 answer : option d"
Answer: d
Problem: a , b and c have rs . 350 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
Options: a ) a ) 200 , b ) b ) 190 , c ) c ) 180 , d ) d ) 170 , e ) e ) 160
Rationale: "a + b + c = 350 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 350 - - - - - - - - - - - - - - - - c = 200 answer : a"
Answer: a
Problem: what is the decimal equivalent of ( 1 / 6 ) ^ 2 ?
Options: a ) 0.0016 , b ) 0.0625 , c ) 0.16 , d ) 0.278 , e ) 0.5
Rationale: "( 1 / 6 ) ² = ( 1 / 6 ) ( 1 / 6 ) = 1 / 36 approach # 1 : use long division to divide 36 into 1 to get 1 / 36 = 0.0278 d"
Answer: d
Problem: there are 32 balls which are red , blue or green . if 15 balls are green and the sum of red balls and green balls is less than 23 , at most how many red balls are there ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "r + g + b = 32 g = 15 r + g < 23 = > r + 15 < 23 = > r < 8 = > at most 7 red balls answer : d"
Answer: d
Problem: the length of a train and that of a platform are equal . if with a speed of 90 k / hr , the train crosses the platform in one minute , then the length of the train ( in metres ) is :
Options: a ) 400 , b ) 525 , c ) 750 , d ) 850 , e ) none
Rationale: "sol . speed = [ 90 * 5 / 18 ] m / sec = 25 m / sec ; time = 1 min . = 60 sec . let the length of the train and that of the platform be x metres . then , 2 x / 60 = 25 ⇔ x = 25 * 60 / 2 = 750 answer c"
Answer: c
Problem: of 30 applicants for a job , 11 had at least 4 years ' experience , 18 had degrees , and 3 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
Options: a ) 14 , b ) 13 , c ) 8 , d ) 7 , e ) 5
Rationale: "c . 8 30 - 3 = 27 27 - 11 - 18 = - 8 then 8 are in the intersection between 4 years experience and degree . answer c"
Answer: c
Problem: what is the sum of all remainders obtained when the first 200 natural numbers are divided by 9 ?
Options: a ) 397 , b ) 401 , c ) 403 , d ) 405 , e ) 399
Rationale: "a positive integer can give only the following 9 remainders when divided by 9 : 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , and 0 . 1 divided by 9 gives the remainder of 1 ; 2 divided by 9 gives the remainder of 2 ; . . . 8 divided by 9 gives the remainder of 8 ; 9 divided by 9 gives the remainder of 0 . we ' ll have 11 such blocks , since 99 / 9 = 11 . the last will be : 91 divided by 9 gives the remainder of 1 ; 92 divided by 9 gives the remainder of 2 ; . . . 98 divided by 9 gives the remainder of 8 ; 99 divided by 9 gives the remainder of 0 . the last number , 100 , gives the remainder of 1 when divided by 9 , thus the sum of all remainders will be : 11 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 0 ) + 1 = 401 . answer : b ."
Answer: b
Problem: linda spent 2 / 4 of her savings on furniture and the rest on a tv . if the tv cost her $ 300 , what were her original savings ?
Options: a ) $ 900 , b ) $ 300 , c ) $ 600 , d ) $ 700 , e ) $ 800
Rationale: "if linda spent 3 / 4 of her savings on furnitute , the rest 4 / 4 - 2 / 4 = 1 / 2 on a tv but the tv cost her $ 300 . so 1 / 2 of her savings is $ 300 . so her original savings are 2 times $ 300 = $ 600 correct answer c"
Answer: c
Problem: what is the speed of the stream if a canoe rows upstream at 3 km / hr and downstream at 12 km / hr
Options: a ) 1 kmph , b ) 4 kmph , c ) 3 kmph , d ) 2 kmph , e ) 4.5 kmph
Rationale: "sol . speed of stream = 1 / 2 ( 12 - 3 ) kmph = 4.5 kmph . answer e"
Answer: e
Problem: the ratio of the number of females to males at a party was 1 : 2 but when 3 females and 3 males left , the ratio became 1 : 3 . how many people were at the party originally ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "the total number of people are x females + 2 x males . 3 * ( x - 3 ) = 2 x - 3 x = 6 there were 3 x = 18 people at the party originally . the answer is c ."
Answer: c
Problem: one fourth of one third of two fifth of a number is 30 . what will be 40 % of that number
Options: a ) a ) 360 , b ) b ) 150 , c ) c ) 180 , d ) d ) 200 , e ) e ) 220
Rationale: "explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 30 then x = 30 * 30 = 900 40 % of 900 = 360 answer : option a"
Answer: a
Problem: 5 percent of 255 =
Options: a ) 5 , b ) 12.5 , c ) 14.5 , d ) 12.75 , e ) 25
Rationale: 255 / 100 = 2.55 1 % = 2.55 5 % = 2.55 * 5 = 12.75 answer : d
Answer: d
Problem: a certain number of men can do a work in 20 days . if there were 4 men less it could be finished in 5 days more . how many men are there ?
Options: a ) 10 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: the original number of men = 4 ( 20 + 5 ) / 5 = 20 men answer is b
Answer: b
Problem: a train running at the speed of 36 km / hr crosses a pole in 9 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 299 meter , c ) 666 meter , d ) 90 meter , e ) 144 meter
Rationale: "speed = 36 * ( 5 / 18 ) m / sec = 10 m / sec length of train ( distance ) = speed * time ( 10 ) * 9 = 90 meter answer : d"
Answer: d
Problem: if n is a prime number greater than 3 , what is the remainder when n ^ 2 is divided by 11 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
Rationale: "there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 3 , square it and see what would be the remainder upon division of it by 11 . n = 5 - - > n ^ 2 = 25 - - > remainder upon division 25 by 11 is 3 . answer : d ."
Answer: d
Problem: point ( m , n ) is on the circle represented by m ^ 2 + n ^ 2 = 10 , and m , n are integers . how many such points are possible ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: m ^ 2 + n ^ 2 = 10 and m , n are integers means that 10 is the sum of two perfect squares . 10 is the sum of only one pair of perfect squares 1 and 9 . so , there can be 8 such points , 4 in each quadrant : ( 1 , 3 ) ; ( 1 , - 3 ) ; ( - 1 , 3 ) ; ( - 1 , - 3 ) ; ( 3 , 1 ) ; ( 3 , - 1 ) ; ( - 3 , 1 ) ; ( - 3 , - 1 ) . answer : e .
Answer: e
Problem: find the area of the quadrilateral of one of its diagonals is 26 cm and its off sets 9 cm and 6 cm ?
Options: a ) 188 cm 2 , b ) 150 cm 2 , c ) 168 cm 2 , d ) 195 cm 2 , e ) 987 cm 2
Rationale: "1 / 2 * 26 ( 9 + 6 ) = 195 cm 2 answer : d"
Answer: d
Problem: irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 170 cookies , what percent of the cookies did nell bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 11.7 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 170 cookies x = 170 / 16.4 = 10 ( approx ) so , nell baked 10 * 2.05 cookies or 20 cookies ( approx ) % share = 20 / 170 = 11.7 approx hence , answer is c ."
Answer: c
Problem: a train speeds past a pole in 23 seconds and a platform 125 m long in 33 seconds . its length is ?
Options: a ) 275 , b ) 287.5 , c ) 288 , d ) 233.5 , e ) 245.6
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 23 = > y = x / 23 x + 125 / 33 = x / 23 x = 287.5 m . answer : b"
Answer: b
Problem: a bookseller sells his books at a 25 % markup in price . if he sells a book for $ 12.5 , how much did he pay for it ?
Options: a ) $ 14.40 , b ) $ 14.00 , c ) $ 11.00 , d ) $ 9.60 , e ) $ 10.00
Rationale: "let the cost price of book = x selling price of book = 12.5 $ markup % = 25 ( 125 / 100 ) x = 12.5 = > x = 10 answer e"
Answer: e
Problem: what will be the compound interest on a sum of rs . 25,000 after 3 years at the rate of 12 p . c . p . a . ?
Options: a ) rs . 9000.30 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none of these
Rationale: "explanation : amount = rs . [ 25000 x ( 1 + 12 / 100 ) 3 ] = rs . 35123.20 c . i . = rs . ( 35123.20 - 25000 ) = rs . 10123.20 answer is c"
Answer: c
Problem: a soft drink company had 5000 small and 12000 big bottles in storage . if 15 % of small 18 % of big bottles have been sold , then the total bottles remaining in storage is
Options: a ) 14090 , b ) 16010 , c ) 15060 , d ) 14930 , e ) 16075
Rationale: 5000 + 12000 - ( 0.15 * 5000 + 0.18 * 12000 ) = 14090 . answer : a .
Answer: a
Problem: 4 - fifths of 3 - eighths of a number is 24 . what is 250 per cent of that number ?
Options: a ) 100 , b ) 160 , c ) 120 , d ) 200 , e ) none of these
Rationale: let the number = x . 4 ⁄ 5 × 3 ⁄ 8 x = 24 or x = 24 × 2 × 5 / 3 = 80 ∴ 250 per cent of the number = 250 ⁄ 100 × 80 = 200 answer d
Answer: d
Problem: rates for having a manuscript typed at a certain typing service are $ 10 per page for the first time a page is typed and $ 6 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 430 , b ) $ 1620 , c ) $ 1650 , d ) $ 1110 , e ) $ 1770
Rationale: "for 100 - 40 - 10 = 50 pages only cost is 10 $ per page for the first time page is typed - 50 * 10 = 500 $ ; for 40 pages the cost is : first time 5 $ + 6 $ of the first revision - 40 * ( 5 + 6 ) = 440 $ ; for 10 pages the cost is : first time 5 $ + 6 $ of the first revision + 6 $ of the second revision - 10 ( 5 + 6 + 6 ) = 170 $ ; total : 500 + 440 + 170 = 1110 $ . answer : d ."
Answer: d