regisss/math_qa huggingface dataset:
Problem: rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 4 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 4 , b ) 25 / 16 , c ) 4 / 5 , d ) 16 / 25 , e ) 16 / 5
Rationale: "the area of rectangle a is ab . c = 5 a / 4 and d = 5 b / 4 . the area of rectangle b is cd = 25 ab / 16 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 16 ) = 16 / 25 . the answer is d ."
Answer: d
Problem: pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 5 : 00 am and pipe b at 6 : 00 am , at what time will the pool be full ?
Options: a ) 13 : 00 , b ) 14 : 00 , c ) 15 : 00 , d ) 17 : 00 , e ) 16 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 5 : 00 a . m and pipe b at 6 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 6 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 5 : 00 a . m , pool is full at 15 : 00 hrs answer : c"
Answer: c
Problem: a student multiplied a number by 3 / 5 instead of 5 / 3 , what is the percentage error in the calculation ?
Options: a ) 22 , b ) 64 , c ) 365 , d ) 29 , e ) 36
Rationale: "let the number be x . then , ideally he should have multiplied by x by 5 / 3 . hence correct result was . by mistake he multiplied x by 3 / 5 . hence the result with error = then , error = error % = = 64 % answer : b"
Answer: b
Problem: a team of 6 entered for a shooting competition . the best marks man scored 85 points . if he had scored 92 points , the average scores for . the team would have been 84 . how many points altogether did the team score ?
Options: a ) 288 , b ) 497 , c ) 168 , d ) 127 , e ) 664
Rationale: explanation : 6 * 84 = 504 - 7 = 497 answer : b
Answer: b
Problem: if 60 percent of 500 is 50 percent of x , then x = ?
Options: a ) 600 , b ) 620 , c ) 650 , d ) 700 , e ) 720
Rationale: "0.6 * 500 = 0.5 * x x = 6 / 5 * 500 = 600"
Answer: a
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 220 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 7.5 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 220 kilometers ? 220 ÷ 40 = 5.5 × 1 gallon = 5.5 gallons correct answer b"
Answer: b
Problem: the sum of 3 numbers is 98 . if the ratio between first and second be 2 : 3 and that between second and third be 5 : 8 , then the second number is ?
Options: a ) 30 , b ) 20 , c ) 58 , d ) 48 , e ) 68
Rationale: let the numbers be x , y and z . then , x + y + z = 98 , x / y = 2 / 3 and y / z = 5 / 8 therefore , x = 2 y / 3 and z = 8 y / 5 . so , 2 y / 3 + y + 8 y / 5 = 98 . 49 y / 15 = 98 y = 30 . answer : a
Answer: a
Problem: a courtyard is 25 meter long and 18 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 22500 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1800 / 20 × 10 ) = 22500 answer : d"
Answer: d
Problem: the perimeter of one square is 24 m & that of another is 32 m . perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be
Options: a ) 20 m
b ) 24 m
c ) 28 m
d ) 40 m
e ) 43 m
Rationale: perimeter of square = 4 * side perimeter of first square = 24 m . side of first square = ∴ area of first square = perimeter of second square = 32 m . side of second square = ∴ area of second square = sum of the areas of two squares = 36 + 64 = 100 m 2 ∴ side of square = ∴ perimeter of square = 4 * 10 = 40 m . d
Answer: d
Problem: the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 2500 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 625 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 2500 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 2500 ) * t = = = > 3 d = ts + 2500 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 2500 t - 2 d = - 2 st + 2500 t 2 d = 2 st - 2500 t d = st - 1250 t x 13 : d = s * t st - 1250 t = s * t s - 1250 = s - 625 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 2500 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 2500 2 = 1250 d = s * t d = 1250 * ( 1 / 2 ) d = 625 answer : b"
Answer: b
Problem: what is the value of 3 x ^ 2 − 2.4 x + 0.3 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.06 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 2.4 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 4 * 0.6 * ( 0.6 ) + 0.3 = - 0.6 * 0.6 + 0.3 = 0.06 correct option : c"
Answer: c
Problem: if x = 1 - 3 t and y = 2 t - 3 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 4 / 5 , d ) 2 / 5 , e ) 0
Rationale: "we are given x = 1 – 3 t and y = 2 t – 3 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 3 t for x and 2 t – 3 for y in the equation x = y . this gives us : 1 – 3 t = 2 t – 3 4 = 5 t 4 / 5 = t the answer is c ."
Answer: c
Problem: find the simple interest on the rs . 2000 at 25 / 4 % per annum for the period from 4 th feb 2005 to 18 th april 2005
Options: a ) rs 25 , b ) rs 30 , c ) rs 35 , d ) rs 40 , e ) none of these
Rationale: explanation : one thing which is tricky in this question is to calculate the number of days . always remember that the day on which money is deposited is not counted while the day on which money is withdrawn is counted . so lets calculate the number of days now , time = ( 24 + 31 + 18 ) days = 73 / 365 years = 1 / 5 years p = 2000 r = 25 / 4 % s . i . = = 2000 × 254 × 5 × 100 = 25 answer : a
Answer: a
Problem: volume of a right circular cylinder is 6 o l . if radius of cylinder is doubled , then what will be the increase in volume ?
Options: a ) 120 l
b ) 180 l
c ) 240 l
d ) 300 l
e ) 360 l
Rationale: pi ∗ r ^ 2 ∗ h = 60 double the radius . . . . . pi ∗ ( 2 r ) ^ 2 ∗ h = pi ∗ 4 ∗ r ^ 2 ∗ h = 4 ∗ 60 = 240 important . . we are looking at the increase so 240 - 60 = 180 answer : b
Answer: b
Problem: you enter a weight loss challenge game and manage to lose 10 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 8.2 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 10 % ) * ( 100 % + 2 % ) = 0.90 * 1.02 = 8.2 % the weigh in records your weight loss at 8.2 % ! the answer is b"
Answer: b
Problem: a person was asked to state his age in years . his reply was , ` ` take my age 5 years hence , multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 30
Rationale: "explanation : let the present age of person be x years . then , 3 ( x + 5 ) - 3 ( x - 5 ) = x < = > ( 3 x + 15 ) - ( 3 x - 15 ) = x < = > x = 30 . . answer : e"
Answer: e
Problem: the radius of a semi circle is 6.3 cm then its perimeter is ?
Options: a ) 32.9 , b ) 32.4 , c ) 32.2 , d ) 32.1 , e ) 32.7
Rationale: "36 / 7 r = 6.3 = 32.4 answer : b"
Answer: b
Problem: a train is 300 meter long is running at a speed of 54 km / hour . in what time will it pass a tunnel of 1200 meter length ?
Options: a ) 90 seconds , b ) 85 seconds , c ) 40 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 300 + 1200 = 1500 meter time = distance / speed = 1500 * ( 15 ) = 100 seconds answer : d
Answer: d
Problem: in a single throw of a die , what is probability of getting a number greater than 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 8 / 9 , e ) 1 / 3
Rationale: "e = { 5,6 } n ( e ) = 2 p ( s ) = n ( e ) / n ( s ) = 2 / 6 = 1 / 3 ans : e"
Answer: e
Problem: a certain bag contains 60 balls — 22 white , 18 green , 8 yellow , 5 red , and 7 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.8 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 8 ) / 60 = 48 / 60 = 0.8 . answer : d ."
Answer: d
Problem: a 10 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6
b ) 1 / 5
c ) 3 / 10
d ) 1 / 3
e ) 4 / 10
Rationale: a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 2 meters from either end . the probability of this is 4 / 10 = 2 / 5 . the answer is e .
Answer: e
Problem: the mean of 50 observations was 40 . it was found later that an observation 45 was wrongly taken as 15 the corrected new mean is
Options: a ) 40 , b ) 36.5 , c ) 46.5 , d ) 20.5 , e ) 40.6
Rationale: "explanation : correct sum = ( 40 * 50 + 45 - 15 ) = 2030 correct mean = = 2030 / 50 = 40.6 answer : e"
Answer: e
Problem: the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 4 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7 , b ) b ) 2 , c ) c ) 8.73 , d ) d ) 5.77 , e ) e ) 3
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 4 x = 5.77 answer : d"
Answer: d
Problem: by selling 14 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 26 , c ) 25 , d ) 23 , e ) 21
Rationale: "80 % - - - 14 120 % - - - ? 80 / 120 * 14 = 21 answer : e"
Answer: e
Problem: a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 → t = 3.5 answer a
Answer: a
Problem: caleb spends $ 70.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 20 , d ) 41 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 70.50 . by solving the equations y = 41 . ans d ."
Answer: d
Problem: tom traveled the entire 100 miles trip . if he did the first 50 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 28.36 mph , b ) 26.55 mph , c ) 28.57 mph , d ) 25.56 mph , e ) 28.45 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 50 + 50 ) / ( ( 50 / 20 ) + ( 50 / 50 ) ) = 60 * 2 / 3 = 28.57 mph c"
Answer: c
Problem: when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y – x ?
Options: a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ."
Answer: d
Problem: a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 30 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 1 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 30 = 6 geese ( males ) and now we know out of the total 20 geese , 6 are male , then 14 have to be female . now the ratio part , male geese ratios = 6 / 30 = 1 / 5 . - a female geese ratios = 14 / 70 = 1 / 5 - b cross multiply equations a and b and you get = 1 . ans d"
Answer: d
Problem: a clock hangs on the wall of a railway station , 71 ft 9 in long and 10 ft 4 in high . those are the dimension of the wall , not the clock ! while waiting for a train we noticed that the hands of the clock were pointing in opposite directions , and were parallel to one of the diagonals of the wall , what was the exact time ?
Options: a ) 7 : 15
b ) 7 : 5
c ) 7 : 25
d ) 7 : 45
e ) 7 : 55
Rationale: it can have four possiblities time could be 7 : 5 1 : 35 11 : 25 5 : 55 answer : b
Answer: b
Problem: how much 60 % of 50 is greater than 40 % of 30 ?
Options: a ) 18 , b ) 28 , c ) 26 , d ) 27 , e ) 23
Rationale: "( 60 / 100 ) * 50 – ( 40 / 100 ) * 30 30 - 12 = 18 answer : a"
Answer: a
Problem: you and your friend spent a total of $ 19 for lunch . your friend spent $ 3 more than you . how much did your friend spend on their lunch ?
Options: a ) $ 9 , b ) $ 3 , c ) $ 4 , d ) $ 6 , e ) $ 11
Rationale: my lunch = l , my friends lunch = l + 3 ( l ) + ( l + 3 ) = 19 l + l + 3 - 3 = 19 - 3 2 l = 16 l = 8 my friends lunch l + 3 = 8 + 3 = $ 11 , the answer is e
Answer: e
Problem: by selling 90 pens , a trader gains the cost of 30 pens . find his gain percentage ?
Options: a ) 33.3 % , b ) 32.3 % , c ) 31.3 % , d ) 30.3 % , e ) 29.3 %
Rationale: "let the cp of each pen be rs . 1 . cp of 90 pens = rs . 90 profit = cost of 30 pens = rs . 30 profit % = 30 / 90 * 100 = 33.3 % answer : a"
Answer: a
Problem: a cistern is normally filled in 2 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 4 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 2 - 1 / x = 1 / 4 , solving 1 / x = 1 / 4 so in 4 hours full cistern will be empty . answer : a"
Answer: a
Problem: two trains of length 100 m and 200 m are 100 m apart . they start moving towards each other on parallel tracks , at speeds 54 kmph and 72 kmph . in how much time will the trains cross each other ?
Options: a ) 70 / 7 sec , b ) 80 / 7 sec , c ) 40 / 7 sec , d ) 60 / 7 sec , e ) 90 / 7 sec
Rationale: "b relative speed = ( 54 + 72 ) * 5 / 18 = 7 * 5 = 35 mps . the time required = d / s = ( 100 + 100 + 200 ) / 35 = 400 / 35 = 80 / 7 sec ."
Answer: b
Problem: effective annual rate of interest corresponding to nominal rate of 6 % per annum compounded half yearly will be
Options: a ) 6.09 % , b ) 6.10 % , c ) 6.12 % , d ) 6.14 % , e ) none of these
Rationale: explanation : let the amount rs 100 for 1 year when compounded half yearly , n = 2 , rate = 6 / 2 = 3 % amount = 100 ( 1 + 3 / 100 ) 2 = 106.09 effective rate = ( 106.09 - 100 ) % = 6.09 % option a
Answer: a
Problem: in a certain business school class , p students are accounting majors , q students are finance majors , r students are marketing majors , and s students are strategy majors . if pqrs = 1365 , and if 1 < p < q < r < s , how many students in the class are finance majors ?
Options: a ) 3 , b ) 5 , c ) 8 , d ) 11 , e ) 17
Rationale: "pqrs = 1365 = 3 * 5 * 7 * 13 since 1 < p < q < r < s , the number of students who are finance majors is q = 5 . the answer is b ."
Answer: b
Problem: a train 500 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 298 m , b ) 300 m , c ) 800 m , d ) 967 m , e ) 1181 m
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 500 + x ) / 60 = 65 / 3 x = 800 m . answer : c"
Answer: c
Problem: the average age of 3 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men . the average age of the two new men is
Options: a ) 22 , b ) 30 , c ) 25 , d ) 38 , e ) 27
Rationale: "total age increased = ( 3 * 2 ) years = 6 years . sum of ages of two new men = ( 21 + 23 + 6 ) years = 50 years average age of two new men = ( 50 / 2 ) years = 25 years . answer : c"
Answer: c
Problem: points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction s of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives s = 1 / 9 . a"
Answer: a
Problem: a van takes 6 hours to cover a distance of 270 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 30 kmph , c ) 70 kmph , d ) 80 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 270 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 270 / 9 = 30 kmph b"
Answer: b
Problem: working together , printer a and printer b would finish the task in 40 minutes . printer a alone would finish the task in 60 minutes . how many pages does the task contain if printer b prints 4 pages a minute more than printer a ?
Options: a ) 250 , b ) 375 , c ) 450 , d ) 480 , e ) 500
Rationale: 40 * a + 40 * b = x pages in 40 mins printer a will print = 40 / 60 * x pages = 2 / 3 * x pages thus in 40 mins printer printer b will print x - 2 / 3 * x = 1 / 3 * x pages also it is given that printer b prints 4 more pages per min that printer a . in 40 mins printer b will print 160 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 160 = > x = 480 pages answer : d
Answer: d
Problem: if 36 men do a work in 70 days , in how many days will 40 men do it ?
Options: a ) 64 , b ) 63 , c ) 65 , d ) 66 , e ) 67
Rationale: "36 * 70 = 40 * x x = 63 days answer : b"
Answer: b
Problem: last year , for every 100 million vehicles that traveled on a certain highway , 75 vehicles were involved in accidents . if 6 billion vehicles traveled on the highway last year , how many of those vehicles were involved in accidents ? ( 1 billion = 1,000 , 000,000 )
Options: a ) 2500 , b ) 4500 , c ) 3500 , d ) 4000 , e ) 1300
Rationale: "to solve we will set up a proportion . we know that “ 100 million vehicles is to 75 accidents as 6 billion vehicles is to x accidents ” . to express everything in terms of “ millions ” , we can use 6,000 million rather than 6 billion . creating a proportion we have : 100 / 75 = 6,000 / x cross multiplying gives us : 100 x = 6,000 * 75 x = 60 * 75 = 4500 answer : b"
Answer: b
Problem: on a certain road , 10 % of the motorists exceed the posted speed limit and receive speeding tickets , but 60 % of the motorists who exceed the posted speed limit do not receive speeding tickets . what percent of the motorists on that road exceed the posted speed limit ?
Options: a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 25 % , e ) 30 %
Rationale: "suppose there are x motorists . 10 % of them exceeded the speed limit and received the ticket , i . e . x / 10 . again , suppose total no . of motorists who exceeded the speed limit are y . 60 % of y exceeded the speed limit but did n ' t received the ticket , i . e . 3 y / 5 . it means 2 y / 5 received the ticket . hence , 2 y / 5 = x / 10 or y / x = 1 / 4 or y / x * 100 = 1 / 4 * 100 = 25 % d"
Answer: d
Problem: a and b can do a piece of work in 48 days , a and c can do it in 60 days , b and c can do it 72 days . in what time can c alone do it ?
Options: a ) 84 days , b ) 84 ½ days , c ) 85 days , d ) 87 days , e ) 89 days
Rationale: explanation : ( a + b ) 1 day work = 1 / 48 ( b + c ) 1 day work = 1 / 72 ( a + c ) 1 day work = 1 / 60 by adding 2 ( a + b + c ) = 1 / 48 + 1 / 72 + 1 / 60 = 37 / 720 ( a + b + c ) 1 day work = 37 / 1440 a 1 day work = 37 / 1440 – 1 / 72 = 17 / 1440 = 85 days ( approximately ) answer : option c
Answer: c
Problem: if x is an integer such that 1 < x < 9 , 2 < x < 15 , 7 > x > – 1 , 4 > x > 0 , and x + 1 < 5 , then x is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "1 < x < 9 , 2 < x < 15 , - 1 < x < 7 0 < x < 4 x + 1 < 5 from above : 2 < x < 4 - - > x = 3 . answer : a ."
Answer: a
Problem: 1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ?
Options: a ) 1 , b ) 255 , c ) 3 , d ) 445 , e ) 235
Rationale: "1 = 1,2 = 2,3 = 9,4 = 16,5 = 25 , then 9 = ? 9 = 3 check the third eqn . answer : c"
Answer: c
Problem: a train 300 m long can cross an electric pole in 10 sec and then find the speed of the train ?
Options: a ) 88 kmph , b ) 89 kmph , c ) 72 kmph , d ) 16 kmph , e ) 108 kmph
Rationale: "length = speed * time speed = l / t s = 300 / 10 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : e"
Answer: e
Problem: if a book is sold at 10 % profit instead of 10 % loss , it would have brought rs 14 more . find out the cost price of the book
Options: a ) 75 , b ) 72 , c ) 60 , d ) 70 , e ) 80
Rationale: "let c . p . of the book be rs . ’ x ’ given , 1.10 x - 0.90 x = 14 = > 0.2 x = 14 = 14 / 0.2 = rs 70 answer : d"
Answer: d
Problem: in the number 11,0 ab , a and b represent the tens and units digits , respectively . if 11,0 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: "you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 25 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e"
Answer: e
Problem: how many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 12.5 , b ) 15.5 , c ) 17.5 , d ) 21.5 , e ) 24.5
Rationale: "let x be the amount that needs to be evaporated . 0.03 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1.5 x = 0.5 / 0.04 = 12.5 liters the answer is a ."
Answer: a
Problem: the average of marks obtained by 120 candidates was 35 . if the avg of marks of passed candidates was 39 & that of failed candidates was 39 and that of failed candidates was 15 , the no . of candidateswho passed the examination is ?
Options: a ) 50 , b ) 90 , c ) 100 , d ) 120 , e ) 140
Rationale: "let the number of candidate who passed = y then , 39 y + 15 ( 120 - y ) = 120 x 35 ⇒ 24 y = 4200 - 1800 ∴ y = 2400 / 24 = 100 c"
Answer: c
Problem: a squirrel runs up a cylindrical post , in a perfect spiral path making one circuit for each rise of 4 feet . how many feet does the squirrel travels if the post is 16 feet tall and 2 feet in circumference ?
Options: a ) 10 feet , b ) 8 feet , c ) 13 feet , d ) 15 feet , e ) 18 feet
Rationale: "total circuit = 16 / 4 = 4 total feet squirrel travels = 4 * 2 = 8 feet answer : b"
Answer: b
Problem: if ( t - 8 ) is a factor of t ^ 2 - kt - 46 , then k =
Options: a ) 16 , b ) 12 , c ) 2 , d ) 6 , e ) 14
Rationale: "t ^ 2 - kt - 48 = ( t - 8 ) ( t + m ) where m is any positive integer . if 48 / 8 = 6 , then we know as a matter of fact that : m = + 6 and thus k = 8 - 6 = 14 t ^ 2 - kt - m = ( t - a ) ( t + m ) where a > m t ^ 2 + kt - m = ( t - a ) ( t + m ) where a < m t ^ 2 - kt + m = ( t - a ) ( t - m ) e"
Answer: e
Problem: what will be the cost of building a fence around a rectangular plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 50 ?
Options: a ) a ) rs . 3944
b ) b ) rs . 3948
c ) c ) rs . 3519.5
d ) d ) rs . 3949
e ) e ) rs . 3923
Rationale: let the side of the rectangle plot be a ft . a * b = 289 = > 1.7 b * b = 289 b = 13.03 a = 22.17 length of the fence = perimeter of the plot = 2 ( a + b ) = 70.39 ft . cost of building the fence = 70.39 * 50 = rs . 3519.5 answer : c
Answer: c
Problem: how many liters of water must be evaporated from 50 liters of a 8 - percent sugar solution to get a 10 - percent solution ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "8 % of a 50 liter solution is 4 l which is 10 % of the solution at the end . the solution at the end must be 40 l . we need to evaporate 10 liters . the answer is b ."
Answer: b
Problem: . in a certain city , 60 percent of the registered voters are democrats and the rest are republicans . in a mayoral race , if 70 percent of the registered voters who are democrats and 20 percent of the registered voters who are republicans are expected to vote for candidate a , what percent of the registered voters are expected to vote for candidate a ?
Options: a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
Rationale: registered voters = 100 d = 60 r = 40 70 % of d ( 60 ) = 42 20 % of r ( 40 ) = 8 total voter % of registered voters = 50 / 100 50 % ans a
Answer: a
Problem: a box contains 12 apples , 11 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 * 5 / 6 = 5 / 12 < 0.5 the answer is e ."
Answer: e
Problem: a train 110 meters long completely crosses a 280 meters long bridge in 38 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 45 , c ) 40 , d ) 66 , e ) 09
Rationale: "s = ( 110 + 280 / 38 = 390 / 38 * 18 / 5 = 40 answer : c"
Answer: c
Problem: in a market , a dozen eggs cost as much as a pound of rice , and a half - liter of kerosene costs as much as 8 eggs . if the cost of each pound of rice is $ 0.33 , then how many f cents does a liter of kerosene cost ? [ one dollar has 100 cents . ]
Options: a ) 0.33 , b ) 0.44 , c ) 0.55 , d ) 44 , e ) 55
Rationale: "main thing to remember is answer is asked in cents , however when we calculate , it comes up as 0.44 $ just multiply by 100 , answer f = 44 . d"
Answer: d
Problem: paulson spends 75 % of his income . his income is increased by 20 % and he increased his expenditure by 10 % . find the percentage increase in his savings
Options: a ) 30 % , b ) 35 % , c ) 40 % , d ) 45 % , e ) 50 %
Rationale: "let the original income = rs . 100 . then , expenditure = rs . 75 and savings = rs . 25 new income = rs . 120 , new expenditure = rs . ( ( 110 / 100 ) * 75 ) = rs . 165 / 2 new savings = rs . ( 120 - ( 165 / 2 ) ) = rs . 75 / 2 increase in savings = rs . ( ( 75 / 2 ) - 25 ) = rs . 25 / 2 increase % = ( ( 25 / 2 ) * ( 1 / 25 ) * 100 ) % = 50 % . answer e 50 %"
Answer: e
Problem: if ( 1 – 1.5 ) n = 1 , then n =
Options: a ) − 400 , b ) − 140 , c ) − 2 , d ) 4 , e ) 400
Rationale: "( 1 – 1.5 ) n = 1 simplify to get : - 0.5 n = 1 rewrite as ( - 1 / 2 ) n = 1 multiply both sides by - 2 to get : n = - 2 answer : c"
Answer: c
Problem: in a college , the ratio of the number of boys to girls is 8 : 5 . if there are 160 girls , the total number of students in the college is
Options: a ) 2447 , b ) 377 , c ) 667 , d ) 416 , e ) 871
Rationale: "explanation : let the number of boys and girls be 8 x and 5 x . total number of students = 13 x = 13 * 32 = 416 . answer : d"
Answer: d
Problem: the average weight of 5 students decreases by 12 kg when one of them weighing 72 kg is replaced by a new student . the weight of the student is
Options: a ) 12 kg , b ) 10 kg , c ) 20 kg , d ) 72 kg , e ) none of these
Rationale: "explanation : let the weight of student be x kg . given , difference in average weight = 12 kg = > ( 72 - x ) / 5 = 12 = > x = 12 answer : a"
Answer: a
Problem: find the least multiple of 23 , which when divided by 1821 and 24 leaves remainders 710 and 13 respectively .
Options: a ) 3002 , b ) 3013 , c ) 3024 , d ) 3036 , e ) none of these
Rationale: solution here ( 18 - 7 ) = 11 , ( 21 - 10 ) = 11 and ( 24 - 13 ) = 11 . l . c . m . of 1821 and 24 is 504 . let required number be 504 k - 11 . least value of k for which ( 504 k - 11 ) is divisible 23 is k = 6 . so , required number = 504 × 6 - 11 = 3024 - 11 = 3013 . answer b
Answer: b
Problem: a boy is travelling from his home to school at 5 km / hr and reached 7 min late . next day he traveled at 10 km / hr and reached 8 min early . distance between home and school ?
Options: a ) 2.5 km , b ) 3.5 km , c ) 4.5 km , d ) 5.5 km , e ) 6.5 km
Rationale: let the distance be x t 1 = x / 5 hr t 2 = x / 10 hr difference in time = 7 + 8 = 15 = 1 / 4 hr x / 5 - x / 10 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer is a
Answer: a
Problem: how many of the positive factors of 16 are not factors of 20
Options: a ) 2 , b ) 3 , c ) 4 , d ) 1 , e ) 5
Rationale: "factors of 16 - 1 , 2 , 4 , 8 , 16 factors of 20 - 1 , 2 , 4 , 5 , 10 , 20 . comparing both , we have 2 factors of 16 which are not factors of 20 - 8,16 answer : a"
Answer: a
Problem: an investor deposited $ 10,000 to open a new savings account that earned 8 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 10,200 , b ) $ 10,202 , c ) $ 10,400 , d ) $ 10,404 , e ) $ 10,800
Rationale: "the amount in the account after 6 months is 1.02 * 1.02 ( $ 10,000 ) = $ 10,404 . the answer is d ."
Answer: d
Problem: a pipe can fill a cistern in 77 minutes . find the time in which 1 / 11 part of the cistern will be filled ?
Options: a ) 5 min , b ) 2 min , c ) 3 min , d ) 1 min , e ) 7 min
Rationale: "full cistern filled in = 77 minutes 1 / 11 part filled in = 77 * 1 / 11 = 7 minutes answer is e"
Answer: e
Problem: a can do a job in 10 days and b in 20 days . if they work on it together for 4 days , then the fraction of the work that is left is ?
Options: a ) 2 / 5 , b ) 8 / 15 , c ) 3 / 11 , d ) 1 / 12 , e ) 6 / 13
Rationale: "a ' s 1 day work = 1 / 10 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 10 + 1 / 20 = 3 / 20 a + b 4 days work = 3 / 20 * 4 = 3 / 5 remaining work = 1 - 3 / 5 = 2 / 5 answer is a"
Answer: a
Problem: a trader sells 20 meters of cloth for rs . 4500 at the profit of rs . 10 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 380 , b ) rs . 215 , c ) rs . 190 , d ) rs . 395 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 20 = rs . 225 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 225 - rs . 10 = rs . 215 . answer : c"
Answer: c
Problem: sahil purchased a machine at rs 10000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
Options: a ) rs . 22000 , b ) rs . 24000 , c ) rs . 26000 , d ) rs . 28000 , e ) none of these
Rationale: "explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 10000 + 5000 + 1000 = 16000 150 % of 16000 = 150 / 100 * 16000 = 24000 option b"
Answer: b
Problem: the ages of 2 persons differ by 35 years . if 10 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30 , b ) 48.5 , c ) 52 , d ) 50 , e ) 55
Rationale: "age of the younger person = x age of the elder person = x + 35 6 ( x - 10 ) = x + 35 - 10 x = 15 age of elder person = 15 + 35 = 50 answer is d"
Answer: d
Problem: tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 38 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 18 , at what time will they be reading the same page ?
Options: a ) 7 : 48 , b ) 8 : 18 , c ) 8 : 48 , d ) 9 : 18 , e ) 9 : 48
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 24 pages in the first 48 minutes . jan can catch tom at a rate of 8 pages per hour , so it will take 3 hours to catch tom . the answer is b ."
Answer: b
Problem: for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the integers between 1 and 50 ?
Options: a ) 1275 , b ) 1542 , c ) 985 , d ) 1024 , e ) 1125
Rationale: "sum = 50 * 51 / 2 = 25 * 51 = 1275 answer is a"
Answer: a
Problem: simplify : 896 x 896 - 204 x 204
Options: a ) 761200 , b ) 761400 , c ) 761800 , d ) 761500 , e ) none of them
Rationale: "( 896 ) ^ 2 - ( 204 ) ^ 2 = ( 896 + 204 ) ( 896 - 204 ) = 1100 x 692 = 761200 . answer is a ."
Answer: a
Problem: a searchlight on top of the watch - tower makes 2 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 5 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: 2 revolutions per minute = 1 revolution every 30 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 30 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 5 seconds ) = 1 - 5 / 30 = 1 - 1 / 6 = 5 / 6 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 30 seconds because that is the max . in this approach it would be 25 / 30 seconds = 5 / 6 . answer is e
Answer: e
Problem: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number selected will be a solution of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: roots of the equation ( x - 5 ) ( x + 10 ) ( 2 x - 5 ) = 0 are x = 5 , x = - 10 and x = 5 / 2 = 2.5 . so , two solutions present in our set of 12 distinct numbers , therefore p = 2 / 12 = 1 / 6 . answer : b .
Answer: b
Problem: a bag contains 10 red jellybeans and 10 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability y that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability y = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 2 / 19 answer : option b"
Answer: b
Problem: how many positive factors of 42 are not factors of 56 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "42 = 2 * 3 * 7 . so , total number of factors for 42 = 2 * 2 * 2 = 8 factors for 42 = 1 , 2,3 , 6,7 , 14,21 and 42 56 = 2 * 2 * 2 * 7 so , total number of factors for 56 = 4 * 2 = 8 factors of 56 = 1 , 2,4 , 7,8 , 14,28 and 56 . factors same in 42 and 56 are 1 , 2,7 and 14 . hence , answer will be d ."
Answer: d
Problem: when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 40 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 60 % ( 100 - 40 ) . therefore 0.5 x amount of flower - nectar = 0.60 x amount of honey = 0.60 x 1 kg therefore amount of flower - nectar needed = ( 0.60 / 0.51 ) kg = 1.2 kgs answer : a"
Answer: a
Problem: sale of rs 6835 , rs . 9927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs , 7000 ?
Options: a ) 4966 , b ) 2477 , c ) 2877 , d ) 7991 , e ) 8881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 42000 - 34009 ) = rs . 7991 answer : d"
Answer: d
Problem: the number of sailors on a ship is 50 % more than the number of officers . the ratio of sailors to officers would be
Options: a ) 33 : 25 , b ) 47 : 20 , c ) 3 : 2 , d ) 22 : 25 , e ) 97 : 50
Rationale: "sailor = 1.50 * officer sailor / officer = 1.50 / 1 = 150 / 100 = 3 / 2 answer will be c"
Answer: c
Problem: in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 5,4 ) , and ( 5,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 2 / 3 , b ) 2 / 5 , c ) 3 / 4 , d ) 3 / 7 , e ) 5 / 8
Rationale: the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 20 . p ( x + y < 4 ) = 8 / 20 = 2 / 5 the answer is b .
Answer: b
Problem: we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value q of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: q - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a .
Answer: a
Problem: 3 numbers are in the ratio of 2 : 3 : 4 . if the sum of the squares of the extremes is 180 , then the middle number is :
Options: a ) 6 , b ) 12 , c ) 15 , d ) 9 , e ) 7
Rationale: number be = 2 x , 3 x , 4 x , ( 2 x ) 2 + ( 4 x ) 2 = 180 20 x = 180 ⇒ x = 9 ⇒ x = 3 , midline number = 3 × 3 = 9 answer : d
Answer: d
Problem: 20 men do a work in 20 days . how many men are needed to finish the work in 5 days ?
Options: a ) 50 , b ) 20 , c ) 80 , d ) 10 , e ) 15
Rationale: "men required to finish the work in 5 days = 20 * 20 / 5 = 80 answer is c"
Answer: c
Problem: a man can row his boat with the stream at 22 km / h and against the stream in 10 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 6 kmph , c ) 7 kmph , d ) 4 kmph , e ) 9 kmph
Rationale: "explanation : ds = 22 us = 10 s = ? s = ( 22 - 10 ) / 2 = 6 kmph answer : b"
Answer: b
Problem: suganya and suriya are partners in a business . suganya invests rs . 35,000 for 8 months and suriya invests rs . 42,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 18,040 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 35000 × 8 ) : ( 42000 × 10 ) = 2 : 3 . suganya ' s share = rs . ( 31570 × 2 / 5 ) = rs . 12628 . answer c"
Answer: c
Problem: roja and pooja start moving in the opposite directions from a pole . they are moving at the speeds of 7 km / hr and 3 km / hr respectively . after 4 hours what will be the distance between them ?
Options: a ) 22 km , b ) 40 km , c ) 65 km , d ) 18 km , e ) 16 km
Rationale: "distance = relative speed * time = ( 7 + 3 ) * 4 = 40 km [ they are travelling in the opposite direction , relative speed = sum of the speeds ] . answer : b"
Answer: b
Problem: if xy denotes x is raised to the power y , find the last two digits of 19413846 + 19614181
Options: a ) 67 , b ) 74 , c ) 82 , d ) 98 , e ) 34
Rationale: 1941 ^ 3846 unit digit = 1 ^ 4 = 1 10 th digit = 4 * 6 = 24 = 2 means last two digit = 41 and 1972 ^ 4181 unit digit = 1 10 th digit = 7 * 2 = 14 mean last two digit = 41 hence , 41 + 41 = 82
Answer: c
Problem: all the milk in container a which was filled to its brim was poured into two containers b and c . the quantity of milk in container b was 62.5 % less than the capacity of container a . if 156 liters was now transferred from c to b , then both the containers would have equal quantities of milk . what was the initial quantity of milk in container a ?
Options: a ) 1248 , b ) 1723 , c ) 1129 , d ) 2613 , e ) 1372
Rationale: "a b has 62.5 % or ( 5 / 8 ) of the milk in a . therefore , let the quantity of milk in container a ( initially ) be 8 k . quantity of milk in b = 8 k - 5 k = 3 k . quantity of milk in container c = 8 k - 3 k = 5 k container : a b c quantity of milk : 8 k 3 k 5 k it is given that if 156 liters was transferred from container c to container b , then both the containers would have equal quantities of milk . 5 k - 156 = 3 k + 156 = > 2 k = 312 = > k = 156 the initial quantity of milk in a = 8 k = 8 * 156 = 1248 liters ."
Answer: a
Problem: the chance of rain on any given day in tel - aviv is 50 % . what is the probability a that it rained in tel - aviv on exactly 4 out of 6 randomly chosen days ?
Options: a ) 15 / 64 , b ) 30 / 64 , c ) 1 / 2 , d ) 1 / 4 , e ) 52 / 64
Rationale: "chances of rain on exactly 4 days and not rain on 2 days = ( 1 / 2 ) ^ 4 * ( 1 / 2 ) ^ 2 = 1 / 64 chosing 4 days out of 6 = 6 ! / ( 4 ! * 2 ! ) = 15 chances of rain on exactly 4 days out of 6 days a = 15 / 64 ans a it is ."
Answer: a
Problem: a 300 m long train crosses a platform in 27 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 286 m , b ) 350 m , c ) 277 m , d ) 278 m , e ) 150 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 27 = 50 / 3 x = 150 m . answer : e"
Answer: e
Problem: of 67 players on a cricket team , 37 are throwers . the rest of the team is divided so one third are left - handed and the rest are right handed . assuming that all throwers are right handed , how many right - handed players are there total ?
Options: a ) 54 , b ) 55 , c ) 57 , d ) 71 , e ) 92
Rationale: "total = 67 thrower = 37 rest = 67 - 37 = 30 left handed = 30 / 3 = 10 right handed = 20 if all thrower are right handed then total right handed is 30 + 20 = 57 so c . 57 is the right answer"
Answer: c
Problem: a can do a half of certain work in 70 days and b one third of the same in 35 days . they together will do the whole work in .
Options: a ) 88 days , b ) 27 days , c ) 78 days , d ) 60 days , e ) 17 days
Rationale: "a = 140 days b = 105 days 1 / 140 + 1 / 105 = 7 / 420 = 1 / 60 = > 60 days answer : d"
Answer: d
Problem: when 1 / 10 percent of 4,000 is subtracted from 1 / 10 of 4,000 , the difference is
Options: a ) 0 , b ) 50 , c ) 396 , d ) 495 , e ) 500
Rationale: "we can break this problem into two parts : 1 ) what is 1 / 10 percent of 4,000 ? 2 ) what is 1 / 10 of 4,000 ? to calculate 1 / 10 percent of 4,000 we must first remember to divide 1 / 10 by 100 . so we have : ( 1 / 10 ) / ( 100 ) to divide a number by 100 means to multiply it by 1 / 100 , so we have : 1 / 10 x 1 / 100 = 1 / 1,000 thus , 1 / 10 percent of 4,000 = 1 / 1,000 x 4,000 = 4 . now let ' s concentrate on part 2 . we need to calculate 1 / 10 of 4,000 . to do this we simply multiply 1 / 10 by 4,000 . 1 / 10 x 4,000 = 400 the answer to part 1 is 4 , and the answer to part 2 is 400 . their difference is 400 – 4 = 396 . answer c ."
Answer: c
Problem: if n = 2.0823 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 ) - 0.0023 , c ) 0.0007 , d ) 0.0047 , e ) 0.0153
Rationale: "n * = 2.08 n * - n = 2.08 - 2.0823 - 0.0023 answer : b"
Answer: b
Problem: if jack walked 7 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 4 , b ) 4.5 , c ) 5.6 , d ) 6.25 , e ) 15
Rationale: "distance walked in 1 hour and 15 mins = 7 miles speed per hour = distance / time = 7 / ( 5 / 4 ) = 5.6 miles per hour answer c"
Answer: c
Problem: a grocery shop has a sale of rs . 6635 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) 4857 , b ) 4184 , c ) 4012 , d ) 4791 , e ) 5291
Rationale: let the sale in the sixth month = x then ( 6635 + 6927 + 6855 + 7230 + 6562 + x ) / 6 = 6500 = > 6635 + 6927 + 6855 + 7230 + 6562 + x = 6 × 6500 = > 34209 + x = 39000 = > x = 39000 − 34209 = 4791 answer : d
Answer: d
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 150 kilometers ?
Options: a ) 3.5 gallons , b ) 2.7 gallons , c ) 5.75 gallons , d ) 3.75 gallons , e ) 7.50 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 150 kilometers ? 150 ã · 40 = 3.75 ã — 1 gallon = 3.75 gallons correct answer is d ) 3.75 gallons"
Answer: d
Problem: a fellow borrowed a certain sum of money at 5 % per annum at simple interest and in 5 years the interest amounted to rs . 2250 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 1060 , e ) 3000
Rationale: "p - 2250 = ( p * 5 * 5 ) / 100 p = 3000 answer : e"
Answer: e
Problem: in a certain country 1 / 3 of 4 = 8 . assuming the same proportion , what would be the value of 1 / 8 of 4 ?
Options: a ) 2 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "e 3"
Answer: e
Problem: the average age of a group of 12 students is 20 years . if 4 more students join the group , the average age increases by 1 year . the average age of the new students is
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "total age of 12 std = 20 * 12 total age of 16 std = 21 * 16 total age of 4 std = ( 21 * 16 ) - 20 * 12 = 96 avg of 4 std = ( 96 ) / 4 = 24 answer : c"
Answer: c
Problem: golu started from his house towards north . after covering a distance of 8 km . he turned towards left and covered a distance of 6 km . what is the shortest distance now from his house ?
Options: a ) 10 km . , b ) 16 km . , c ) 14 km , d ) 2 km . , e ) 4 km .
Rationale: c - - - - - - - - - - - - - b ! ! ! ! ! a ab = 8 km bc = 6 km ac = sqrtof ( 8 ^ 2 + 6 ^ 2 ) ac = 10 km answer : a
Answer: a