regisss/math_qa huggingface dataset:
Problem: in 1950 , richard was 4 times as old as robert . in 1955 , richard was 3 times as old as robert . in which year was richard 1.3 times as old as robert ?
Options: a ) 1960 , b ) 1965 , c ) 1970 , d ) 1975 , e ) 2040
Rationale: "in 1950 : ri = 4 ro - - - - - - - - - - - - - - eq 1 in 1955 : ri + 5 = 3 ( ro + 5 ) - - - - - - - - - eq 2 thus in 1950 , solving eq 1 and eq 2 ro = 10 , ri = 40 now for each year we can calculate : 1960 : ri = 50 , ro = 20 1965 : ri = 55 , ro = 25 2040 : ri = 100 , ro = 130 thus ans : e"
Answer: e
Problem: the simple interest on a sum of money will be rs . 800 after 10 years . if the principal is trebled after 5 years what will be the total interest at the end of the tenth year ?
Options: a ) 8981 , b ) 3799 , c ) 1200 , d ) 1600 , e ) 1732
Rationale: "p - - - 10 - - - - 800 p - - - 5 - - - - - 400 3 p - - - 5 - - - - - 1200 - - - - - - = > 1600 answer : d"
Answer: d
Problem: a certain clock marks every hour by striking a number of times equal to the hour , and the time required for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stroke and the end of the last stroke is 66 seconds . at 12 : 00 , how many seconds elapse between the beginning of the first stroke and the end of the last stroke ?
Options: a ) a . 138 , b ) b . 50 , c ) c . 48 , d ) d . 46 , e ) e . 44
Rationale: "at 6 : 00 it ' ll chime 6 times . if we assume that the time taken to chime is x , then time between chimes is also x . so you have 6 chimes , which is 6 x and 5 time intervals between chimes . this means that 11 x = 66 seconds . thus x = 6 seconds . by a similar logic , at 12 : 00 , there are 12 chimes and 11 intervals so the total time is ( 12 + 11 ) x = 23 x = 138 seconds . answer a"
Answer: a
Problem: each week , harry is paid x dollars per hour for the first 30 hours and 1.5 x dollars for each additional hour worked that week . each week , annie is paid x dollars per hour for the first 40 hours and 2 x dollars for each additional hour worked that week . last week annie worked a total of 50 hours . if harry and annie were paid the same amount last week , how many hours did harry work last week ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "annie earned 40 x + 10 ( 2 x ) = 60 x let h be the number of hours that harry worked . harry earned 30 x + 1.5 x ( h - 30 ) = 60 x ( 1.5 x ) ( h ) = 75 x h = 50 hours the answer is c ."
Answer: c
Problem: a box measuring 25 inches long by 30 inches wide by 15 inches deep is to be filled entirely with identical cubes . no space is to be left unfilled . what is the smallest number of cubes that can accomplish this objective ?
Options: a ) 80 , b ) 82 , c ) 84 , d ) 88 , e ) 90
Rationale: "least number of cubes will be required when the cubes that could fit in are biggest . 5 is the biggest number that could divide all three , 25 , 30 and 15 . thus side of cube must be 5 , and total number of cubes = 25 / 5 * 30 / 5 * 15 / 5 = 90 ans e ."
Answer: e
Problem: in lottery , there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a prize ?
Options: a ) 1 / 7 , b ) 2 / 7 , c ) 3 / 7 , d ) 4 / 7 , e ) 1
Rationale: total number of outcomes possible , n ( s ) = 10 + 25 = 35 . total number of prize , n ( e ) = 10 p ( e ) = n ( e ) / n ( s ) = 10 / 35 = 2 / 7 answer is option b
Answer: b
Problem: 0.999991 + 0.111119 = ?
Options: a ) 1 , b ) 1.0001 , c ) 1.0021 , d ) 1.11111 , e ) 1.1111
Rationale: "0.999991 + 0.111119 = 0.999991 + 0.11111 + 0.00009 = ( 0.999991 + 0.00009 ) + 0.11111 = 1 + 0.11111 = 1.11111 d"
Answer: d
Problem: from january 1 , 1991 , to january 1 , 1993 , the number of people enrolled in health maintenance organizations increased by 30 percent . the enrollment on january 1 , 1993 , was 45 million . how many million people , to the nearest million , were enrolled in health maintenance organizations on january 1 , 1991 ?
Options: a ) 35 , b ) 39 , c ) 40 , d ) 41 , e ) 42
Rationale: "1.30 x = 45 - - > 13 / 10 * x = 45 - - > x = 45 * 10 / 13 = 450 / 13 = ~ 35 . answer : a ."
Answer: a
Problem: if $ 5,000 is invested in an account that earns 10 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 10
Rationale: solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.10 / 2 ) ^ 2 = 5410 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 10 / 100 ) = 5400 difference = 5410 - 5400 = 10 $ e
Answer: e
Problem: line q has the equation 5 y – 3 x = 15 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )
Options: a ) 9 , b ) 11 , c ) 13 , d ) 15 , e ) 17
Rationale: "5 y - 3 x = 15 and so y = 3 x / 5 + 3 when x = 0 , then y = 3 . when y = 0 , then x = - 5 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 5 , 0 ) , 0 = - 5 ( - 5 ) / 3 + c the y - intercept is c = - 25 / 3 < - 8 . thus the perpendicular line s can have y - intercepts from - 8 up to 2 . the number of possible lines is 8 + 2 + 1 = 11 the answer is b ."
Answer: b
Problem: mr . kramer , the losing candidate in a two - candidate election , received 942,568 votes , which was exactly 35 percent of all votes cast . approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 17 % , e ) 23 %
Rationale: "lets assume that candidate got 35 % votes and total votes is 100 . candidate won = 35 remaining = 65 to get 50 % , candidate requires 15 votes from 100 which is 15 % and 15 votes from 65 . 15 / 65 = 23.07 which is approx 23 % . hence the answer is e"
Answer: e
Problem: find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 5 cm ?
Options: a ) 827 cm 2 , b ) 216 cm 2 , c ) 95 cm 2 , d ) 80 cm 2 , e ) 176 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 5 ) = 95 cm 2 answer : c"
Answer: c
Problem: a family pays $ 900 per year for an insurance plan that pays 80 percent of the first $ 1,000 in expenses and 100 percent of all medical expenses thereafter . in any given year , the total amount paid by the family will equal the amount paid by the plan when the family ' s medical expenses total .
Options: a ) $ 1,000 , b ) $ 1,200 , c ) $ 1,300 , d ) $ 1,800 , e ) $ 2,200
Rationale: "upfront payment for insurance plan = 900 $ family needs to pay 20 % of first 1000 $ in expense = 200 $ total amount paid by family when medical expenses are equal to or greater than 1000 $ = 900 + 200 = 1100 $ total amount paid by insurance plan for first 1000 $ = 900 $ total amount paid by family will equal amount paid by plan when medical expense = 1300 $ ( since insurance plan will pay 100 % of amount that exceeds 1100 $ ) answer c"
Answer: c
Problem: at 1 : 00 pm , there were 10.0 grams of bacteria . the bacteria increased to x grams at 4 : 00 pm , and 28.9 grams at 7 : 00 pm . if the amount of bacteria present increased by the same fraction during each of the 3 - hour periods , how many grams of bacteria were present at 4 : 00 pm ?
Options: a ) 16.2 , b ) 16.4 , c ) 16.6 , d ) 16.8 , e ) 17.0
Rationale: "let x be the factor by which the bacteria increases every three hours . at 4 : 00 pm , the amount of bacteria was 10 x and at 7 : 00 pm it was 10 x ^ 2 . 10 x ^ 2 = 28.9 x ^ 2 = 2.89 x = 1.7 at 4 : 00 pm , the amount of bacteria was 10 ( 1.7 ) = 17 grams . the answer is e ."
Answer: e
Problem: rahul played weel in this season . his current batting averagge is 53 . if he score 78 runs in today match . his batting average will become 58 . how many matches had he played in this season .
Options: a ) 4 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "53 x + 78 = 58 ( x + 1 ) = > 5 x = 20 = > x = 4 answer : a"
Answer: a
Problem: the length of a rectangle is two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units
b ) 158 sq . units
c ) 187 sq . units
d ) 607 sq . units
e ) 815 sq . units
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : a
Answer: a
Problem: 33 1 / 3 % of 390 ?
Options: a ) 80 , b ) 90 , c ) 110 , d ) 120 , e ) 130
Rationale: "33 1 / 3 % = 1 / 3 1 / 3 × 390 = 130 e )"
Answer: e
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 , 6600 ?
Options: a ) 5591 , b ) 2477 , c ) 2877 , d ) 2676 , e ) 1881
Rationale: "total sale for 5 months = rs . ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs . 34009 . required sale = rs . [ ( 6600 x 6 ) - 34009 ] = rs . ( 39600 - 34009 ) = rs . 5591 answer : a"
Answer: a
Problem: a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 186 , how many hours overtime did he work ?
Options: a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 11
Rationale: at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 186 - $ 120 = $ 66 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 66 / $ 6 = 11 ans is e
Answer: e
Problem: 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days c do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time c = 3 days to finish the task imo a
Answer: a
Problem: a man can row 9 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and black . what is the total distance traveled by the man ?
Options: a ) 5.98 , b ) 9.98 , c ) 9.06 , d ) 9.87 , e ) 9.82
Rationale: "m = 9 s = 1.2 ds = 7.2 us = 10.8 x / 10.8 + x / 7.8 = 1 x = 4.53 d = 4.53 * 2 = 9.06 answer : c"
Answer: c
Problem: jacob is 12 years old . he is 4 times as old as his brother . how old will jacob be when he is twice as old ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 18
Rationale: "j = 12 ; j = 4 b ; b = 12 / 4 = 3 ; twice as old so b = 3 ( now ) + ( 3 ) = 6 ; jacob is 12 + 6 = 18 answer : e"
Answer: e
Problem: a type q machine can complete a job in 5 hours and a type b machine can complete the job in 7 hours . how many hours will it take 2 type q machines and 3 type b machines working together and independently to complete the job ?
Options: a ) 1 / 5 , b ) 29 / 35 , c ) 5 / 6 , d ) 35 / 29 , e ) 35 / 12
Rationale: now d should be the answer . q need 5 hours to complete and b needs 7 hours to compete so 2 q + 3 b will complete 2 / 5 + 3 / 7 or 29 / 35 portion of the job in 1 hour so the whole job will take 35 / 29 hours . . . . = d
Answer: d
Problem: a fellow borrowed a certain sum of money at 3 % per annum at simple interest and in 3 years the interest amounted to rs . 1820 less than the sum lent . what was the sum lent ?
Options: a ) 1050 , b ) 1220 , c ) 1250 , d ) 2000 , e ) 1110
Rationale: "p - 1820 = ( p * 3 * 3 ) / 100 p = 2000 answer : d"
Answer: d
Problem: a sum amounts to rs . 3969 in 2 years at the rate of 5 % p . a . if interest was compounded yearly then what was the principal ?
Options: a ) s . 3600 , b ) s . 5000 , c ) s . 4500 , d ) s . 4800 , e ) s . 5800
Rationale: "ci = 3969 , r = 5 , n = 2 ci = p [ 1 + r / 100 ] ^ 2 = p [ 1 + 5 / 100 ] ^ 2 3969 = p [ 21 / 20 ] ^ 2 3969 [ 20 / 21 ] ^ 2 3600 answer : a"
Answer: a
Problem: a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party r . if one registered voter has a favorable impression of both parties for every two registered voters who have a favorable impression only of party b , then what percentage of the country ’ s registered voters have a favorable impression of both parties ( assuming that respondents to the poll were given a choice between favorable and unfavorable impressions only ) ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
Rationale: "s = 100 not ( r and b ) = 35 only r = 20 ( r and b ) / b = 1 / 2 let ( r and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
Answer: a
Problem: how many pieces of 85 cm length can be cut from a rod of 38.25 meters long ?
Options: a ) 25 , b ) 35 , c ) 45 , d ) 55 , e ) 65
Rationale: "number of pieces = 3825 / 85 = 45 the answer is c ."
Answer: c
Problem: gretzky street begins at orr street and runs directly east for 5.6 kilometers until it ends when it meets howe street . gretzky street is intersected every 350 meters by a perpendicular street , and each of those streets other than orr street and howe street is given a number beginning at 1 st street ( one block east of orr street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of howe street . what is the highest - numbered street that intersects gretzky street ?
Options: a ) 12 th , b ) 13 th , c ) 14 th , d ) 15 th , e ) 16 th
Rationale: 5.6 km / 350 m = 16 . however , the street at the 5.6 - km mark is not 16 th street ; it is howe street . therefore , the highest numbered street is 15 th street . the answer is d .
Answer: d
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.9 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 13 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.9 - 19 x 15 ) kg = 13 kg . correct option : d"
Answer: d
Problem: the difference between a two - digit number and the number obtained by interchanging the digits is 36 . what is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1 : 2 ?
Options: a ) 4 , b ) 8 , c ) 16 , d ) 12 , e ) 14
Rationale: "since the number is greater than the number obtained on reversing the digits , so the ten ' s digit is greater than the unit ' s digit . let ten ' s and unit ' s digits be 2 x and x respectively . then , ( 10 x 2 x + x ) - ( 10 x + 2 x ) = 36 9 x = 36 x = 4 . required difference = ( 2 x + x ) - ( 2 x - x ) = 2 x = 8 . answer : b"
Answer: b
Problem: excluding stoppages , the average speed of a bus is 80 km / hr and including stoppages , the average speed of the bus is 40 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 30 min
Rationale: "in 1 hr , the bus covers 80 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 80 - 40 ) km i . e 40 km at 80 km / hr . stoppage time = 40 / 80 hrs = 30 min answer : e"
Answer: e
Problem: what is the smallest integer n for which 25 ^ n > 5 ^ 12 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "to solve , we want to get the bases the same . thus we need to break 25 ^ n into prime factors . 25 ^ n = ( 5 ^ 2 ) ^ n = 5 ^ ( 2 n ) ( remember that when we have a power to a power , we multiply the exponents . ) we can use the new value in the given inequality : 5 ^ ( 2 n ) > 5 ^ 12 since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents . 2 n > 12 n > 6 because n is greater than 6 , the smallest integer that satisfies the inequality 25 ^ n > 5 ^ 12 is 7 . the answer is b ."
Answer: b
Problem: a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 4 , and the ratio of soap to salt is five times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is quartered by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 26 : 64 , b ) 64 : 9 , c ) 9 : 64 , d ) 9 : 60 , e ) 20 : 64
Rationale: "water : soap = 3 : 4 soap : salt = 15 : 20 = > for 15 soap , salt = 20 = > for 4 soap , salt = ( 20 / 15 ) * 4 = 80 / 15 = 16 / 3 so , water : soap : salt = 3 : 4 : 16 / 3 = 9 : 12 : 16 after open container , water : soap : salt = 2.25 : 12 : 16 so , water : salt = 2.25 : 16 = 9 : 64 answer : c"
Answer: c
Problem: by selling an article for $ 110 , a person gains $ 10 . what is the gain % ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 20 % , e ) 10 %
Rationale: "s . p . = $ 110 gain = $ 10 c . p . = 110 - 10 = 100 gain % = 10 / 100 * 100 % = 10 % answer is e"
Answer: e
Problem: tough and tricky questions : functions . let a be a positive integer . let n # a equal n ^ ( 2 a ) if a is odd and n ^ ( 3 a ) if a is even . then ( 4 # 3 ) + ( 3 # 4 ) – ( 3 # 3 ) is equal to
Options: a ) 64 , b ) 82 , c ) 128 , d ) 512 , e ) 4096
Rationale: answer : 4 ^ 6 + 3 ^ 6 - 3 ^ 6 = 4 ^ 6 = 4096 ans e
Answer: e
Problem: find the smallest number of 6 digits which is exactly divisible by 111 .
Options: a ) 100011 , b ) 111111 , c ) 101111 , d ) 201111 , e ) 211111
Rationale: smallest number of 6 digits is 100000 . on dividing 100000 by 111 , we get 100 as remainder . number to be added = ( 111 - 100 ) - 11 . hence , required number = 100011 option a
Answer: a
Problem: a company recently conducted a survey and found that 35,000 of its customers live in rural areas . if the number of customers who live in urban areas is 140 percent greater than the number of customers who live in rural areas , how many customers live in urban areas ?
Options: a ) 78,000 , b ) 80,000 , c ) 82,000 , d ) 84,000 , e ) 86,000
Rationale: "the number of customers in urban areas is 35,000 + 1.4 * 35,000 = 84,000 . the answer is d ."
Answer: d
Problem: in plutarch enterprises , 60 % of the employees are marketers , 20 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 290,000 , e ) $ 340,000
Rationale: "for sake of ease , let ' s say there are 10 employees : 6 marketers , 2 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 6 * $ 50,000 ) and the engineers ( 2 * $ 80,000 ) > > > $ 800,000 - $ 300,000 - $ 160,000 = $ 340,000 . the correct answer is e ."
Answer: e
Problem: two stations a and b are 20 km apart on a straight line . one train starts from a at 7 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 8
Rationale: "suppose they meet x hours after 7 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 20 45 x = 45 x = 1 . so , they meet at 8 a . m . answer : option e"
Answer: e
Problem: a bag contains 6 red , 3 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
Options: a ) 2 / 7 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
Rationale: "total number of balls = 6 + 3 + 4 = 13 n ( s ) = 13 c 3 = 286 n ( e ) = 6 c 1 * 3 c 1 * 4 c 1 = 72 probability = 72 / 286 = 1 / 4 answer is d"
Answer: d
Problem: a crate measures 2 feet by 8 feet by 12 feet on the inside . a stone pillar in the shape of a right circular cylinder must fit into the crate for shipping so that it rests upright when the crate sits on at least one of its six sides . what is the radius , in feet , of the pillar with the largest volume that could still fit in the crate ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: "we can find the radius of all the three cases of cylinders . the only crux to find the answer faster is that : voulme is pi * r ^ 2 * h . the volume is a function of r ^ 2 . so r has to be the highest to find the largest volume . so r = 2 for the surface 8 * 12 face . volume = 8 pi answer a"
Answer: a
Problem: if 0.3 of a number is equal to 0.06 of another number , the ratio of the numbers i
Options: a ) 3 : 15 , b ) 1 : 2 , c ) 3 : 20 , d ) 20 : 3 , e ) none
Rationale: "sol . 0.3 a = 0.06 b â ‡ ” a / b = 0.06 / 0.30 = 6 / 30 = 3 / 15 . â ˆ ´ a : b = 3 : 15 . answer a"
Answer: a
Problem: if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 93 , what is the value of x ?
Options: a ) 95 , b ) 91 , c ) 102 , d ) 101 , e ) 85
Rationale: "am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 93 x = 91 answer : b"
Answer: b
Problem: a person crosses a 1800 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 4.1 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 9
Rationale: "speed = 1800 / ( 12 x 60 ) m / sec = 2.5 m / sec . converting m / sec to km / hr = 2.5 x ( 18 / 5 ) km / hr = 9 km / hr . answer : e"
Answer: e
Problem: calculate the amount that an investor needs to be invest to earn $ 1023 in interest in 24 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 12 % compounded semi - annually ?
Options: a ) 3980 , b ) 3600 , c ) 3700 , d ) 3800 , e ) 3900
Rationale: "the approach is substitution , our interest requirement is $ 1023 after 24 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields $ 1023 in 24 months 3900 yielded $ 1023 using the formula a = p ( 1 + r / n ) nt hence answer is e"
Answer: e
Problem: a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates c apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates c / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Problem: a person can row at 9 kmph and still water . he takes 4 1 / 2 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 1 kmph ?
Options: a ) 33 , b ) 77 , c ) 26 , d ) 28 , e ) 20
Rationale: "let the distance between a and b be x km . total time = x / ( 9 + 1 ) + x / ( 9 - 1 ) = 4.5 = > x / 10 + x / 8 = 9 / 2 = > ( 4 x + 5 x ) / 40 = 9 / 2 = > x = 20 km . answer : e"
Answer: e
Problem: the distance from steve ' s house to work is 35 km . on the way back steve drives twice as fast as he did on the way to work . altogether , steve is spending 6 hours a day on the roads . what is steve ' s speed on the way back from work ?
Options: a ) 5 . , b ) 10 . , c ) 14 . , d ) 15 . , e ) 17.5
Rationale: time is in the ratio 2 : 1 : : to : fro office therefore , 2 x + 1 x = 6 hrs time take to come back - 2 hrs , distance travelled - 35 km = > speed = 17.5 kmph e
Answer: e
Problem: the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the 4 walls of the room at rs . 3 per square feet if there is one door of dimensions 6 feet * 3 feet and 3 windows of dimensions 4 feet * 3 feet each ?
Options: a ) s . 4528 , b ) s . 4520 , c ) s . 4527 , d ) s . 4530 , e ) s . 2718
Rationale: area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 3 = rs . 2718 answer : e
Answer: e
Problem: the greatest number which on dividing 1657 and 2037 leaves remainders 6 and 5 respectively , is :
Options: a ) 123 , b ) 127 , c ) 235 , d ) 305 , e ) 505
Rationale: "explanation : required number = h . c . f . of ( 1657 - 6 ) and ( 2037 - 5 ) = h . c . f . of 1651 and 2032 = 127 . answer : b"
Answer: b
Problem: in an examination , 300 students appeared . out of these students ; 28 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 01
Rationale: "the number of students with first division = 28 % of 300 = 28 / 100 × 300 = 8400 / 100 = 84 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 84 + 162 ) = 54 answer : c"
Answer: c
Problem: the average of first 13 even numbers is ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "sum of 13 even numbers = 13 * 14 = 110 average = 182 / 13 = 14 answer : e"
Answer: e
Problem: a 250 m long train is running at a speed of 55 km / hr . it crossed a platform of length 520 m in ?
Options: a ) 41.1 sec , b ) 20.2 sec , c ) 31.8 sec , d ) 50.4 sec , e ) none of the above
Rationale: "speed = 55 km / hr ( to convert km / hr in to m / s ) = 55 x 5 / 18 m / s distance = 250 m + 520 m ( if questions is about train crossing a post you need to consider only the length of train , ) = 770 m time = distance / speed = 770 x 18 / ( 5 x 55 ) = 50.4 sec ans is : d"
Answer: d
Problem: what is 15 percent of 54 ?
Options: a ) 7.3 , b ) 8.1 , c ) 9.5 , d ) 10.2 , e ) 11.6
Rationale: "( 15 / 100 ) * 54 = 8.1 the answer is b ."
Answer: b
Problem: a sum of money at simple interest amount to rs 720 after 2 years and to rs 1020 after a further period of 5 years . the sum is :
Options: a ) 600 , b ) 450 , c ) 650 , d ) 500 , e ) 550
Rationale: simple interest for 5 year = rs . ( 1020 - 720 ) = rs . 300 . simple interest for 2 year = rs . ( 300 / 5 × 2 ) = rs . 120 . principal = rs . ( 720 - 120 ) = rs . 600 . answer : a
Answer: a
Problem: an amount of rs . 100000 is invested in two types of shares . the first yields an interest of 9 % p . a and the second , 11 % p . a . if the total interest at the end of one year is 9 2 / 3 % , then the amount invested in each share was ?
Options: a ) 23777 , b ) 35000 , c ) 29977 , d ) 26777 , e ) 19871
Rationale: let the sum invested at 9 % be rs . x and that invested at 11 % be rs . ( 100000 - x ) . then , ( x * 9 * 1 ) / 100 + [ ( 100000 - x ) * 11 * 1 ] / 100 = ( 100000 * 29 / 3 * 1 / 100 ) ( 9 x + 1100000 - 11 x ) / 100 = 29000 / 3 = 9700 ( 9 x + 1100000 - 11 x ) = 970000 x = 65000 sum invested at 9 % = rs . 65000 sum invested at 11 % = rs . ( 100000 - 65000 ) = rs . 35000 . answer : b
Answer: b
Problem: a sum was put at simple interest at a certain rate for 10 years . had it been put at 5 % higher rate , it would have fetched rs . 100 more . what was the sum ?
Options: a ) s . 350 , b ) s . 700 , c ) s . 200 , d ) s . 600 , e ) s . 500
Rationale: "at 5 % more rate , the increase in s . i for 10 years = rs . 100 ( given ) so , at 5 % more rate , the increase in si for 1 year = 100 / 10 = rs . 10 / - i . e . rs . 10 is 5 % of the invested sum so , 1 % of the invested sum = 10 / 5 therefore , the invested sum = 10 × 100 / 5 = rs . 200 answer : c"
Answer: c
Problem: a merchant gets a 5 % discount on each meter of fabric he buys after the first 2,000 meters and a 7 % discount on every meter after the next 1,500 meters . the price , before discount , of one meter of fabric is $ 2 , what is the total amount of money the merchant spends on 6,000 meters of fabric ?
Options: a ) $ 9,300 , b ) $ 10,400 , c ) $ 11,500 , d ) $ 12,600 , e ) $ 13,700
Rationale: "for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 2500 = $ 4650 the total price is $ 4000 + $ 2850 + $ 4650 = $ 11,500 the answer is c ."
Answer: c
Problem: there are 6 red balls and 4 blue balls in a jar . if 3 balls are selected from the jar , what is the probability that all 3 balls selected are blue balls ?
Options: a ) 1 / 18 , b ) 1 / 24 , c ) 1 / 30 , d ) 1 / 36 , e ) 1 / 48
Rationale: the number of ways of choosing 3 balls from the jar is 10 c 3 = 120 . the number of ways of choosing 3 blue balls is 4 c 3 = 4 . p ( 3 blue balls ) = 4 / 120 = 1 / 30 . the answer is c .
Answer: c
Problem: in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50,000 a year , and engineers make an average of $ 80,000 . what is the average salary for managers if the average for all employees is also $ 80,000 ?
Options: a ) $ 80,000 , b ) $ 130,000 , c ) $ 240,000 , d ) $ 370,000 , e ) $ 320,000
Rationale: for sake of ease , let ' s say there are 10 employees : 7 marketers , 1 engineers , and 2 manager . average company salary * number of employees = total company salary > > > $ 80,000 * 10 = $ 800,000 subtract the combined salaries for the marketers ( 7 * $ 50,000 ) and the engineers ( $ 80,000 ) > > > $ 800,000 - $ 350,000 - $ 80,000 = $ 370,000 . the correct answer is d .
Answer: d
Problem: working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel eight times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 8 and w = 8 s then we have 1 / ( 8 * s ) + 1 / s = 1 / 8 < = > 9 / ( 8 * s ) = 1 / 8 < = > s = 9 ans : d
Answer: d
Problem: a boat running up stram takes 6 hours to cover a certain distance , while it takes 7 hours to cover the same distance running down stream . what is the ratio between the speed of the boat and the speed of water current respectively ?
Options: a ) 2 : 3 , b ) 5 : 6 , c ) 4 : 5 , d ) 13 : 1 , e ) 8 : 1
Rationale: "explanation : let speed of boat is x km / h and speed stream is y km / hr 6 ( x + y ) = 7 ( x - y ) 6 x + 6 y = 7 x - 7 y 13 y = x 13 y = x x / y = 13 / 1 13 : 1 answer : option d"
Answer: d
Problem: company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.6 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 14 / 31 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.6 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 32 hours . total hours = 72 then the fraction would be 32 / 72 = 4 / 9 . therefore answer e
Answer: e
Problem: a car traveled 75 % of the way from town a to town b at an average speed of 50 miles per hour . the car travels at an average speed of s miles per hour for the remaining part of the trip . the average speed for the entire trip was 60 miles per hour . what is s ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 300 , e ) 237.5
Rationale: "total distance = 100 miles ( easier to work with % ) 75 % of the distance = 75 miles 25 % of the distance = 25 miles 1 st part of the trip → 75 / 50 = 1.5 2 nd part of the trip → 25 / s = t total trip → ( 75 + 25 ) / 60 = 1.5 + t » 100 / 60 = 1.5 + t » 2.5 = 1.5 + t » t = 0.1667 back to 2 nd part of the trip formula : 25 / s = 0.1667 » s = 150 ans a"
Answer: a
Problem: when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.02 , what is value of j ?
Options: a ) 300 , b ) 600 , c ) 500 , d ) 112 , e ) 620
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.02 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.02 = 12 / j 0.02 * j = 12 j = 12 / 0.02 = 1200 / 2 = 600 / 1 = 600 so j = 600 , answer = b ."
Answer: b
Problem: joshua and jose work at an auto repair center with 5 other workers . for a survey on health care insurance , 2 of the 6 workers will be randomly chosen to be interviewed . what is the probability that joshua and jose will both be chosen ?
Options: a ) 1 / 21 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
Rationale: "two methods 1 ) probability of chosing josh first = 1 / 7 probability of chosing jose second = 1 / 6 total = 1 / 42 probability of chosing jose first = 1 / 7 probability of chosing josh second = 1 / 6 total = 1 / 42 final = 1 / 42 + 1 / 42 = 1 / 21 a"
Answer: a
Problem: in the coordinate plane , points ( x , 2 ) and ( 10 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 2 ) = ( 4 , 2 ) and ( 10 , y ) = ( 10,5 ) - - > 4 + 5 = 2 + 5 = 9 . answer : c ."
Answer: c
Problem: the average score of a cricketer in 2 matches is 20 and in other 3 matches is 30 . then find the average score in all the 5 matches ?
Options: a ) 26 , b ) 27 , c ) 30 , d ) 35 , e ) 42
Rationale: "average in 5 matches = ( 2 * 20 + 3 * 30 ) / 2 + 3 = 40 + 90 / 5 = 130 / 5 = 26 answer is a"
Answer: a
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 10 mat - weavers in 10 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 16
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 10 : : 4 : x days 4 : 10 4 * 4 * x = 10 * 10 * 4 x = ( 10 * 10 * 4 ) / ( 4 x 4 ) x = 25 . answer is a ."
Answer: a
Problem: rahul played weel in this season . his current batting averagge is 51 . if he score 78 runs in today match . his batting average will become 54 . how many matches had he played in this season .
Options: a ) 8 , b ) 10 , c ) 9 , d ) 6 , e ) 5
Rationale: "51 x + 78 = 54 ( x + 1 ) = > 3 x = 24 = > x = 8 answer : a"
Answer: a
Problem: in 1998 the profits of company n were 10 percent of revenues . in 1999 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 1999 were what percent of the profits in 1998 ?
Options: a ) 80 % , b ) 105 % , c ) 120 % , d ) 112 % , e ) 138 %
Rationale: "0,112 r = x / 100 * 0.1 r answer d"
Answer: d
Problem: a garrison of 400 men had a provision for 31 days . after 25 days 320 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 30 days , c ) 10 days , d ) 16 days , e ) 18 days
Rationale: "400 - - - 31 400 - - - 6 80 - - - ? 400 * 6 = 80 * x = > x = 30 days . answer : b"
Answer: b
Problem: a jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . the train is running at 45 kmph in the same direction . how much time does it take for the train to pass the jogger ?
Options: a ) 46 , b ) 36 , c ) 18 , d ) 22 , e ) 23
Rationale: explanation : distance to be covered = 240 + 120 = 360 m relative speed = 36 km / hr = 36 × 10 / 36 = 10 m / s time = distance / speed = 360 / 10 = 36 seconds answer : option b
Answer: b
Problem: the dimensions of a field are 10 m by 10 m . a pit 5 m long , 5 m wide and 3 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 2 m , b ) 2.5 m , c ) 1.5 m , d ) 1.25 m , e ) 1 m
Rationale: "the volume of the earth removed is 5 * 5 * 3 = 75 m ^ 3 . the remaining area of the field is 10 * 10 - 5 * 5 = 75 m ^ 2 . 75 m ^ 3 of the earth evenly spread over the area of 75 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 75 / 75 = 1 m . answer : e"
Answer: e
Problem: suganya and suriya are partners in a business . suganya invests rs . 32,000 for 8 months and suriya invests rs . 28,000 for 10 months . out of a profit of rs . 30,570 . suganya ' s share is
Options: a ) rs . 9471 , b ) rs . 12,628 , c ) rs . 912.54 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 32000 ã — 8 ) : ( 28000 ã — 10 ) = 32 : 35 . suganya ' s share = rs . ( 31570 ã — 2 / 67 ) = rs . 912.54 . answer c"
Answer: c
Problem: a number when divided by a divisor leaves a remainder of 24 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 13 , b ) 59 , c ) 35 , d ) 37 , e ) 12
Rationale: "explanatory answer decoding ` ` a number when divided by a divisor leaves a remainder of 24 ' ' let the original number be ' a ' . let the divisor be ' d ' . let the quotient of dividing ' a ' by ' d ' be ' x ' . therefore , we can write the division as a / d = x and the remainder is 24 . i . e . , a = dx + 24 decoding ` ` when twice the original number is divided by the same divisor , the remainder is 11 ' ' twice the original number is divided by d means 2 a is divided by d . we know that a = dx + 24 . therefore , 2 a = 2 ( dx + 48 ) or 2 a = 2 dx + 48 when ( 2 dx + 48 ) is divided by ' d ' the remainder is 11 . 2 dx is divisible by ' d ' and will therefore , not leave a remainder . the remainder of 11 would be the remainder of dividing 48 by d . the question is ` ` what number will leave a remainder of 11 when it divides 48 ? ' ' when 37 divides 48 , the remainder is 11 . hence , the divisor is 37 . choice d"
Answer: d
Problem: an uneducated retailer marks all his goods at 65 % above the cost price and thinking that he will still make 25 % profit , offers a discount of 25 % on the marked price . what is his actual profit on the sales ?
Options: a ) 12.50 % , b ) 13.50 % , c ) 14 % , d ) 23.75 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 165 . s . p . = 75 % of rs . 165 = rs . 123.75 . ∴ gain % = 23.75 % . answer d"
Answer: d
Problem: a boat can travel with a speed of 16 km / hr in still water . if the rate of stream is 5 km / hr , then find the time taken by the boat to cover distance of 126 km downstream .
Options: a ) 4 hours , b ) 5 hours , c ) 6 hours , d ) 7 hours , e ) 8 hours
Rationale: explanation : it is very important to check , if the boat speed given is in still water or with water or against water . because if we neglect it we will not reach on right answer . i just mentioned here because mostly mistakes in this chapter are of this kind only . lets see the question now . speed downstream = ( 16 + 5 ) = 21 kmph time = distance / speed = 126 / 21 = 6 hours option c
Answer: c
Problem: if 7 a = 2 b = 15 , then 42 ab =
Options: a ) 75 , b ) 125 , c ) 675 , d ) 1100 , e ) 1250
Rationale: "7 a * 2 b = 15 * 15 = 225 14 ab = 225 i . e . 42 ab = 675 answer : option c"
Answer: c
Problem: 10 friends went to a hotel and decided to pay the bill amount equally . but 9 of them could pay rs . 50 each as a result 10 th has to pay rs . 180 extra than his share . find the amount paid by him .
Options: a ) 130 , b ) 140 , c ) 110 , d ) 120 , e ) none
Rationale: "explanation : average amount paid by 9 persons = rs . 50 increase in average due to rs . 50 paid extra by the 10 th men = rs . 180 / 9 = rs . 20 therefore , average expenditure of 10 friends = rs . 50 + rs . 20 = rs . 70 therefore , amount paid by the 10 th men = rs . 70 + rs . 50 = rs . 120 correct option : d"
Answer: d
Problem: if 0.75 : x : : 5 : 7 , then x is equal to :
Options: a ) 1.05 , b ) 1.16 , c ) 1.2 , d ) 1.3 , e ) none of these
Rationale: "explanation : ( x * 5 ) = ( 0.75 * 7 ) x = 5.25 / 5 = 1.05 answer : a"
Answer: a
Problem: a new tower has just been built at the verbico military hospital ; the number of beds available for patients at the hospital is now 7 times the number available before the new tower was built . currently , 1 / 3 of the hospital ' s original beds , as well as 1 / 5 of the beds in the new tower , are occupied . for the purposes of renovating the hospital ' s original wing , all of the patients in the hospital ' s original beds must be transferred to beds in the new tower . if patients are neither admitted nor discharged during the transfer , what fraction of the beds in the new tower will be unoccupied once the transfer is complete ?
Options: a ) 67 / 90 , b ) 29 / 60 , c ) 17 / 30 , d ) 19 / 30 , e ) 11 / 15
Rationale: "i think a - 67 / 90 is the correct answer . here goes : lets assume originally the number of beds = x after the new tower , the total combined no of beds = 7 x so old = x , new = 6 x now 1 / 3 of x are occupied and 1 / 5 of 6 x are occupied which simplifies to ( 6 / 5 ) x we are shifting 1 / 3 of x to the new ward so there will now be : 1 / 3 of x plus 6 / 5 of x occupied in the new ward . add them up to get 23 / 15 of x there are 6 x beds in new tower so ratio is : ( 23 / 15 ) x / 6 x = 23 / 90 of x subtract that from 90 / 90 of x and you get the number of un - occupied beds to total capacity of new tower = 67 / 90 . a"
Answer: a
Problem: a man rows 750 m in 675 seconds against the stream and returns in 7 and half minutes . his rowing speed in s ɵ ll water is
Options: a ) 4 kmph , b ) 5 kmph , c ) 6 kmph , d ) 7 kmph , e ) none of these
Rationale: explanation : rate upstream = ( 750 / 675 ) = 10 / 9 m / sec rate downstream ( 750 / 450 ) m / sec = 5 / 3 m / sec rate in still water = ( 1 / 2 ) * [ ( 10 / 9 ) + ( 5 / 3 ) ] m / sec . = 25 / 18 m / sec = ( 25 / 18 ) * ( 18 / 5 ) kmph = 5 kmph answer : b
Answer: b
Problem: a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3500 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 2100 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3500 / 25 = 140 so , a ’ s amount = 120 × 15 = rs . 2100 . answer : option c"
Answer: c
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 7350 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) 287 , b ) 1287 , c ) 125 , d ) 988 , e ) 175
Rationale: "3 x * 2 x = 7350 = > x = 35 2 ( 105 + 70 ) = 350 m 350 * 1 / 2 = rs . 175 answer : e"
Answer: e
Problem: the probability that a number selected at random from the first 50 natural numbers is a composite number is - .
Options: a ) 17 / 25 , b ) 17 / 27 , c ) 17 / 18 , d ) 17 / 22 , e ) 17 / 09
Rationale: "the number of exhaustive events = ⁵ ⁰ c ₁ = 50 . we have 15 primes from 1 to 50 . number of favourable cases are 34 . required probability = 34 / 50 = 17 / 25 . answer : a"
Answer: a
Problem: there are certain number of hats and gloves in a box . they are of 41 red , 23 green , 11 orange . power gone but a woman can differentiate between hats and gloves . how many draws are required to obtain a pair of each color ?
Options: a ) 66 , b ) 67 , c ) 68 , d ) 69 , e ) 70
Rationale: the worst case senario will be first take 40 red then take 22 green then take 1 + 1 red + green then take 2 orange . so total 40 + 22 + 2 + 2 = 66 answer : a
Answer: a
Problem: 19.19 / 2000 is equal to :
Options: a ) 1.01252633 , b ) 0.01262533 , c ) 0.12526333 , d ) 0.012793333 , e ) 0.12725333
Rationale: "19.19 / 2000 = 2525 / 200000 = 0.012793333 answer : d"
Answer: d
Problem: the average weight of 20 persons sitting in a boat had some value . a new person added to them whose weight was 49 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 20 persons ?
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: "20 x + 49 = 21 ( x – 5 ) x = 56 answer : b"
Answer: b
Problem: harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 3 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 1 / 2 , e ) 4 / 7
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 3 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 3 x = 9 x august tips as a fraction of total tips = 3 x / 9 x = 1 / 3 . so answer is a"
Answer: a
Problem: how many shots of 1 cm radius can be prepared from a sphere of 3 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 88 , e ) 99
Rationale: "4 / 3 π * 3 * 3 * 3 = 4 / 3 π * 1 * 1 * 1 * x x = 27 answer : c"
Answer: c
Problem: two trains each 190 m in length each , are running on two parallel lines in opposite directions . if one goes at the speed of 65 km / h while the other travels at 50 km / h . how long will it take for them to pass each other completely .
Options: a ) 10.7 sec , b ) 2.7 sec , c ) 11.9 sec , d ) 12.7 sec , e ) 25.7 sec
Rationale: "explanation : d = 190 m + 190 m = 380 m rs = 65 + 50 = 115 * 5 / 18 = 319 / 10 t = 380 * 10 / 319 = 11.9 sec answer : option c"
Answer: c
Problem: a 600 m long train crosses a tree in 60 sec , how much time will it take to pass a platform 450 m long ?
Options: a ) 288 , b ) 190 , c ) 188 , d ) 188 , e ) 105
Rationale: "l = s * t s = 600 / 60 s = 10 m / sec . total length ( d ) = 1050 m t = d / s t = 1050 / 10 t = 105 sec answer : e"
Answer: e
Problem: the price of rice falls by 10 % . how much rice can be bought now with the money that was sufficient to buy 20 kg of rice previously ?
Options: a ) 5 kg , b ) 15 kg , c ) 25 kg , d ) 30 kg , e ) none
Rationale: "solution : let rs . 100 be spend on rice initially for 20 kg . as the price falls by 10 % , new price for 20 kg rice , = ( 100 - 10 % of 100 ) = 90 new price of rice = 90 / 20 = rs . 4,5 per kg . rice can bought now at = 100 / 4,5 = 22,22 kg . answer : option e"
Answer: e
Problem: the least number , which when divided by 12 , 15 , 20 and 63 leaves in each case a remainder of 8 is :
Options: a ) 448 , b ) 488 , c ) 542 , d ) 1268 , e ) 560
Rationale: "required number = ( l . c . m . of 12 , 15 , 20 , 63 ) + 8 = 1260 + 8 = 1268 . answer : d"
Answer: d
Problem: in a class of 50 students , 3 / 5 went away do painting , 1 / 5 went to play in the field . how many students are left in the classroom ?
Options: a ) 20 , b ) 30 , c ) 5 , d ) 8 , e ) 10
Rationale: 3 / 5 + 1 / 5 are the students who have left the classroom 3 / 5 + 1 / 5 = ( 3 + 1 ) / 5 , since denominator is same for both fractions = 4 / 5 remaining students in the classroom = 1 - 4 / 5 = 5 / 5 - 4 / 5 = ( 5 - 4 ) / 5 = 1 / 5 1 / 5 of 50 = 10 ans : e
Answer: e
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 300 kg . in the first week 30 percent is cut away . in the second week 30 percent of the remainder is cut away . in the third week the statue is completed when 15 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "d 125 kg 300 ã — 0.7 ã — 0.7 ã — 0.85 = 125 kg ."
Answer: d