regisss/math_qa huggingface dataset:
Problem: 24 oz of juice p and 25 oz of juice v are mixed to make smothies a and y . the ratio of p to v in smothie a is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie a ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . p 1 + p 2 = 24 v 1 + v 2 = 25 p 1 = 4 v 1 p 2 = v 2 / 5 4 v 1 + v 2 / 5 = 24 v 1 + v 2 = 25 4 v 2 - v 2 / 5 = 76 19 v 2 / 5 = 76 = > v 2 = 20 = > v 1 = 5 = > p 1 = 20 answer - d
Answer: d
Problem: during a certain season , a team won 60 percent of its first 100 games and 50 percent of its remaining games . if the team won 70 percent of its games for the entire season , what was the total number of games that the team played ?
Options: a ) 80 , b ) 70 , c ) 56 , d ) 50 , e ) 105
Rationale: "we are first given that a team won 60 percent of its first 100 games . this means the team won 0.6 x 100 = 60 games out of its first 100 games . we are next given that the team won 50 percent of its remaining games . if we use variable t to represent the total number of games in the season , then we can say t – 100 equals the number of remaining games in the season . thus we can say : 0.5 ( t – 100 ) = number of wins for remaining games 0.5 t – 50 = number of wins for remaining games lastly , we are given that team won 70 percent of all games played in the season . that is , they won 0.7 t games in the entire season . with this we can set up the equation : number of first 100 games won + number of games won for remaining games = total number of games won in the entire season 60 + 0.5 t – 50 = 0.7 t 10 = 0.2 t 100 = 2 t 50 = t answer is d ."
Answer: d
Problem: in a certain pond , 20 fish were caught , tagged , and returned to the pond . a few days later , 20 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what ` s the approximate number of fish in the pond ?
Options: a ) 400 , b ) 625 , c ) 1250 , d ) 2500 , e ) 500
Rationale: "if x is total number of fish in the pond : 4 = 20 / x * 100 = > x = 500 so answer is e"
Answer: e
Problem: a certain bus driver is paid a regular rate of $ 18 per hour for any number of hours that does not exceed 40 hours per week . for any overtime hours worked in excess of 40 hours per week , the bus driver is paid a rate that is 75 % higher than his regular rate . if last week the bus driver earned $ 976 in total compensation , how many total hours did he work that week ?
Options: a ) 36 , b ) 40 , c ) 44 , d ) 48 , e ) 52
Rationale: "for 40 hrs = 40 * 18 = 720 excess = 976 - 720 = 252 for extra hours = . 75 ( 18 ) = 13.5 + 18 = 31.5 number of extra hrs = 252 / 31.5 = 8 total hrs = 40 + 8 = 48 answer d 48"
Answer: d
Problem: a shopkeeper buys two articles for rs . 1000 each and then sells them , making 75 % profit on the first article and 75 % loss on second article . find the net profit or loss percent ?
Options: a ) 200 , b ) 768 , c ) 276 , d ) 750 , e ) 279
Rationale: "profit on first article = 75 % of 1000 = 750 . this is equal to the loss he makes on the second article . that , is he makes neither profit nor loss . answer : d"
Answer: d
Problem: a spirit and water solution is sold in a market . the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . a solution of 1 liter of spirit and 1 liter of water costs 50 cents . how many cents does a solution of 1 liter of spirit and 2 liters of water cost ?
Options: a ) 13 , b ) 33 , c ) 50 , d ) 51 , e ) 52
Rationale: "the cost per liter of the solution is directly proportional to the part ( fraction ) of spirit ( by volume ) the solution has . it means there is no effect of change in volume of water to the costing of the solution so a solution of 1 liter of spirit and 2 liters of water will cost 50 cents answer = 50 answer : c"
Answer: c
Problem: in a company of 180 employees , 110 are females . a total of 90 employees have advanced degrees and the rest have a college degree only . if 35 employees are males with a college degree only , how many employees are females with advanced degrees ?
Options: a ) 50 , b ) 55 , c ) 60 , d ) 65 , e ) 70
Rationale: "the number of males is 180 - 110 = 70 . the number of males with advanced degrees is 70 - 35 = 35 . the number of females with advanced degrees is 90 - 35 = 55 . the answer is b ."
Answer: b
Problem: how many positive integers less than 8,000 are there in which the sum of the digits equals 5 ?
Options: a ) 57 , b ) 56 , c ) 55 , d ) 54 , e ) 53
Rationale: "basically , the question asks how many 4 digit numbers ( including those in the form 0 xxx , 00 xx , and 000 x ) have digits which add up to 5 . think about the question this way : we know that there is a total of 5 to be spread among the 4 digits , we just have to determine the number of ways it can be spread . let x represent a sum of 1 , and | represent a seperator between two digits . as a result , we will have 5 x ' s ( digits add up to the 5 ) , and 3 | ' s ( 3 digit seperators ) . so , for example : xx | x | x | x = 2111 | | xxx | xx = 0032 etc . there are 8 c 3 ways to determine where to place the separators . hence , the answer is 8 c 3 = 56 . b"
Answer: b
Problem: c and d started a business by investing rs . 1000 / - and rs . 1500 / - respectively . find the d ’ s share out of a total profit of rs . 500 :
Options: a ) 400 , b ) 300 , c ) 200 , d ) 100 , e ) 150
Rationale: c = rs . 1000 / - d = rs . 1500 / - c share 2 parts & d share 3 parts total 5 parts - - - - - > rs . 500 / - - - - - > 1 part - - - - - - - > rs . 100 / - d share = 3 parts - - - - - > rs . 300 / - d
Answer: d
Problem: a train 400 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 , b ) 56 , c ) 29 , d ) 27 , e ) 21
Rationale: "s = ( 400 + 300 ) / 45 = 700 / 45 * 18 / 5 = 56 answer : b"
Answer: b
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 70 , what is the greatest possible value of q minus r ?
Options: a ) 63 , b ) 64 , c ) 65 , d ) 66 , e ) 67
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 70 . the greatest multiple of 9 which is less than 70 is 63 . the answer is a ."
Answer: a
Problem: at a certain paint store forest green is made by mixing 4 parts blue paint with 3 parts yellow paint . verdant green is made by mixing 4 parts yellow paint with 3 parts blue paint . how many liters of yellow paint must be added to 7 liters of forest green to change it to verdant green ?
Options: a ) 5 / 3 , b ) 2 / 7 , c ) 7 / 3 , d ) 1 / 7 , e ) 1 / 4
Rationale: 7 liter of forset green have 4 liter of blue and 3 liter of yellow suppose we add x liter of yellow to make it a verdant green so the ratio of blue to yellow in verdant green is ¾ so the equation is blue / yellow = 4 / ( 3 + x ) = ¾ 9 + 3 x = 16 = > x = 7 / 3 answer : c
Answer: c
Problem: the sum of three consecutive multiples of 3 is 90 . what is the largest number ?
Options: a ) 30 , b ) 33 , c ) 36 , d ) 39 , e ) 42
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 90 9 x = 81 x = 9 largest number = 3 x + 6 = 33 answer : b"
Answer: b
Problem: what will be the difference between simple and compound interest @ 25 % per annum on a sum of $ 3600 after 2 years ?
Options: a ) $ 150 , b ) $ 220 , c ) $ 225 , d ) $ 182 , e ) $ 189
Rationale: "s . i . = 3600 * 25 * 2 / 100 = $ 1800 c . i . = 3600 * ( 1 + 25 / 100 ) ^ 2 - 3600 = $ 2025 difference = 2025 - 1800 = $ 225 answer is c"
Answer: c
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 8 people to do 8 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 8 , e ) 11
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 8 people can do 8 / 3 of the work in one day . 8 people can do 8 times the work in 3 days . the answer is c ."
Answer: c
Problem: a is half good a work man as b and together they finish a job in 32 days . in how many days working alone b finish the job ?
Options: a ) 98 days , b ) 21 days , c ) 48 days , d ) 18 days , e ) 19 days
Rationale: "wc = 1 : 2 2 x + x = 1 / 32 = > x = 1 / 96 2 x = 1 / 96 = > 48 days answer : c"
Answer: c
Problem: the measurement of a rectangular box with lid is 25 cmx 24 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288 , b ) 2302 , c ) 2304 , d ) 8640 , e ) 964
Rationale: "d = 24 , r = 12 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 12 * 12 * 12 = 2304 π cm 3 answer : c"
Answer: c
Problem: if the sides of a square are multiplied by 10 , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 1 %
b ) 10 %
c ) 100 %
d ) 500 %
e ) 1000 %
Rationale: let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 10 x , so the area is 100 x ^ 2 . the area of the original square is 1 / 100 = 1 % times the area of the new square . the answer is a .
Answer: a
Problem: machine t takes 2 more hours than machine b to make 20 widgets . if working together , the machines can make 25 widgets in 3 hours , how long will it take machine t to make 40 widgets ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: i approached this one by plugging in numbers . . . started with c . if 40 are made in 8 hours , then 20 are made in 4 hours . so time of t is 4 , and time of b is 2 . rate together : 20 / 4 + 20 / 2 = 5 + 10 = 15 . so in 1 hour , together make 15 widgets . in 3 hours = 45 . way too much . we can eliminate right away c , b , and a - because b and t reduces the time - the total # of widgets made will be even higher . now between d and e - > try only one . . if it does n ' t work , then the other one is the answer . i picked e : 12 h to make 40 widgets , and 6 hours to make 20 . this is the time of t . time of b = 4 hours . 20 / 6 + 20 / 4 = 10 / 3 + 20 / 4 find lcm of 3 and 4 = 12 . multiply first by 4 , and second by 3 : 40 + 60 / 12 = 100 / 12 divide by 4 : 25 / 3 so this is the rate given . e is the correct answer
Answer: e
Problem: seller selling an apple for rs . 16 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 17 , d ) 18 , e ) 20
Rationale: "sp = 16 loss = cp 17 loss = cp − sp = cp − 16 ⇒ cp 17 = cp − 16 ⇒ 16 cp 17 = 16 ⇒ cp 17 = 1 ⇒ cp = 17 c"
Answer: c
Problem: what is the smallest number which when increased by 3 is divisible by 9 , 70 , 25 and 21 ?
Options: a ) 2927 , b ) 3147 , c ) 3387 , d ) 3567 , e ) 3797
Rationale: "when increased by 3 , the number must include at least 2 * 3 ^ 2 * 5 ^ 2 * 7 = 3150 the answer is b ."
Answer: b
Problem: carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 8 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 8 = 42 42 / 12 = 3.5 feet answer : e"
Answer: e
Problem: an employee whose hourly wage was increased by 25 percent decided to reduce the number of hours worked per week so that the employee ' s total weekly income would remain unchanged . by what percent should the number of hours worked be reduced ?
Options: a ) 9 , b ) 13 , c ) 16 , d ) 20 , e ) 25
Rationale: let original hourly wage be x and let the no of hours worked be y total wage will be = x * y after the increment the wage will be = 1.25 x now we need to find number of hours worked so that x * y = 1.25 x * z i . e z = 4 / 5 y % decrease = ( y - 4 / 5 y ) / y * 100 = 100 / 5 = 20 % . thus my answer is d
Answer: d
Problem: 45 men working 8 hours per day dig 40 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: "( 45 * 8 ) / 40 = ( x * 6 ) / 50 = > x = 75 75 – 45 = 30 answer : c"
Answer: c
Problem: there are 150 ' zeroes ' and 151 ' ones ' written on a black board . a step involves choosing 3 digits and replacing them with a single digit . if all the 3 digits are identical , they are replaced with the same digit . otherwise , the digit that appears twice replaces the 3 chosen digits . what is the minimum number of steps after which there will be no zero written on the blackboard ?
Options: a ) 11 , b ) 37 , c ) 36 , d ) 76 , e ) 33
Rationale: if we strike out 3 zeros , we are in effect reducing two zeroes . so we need 74 steps to reduce 148 zeroes . there are 2 zeroes and 151 ones left now . the remaining zeroes can be reduced in 2 steps . hence the answer is 76 . answer : d
Answer: d
Problem: a and b complete a work in 9 days . a alone can do it in 18 days . if both together can do the work in how many days ?
Options: a ) 6 days , b ) 8 days , c ) 5 days , d ) 7 days , e ) 15 days
Rationale: "1 / 9 + 1 / 18 = 1 / 6 6 / 1 = 6 days answer : a"
Answer: a
Problem: in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 5 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 146
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 5 % so total man = 150 * . 95 = 142.5 women will be = 175 - 142.5 = 32.5 so population after two years = [ 135 ^ 2 + 32.5 ^ 2 ] ^ . 5 = 146.15 = 146 so population after two year = 146 answer : e"
Answer: e
Problem: if an object travels 200 feet in 4 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 36 , b ) 34 , c ) 356 , d ) 12 , e ) 45
Rationale: 1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 200 feet in 4 sec then it travels 200 / 4 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 50 feet in 1 hour = 180000 feet in 1 hr = 180000 / 5280 miles in 1 hour = 18000 / 528 miles / hr ~ 34 miles / hr answer - b
Answer: b
Problem: a cube of side 3 meter length is cut into small cubes of side 15 cm each . how many such small cubes can be obtained ?
Options: a ) 8078 , b ) 1040 , c ) 1058 , d ) 1021 , e ) 8000
Rationale: "along one edge , the number of small cubes that can be cut = 300 / 15 = 20 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 20 * 20 * 20 = 8000 answer : e"
Answer: e
Problem: a hall is 15 m long and 12 m broad . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of 4 walls , the volume of the hall is :
Options: a ) 3348 , b ) 3898 , c ) 1200 , d ) 2881 , e ) 7881
Rationale: answer : c ) 1200
Answer: c
Problem: if the sides of a triangle are 30 cm , 28 cm and 12 cm , what is its area ?
Options: a ) 120 cm 2 , b ) 112 cm 2 , c ) 776 cm 2 , d ) 666 cm 2 , e ) 168 cm 2
Rationale: "the triangle with sides 30 cm , 28 cm and 12 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 12 = 168 cm 2 answer : e"
Answer: e
Problem: the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 3 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 45 , b ) 65 , c ) 75 , d ) 89 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 3 = 71 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 – 316 = 4 a = e + 4 = 71 + 4 = 75 c"
Answer: c
Problem: if the price of a certain computer increased 30 percent from d dollars to 377 dollars , then 2 d =
Options: a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 580
Rationale: "before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 377 ( given ) i . e . d = 377 / 1.3 = $ 290 i . e . 2 d = 2 * 290 = 580 answer : option e"
Answer: e
Problem: you have been given a physical balance and 7 weights of 52 , 50 , 48 , 44 , 45 , 46 , and 78 kgs . . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 183 kgs . ?
Options: a ) 178 , b ) 180 , c ) 181 , d ) 182 , e ) 183
Rationale: "balance = 52 + 50 + 48 + 44 + 45 + 46 + 78 - 183 answer : e"
Answer: e
Problem: on a sum of money , the s . i . for 2 years is $ 600 , while the c . i . is $ 615 , the rate of interest being the same in both the cases . the rate of interest is ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "difference in c . i . and s . i for 2 years = $ 615 - $ 600 = $ 15 s . i for one year = $ 300 s . i . on $ 300 for 1 year = $ 15 rate = ( 100 * 15 ) / ( 300 ) = 5 % the answer is b ."
Answer: b
Problem: a is a working partner and b is a sleeping partner in the business . a puts in rs . 2000 and b rs . 3000 , a receives 10 % of the profit for managing the business the rest being divided in proportion of their capitals . out of a total profit of rs . 9600 , money received by a is ?
Options: a ) 1978 , b ) 2707 , c ) 7728 , d ) 4416 , e ) 7291
Rationale: "2 : 3 = > 2 : 3 9600 * 10 / 100 = 960 9600 - 960 = 8640 8640 * 2 / 5 = 3456 + 960 = 4416 answer : d"
Answer: d
Problem: annie and sam set out together on bicycles traveling at 15 and 12 km per hour respectively . after 40 minutes , annie stops to fix a flat tire . if it takes annie 35 minutes to fix the flat tire and sam continues to ride during this time , how many minutes will it take annie to catch up with sam assuming that annie resumes riding at 15 km per hour ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 100
Rationale: "annie gains 3 km per hour ( or 1 km every 20 minutes ) on sam . after 40 minutes annie is 2 km ahead . sam rides 1 km every 5 minutes . in the next 35 minutes , sam rides 7 km so sam will be 5 km ahead . it will take annie 100 minutes to catch sam . the answer is e ."
Answer: e
Problem: find the unknown term 8 , 86 , x , - 4 , - 12
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
Rationale: 8 , 86 , x , - 4 , - 12 i guess each differ in d range of 2 8 - 8 = 0 8 - 6 = 2 6 - 2 = 4 2 - 6 = - 4 - 4 - 8 = - 12 answer : a
Answer: a
Problem: if a train , travelling at a speed of 360 kmph , crosses a pole in 5 sec , then the length of train is ?
Options: a ) 381 m , b ) 112 m , c ) 500 m , d ) 125 m , e ) 433 m
Rationale: "c c = 360 * 5 / 18 * 5 = 500 m"
Answer: c
Problem: if y is the smallest positive integer such that 1260 multiplied by y is the square of an integer , then y must be
Options: a ) 25 , b ) 35 , c ) 60 , d ) 75 , e ) 140
Rationale: "1260 = 2 ^ 2 * 3 ^ 2 * 5 * 7 to be perfect square , we need to multiply by at least 5 * 7 = 35 . the answer is b ."
Answer: b
Problem: a certain company retirement plan has arule of 70 provision that allows an employee to retire when the employee ' s age plus years of employment with the company total at least 70 . in what year could a female employee hired in 1988 on her 32 nd birthday first be eligible to retire under this provision ?
Options: a ) 2003 , b ) 2004 , c ) 2005 , d ) 2006 , e ) 2007
Rationale: "she must gain at least 70 points , now she has 32 and every year gives her two more points : one for age and one for additional year of employment , so 32 + 2 * ( # of years ) = 70 - - > ( # of years ) = 19 - - > 1988 + 19 = 2007 . answer : e ."
Answer: e
Problem: a coin is tossed 3 times . what is the probability of getting exactly 2 heads ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 3 / 8 , d ) 5 / 8 , e ) 3 / 16
Rationale: "the number of possible outcomes is 2 ^ 3 = 8 there are 3 ways to get exactly 2 heads . p ( exactly 2 heads ) = 3 / 8 the answer is c ."
Answer: c
Problem: 3 , 4.5 , 6.75 , 10.13 , 15.18 , ( . . . )
Options: a ) 60 , b ) 60.75 , c ) 22.78 , d ) 32.52 , e ) 88
Rationale: "3 ( 3 ã — 3 ) ã · 2 = 4.5 ( 4.5 ã — 3 ) ã · 2 = 6.75 ( 6.75 ã — 3 ) ã · 2 = 10.13 ( 10.18 ã — 3 ) ã · 2 = 15.18 ( 15.18 ã — 3 ) ã · 2 = 60.75 answer is c"
Answer: c
Problem: a certain protective additive increases from 45 days to 60 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: "general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 60 − 45 / 45 ∗ 100 = 33 1 / 3 answer : b ."
Answer: b
Problem: if x * y = xy + 2 ( x + y ) for all integers x and y , then 2 * ( – 3 ) =
Options: a ) – 16 , b ) – 11 , c ) – 8 , d ) 4 , e ) 16
Rationale: 2 * ( - 3 ) = 2 * ( - 3 ) + 2 ( 2 + ( - 3 ) ) = - 6 - 2 = - 8 option ( c )
Answer: c
Problem: a can run 4.5 km distance in 1 min 30 seconds , while b can run this distance in 3 min . by how much distance can a beat b ?
Options: a ) 2250 m , b ) 1000 m , c ) 1250 m , d ) 1800 m , e ) 2000 m
Rationale: a takes time 1.30 minutes = 90 sec b takes time 3 minutes = 180 sec diffrence = 180 - 90 = 90 sec now we are to find distance covered in 90 sec by b 180 sec = 4500 m 1 sec = 25 m 90 sec = 25 x 90 = 2250 m answer : a
Answer: a
Problem: a , b and c rents a pasture for rs . 957 . a put in 12 horses for 8 months , b 16 horses for 9 months and 18 horses for 6 months . how much should c pay ?
Options: a ) 270 , b ) 289 , c ) 297 , d ) 255 , e ) 552
Rationale: "12 * 8 : 16 * 9 = 18 * 6 8 : 12 : 9 9 / 29 * 957 = 297 answer : c"
Answer: c
Problem: a student got 74 % in math and 84 % in history . to get an overall average of 75 % , how much should the student get in the third subject ?
Options: a ) 61 % , b ) 63 % , c ) 65 % , d ) 67 % , e ) 69 %
Rationale: 74 + 84 + x = 3 * 75 x = 67 the answer is d .
Answer: d
Problem: the sector of a circle has radius of 7 cm and central angle 135 o . find its perimeter ?
Options: a ) 91.5 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 30.5 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 7 ) + 2 ( 7 ) = 16.5 + 14 = 30.5 cm answer : d"
Answer: d
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 128 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 128 = x * 1 x / 2 x ² = 256 x = 16 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 16 / 2 = 8 m answer : a"
Answer: a
Problem: two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds . the ratio of their speeds is :
Options: a ) 3 : 1 , b ) 3 : 2 , c ) 2 : 7 , d ) 3 : 25 , e ) 3 : 4
Rationale: "let the speeds of the two trains be x m / sec and y m / sec respectively . then , length of the first train = 47 x meters , and length of the second train = 38 y meters . ( 47 x + 37 y ) / ( x + y ) = 40 = = > 47 x + 38 y = 40 x + 40 y = = > 7 x = 2 y = = > x / y = 2 / 7 answer : option c"
Answer: c
Problem: the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 13 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is
Options: a ) 345600 , b ) 153400 , c ) 153600 , d ) 154000 , e ) 154200
Rationale: "perimeter = distance covered in 8 min . = 18000 x 8 m = 2400 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2400 or x = 240 . length = 720 m and breadth = 480 m . area = ( 720 x 480 ) m 2 = 345600 m 2 . a"
Answer: a
Problem: a train 200 m long running at 80 kmph crosses a platform in 22 sec . what is the length of the platform ?
Options: a ) 338 , b ) 277 , c ) 350 , d ) 288 , e ) 271
Rationale: "d = 80 * 5 / 18 = 22 = 488 – 200 = 288 answer : d"
Answer: d
Problem: a fruit seller sells mangoes at the rate of rs . 9 per kg and thereby loses 20 % . at what price per kg , he should have sold them to make a profit of 5 % ?
Options: a ) rs . 11.81 , b ) rs . 12 , c ) rs . 12.25 , d ) rs . 12.31 , e ) none
Rationale: "solution 85 : 9 = 105 : x x = ( 9 × 105 / 80 ) = rs . 11.81 hence , s . p per kg = rs . 11.81 answer a"
Answer: a
Problem: if the simple interest on a certain sum of money for 8 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4.1 % , b ) 7 % , c ) 2.5 % , d ) 2.8 % , e ) 3 %
Rationale: explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 8 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 8 ) = 20 / 8 = 2.5 % answer : option c
Answer: c
Problem: two pipes a and b can fill a tank in 20 and 30 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 min , b ) 15 min , c ) 25 min , d ) 50 min , e ) 55 min
Rationale: "part filled by a in 1 min = 1 / 20 part filled by b in 1 min = 1 / 30 part filled by ( a + b ) in 1 min = ( 1 / 20 + 1 / 30 ) = 1 / 12 so both pipes can fill the tank in 12 minutes . answer : a"
Answer: a
Problem: the captain of a cricket team of 11 members is 24 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 20 years , b ) 21 years , c ) 22 years , d ) 23 years , e ) 24 years
Rationale: "explanation : let the average age of the whole team by x years . 11 x â € “ ( 24 + 27 ) = 9 ( x - 1 ) 11 x â € “ 9 x = 42 2 x = 42 x = 21 . so , average age of the team is 21 years . answer b"
Answer: b
Problem: the sum of 111 consecutive integers is 11211 . what is the greatest integer in the set ?
Options: a ) 148 , b ) 150 , c ) 152 , d ) 154 , e ) 156
Rationale: "let x be the first integer in the set , then x + 110 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 110 ) = 111 x + 110 * 111 / 2 = 111 ( x + 55 ) then x + 55 = 101 x = 46 the largest integer in the set is 46 + 110 = 156 the answer is e ."
Answer: e
Problem: according to the formula f = 9 / 5 ( c ) + 32 , if the temperature in degrees farenheit ( f ) increases by 28 , by how much does the temperature in degrees celsius ( c ) increase ?
Options: a ) 9 , b ) 15.55 , c ) 47 , d ) 48 3 / 5 , e ) 59
Rationale: you can plug in values . c = 5 / 9 * ( f - 32 ) f = 32 - - > c = 0 ; f = 32 + 28 = 60 - - > c = 5 / 9 * 28 = 15.55 . increase = 15.55 degrees . answer : b .
Answer: b
Problem: how many positive integers less than 24 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 19 , b ) 25 , c ) 24 , d ) 22 , e ) 20
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 2 odd multiples of 5 : { 5 , 15 } 9 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 2 + 9 - 1 = 19 . answer : a ."
Answer: a
Problem: without stoppages , a train travels certain distance with an average speed of 250 km / h , and with stoppages , it covers the same distance with an average speed of 125 km / h . how many minutes per hour the train stops ?
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "due to stoppages , it covers 125 km less . time taken to cover 125 km = 125 â  „ 250 h = 1 â  „ 2 h = 1 â  „ 2 ã — 60 min = 30 min answer b"
Answer: b
Problem: cara took out a charge account at the general store and agreed to pay 5 % simple annual interest . if she charges $ 54 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 55.70 , b ) $ 56.20 , c ) $ 56.70 , d ) $ 57.20 , e ) $ 57.70
Rationale: 1.05 * $ 54 = $ 56.70 the answer is c .
Answer: c
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter t of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: "as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) t = 7 * 3 = 21 . c"
Answer: c
Problem: the length of a rectangle is double its width . if the length is diminished by 5 cm and the width is increased by 5 cm then its area is increased by 75 cm square . what is the length of the rectangle ?
Options: a ) 20
b ) 30
c ) 40
d ) 56
e ) 65
Rationale: sol . according to question ( l - 5 ) ( b + 5 ) - lb = 75 and l = 2 b so , b = 20 , l = 40 ans . ( c )
Answer: c
Problem: a and b go around a circular track of length 1500 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 120 sec , b ) 165 sec , c ) 300 sec , d ) 167 sec , e ) 168 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 1500 / ( 36 * 5 / 18 ) , 1500 / ( 54 * 5 / 18 ) } = lcm ( 150 , 100 ) = 300 sec . answer : c"
Answer: c
Problem: a train 300 m long takes 9 sec to cross a man walking at 3 kmph in a direction opposite to that of the train . find the speed of the train ?
Options: a ) 100 kmph , b ) 90 kmph , c ) 120 kmph , d ) 117 kmph , e ) 125 kmph
Rationale: "let the speed of the train be x kmph speed of the train relative to man = x + 3 = ( x + 3 ) * 5 / 18 m / sec 300 / [ ( x + 3 ) * 5 / 18 ] = 9 9 ( x + 3 ) = 1080 x = 117 kmph answer is d"
Answer: d
Problem: the perimeters of 2 squares are 40 cm and 32 cm . find the perimeter of a third square whose area is equal to the difference of the areas of the two squares ?
Options: a ) 20 cm , b ) 24 cm , c ) 32 cm , d ) 28 cm , e ) 30 cm
Rationale: "side of the 1 st square = 40 / 4 = 10 cm side of the 2 nd square = 32 / 4 = 8 cm area of the 3 rd square = 10 ^ 2 - 8 ^ 2 = 36 cm ^ 2 side of the 3 rd square = 6 cm required perimeter = 6 * 4 = 24 cm answer is b"
Answer: b
Problem: if there are 210 workers in a factory , and on a certain day , 198 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 94.3 % , b ) 95.3 % , c ) 93.3 % , d ) 92.3 % , e ) 91.3 %
Rationale: 198 / 210 * 100 = 94.28 94.3 % correct answer a
Answer: a
Problem: a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 210 kilometers ?
Options: a ) 8.25 gallons , b ) 7.5 gallons , c ) 6.55 gallons , d ) 5.25 gallons , e ) 4.5 gallons
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 210 kilometers ? 210 / 40 = 5.25 * 1 gallon = 5.25 gallons correct answer d"
Answer: d
Problem: on a certain farm the ratio of horses to cows is 4 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 7 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 40 , c ) 50 , d ) 60 , e ) 80
Rationale: "originally , there were 4 k horses and k cows . 3 ( 4 k - 15 ) = 7 ( k + 15 ) 12 k - 7 k = 105 + 45 5 k = 150 k = 30 the difference between horses and cows is ( 4 k - 15 ) - ( k + 15 ) = 3 k - 30 = 60 the answer is d ."
Answer: d
Problem: two pipes p and q can fill a cistern in 11 and 15 minutes respectively . both are opened together , but at the end of 3 minutes the first is turned off . how much longer will the cistern take to fill ?
Options: a ) 1 / 8 , b ) 1 / 4 , c ) 2 / 4 , d ) 10 / 11 , e ) 1 / 4
Rationale: "3 / 11 + x / 15 = 1 x = 10 10 / 11 answer : d"
Answer: d
Problem: rani bought more apples than oranges . she sells apples at ₹ 23 apiece and makes 15 % profit . she sells oranges at ₹ 10 apiece and makes 25 % profit . if she gets ₹ 653 after selling all the apples and oranges , find her profit percentage q .
Options: a ) 16.8 % , b ) 17.4 % , c ) 17.9 % , d ) 18.5 % , e ) 19.1 %
Rationale: given : selling price of an apple = 23 - - > cost price = 23 / 1.15 = 20 selling price of an orange = 10 - - > cost price = 10 / 1.25 = 8 a > o 23 * ( a ) + 10 * ( o ) = 653 653 - 23 * ( a ) has to be divisible by 10 - - > units digit has to be 0 values of a can be 1 , 11 , 21 , 31 , . . . . - - > 1 can not be the value between 11 and 21 , if a = 11 , o = 30 - - > not possible if a = 21 , o = 17 - - > possible cost price = 20 * 21 + 8 * 17 = 420 + 136 = 556 profit = 653 - 556 = 97 profit % q = ( 97 / 556 ) * 100 = 17.4 % answer : b
Answer: b
Problem: at a summer camp with 1,800 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 1,800 campers will the 8 - to 12 - year - olds represent ?
Options: a ) 68 % , b ) 66 % , c ) 66 2 / 3 % , d ) 60 % , e ) 70 %
Rationale: total - 1,800 participants campers are aged 8 to 12 = ( 1 / 2 ) * 1800 = 900 next year , campers are aged 8 to 12 = ( 4 / 3 ) * 900 = 1200 percentage = ( 1200 / 1800 ) * 100 = 66 2 / 3 % answer : option c
Answer: c
Problem: village p ’ s population is 800 greater than village q ' s population . if village q ’ s population were reduced by 500 people , then village p ’ s population would be 3 times as large as village q ' s population . what is village q ' s current population ?
Options: a ) 1100 , b ) 1150 , c ) 1200 , d ) 1250 , e ) 1300
Rationale: "p = q + 800 . p = 3 ( q - 500 ) . 3 ( q - 500 ) = q + 800 . 2 q = 2300 . q = 1150 . the answer is b ."
Answer: b
Problem: the sale price of a trolley bag including the sale tax is rs . 420 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :
Options: a ) rs 625 , b ) rs 300 , c ) rs 350 , d ) rs 375 , e ) none of these
Rationale: explanation : 112 % of s . p . = 420 s . p . = rs . ( 420 x 100 / 112 ) = rs . 375 . c . p . = rs ( 100 / 125 x 375 ) = rs 300 answer : b
Answer: b
Problem: how many bricks each measuring 20 cm x 13.25 cm x 8 cm , will be needed to build a wall 7 m x 8 m x 15.5 m
Options: a ) 5600 , b ) 4600 , c ) 4094 , d ) 7200 , e ) none of these
Rationale: "explanation : no . of bricks = volume of the wall / volume of 1 brick = ( 700 x 800 x 15.5 ) / ( 20 x 13.25 x 8 ) = 4094 answer : c"
Answer: c
Problem: one - tenth of the students at a nursery school are 4 years old or older . if 20 students have not yet reached their third birthday , and a total of 50 students are not between 3 years old and 4 years old , how many children are in the nursery school ?
Options: a ) 150 , b ) 300 , c ) 450 , d ) 490 , e ) 620
Rationale: x / 10 students are > 4 yrs 20 students are < 3 yrs x / 10 + 20 = 50 x / 10 = 30 x = 300 answer : b
Answer: b
Problem: if p / q = 3 / 4 then 3 p + 4 q = ?
Options: a ) 25 / 4 , b ) 25 / 2 , c ) 20 / 4 , d ) 35 / 4 , e ) 25 / 3
Rationale: 3 p + 4 q = ? divided by q , 3 ( p / q ) + 4 = x 3 * ( 3 / 4 ) + 4 = 25 / 4 answer : a
Answer: a
Problem: x and y started a business by investing rs . 36000 and rs . 42000 respectively after 4 months z joined in the business with an investment of rs . 48000 , then find share of z in the profit of rs . 13970 ?
Options: a ) 3200 , b ) 4064 , c ) 3250 , d ) 3825 , e ) 3985
Rationale: "ratio of investment , as investments is for different time . investment x number of units of time . ratio of investments x : y : z = 36000 : 42000 : 48000 = > 6 : 7 : 8 . x = 6 x 12 months = 72 , y = 7 x 12 = 84 , z = 8 x 8 = 64 = > 18 : 21 : 16 . ratio of investments = > x : y : z = 18 : 21 : 16 . investment ratio = profit sharing ratio . z = 13970 ã — 16 / 55 = rs . 4064 . share of z in the profit is rs . 4064 . option b"
Answer: b
Problem: the banker â € ™ s discount of a certain sum of money is rs . 42 and the true discount on the same sum for the same time is rs . 36 . the sum due is
Options: a ) 252 , b ) 280 , c ) 360 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 42 * 36 / 42 - 36 ] = rs . [ 42 * 36 / 6 ] = rs . 252 answer a"
Answer: a
Problem: the cost of 20 pens and 12 pencils is rs . 400 and the cost of 6 pens and 4 pencils is rs . 100 . find the cost of each pen ?
Options: a ) rs . 50 , b ) rs . 100 , c ) rs . 150 , d ) rs . 25 , e ) rs . 125
Rationale: "20 p + 12 q = 400 - - - ( 1 ) 6 p + 4 q = 100 8 p + 8 q = 192 - - - ( 2 ) ( 1 ) - ( 2 ) = > 8 p = 160 = > p = 50 answer : a"
Answer: a
Problem: two trains of equal lengths take 10 sec and 15 sec , respectively , to cross a telegraph post . if the length of each train is 120 m , in what time will they cross each other , travelling in opposite directions ?
Options: a ) 17 sec , b ) 12 sec , c ) 18 sec , d ) 19 sec , e ) 52 sec
Rationale: speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 120 + 120 ) / 20 = 12 sec . answer : b
Answer: b
Problem: if there is an equal probability of a child being born a boy or a girl , what is the probability that a couple who have 5 children have two children of the same sex and one of the opposite sex ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 4 , d ) 5 / 16 , e ) 3 / 5
Rationale: "no of ways of selecting a gender - 2 c 1 no of ways of selecting any 2 children out of 5 = 5 c 2 total possible outcomes - 2 ^ 5 ( each child can be either a girl or a boy ) probability = 2 c 1 * 5 c 2 / 2 ^ 5 = 2 * 5 / 2 * 2 * 2 * 2 * 2 = 10 / 32 = 5 / 16 ans = d"
Answer: d
Problem: 2 men and 3 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: "first arrange 3 women . 3 women can be arranged in 3 places in 3 ! ways . now w blank w blankw we have to fill the two blanks with 2 men . we can arrange 2 persons in 2 places in 2 ! ways . 3 ! * 2 ! = 12 ways . a is the answer"
Answer: a
Problem: a constructor estimates that 3 people can paint mr khans house in 4 days . if he uses 4 people instead of 3 , how long will they take to complete the job ?
Options: a ) 2 , b ) 8 , c ) 1 , d ) 3 , e ) 4
Rationale: explanation : use formula for a work members × days = constant 3 × 4 = 4 × a a = 3 so answer is 3 days answer : d
Answer: d
Problem: ( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + 0.082 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.72
Rationale: "given expression = ( 0.82 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.82 ) ( power 2 ) + ( 0.82 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.82 - 0.1 ) = 0.72 answer is e"
Answer: e
Problem: for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 16.2 . , e ) 16.4
Rationale: [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.6 = 6 * 0 + 2 * 7.2 + 8 - 6.6 = 0 + 14.4 + 1.4 15.8 answer c
Answer: c
Problem: a train traveling at 144 kmph crosses a platform in 30 seconds and a man standing on the platform in 12 seconds . what is the length of the platform in meters ?
Options: a ) 240 meters , b ) 360 meters , c ) 480 meters , d ) 600 meters , e ) can not be determined
Rationale: "answer distance covered by the train when crossing a man and when crossing a platform when a train crosses a man standing on a platform , the distance covered by the train is equal to the length of the train . however , when the same train crosses a platform , the distance covered by the train is equal to the length of the train plus the length of the platform . the extra time that the train takes when crossing the platform is on account of the extra distance that it has to cover . i . e . , length of the platform . compute length of platform length of the platform = speed of train * extra time taken to cross the platform . length of platform = 144 kmph * 12 seconds convert 144 kmph into m / sec 1 kmph = 5 / 18 m / s ( this can be easily derived . but if you can remember this conversion , it saves a good 30 seconds ) . ∴ 144 kmph = 5 / 18 ∗ 144 = 40 m / sec therefore , length of the platform = 40 m / s * 12 sec = 480 meters . choice c"
Answer: c
Problem: the cost of registration at a professional association meeting was $ 50 per person ; a lunch for registrants only was available for an additional $ 22 per person . if the number of registrants who paid for lunch was 40 more than the number who did not , and if receipts for registration and lunch totaled $ 39,480 , how many people paid just for registration at the meeting ?
Options: a ) 700 , b ) 800 , c ) 300 , d ) 1,500 , e ) 1,800
Rationale: "hope this might be useful to you . let the number of people who have opted only to register = x now since the registration cost is 50 $ per person , the total amount sums to = 50 x $ as per the information given in the question , the number of registrants who paid for lunch was 40 more than the number who did not . that means , total number of people who registered and paid for lunch = 40 + x . for the people who registered for lunch the cost is 50 $ ( for the event registration ) + 22 $ ( for lunch ) = 72 $ . total amount in this case sums to = 72 ( 40 + x ) = 2880 + 72 x now , total amount received was 39480 thus , from the above data , 50 x + 2880 + 72 x = 39480 122 x = 39480 - 2880 122 x = 36600 x = 300 . hence the correct ans is 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 25.6 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 ) 15.1 , b ) 15.4 , c ) 15.7 , d ) 16.0 , e ) 16.3
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 = 25.6 x ^ 2 = 2.56 x = 1.6 at 4 : 00 pm , the amount of bacteria was 10 ( 1.6 ) = 16 grams . the answer is d .
Answer: d
Problem: a bag contains 6 red , 4 blue and 2 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 1 / 13 , b ) 2 / 23 , c ) 5 / 26 , d ) 5 / 22 , e ) 3 / 23
Rationale: "p ( both are red ) , = 6 c 212 c 2 = 6 c 212 c 2 = 15 / 66 = 5 / 22 d"
Answer: d
Problem: the true discount on a bill of rs . 2560 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 432 , b ) rs . 422 , c ) rs . 419 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2560 td = rs . 360 pw = f - td = 2560 - 360 = rs . 2200 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 2200 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2160 for unexpired time = 360 / 2200 × 2560 = 0.16 × 2560 = rs . 419 answer : option c"
Answer: c
Problem: a man took loan from a bank at the rate of 4 % p . a . s . i . after 10 years he had to pay rs . 2000 interest only for the period . the principal amount borrowed by him was ?
Options: a ) 5000 , b ) 4500 , c ) 3200 , d ) 6000 , e ) 1592
Rationale: "principal = ( 100 * 2000 ) / ( 4 * 10 ) = rs . 5000 answer : a"
Answer: a
Problem: the mean of 50 observations was 36 . it was found later that an observation 46 was wrongly taken as 23 . the corrected new mean is
Options: a ) 35.24 , b ) 36.16 , c ) 36.24 , d ) 36.46 , e ) none
Rationale: "solution correct sum = ( 36 x 50 + 46 - 23 ) = 1823 . â ˆ ´ correct mean = 1823 / 50 = 36.46 . answer d"
Answer: d
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 300 oranges . how many oranges he had originally ?
Options: a ) 420 , b ) 700 , c ) 220 , d ) 500 , e ) none of these
Rationale: "explanation : he sells 40 % of oranges and still there are 300 oranges remaining = > 60 % of oranges = 300 ⇒ ( 60 × total oranges ) / 100 = 300 ⇒ total oranges / 100 = 5 ⇒ total oranges = 5 × 100 = 500 answer : option d"
Answer: d
Problem: average weight of 15 boys in a class is 48 kgs . the average weight of the class of 25 students is 45 kgs . what is the average weight of the 15 girls in the class ?
Options: a ) 45 , b ) 47.3 , c ) 39.8 , d ) 45.5 , e ) 40.5
Rationale: total weight of boys in class 15 x 48 = 720 kg total weight of all student in the class room 25 x 45 = 1125 kg total no of girls in the class 1125 - 720 = 405 kg average weight of girls 405 / 10 = 40.5 kg correct ans is e
Answer: e
Problem: the sum of two numbers is 84 , and one of them is 12 more than the other . what are the two numbers ?
Options: a ) 48 , 36 , b ) 36 , 48 , c ) 32 , 48 , d ) 48 , 32 , e ) 32 , 42
Rationale: 2 x = 84 − 12 = 72 . x = 72 / 2 = 36 . this is the first number . therefore the other number is x + 12 = 36 + 12 = 48 . the sum of 36 + 48 is 84 . answer is b .
Answer: b
Problem: 12.5 * 3.2 * 6.8 = ?
Options: a ) 352 , b ) 272 , c ) 224 , d ) 646 , e ) 742
Rationale: "b 272 ? = 12.5 * 3.2 * 6.8 = 352"
Answer: b
Problem: a man started driving at a constant speed , from the site of a blast , the moment he heard the blast . he heard a second blast after a time of 30 mins and 25 seconds . if the second blast occurred exactly 30 mins after the first , how many meters was he from the site when he heard the second blast ? ( speed of sound = 330 m / s )
Options: a ) 8250 , b ) 9350 , c ) 10,450 , d ) 11,550 , e ) 12,650
Rationale: "the distance the sound traveled to the man is 25 * 330 = 8250 meters the answer is a ."
Answer: a
Problem: john had a stock of 1400 books in his bookshop . he sold 62 on monday , 62 on tuesday , 60 on wednesday , 48 on thursday and 40 on friday . what percentage of the books were not sold ?
Options: a ) 81.57 % , b ) 36.5 % , c ) 80.67 % , d ) 56.5 % , e ) 80.57 %
Rationale: "let n be the total number of books sold . hence n = 62 + 62 + 60 + 48 + 40 = 272 let m be the books not sold m = 1400 - n = 1400 - 272 = 1128 percentage books not sold / total number of books = 1128 / 1200 = 0.81 = 80.57 % correct answer e"
Answer: e
Problem: if you multiply all the numbers on your mobile phone except 0 and 9 , what is the answer ?
Options: a ) 25869 , b ) 48586 , c ) 40320 , d ) 58964 , e ) 45698
Rationale: "we have to multiply 1 to 8 to find the answer . therefore 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 40320 answer is c"
Answer: c
Problem: a train 250 m long is running at a speed of 68 kmph . how long does it take to pass a man who is running at 8 kmph in the same direction as the train ?
Options: a ) 15 sec , b ) 9 sec , c ) 12 sec , d ) 15 sec , e ) 18 sec
Rationale: "speed of the train relative to man = ( 68 - 8 ) kmph = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec time taken by the train to cross the man = time taken by it to cover 250 m at 50 / 3 m / sec = 250 * 3 / 50 sec = 15 sec answer : a ."
Answer: a