regisss/math_qa huggingface dataset:
Problem: a store ’ s selling price of $ 2240 for a certain computer would yield a profit of 40 percent of the store ’ s cost for the computer . what selling price would yield a profit of 50 percent of the computer ’ s cost ?
Options: a ) $ 2400 , b ) $ 2464 , c ) $ 2650 , d ) $ 2732 , e ) $ 2800
Rationale: "2240 = x * 1.4 = x * ( 7 / 5 ) . therefore , x = 2240 * 5 / 7 . 2240 is easily divided by 7 to be 320 , which is then easily multiplied by 5 to give x = 1600 . to get 50 % profit , you need 1600 * 1.5 = 2400 . answer : a"
Answer: a
Problem: two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 80 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 8 : 5
b ) 9 : 25
c ) 5 : 8
d ) 25 : 9
e ) can not be determined from the information provided
Rationale: same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 40 / speed b since the times are same , 50 pi / speed a = 80 pi / speed b speeda / speed b = 50 pi / 80 pi = 5 / 8 correct option : c
Answer: c
Problem: what is the area inscribed by the lines y = 3 , x = 2 , y = x + 3 on an xy - coordinate plane ?
Options: a ) a ) 1 , b ) b ) 2 , c ) c ) 4 , d ) d ) 6 , e ) e ) 10
Rationale: "first , let ' s graph the lines y = 3 and x = 2 at this point , we need to find the points where the line y = x + 3 intersects the other two lines . for the vertical line , we know that x = 2 , so we ' ll plug x = 2 into the equation y = x + 3 to get y = 2 + 3 = 5 perfect , when x = 2 , y = 5 , so one point of intersection is ( 2,5 ) for the horizontal line , we know that y = 3 , so we ' ll plug y = 3 into the equation y = x + 3 to get 3 = x + 3 . solve to get : x = 0 so , when y = 3 , x = 0 , so one point of intersection is ( 0,3 ) now add these points to our graph and sketch the line y = x + 3 at this point , we can see that we have the following triangle . the base has length 2 and the height is 2 area = ( 1 / 2 ) ( base ) ( height ) = ( 1 / 2 ) ( 2 ) ( 2 ) = 2 answer : b"
Answer: b
Problem: tough and tricky questions : distance / rate . on a reconnaissance mission , a state - of - the - art nuclear powered submarine traveled 300 miles to reposition itself in the proximity of an aircraft carrier . this journey would have taken 1 hour less if the submarine had traveled 10 miles per hour faster . what was the average speed , in miles per hour , for the actual journey ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 50
Rationale: say , if speed is 60 , 300 / 50 = 6 hrs and 300 / 60 = 5 hrs ( a reduction of 1 hr - > correct answer ) answer ( e )
Answer: e
Problem: a , b and c enter into partnership . a invests some money at the beginning , b invests double the amount after 6 months , and c invests thrice the amount after 8 months . if the annual gain be rs . 12000 . a ' s share is ?
Options: a ) 2500 , b ) 3500 , c ) 4500 , d ) 2800 , e ) 4000
Rationale: "x * 12 : 2 x * 6 : 3 x * 4 1 : 1 : 1 1 / 3 * 12000 = 4000 answer : e"
Answer: e
Problem: one computer can upload 100 megabytes worth of data in 3 seconds . two computers , including this one , working together , can upload 1300 megabytes worth of data in 30 seconds . how long would it take for the second computer , working on its own , to upload 100 megabytes of data ?
Options: a ) 6 , b ) 10 , c ) 9 , d ) 11 , e ) 13
Rationale: since the first computer can upload 100 megabytes worth of data in 3 seconds then in 3 * 10 = 30 seconds it can upload 10 * 100 = 1000 megabytes worth of data , hence the second computer in 30 seconds uploads 1300 - 1000 = 300 megabytes worth of data . the second computer can upload 100 megabytes of data in 10 seconds . answer : b .
Answer: b
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 40 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 40 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 140 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 140 - 90 ) / 90 * 100 = 40 % answer : d ."
Answer: d
Problem: two trains 130 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 , b ) 10.7 , c ) 10.3 , d ) 10.44 , e ) 10.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 130 + 160 = 290 m . required time = 290 * 9 / 250 = 261 / 25 = 10.44 sec . ' answer : d"
Answer: d
Problem: in a company with 48 employees , some part - time and some full - time , exactly ( 1 / 3 ) of the part - time employees and ( 1 / 4 ) of the full - time employees take the subway to work . what is the greatest possible number w of employees who take the subway to work ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: p / 3 + f / 4 = p / 3 + ( 48 - p ) / 4 = 12 + p / 2 p / 3 + f / 3 = ( p + f ) / 3 = 48 / 3 = 16 p / 4 + f / 4 = 12 p / 3 + f / 3 > p / 3 + f / 4 > p / 4 + f / 4 - - > 16 > 12 + p / 12 > 12 greatest possible w : 12 + p / 12 = 15 - - > p = 36 ( integer - - > good ) 15 or d is the answer
Answer: d
Problem: how many pieces of 75 cm can be cut from a rope 57 meters long ?
Options: a ) 30 , b ) 40 , c ) 76 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 57 meters long is = ( 57 meters ) / ( 75 cm ) = ( 57 meters ) / ( 0.75 meters ) = 76 answer : c"
Answer: c
Problem: if r is a positive integer and r ^ 2 is divisible by 12 , then the largest positive integer that must divide r ^ 3 is
Options: a ) 2 ^ 3 , b ) 2 ^ 6 , c ) 3 ^ 3 , d ) 6 ^ 3 , e ) 12 ^ 2
Rationale: since r is an integer so r can not have a 2 and sqrt 3 ( because squaring this will give us a 2 ^ 2 and 3 ( making the product as 12 , and making r ^ 2 as a multiple of 12 ) ) r ^ 2 is divisible by 12 ( 12 = 2 * 2 * 3 ) , so , r should have at least one 2 and one 3 so that r ^ 2 has a 2 ^ 2 and two 3 so , r will have a 2 and a 3 . or r will be a multiple of 6 so , largest possible integer than should divide r ^ 3 is 6 ^ 3 so , answer will be d
Answer: d
Problem: if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 10 percent , how much would she earn per week ?
Options: a ) $ 374 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "soln : - ( 406 / 116 ) 110 = 385 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 11 = 385 ( 350 + 35 ) answer : c"
Answer: c
Problem: what is the average of first 21 multiples of 6 ?
Options: a ) a ) 66 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 82
Rationale: "required average = 6 ( 1 + 2 + . . . . + 21 ) / 21 ( 6 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 66 a"
Answer: a
Problem: a contractor undertook to do a piece of work in 8 days . he employed certain number of laboures but 3 of them were absent from the very first day and the rest could finish the work in only 14 days . find the number of men originally employed ?
Options: a ) 6 , b ) 7.5 , c ) 5 , d ) 6 , e ) 7
Rationale: "let the number of men originally employed be x . 8 x = 14 ( x â € “ 3 ) or x = 7 answer e"
Answer: e
Problem: what is the sum of two consecutive even numbers , the difference of whose squares is 84 ?
Options: a ) 42 , b ) 84 , c ) 48 , d ) 24 , e ) 43
Rationale: let the numbers be x and x + 2 . then , ( x + 2 ) 2 - x 2 = 84 4 x + 4 = 84 4 x = 80 x = 20 . the required sum = x + ( x + 2 ) = 2 x + 2 = 42 . answer a 42
Answer: a
Problem: a man rows his boat 90 km downstream and 40 km upstream , taking 2 1 / 2 hours each time . find the speed of the stream ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 15
Rationale: "speed downstream = d / t = 90 / ( 2 1 / 2 ) = 36 kmph speed upstream = d / t = 40 / ( 2 1 / 2 ) = 16 kmph the speed of the stream = ( 36 - 16 ) / 2 = 15 kmph answer : e"
Answer: e
Problem: in the youth summer village there are 300 people , 200 of them are not working , 100 of them have families and 125 of them like to sing in the shower . what is the largest possible number of people in the village , which are working , that do n ' t have families and that are singing in the shower ?
Options: a ) 150 , b ) 125 , c ) 175 , d ) 200 , e ) 100
Rationale: "total = 300 not working = 200 having family = 100 like to sing in shower = 125 working = 300 - 200 = 100 not having family = 300 - 100 = 200 like to sing in shower = 125 largest possible number is the lowest possible among the above thus 100 e"
Answer: e
Problem: a 15 by 20 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 5 π , b ) 10 π , c ) 15 π , d ) 20 π , e ) 25 π
Rationale: "the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : e"
Answer: e
Problem: if x > 0 , x / 5 + x / 25 is what percent of x ?
Options: a ) 6 % , b ) 24 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 5 + 100 / 25 = 20 + 4 = 24 24 is 24 % of 100 = b"
Answer: b
Problem: each month , after jill pays for rent , utilities , food , and other necessary expenses , she has one fifth of her net monthly salary left as discretionary income . of this discretionary income , she puts 30 % into a vacation fund , 20 % into savings , and spends 35 % on eating out and socializing . this leaves her with $ 102 dollar , which she typically uses for gifts and charitable causes . what is jill ’ s net monthly salary ?
Options: a ) $ 3400 , b ) $ 3200 , c ) $ 6000 , d ) $ 6400 , e ) $ 9600
Rationale: "let x be the monthly salary 15 % of 1 / 5 * x = 102 x = 3400 answer a"
Answer: a
Problem: if f ( f ( n ) ) + f ( n ) = 2 n + 3 , f ( 0 ) = 1 then f ( 2017 ) = ?
Options: a ) 2018 , b ) 2088 , c ) 270 , d ) 1881 , e ) 1781
Rationale: "f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) = 3 - 1 = 2 , f ( 1 ) = 2 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) = 5 - 2 = 3 , f ( 2 ) = 3 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) = 7 - 3 = 4 , f ( 3 ) = 4 . . . . . . . . . . . . . . f ( 2017 ) = 2018 ans : a"
Answer: a
Problem: the h . c . f . of two numbers is 32 and the other two factors of their l . c . m . are 13 and 14 . the larger of the two numbers is :
Options: a ) 448 , b ) 299 , c ) 421 , d ) 460 , e ) 365
Rationale: "clearly , the numbers are ( 32 x 13 ) and ( 32 x 14 ) . larger number = ( 32 x 14 ) = 448 . answer : option a"
Answer: a
Problem: a solution is 90 % glycerin . if there are 4 gallons of the solution , how much water , in gallons must be addded to make a 75 % glycerin solution
Options: a ) 1.8 , b ) 1.4 , c ) 1.2 , d ) 1.0 , e ) 0.8
Rationale: in 4 gallons of the solution there are 0.9 ∗ 4 = 3.80 gallons of glycerin . we want to add ww gallons of water to 4 gallons of solution so that these 3.6 gallons of glycerin to be 75 % of new solution : 0.9 ∗ 4 = 0.75 ( 4 + w ) - - > w = 0.8 answer : e .
Answer: e
Problem: of the 120 passengers on flight 750 , 30 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 28 , c ) 50 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 3 * 120 = 36 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 36 - 8 = 28 answer b"
Answer: b
Problem: 1240 men have provisions for 12 days . if 300 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 9.7 , d ) 8.6 , e ) 12.1
Rationale: "1240 * 12 = 1540 * x x = 9.7 answer : c"
Answer: c
Problem: on a certain transatlantic crossing , 15 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 60 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?
Options: a ) 37.5 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %
Rationale: 0.15 p = rt + c 0.6 ( rt ) = no c = > 0.40 ( rt ) had c 0.15 p = 0.40 ( rt ) rt / p = 37.5 % answer - a
Answer: a
Problem: in how many seconds will a train 150 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 150 / 10 = 15 seconds the answer is c ."
Answer: c
Problem: two numbers n and 16 have lcm = 48 and gcf = 4 . find n .
Options: a ) 35 , b ) 56 , c ) 76 , d ) 87 , e ) 12
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 16 * n = 48 * 4 n = 48 * 4 / 16 = 12 correct answer e"
Answer: e
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 65000 ?
Options: a ) 81000 , b ) 81007 , c ) 81008 , d ) 81066 , e ) 82265.6
Rationale: "65000 * 9 / 8 * 9 / 8 = 82265.6 answer : e"
Answer: e
Problem: a track covers a distance of 550 metres in 1 minute whereas a bus covers a distance of 33 kms in 45 minute . the ratio of their speeds is :
Options: a ) 4 : 3 , b ) 3 : 5 , c ) 3 : 4 , d ) 50 : 3 , e ) none
Rationale: solution : speed of track = 550 per minute . speed of bus = 33 kms / 45 = 33000 / 45 = 733.33 m / minute ratio of their speeds = 550 / 733.33 = 3 : 4 . answer : option c
Answer: c
Problem: the length of rectangle is thrice its breadth and its perimeter is 64 m , find the area of the rectangle ?
Options: a ) 432 sq m , b ) 192 sq m , c ) 452 sq m , d ) 428 sq m , e ) 528 sq m
Rationale: "2 ( 3 x + x ) = 64 l = 24 b = 8 lb = 24 * 8 = 192 answer : b"
Answer: b
Problem: the instructions state that cheryl needs 3 / 8 square yards of one type of material and 1 / 3 square yards of another type of material for a project . she buys exactly that amount . after finishing the project , however , she has 15 / 40 square yards left that she did not use . what is the total amount of square yards of material cheryl used ?
Options: a ) 1 / 12 , b ) 1 / 9 , c ) 2 / 3 , d ) 1 / 3 , e ) 2 1 / 9
Rationale: "total bought = 3 / 8 + 1 / 3 left part 15 / 40 - - - > 3 / 8 so used part 3 / 8 + 1 / 3 - 3 / 8 = 1 / 3 ans d"
Answer: d
Problem: what number has a 1 : 20 ratio to the number 10 ?
Options: a ) 10 , b ) 1 / 2 , c ) 2 , d ) 1 / 4 , e ) 20
Rationale: "1 : 20 = x : 10 20 x = 10 ; x = 10 / 20 x = 1 / 2 answer : b"
Answer: b
Problem: running at the same rate , 8 identical machines can produce 560 paperclips a minute . at this rate , how many paperclips could 10 machines produce in 6 minutes ?
Options: a ) 1344 , b ) 4200 , c ) 8400 , d ) 50400 , e ) 67200
Rationale: 8 machines produce 560 in 1 min 8 machines produce 560 * 6 in 6 min 10 machine produce 560 * 6 * ( 10 / 8 ) in 6 minutes 560 * 6 * 10 / 8 = 4200 answer is b .
Answer: b
Problem: speed of a boat in standing water is 16 kmph and the speed of the stream is 2 kmph . a man rows to a place at a distance of 7020 km and comes back to the starting point . the total time taken by him is :
Options: a ) 914.2 hours , b ) 900 hours , c ) 915 hours , d ) 891.4 hours , e ) 915 hours
Rationale: "explanation : speed downstream = ( 16 + 2 ) = 18 kmph speed upstream = ( 16 - 2 ) = 14 kmph total time taken = 7020 / 18 + 7020 / 14 = 390 + 501.4 = 891.4 hours answer : option d"
Answer: d
Problem: the angle between the minute hand and the hour hand of a clock when the time is 4.20 ° is
Options: a ) 0 ° , b ) 5 ° , c ) 10 ° , d ) 20 ° , e ) none
Rationale: "sol . angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min . = ( 360 / 60 x 20 ) ° = 120 ° ∴ required angle = ( 130 - 120 ) ° = 10 ° answer c"
Answer: c
Problem: a man invests some money partly in 9 % stock at 96 and partly in 12 % stock at 120 . to obtain equal dividends from both , he must invest the money in the ratio :
Options: a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 5 , d ) 16 : 15 , e ) none
Rationale: "solution for an income of rs . 1 in 9 % stock at 96 , investment = rs . ( 96 / 9 ) = rs . 32 / 3 . for an income of rs . 1 in 12 % stock at 120 , investment = rs . ( 120 / 12 ) = rs . 10 . ∴ ratio of investments = 32 / 3 : 10 = 32 : 30 = 16 : 15 answer d"
Answer: d
Problem: at 6 ' o clock clock ticks 6 times . the time between first and last ticks was 30 sec . how much time it takes at 8 ' o clock .
Options: a ) 54 sec , b ) 48 sec , c ) 42 sec , d ) 70 sec , e ) 60 sec
Rationale: at 6 ' 0 clock , clock ticks 6 times . so , there must be 5 intervals between clock ticks . time between first and last ticks = 30 sec so , 1 interval = 30 / 5 = 6 sec so 6 ' o clock 5 * 6 = 30 sec 7 ' o clock 6 * 6 = 36 sec 8 ' o clock 7 * 6 = 42 sec so , 42 sec at 8 ' o clock . answer : c
Answer: c
Problem: 9 fencers participate in a fencing championship . assuming all competitors have an equal chance of winning , how many possibilities are there with respect to how a first - place and second - place medal can be awarded ?
Options: a ) 72 , b ) 75 , c ) 81 , d ) 84 , e ) 88
Rationale: 9 * 8 = 72 the answer is a .
Answer: a
Problem: what is the units digit of 2222 ^ ( 333 ) * 3333 ^ ( 222 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "( 2222 ^ 333 ) * ( 3333 ^ 222 ) = 2222 ^ 111 * ( 2222 ^ 222 * 3333 ^ 222 ) here please pay attention to the fact that the unit digit of multiplication of 2222 and 3333 is 6 ( 2222 ^ 222 * 3333 ^ 222 ) . since 6 powered in any number more than 0 results in 6 as a units digit , as a result we have - 6 * 2222 ^ 111 2 has a cycle of 4 . 111 = 27 * 4 + 3 . 2 ^ 3 = 8 6 * 8 = 48 so the units digit is 8 , and the answer is e"
Answer: e
Problem: in a factory , an average of 70 tv ' s are produced per day for the fist 25 days of the months . a few workers fell ill for the next 5 days reducing the daily avg for the month to 68 sets / day . the average production per day for day last 5 days is ?
Options: a ) 20 , b ) 36 , c ) 48 , d ) 50 , e ) 58
Rationale: "production during these 5 days = total production in a month - production in first 25 days . = 30 x 68 - 25 x 70 = 290 ∴ average for last 5 days = 290 / 5 = 58 e"
Answer: e
Problem: alex has 4 pens worth of { 22 , 25 , 30 , 40 } , what is the total mean and median of the worth of pens ?
Options: a ) 3.42 , b ) 6.16 , c ) 8.32 , d ) 2.0 , e ) 1.75
Rationale: this is a good question to understand the difference between mean and median . mean : average of all the numbers . ( sum of all the elements divided by the number of elements ) median : arrange the elements of the set in increasing order . if the number of terms is odd , the middle term is the median . if the number of terms is even , the average of middle two terms is the median coming to this question , mean = ( 22 + 25 + 30 + 40 ) / 4 = 29.25 median = ( 25 + 30 ) / 2 = 27.5 total = 1.75 option e
Answer: e
Problem: there were 35 students in a hostel . due to the admission of 7 new students , ; he expenses of the mess were increased by rs . 42 per day while the average expenditure per head diminished by rs 1 . what was the original expenditure of the mess ?
Options: a ) 320 , b ) 120 , c ) 400 , d ) 420 , e ) 514
Rationale: "sol . let the original average expenditure be rs . x . then , 42 ( x - 1 ) - 35 x = 42  7 x = 84  x = 12 . original expenditure = rs . ( 35 x 12 ) = rs . 420 . . answer d"
Answer: d
Problem: 1 , 0.5 , 0.5 , 0.75 , 1.5 , ____
Options: a ) 1.25 , b ) 5.75 , c ) 3.25 , d ) 3.75 , e ) none
Rationale: "1 , 0.5 , 0.5 , 0.75 , 1.5 , . . . . . 1 * 0.5 = 0.5 0.5 * 1 = 0.5 0.5 * 1.5 = 0.75 0.75 * 2 = 1.5 so , 1.5 * 2.5 = 3.75 answer : d"
Answer: d
Problem: what percent of 15 kg is 30 gms ?
Options: a ) 25 , b ) 66 , c ) 20 , d ) 19 , e ) 17
Rationale: "explanation : required percentage = ( 30 / 15000 * 100 ) % = 1 / 5 % = 0.2 % answer : c ) . 20 %"
Answer: c
Problem: if $ 100 invested at a certain rate of simple interest amounts to $ 140 at the end of 3 years , how much will $ 150 amount to at the same rate of interest in 6 years ?
Options: a ) $ 190 , b ) $ 180 , c ) $ 200 , d ) $ 240 , e ) $ 270
Rationale: 100 amounts to 140 in 3 years . i . e ( principal + interest ) on 120 in 3 years = 140 100 + 100 * ( r / 100 ) * ( 3 ) = 140 = > r = 40 / 3 150 in 6 years = principal + interest = 150 + 150 * ( r / 100 ) * ( 6 ) = 270 answer is e .
Answer: e
Problem: the owner of a furniture shop charges his customer 100 % more than the cost price . if a customer paid rs . 1000 for a computer table , then what was the cost price of the computer table ?
Options: a ) 800 , b ) 650 , c ) 500 , d ) 600 , e ) 250
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 1000 ( 100 / 200 ) = rs . 500 . answer : c"
Answer: c
Problem: if a father said to his elder son , ` ` i was as old as you are at the present at the time of your birth ' ' . if the father ' s age is 25 years now , what was the son ' s age 4 years back ?
Options: a ) 7.5 , b ) 8.5 , c ) 9 , d ) 9.5 , e ) 10
Rationale: let son ' s present age be a years . then , ( 25 − a ) = a ⇒ 2 a = 25 ⇒ a = 25 / 2 = 12.5 son ' s age 4 years back = 12.5 - 4 = 8.5 answer : b
Answer: b
Problem: a circle graph shows how the megatech corporation allocates its research and development budget : 13 % microphotonics ; 24 % home electronics ; 15 % food additives ; 29 % genetically modified microorganisms ; 8 % industrial lubricants ; and the remainder for basic astrophysics . if the arc of each sector of the graph is proportional to the percentage of the budget it represents , how many degrees of the circle are used to represent basic astrophysics research ?
Options: a ) 8 ° , b ) 40 ° , c ) 18 ° , d ) 36 ° , e ) 52 °
Rationale: "here all percentage when summed we need to get 100 % . as per data 13 + 24 + 15 + 29 + 8 = 89 % . so remaining 11 % is the balance for the astrophysics . since this is a circle all percentage must be equal to 360 degrees . 100 % - - - - 360 degrees then 11 % will be 40 degrees . . imo option b ."
Answer: b
Problem: 7 , 10.5 , 15.75 , 23.63 , 35.43 , ( . . . )
Options: a ) 52.112 , b ) 53.156 , c ) 54 , d ) 89 , e ) 88
Rationale: "7 ( 7 ã — 3 ) ã · 2 = 10.5 ( 10.5 ã — 3 ) ã · 2 = 15.75 ( 15.75 ã — 3 ) ã · 2 = 23.63 ( 23.63 ã — 3 ) ã · 2 = 35.43 ( 35.43 ã — 3 ) ã · 2 = 53.156 answer is b"
Answer: b
Problem: jim ’ s taxi service charges an initial fee of $ 2.25 at the beginning of a trip and an additional charge of $ 0.25 for each 2 / 5 of a mile traveled . what is the total charge for a trip of 3.6 miles ?
Options: a ) $ 3.15 , b ) $ 4.5 , c ) $ 4.80 , d ) $ 5.05 , e ) $ 5.40
Rationale: "let the fixed charge of jim ’ s taxi service = 2.25 $ and charge per 2 / 5 mile ( . 4 mile ) = . 25 $ total charge for a trip of 3.6 miles = 2.25 + ( 3.6 / . 4 ) * . 25 = 2.25 + 9 * . 25 = 4.5 $ answer b"
Answer: b
Problem: payal finished 2 / 3 of a book . she calculated that she finished 20 more pages than she has yet to read . how long is her book ?
Options: a ) a ) 60 , b ) b ) 150 , c ) c ) 130 , d ) d ) 90 , e ) e ) 210
Rationale: let x be the total number of pages in the book , then she finished 2 / 3 * x pages . then she has x − 2 / 3 * x = 1 / 3 * x pages left . 2 / 3 * x − 1 / 3 * x = 20 1 / 3 * x = 20 x = 60 so the book is 270 pages long . answer is a .
Answer: a
Problem: the surface of a cube is 384 sq cm . find its volume ?
Options: a ) 8 cc , b ) 9 cc , c ) 512 cc , d ) 4 cc , e ) 6 cc
Rationale: "6 a 2 = 384 = 6 * 64 a = 8 = > a 3 = 512 cc answer : c"
Answer: c
Problem: the tax on a commodity is diminished by 10 % and its consumption increased by 15 % . the effect on revenue is ?
Options: a ) 2 % decrease , b ) 3.5 % increase , c ) 9 % decrease , d ) 3 % decrease , e ) 2 % increase
Rationale: "100 * 100 = 10000 90 * 115 = 10350 - - - - - - - - - - - 10000 - - - - - - - - - - - 350 100 - - - - - - - - - - - ? = > 3.5 % decrease answer : b"
Answer: b
Problem: a monkey ascends a greased pole 19 metres high . he ascends 2 metres in first minute and slips down 1 metre in the alternate minute . in which minute , he reaches the top ?
Options: a ) 21 st , b ) 22 nd , c ) 23 rd , d ) 35 th , e ) none of these
Rationale: "in 2 minutes , he ascends = 1 metre â ˆ ´ 17 metres , he ascends in 34 minutes . â ˆ ´ he reaches the top in 35 th minute . answer d"
Answer: d
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 4 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .
Options: a ) 20 cm , b ) 25 cm , c ) 26 cm , d ) 100 / 3 cm , e ) 23 cm
Rationale: explanation : let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 4 ) - 2 x * x = 75 = > 3 x - 25 = 75 = > x = 100 / 3 . length of the rectangle = 100 / 3 cm . answer : option d
Answer: d
Problem: there is a 1 km long wire placed on some number of poles which are in equal distance . if the number of poles is reduced by 1 then the distance of wire between each poles increases 1 ( 2 / 3 ) . how many poles are there initially .
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
Rationale: 26 answer : c
Answer: c
Problem: by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at :
Options: a ) rs . 80 , b ) rs . 96 , c ) rs . 106 , d ) rs . 108 , e ) rs . 118
Rationale: michel earns rs 135 by investing rs 1620 to earn rs 8 how much he have to invest ? = ( 8 * 1620 ) / 135 = rs 96 answer : b
Answer: b
Problem: the initial price of an article is rs . 2000 which increases 30 % increse in its price in the first year , a 20 % decrease in the second year and a 10 % increase in the next year . what is the final price of the article ?
Options: a ) rs . 1748 , b ) rs . 1948 , c ) rs . 1848 , d ) rs . 2048 , e ) rs . 2148
Rationale: the initial price of the article , four years age is rs . 2000 in the 1 st year , price of the article = 2000 + 600 = rs . 2600 . in the 2 nd year , price = 2600 - 20 % of 2600 = 2200 - 520 = rs . 1680 . in the 3 rd year , price = 1680 + 10 % of 1680 = 1680 + 168 = rs . 1848 . required price = rs . 1848 answer : c
Answer: c
Problem: at what rate percent on simple interest will rs . 750 amount to rs . 900 in 16 years ?
Options: a ) 6.25 % , b ) 1.25 % , c ) 4 % , d ) 5 % , e ) 3.25 %
Rationale: "150 = ( 750 * 16 * r ) / 100 r = 1.25 % answer : b"
Answer: b
Problem: if there are only 2 wheelers and 4 wheelers parked in a school located at the heart of the city , find the number of 4 wheelers parked there if the total number of wheels is 58 ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "four wheeler = 14 * 4 = 56 ( max ) 2 wheel = 1 so no of 4 wheeler = 14 answer : d"
Answer: d
Problem: if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly once in 3 consecutive flips ?
Options: a ) 0.125 , b ) 0.375 , c ) 0.325 , d ) 0.5 , e ) 0.666
Rationale: total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 * 2 = 8 ways for 2 t and 1 th thus probability is = p ( htt ) + p ( tth ) + p ( tht ) = 1 / 8 + 1 / 8 + 1 / 8 = 3 / 8 = . 375 answer : b
Answer: b
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 2 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 120 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 120 x = 120 min answer : e"
Answer: e
Problem: if the ratio of two number is 5 : 7 and lcm of the number is 320 then what is the number .
Options: a ) 15 , b ) 9 , c ) 10 , d ) 11 , e ) 35
Rationale: "product of two no = lcm * hcf 5 x * 7 x = 320 * x x = 9 answer : b"
Answer: b
Problem: find the principle on a certain sum of money at 5 % per annum for 3 1 / 5 years if the amount being rs . 2030 ?
Options: a ) rs . 2000 , b ) rs . 1750 , c ) rs . 2010 , d ) rs . 2005 , e ) none of these
Rationale: "explanation : 2030 = p [ 1 + ( 5 * 16 / 5 ) / 100 ] p = 1750 answer : option b"
Answer: b
Problem: machine a can process 6000 envelopes in 3 hours . machines b and c working together but independently can process the same number of envelopes in 2.5 hours . if machines a and c working together but independently process 3000 envelopes in 1 hour , then how many hours would it take machine b to process 7000 envelopes .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 60 / 7
Rationale: "you can either take the amount of work done as the same as karishma has done or take the work done by each in the same time . i will do the latter 1 . work done in 1 hr by a is 2000 envelopes 2 . work done in 1 hr by a and c is 3000 envelopes 3 . so work done in 1 hr by c is 1000 envelopes 4 . work done in 1 hr by b and c is 2400 envelopes 5 . so work done in 1 hr by b is 1400 envelopes 6 . so to process 7000 envelopes b will take 7000 / 1400 hrs = 5 hrs so the answer is choice d"
Answer: d
Problem: abcd is a square aegf is a rectangle . . such that the rectangle shares 25 % of the area of the suare also ae lies on the line ab and ag lies on segment of ad . if the square shares half the area of the rectangle what is the ratio ae : ag ?
Options: a ) 1 : 4
b ) 8 : 1
c ) 4 : 1
d ) 3 : 1
e ) 1 : 3
Rationale: a - - - - - - - - - - - - b - - - - - - - - e | | 50 % | g - - - - - - - - - - - - | - - - - - - - - f | | | 75 % | d - - - - - - - - - - - c remaining square 75 % and remaining rectangle 50 % rectangle share 25 % area of square so , ab x ag = ( ad x ab ) / 4 ad = 4 ag - - - - - - - - - - - - - - - - - - ( 1 ) square share half the area of rectangle so , ag x ab = ( ae x ag ) / 2 ab = ae / 2 - - - - - - - - - - - - - - - - - - ( 2 ) in square all sides are equal i . e . ab = bc = cd = ad so , equation ( 1 ) and ( 2 ) both are equal ae / 2 = 4 ag ae / ag = 8 ae : ag = 8 : 1 answer : b
Answer: b
Problem: 2 cow ’ s and 10 goats are brought for rs . 1500 . if the average price of a goat be rs . 70 . what is the average price of a cow .
Options: a ) 420 , b ) 400 , c ) 430 , d ) 410 , e ) 450
Rationale: "explanation : average price of a goat = rs . 70 total price of 8 goats = 10 * 70 = rs . 700 but total price of 2 cows and 8 goats = rs . 1500 total price of 2 cows is = 1500 - 700 = 800 average price of a cow = 800 / 2 = rs . 400 answer : b"
Answer: b
Problem: if x < y < z and y - x > 5 , where x is an even integer and y and z are odd integers , what is the least possible value f of z - x ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] f = z - x = x + 9 - x = 9 ans : d"
Answer: d
Problem: the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by two - thirds of the males and one - third of the females in the class ?
Options: a ) 160 , b ) 168 , c ) 191 , d ) 192 , e ) 204
Rationale: "2 / 3 * 2 / 5 + 1 / 3 * 3 / 5 = 4 / 15 + 3 / 15 = 7 / 15 the number of degrees is 7 / 15 * 360 = 168 degrees the answer is b ."
Answer: b
Problem: last year manfred received 26 paychecks . each of his first 6 paychecks was $ 750 ; each of his remaining paychecks was $ 60 more than each of his first 6 paychecks . to the nearest dollar , what was the average ( arithmetic mean ) amount of his pay checks for the year ?
Options: a ) $ 752 , b ) $ 796 , c ) $ 765 , d ) $ 773 , e ) $ 775
Rationale: "= ( 750 * 6 + 810 * 20 ) / 26 = 796 answer is b . posted from my mobile device"
Answer: b
Problem: in the set of positive integers from 1 to 60 , what is the sum of all the odd multiples of 5 ?
Options: a ) 180 , b ) 185 , c ) 190 , d ) 160 , e ) 165
Rationale: 1 - 60 5 - 15 - 25 - 35 - 45 are valid multiples of 5 . add them 5 + 15 + 25 + 35 + 45 + 55 = 180 a
Answer: a
Problem: a train is 360 meter long is running at a speed of 54 km / hour . in what time will it pass a bridge of 140 meter length ?
Options: a ) 65 seconds , b ) 33.33 seconds , c ) 40 seconds , d ) 97 seconds , e ) 26 seconds
Rationale: "speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 * ( 1 / 15 ) = 33.33 seconds answer : b"
Answer: b
Problem: if a certain number is divided by 12 , the quotient , dividend , and divisor , added together , will amount to 64 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 48 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 12 + x + 12 = 64 . and x - 624 / 13 = 48 ."
Answer: a
Problem: the ages of two persons differ by 24 years . if 5 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 20,20 , b ) 20,10 , c ) 25,15 , d ) 35,11 , e ) none of these
Rationale: "explanation : let their ages be x and ( x + 24 ) years . 5 ( x - 5 ) = ( x + 24 - 5 ) or 4 x = 44 or x = 11 . their present ages are 35 years and 11 years option d"
Answer: d
Problem: what is the remainder when the number t = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: "14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus t = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )"
Answer: a
Problem: the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 15000 , then find the annual income of a ?
Options: a ) 187888 , b ) 276889 , c ) 267777 , d ) 504000 , e ) 297112
Rationale: "b ' s monthly income = 15000 * 112 / 100 = rs . 16800 b ' s monthly income = 2 parts - - - - > rs . 16800 a ' s monthly income = 5 parts = 5 / 2 * 16800 = rs . 42000 a ' s annual income = rs . 42000 * 12 = rs . 504000 answer : d"
Answer: d
Problem: if an article is sold at 18 % profit instead of 9 % profit , then the profit would be $ 72 more . what is the cost price ?
Options: a ) $ 500 , b ) $ 600 , c ) $ 700 , d ) $ 800 , e ) $ 900
Rationale: "9 % * cost price = $ 72 1 % * cost price = $ 72 / 9 = $ 8 the cost price is $ 800 . the answer is d ."
Answer: d
Problem: by approximately what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ?
Options: a ) 173 % , b ) 516 % , c ) 461 % , d ) 350 % , e ) 290 %
Rationale: "what percent is x greater than 1 / 3 if ( 2 / 3 ) ( x ) = 1 ? = > x = 3 / 2 % change = [ ( 3 / 2 - 1 / 3 ) / ( 1 / 3 ) ] * 100 = 350 ans d , 350 %"
Answer: d
Problem: a train 1500 m long can cross an electric pole in 50 sec and then find the speed of the train ?
Options: a ) 106 , b ) 107 , c ) 108 , d ) 109 , e ) 110
Rationale: "length = speed * time speed = l / t s = 1500 / 50 s = 30 m / sec speed = 30 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 108 kmph answer : c"
Answer: c
Problem: in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 35 % of all the employees are men . what % of all the employee went to the picnic ?
Options: a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
Rationale: total men in company 35 % means total women in company 65 % ( assume total people in company 100 % ) no of men emplyess attended picnic = 35 x ( 20 / 100 ) = 7 no of women empolyees attened picnin = 65 x ( 40 / 100 ) = 26 total percentage of empolyess attened the picnic = 7 + 26 = 33 % answer : a
Answer: a
Problem: a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 60 sq . feet , how many feet of fencing will be required ?
Options: a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 26
Rationale: "we have : l = 20 ft and lb = 60 sq . ft . so , b = 3 ft . length of fencing = ( l + 2 b ) = ( 20 + 6 ) ft = 26 ft . answer : e"
Answer: e
Problem: if an integer w is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that w ( w + 1 ) ( w + 2 ) will be divisible by 8 ?
Options: a ) 1 / 4 , b ) 3 / 8 , c ) 1 / 2 , d ) 5 / 8 , e ) 3 / 4
Rationale: for w total numbers 8 * 12 there are 12 numbers divisible by 8 - > 3 * 12 ( if 8 is an example - ( 6 , 78 ) , ( 7 , 89 ) , ( 8 , 910 ) ) and 12 numbers divisible by 4 but not divisible by 8 - > 2 * 12 ( if 4 is an example ( 2 , 34 ) and ( 4 , 56 ) ) the answer 5 / 8 - > d
Answer: d
Problem: tickets numbered from 1 to 24 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 1 / 7
Rationale: here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 , 23 , 24 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 , 24 ] p ( e ) = n ( e ) / n ( s ) = 8 / 24 = 1 / 3 the answer is a .
Answer: a
Problem: the difference of two numbers is 20 % of the larger number . if the smaller number is 12 , the larger one is :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) none of these
Rationale: "let the larger number be x . then , x - 12 = 20 % of x < > x - ( x / 5 ) = 12 4 x / 5 = 12 < = > x = ( 12 ∗ 5 ) / 5 = 15 . answer : a"
Answer: a
Problem: sandy is younger than molly by 14 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 36 , b ) 45 , c ) 54 , d ) 63 , e ) 72
Rationale: "s = m - 14 s / m = 7 / 9 9 s = 7 m 9 ( m - 14 ) = 7 m m = 63 the answer is d ."
Answer: d
Problem: carrie likes to buy t - shirts at the local clothing store . they cost $ 8.75 each . one day , she bought 18 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 70 , c ) $ 200 , d ) $ 171.6 , e ) $ 190
Rationale: $ 8.75 * 18 = $ 70 . answer is b .
Answer: b
Problem: a pharmaceutical company received $ 3 million in royalties on the first $ 20 million in sales of and then $ 8 million in royalties on the next $ 108 million in sales . by approximately what percentage did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 46 % , d ) 52 % , e ) 56 %
Rationale: "( 8 / 108 ) / ( 3 / 20 ) = 30 / 54 = 49,3 % it means that 8 / 108 represents only 49,3 % . therefore a decrease of 46 % . answer c"
Answer: c
Problem: a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 14 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 17 , e ) 72
Rationale: "explanation : as there is meal for 70 adults and 14 have their meal , the meal left can be catered to 56 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 56 adults = 72 children hence , the meal can be catered to 72 children . answer : e"
Answer: e
Problem: a batch of cookies was divided amomg 2 tins : 2 / 3 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 11 , d ) 7 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 2 / 3 r = 1 / 2 b = 1 / 4 we can solve for g which is 5 / 12 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 5 / 12 + 1 / 2 ) = 5 / 12 x = 5 / 11 answer : c . 5 / 11"
Answer: c
Problem: robert ' s salary was decreased by 60 % and subsequently increased by 60 % . how much percentage does he lose ?
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 36 % , e ) 50 %
Rationale: let original salary be $ 100 salary after decreasing 60 % = 100 - 100 x 60 / 100 = $ 40 salary after increasing 60 % on $ 40 = 40 + 40 x 60 / 100 = $ 64 percentage of loss = 100 - 64 = 36 % answer : d
Answer: d
Problem: a candidate got 34 % of the votes polled and he lost to his rival by 640 votes . how many votes were cast ?
Options: a ) 2000 , b ) 2400 , c ) 2800 , d ) 3200 , e ) 3600
Rationale: "let x be the total number of votes . 0.34 x + 640 = 0.66 x 0.32 x = 640 x = 640 / 0.32 = 2000 the answer is a ."
Answer: a
Problem: if x ¤ y = ( x + y ) ^ 2 - ( x - y ) ^ 2 . then √ 11 ¤ √ 11 =
Options: a ) 44 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: x = √ 11 and y also = √ 11 applying the function ( √ 11 + √ 11 ) ^ 2 - ( √ 11 - √ 11 ) ^ 2 = ( 2 √ 11 ) ^ 2 - 0 = 4 x 11 = 44 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 11 and y = √ 11 you get the answer 44 . answer a
Answer: a
Problem: of the people who responded to a market survey , 200 preferred brand x and the rest preferred brand y . if the respondents indicated a preference for brand x over brand y by ratio of 4 to 1 , how many people responded to the survey ?
Options: a ) 80 , b ) 160 , c ) 250 , d ) 350 , e ) 480
Rationale: "ratio = 4 : 1 = > 4 x respondents preferred brand x and x preferred brand y since , no . of respondents who preferred brand x = 200 = > 4 x = 200 = > x = 50 hence total no . of respondents = 200 + 50 = 250 hence c is the answer ."
Answer: c
Problem: 5358 x 55 = ?
Options: a ) 272258 , b ) 272358 , c ) 294690 , d ) 274258 , e ) 274358
Rationale: "5358 x 51 = 5358 x ( 50 + 5 ) = 5358 x 50 + 5358 x 5 = 267900 + 26790 = 294690 . c )"
Answer: c
Problem: the average of 5 numbers is 7.4 . if one of the numbers is multiplied by a factor of 3 , the average of the numbers increases to 9.2 . what number is multiplied by 3 ?
Options: a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.5 , e ) 6.0
Rationale: "the average of 5 numbers is 7.4 the sum of 5 numbers will be 7.4 x 5 = 37 the average of 5 number after one of the number is multiplied by 3 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 37 = 9 let the number multiplied by 3 be n then , 3 n = n + 9 or 2 n = 9 or n = 4.5 answer : - d"
Answer: d
Problem: the average marks obtained by 120 candidates in a certain examination is 35 . find the total marks .
Options: a ) 3800 , b ) 4500 , c ) 5200 , d ) 3400 , e ) 4200
Rationale: "following the above formula , we have the total marks = 120 * 35 = 4200 answer is e"
Answer: e
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 280 6 ounces servings of orange juice ?
Options: a ) a ) 35 , b ) b ) 34 , c ) c ) 50 , d ) d ) 67 , e ) e ) 100
Rationale: "its a . total juice rquired = 280 * 6 = 1680 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1680 / 48 = 35 . answer a"
Answer: a
Problem: a box contains either blue or red flags . the total number of flags in the box is an even number . a group of children are asked to pick up two flags each . if all the flags are used up in the process such that 60 % of the children have blue flags , and 45 % have red flags , what percentage of children have flags of both the colors ?
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) it can not be determined
Rationale: "solution : let the total number of flags be 100 ( even number ) let the total number of ' blue ' flags alone be ' a ' let the total number of ' red ' flags alone be ' b ' let the total number of ' both ' flags be ' c ' we have given , total number of blue flags = 60 % = 60 = a + c total number of red flags = 45 % = 45 = b + c total number of flags = a + b + c = 100 ( since all the flag have been utilized ) so , substituting for c in the third equation , we have , 60 - c + c + 45 - c = 100 c = 5 option a ."
Answer: a
Problem: if the perimeter of a rectangular playground is 1200 m , its length when its breadth is 500 m is ?
Options: a ) 300 , b ) 200 , c ) 100 , d ) 400 , e ) 500
Rationale: 2 ( l + 500 ) = 1200 = > l = 100 m answer : c
Answer: c
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 115 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 13.03 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 115 : ( 115 / 15 ) ) then typical dosage would be 2 * 7.67 = 15.33 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 15.33 ) * 100 = 13.03 % e is the answer ."
Answer: e
Problem: what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 500 inclusive ?
Options: a ) 190 , b ) 255 , c ) 200 , d ) 205 , e ) 210
Rationale: this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 500 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 50 ( 10 ) = 500 so we know that there are 50 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 500 = 510 20 + 490 = 510 30 + 480 = 510 etc . since there are 50 total terms , this pattern will create 25 ' pairs ' of 510 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 25 ) ( 510 ) / ( 50 ) = 255 final answer : b
Answer: b
Problem: 64 ã — 64 ã — 64 ã — 64 x 64 = 8 ^ ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 10 , e ) none of these
Rationale: "64 ã — 64 ã — 64 ã — 64 x 64 = 8 ^ ? or , 8 ( 2 ) ã — 8 ( 2 ) ã — 8 ( 2 ) ã — 8 ( 2 ) x 8 ( 2 ) = 8 ? or 7 ( 10 ) = 8 ? or , ? = 10 answer d"
Answer: d
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 14 km ?
Options: a ) 3 , b ) 6 , c ) 8 , d ) 9 , e ) 7
Rationale: m = 4 s = 2 us = 4 - 2 = 2 d = 14 t = 14 / 2 = 7 answer : e
Answer: e
Problem: find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 15 of money ?
Options: a ) 1500 , b ) 2677 , c ) 1997 , d ) 2677 , e ) 1971
Rationale: p = 15 ( 100 / 10 ) 2 = > p = 1500 answer : a
Answer: a
Problem: one bottle is half - full of oil and another bottle with twice the capacity is one quarter full of oil . if water is added so that both the bottles are full and the contents of both are then poured into a third bottle that is empty and large enough to hold the contents of both , what fractions of the contents in the third bottle is oil ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 3 / 8 , d ) 2 / 3 , e ) 1 / 2
Rationale: let assume that 1 st bottle capacity = 1 litre ; therefore , it contain 1 / 2 litre oil and 1 / 2 litre water . ( i . e ) water = 1 / 2 litre oil = 1 / 2 litre 2 nd bottle is twice the capacity i . e . 2 litre capacity it means , 1 / 2 litre filled with oil and 1 ( 1 / 2 ) litre filled with water . i . e . oil = 1 / 2 liter water = 1 ( 1 / 2 ) litre in total the third bottle will contain , 1 litre oil and 2 litre water . i . e . , oil = 1 litre water = 2 liter therefore , oil proportion is 1 / 3 answer : b
Answer: b