regisss/math_qa huggingface dataset:
Problem: brenda and sally run in opposite direction on a circular track , starting at diametrically opposite points . they first meet after brenda has run 50 meters . they next meet after sally has run 150 meters past their first meeting point . each girl runs at a constant speed . what is the length of the track in meters ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 500
Rationale: "nice problem . + 1 . first timetogetherthey run half of the circumference . second timetogetherthey run full circumference . first time brenda runs 50 meters , thus second time she runs 2 * 50 = 100 meters . since second time ( when they run full circumference ) brenda runs 200 meters and sally runs 150 meters , thus the circumference is 100 + 150 = 250 meters . answer : a ."
Answer: a
Problem: a man buys a cycle for rs . 1900 and sells it at a loss of 18 % . what is the selling price of the cycle ?
Options: a ) s . 1590 , b ) s . 1560 , c ) s . 1558 , d ) s . 1252 , e ) s . 1062
Rationale: "s . p . = 82 % of rs . 1900 = rs . 82 x 1900 / 100 = rs . 1558 answer : option c"
Answer: c
Problem: at the end of the day , february 14 th , a florist had 120 roses left in his shop , all of which were red , white or pink in color and either long or short - stemmed . a third of the roses were short - stemmed , 20 of which were white and 10 of which were pink . the percentage of pink roses that were short - stemmed equaled the percentage of red roses that were short - stemmed . if none of the long - stemmed roses were white , what percentage of the long - stemmed roses were red ?
Options: a ) 20 % , b ) 50 % , c ) 55 % , d ) 75 % , e ) 80 %
Rationale: "r + w + p = 120 s + l = 120 1 / 3 * 120 = 40 short - stemmed white = 20 short - stemmed pink = 10 = > short - stemmed red = 10 10 / p = 10 / r = > r = p so total long stemmed = 80 and long stemmed red + long stemmed pink = 80 so long stemmed red / long stemmed = ? total white = 20 ( as no long stemmed white ) = > r + r + 20 = 120 = > 2 r = 100 and r = 50 long stemmed r = 50 - 10 = 40 so long stemmed red / r = 40 / 80 = 50 % answer - b"
Answer: b
Problem: the difference between a two - digit number and the number obtained by interchanging the positions of its digits is 27 . what is the difference between the two digits of that number ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "sol . let the ten ’ s digit be x and unit ’ s digit be y , then , ( 10 x + y ) - ( 10 y + x ) = 27 ⇔ 9 ( x - y ) = 27 ⇔ x - y = 3 answer a"
Answer: a
Problem: a fair price shopkeeper takes 10 % profit on his goods . he lost 60 % goods during theft . his loss percent is :
Options: a ) 72 % , b ) 42 % , c ) 56 % , d ) 12 % , e ) 22 %
Rationale: "explanation : suppose he has 100 items . let c . p . of each item be re . 1 . total cost = rs . 100 . number of items left after theft = 40 . s . p . of each item = rs . 1.10 total sale = 1.10 * 40 = rs . 44 hence , loss % = 56 / 100 * 100 = 56 % answer : c"
Answer: c
Problem: a corporation that had $ 115.19 billion in profits for the year paid out $ 230.10 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: required answer = [ employee benefit / profit ] * 100 = [ ( 230.10 million ) / ( 115.19 billion ) ] * 100 = [ ( 230.10 * 10 ^ 6 ) / ( 115.19 * 10 ^ 9 ) ] * 100 = ( 2 / 1000 ) * 100 = 0.2 % so answer is ( e )
Answer: e
Problem: 39 men can complete a piece of work in 18 days . in how many days will 27 men complete the same work ?
Options: a ) 24 , b ) 77 , c ) 26 , d ) 25 , e ) 13
Rationale: "explanation : less men , means more days { indirect proportion } let the number of days be x then , 27 : 39 : : 18 : x [ please pay attention , we have written 27 : 39 rather than 39 : 27 , in indirect proportion , if you get it then chain rule is clear to you : ) ] { \ color { blue } x = \ frac { 39 \ times 18 } { 27 } } x = 26 so 26 days will be required to get work done by 27 men . answer : c"
Answer: c
Problem: two cars a and b start from boston and new york respectively simultaneously and travel towards each other at constant speeds along the same route . after meeting at a point between boston and new york the two cars a and b proceed to their respective destinations of new york and boston . car a reaches new york 80 minutes after the two cars have met and car b reaches boston 90 minutes after they have met . how long did car a take to cover the distance between boston and new york ?
Options: a ) 1 hour , b ) 1 hour 10 minutes , c ) 2 hours 30 minutes , d ) 1 hour 40 minutes , e ) 2 hours 20 minutes
Rationale: both cars leave at the same time both cars travel at constant speed stealing a useful piece of information from paragkan : if two objects a and b start from opposite points and , after having met en route , reach their respective destinations in a and b mins ( or any other measure of time ) respectively , then the ratio of their speeds ratio of speed : ( a / b ) = sq . rt ( b / a ) sq . rt ( b / a ) sq . rt ( 90 / 80 ) sq . rt ( 3 / 2 ) so , for every three units of distance a travels , b travels two . because we know the ratio of speed and the time it took b to travel the distance a has n ' t yet covered , we can find the time it took a to cover the distance b did in 90 minutes . 90 * ( 2 / 3 ) where 2 / 3 represents the lesser amount of time it took a to travel the distance b did in 90 minutes . = 60 minutes . therefore , a took 80 minutes to travel the first portion then 60 minutes to travel the distance b did in 90 minutes . a spent ( 80 + 60 ) = 140 minutes on the road . e . 2 hours 20 minutes
Answer: e
Problem: a metallic sphere of radius 24 cm is melted and drawn into a wire , whose radius of cross section is 16 cm . what is the length of the wire ?
Options: a ) 26 cm , b ) 45 cm , c ) 58 cm , d ) 63 cm , e ) 72 cm
Rationale: "volume of the wire ( in cylindrical shape ) is equal to the volume of the sphere . π ( 16 ) ^ 2 * h = ( 4 / 3 ) π ( 24 ) ^ 3 = > h = 72 cm answer : e"
Answer: e
Problem: two pipes can fill a tank in 18 minutes and 6 minutes . an outlet pipe can empty the tank in 45 minutes . if all the pipes are opened when the tank is empty , then how many minutes will it take to fill the tank ?
Options: a ) 1 / 15 , b ) 1 / 6 , c ) 1 / 11 , d ) 1 / 10 , e ) 1 / 12
Rationale: "part of the filled by all the three pipes in one minute = 1 / 18 + 1 / 6 - 1 / 45 = 1 / 6 so , the tank becomes full in 6 minutes . answer : b"
Answer: b
Problem: how many multiples of 4 are there between 32 and 252 ?
Options: a ) 67 , b ) 64 , c ) 54 , d ) 56 , e ) 60
Rationale: "it should be mentioned whether 32 and 252 are inclusive . if 32 and 252 are inclusive , then the answer is ( 252 - 32 ) / 4 + 1 = 56 . if 32 and 252 are not inclusive , then the answer is ( 248 - 36 ) / 4 + 1 = 54 . since oa is c , then we have not inclusive case ."
Answer: c
Problem: a train 260 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 32 , c ) 26 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 260 + 140 = 400 m required time = 400 * 2 / 25 = 32 sec answer : b"
Answer: b
Problem: set # 1 = { a , b , c , d , e , f } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 4 / 9
Rationale: so not a vowel in set - 1 : 4 / 6 and not a vowel in ser - 2 : 5 / 6 now , 4 / 6 ∗ 5 / 6 = 5 / 9 this is for not a vowel . then for at least one vowel will be = 1 − 5 / 9 = 4 / 9 answer will be e .
Answer: e
Problem: if a no . when divided by 44 , gives 432 as quotient and 0 as remainder . what will be the remainder when dividing thesame no . by 31
Options: a ) 2 , b ) 4 , c ) 5 , d ) 7 , e ) 8
Rationale: p ÷ 44 = 432 = > p = 432 * 44 = 19008 p / 31 = 19008 / 31 = 613 , remainder = 5 c
Answer: c
Problem: the age of somu is one - third his father ' s . 7 years back he was one - fifth of his father ' s age . what is his persent age ?
Options: a ) 11 , b ) 13 , c ) 14 , d ) 12 , e ) 10
Rationale: "explanation : let somu ' s age be x and that of his father be 3 x . so , x - 7 = 3 x - 7 / 5 = x = 14 answer : option c"
Answer: c
Problem: sam ’ s car was fined when he gave joe and peter a ride , so they decided to help sam pay the fine . joe paid $ 6 more than 1 / 4 of the fine and peter paid $ 6 less than 1 / 3 of the fine , leaving pay $ 10 less than 1 / 2 the fine to complete the payment . what fraction of the fine did sam pay ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 35 , d ) $ 44 , e ) $ 45
Rationale: "call the fine f . joe paid ( 1 / 4 ) f + 4 and peter paid ( 1 / 3 ) f – 4 , leaving ( 1 / 2 ) f – 5 left . if we add those three up , they should add up to f . f = [ ( 1 / 4 ) f + 6 ] + [ ( 1 / 3 ) f – 6 ] + [ ( 1 / 2 ) f – 10 ] f = ( 1 / 4 ) f + ( 1 / 3 ) f + ( 1 / 2 ) f – 10 multiply all terms by 12 to clear the fractions . 12 f = 3 f + 4 f + 6 f – 120 12 f = 13 f – 120 – f = – 120 f = 120 well , if the fine cost $ 120 , then sam paid the part not covered by joe or peter . half the fine is $ 60 , and sam paid $ 10 less than this : $ 50 . answer = a"
Answer: a
Problem: the average wages of a worker during a fortnight comprising 15 consecutive working days was $ 90 per day . during the first 7 days , his average wages was $ 87 per day and the average wages during the last 7 days was $ 91 per day . what was his wage on the 8 th day ?
Options: a ) $ 83 , b ) $ 90 , c ) $ 92 , d ) $ 97 , e ) $ 104
Rationale: "average daily wage of a worker for 15 consecutive working days = 90 $ during the first 7 days , the daily average daily wage = 87 $ during the last 7 days , the daily average daily wage = 91 $ wage on 8 th day = 90 * 15 - ( 87 * 7 + 91 * 7 ) = 1350 - ( 609 + 637 ) = 1350 - 1246 = 104 answer e"
Answer: e
Problem: it is decided to construct a 2 metre broad pathway around a rectangular plot on the inside . if the area of the plots is 96 sq . m . and the rate of construction is rs . 50 per square metre . , what will be the total cost of the construction ?
Options: a ) rs . 3500
b ) rs . 4200
c ) insufficient data
d ) rs . 4400
e ) none of these
Rationale: explanation : let length and width of the rectangular plot be l and b respectively total area of the rectangular plot = 96 sq . m . = > lb = 96 width of the pathway = 2 m length of the remaining area in the plot = ( l - 4 ) breadth of the remaining area in the plot = ( b - 4 ) area of the remaining area in the plot = ( l - 4 ) ( b - 4 ) area of the pathway = total area of the rectangular plot - remaining area in the plot = 96 - [ ( l - 4 ) ( b - 4 ) ] = 96 - [ lb - 4 l - 4 b + 16 ] = 96 - [ 96 - 4 l - 4 b + 16 ] = 96 - 96 + 4 l + 4 b - 16 = 4 l + 4 b - 16 = 4 ( l + b ) - 16 we do not know the values of l and b and hence area of the pathway can not be found out . so we can not determine total cost of the construction . answer : option c
Answer: c
Problem: in a class , there are 18 boys who are over 160 cm tall . if these constitute 3 - fourths of the boys and the total number of boys is two - thirds of the total number of students in the class , what is the number of girls in the class ?
Options: a ) 11 , b ) 12 , c ) 28 , d ) 27 , e ) 19
Rationale: let the number of boys be x . then , ( 3 / 4 ) x = 18 or x = 18 x ( 4 / 3 ) = 24 . if total number of students is y , then ( 2 / 3 ) y = 24 or y = 24 x ( 3 / 2 ) = 36 . therefore number of girls in the class = ( 36 - 24 ) = 12 . answer : b
Answer: b
Problem: a and b invests rs . 10000 each , a investing for 6 months and b investing for all the 12 months in the year . if the total profit at the end of the year is rs . 24000 , find their shares ?
Options: a ) 8000 , 16000 , b ) 1599,2000 , c ) 7290,3000 , d ) 15000,4000 , e ) 72821,5000
Rationale: "the ratio of their profits a : b = 6 : 12 = 1 : 2 share of a = 1 * 24000 / 3 = 8000 share of b = 2 * 24000 / 3 = 16000 answer : a"
Answer: a
Problem: the perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 87 cm 2 , b ) 28 cm 2 , c ) 98 cm 2 , d ) 26 cm 2 , e ) 50 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 40 / 2 = 50 cm 2 answer : e"
Answer: e
Problem: if 75 percent of a class answered the first question on a certain test correctly , 70 percent answered the second question on the test correctly , and 20 percent answered neither of the questions correctly , what percent answered both correctly ?
Options: a ) 10 % , b ) ( 8 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: { total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 70 % - { both } + 20 % - - > { both } = 65 % . answer : e .
Answer: e
Problem: if a man lost 4 % by selling oranges at the rate of 72 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 41 , b ) 48 , c ) 49 , d ) 44 , e ) 43
Rationale: "96 % - - - - 72 144 % - - - - ? 96 / 144 * 72 = 48 answer : b"
Answer: b
Problem: a man swims downstream 40 km and upstream 16 km taking 4 hours each time , what is the speed of the man in still water ?
Options: a ) 7 , b ) 7.5 , c ) 6.8 , d ) 7.8 , e ) 8.0
Rationale: "40 - - - 4 ds = 10 ? - - - - 1 20 - - - - 4 us = 5 ? - - - - 1 m = ? m = ( 10 + 5 ) / 2 = 7.5 answer : b"
Answer: b
Problem: | 5 - 2 | - | 6 - 9 | = ?
Options: a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
Rationale: "| 5 - 2 | - | 6 - 9 | = | 3 | - | - 3 | = 3 - 3 = 0 correct answer d"
Answer: d
Problem: find value of x : 121 × 54 = x
Options: a ) 34545 , b ) 46576 , c ) 67887 , d ) 57687 , e ) 75625
Rationale: 121 × 54 = 121 × ( 102 ) 4 = 121 × 1000016 = 7.5625 × 10000 = 75625 e
Answer: e
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 it will take to fill the tank ?
Options: a ) 10 mins , b ) 12 mins , c ) 15 mins , d ) 20 mins , e ) 30 mins
Rationale: "explanation : in this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result , as 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 mins . answer : option b"
Answer: b
Problem: how many integers are between 4 and 87 / 8 , inclusive ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 9 , e ) 10
Rationale: "87 / 8 = 10 . xx we are not concerned about the exact value of 87 / 8 as we just need the integers . since the values are small , we can write down the integers . the different integers between 4 and 87 / 8 would be 4 , 5 , 6 , 7 , 8 , 9 , 10 total number of integers = 7 option c"
Answer: c
Problem: aishwarya rai walks into a bank to cash out her check . by mistake the bank teller gives her dollar amount in change , and her cent amount in dollars . on the way home she spends 5 cent , and then suddenly she notices that she has twice the amount of her check . how much was her check amount ?
Options: a ) 21.55 , b ) 25.89 , c ) 30.56 , d ) 31.55 , e ) 31.63
Rationale: e the check was for dollars 31.63 . the bank teller gave her dollars 63.31 she spent . 05 , and then she had dollars 63.26 , which is twice the check . let x be the dollars of the check , and y be the cent . the check was for 100 x + y cent he was given 100 y + x cent also 100 y + x - 5 = 2 ( 100 x + y ) expanding this out and rearranging , we find : 98 y = 199 x + 5 or 199 x ≡ - 5 ( mod 98 ) or 98 * 2 * x + 3 x ≡ - 5 ( mod 98 ) 3 x ≡ - 5 ≡ 93 ( mod 98 ) this quickly leads to x = 31
Answer: e
Problem: the length of a room is 9 m and width is 4.75 m . what is the cost of paying the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) 25650 , b ) 25750 , c ) 26550 , d ) 30750 , e ) 38475
Rationale: "area = 9 × 4.75 sq . metre . cost for 1 sq . metre . = rs . 900 hence total cost = 9 × 4.75 × 900 = 9 × 4275 = rs . 38475 answer is e ."
Answer: e
Problem: if 2 ^ 5 , 3 ^ 3 , and 13 ^ 2 are all factors of the product of 936 and w where w is a positive integer , what is the smallest possible value of w ?
Options: a ) 26 , b ) 39 , c ) 42 , d ) 65 , e ) 156
Rationale: "here 156 has three two ' s two three ' s and one 13 rest of them must be in w so w = 13 * 3 * 4 = 156 answer : e"
Answer: e
Problem: a sum of money at simple interest amounts to rs . 815 in 2 years and to rs . 854 in 4 years . the sum is :
Options: a ) s . 650 , b ) s . 690 , c ) s . 698 , d ) s . 700 , e ) s . 737
Rationale: "s . i . for 1 year = rs . ( 854 - 815 ) = rs . 39 . s . i . for 2 years = rs . ( 39 x 2 ) = rs . 78 . principal = rs . ( 815 - 78 ) = rs . 737 . answer : option e"
Answer: e
Problem: i chose a number and divide it by 12 . then i subtracted 240 from the result and got 8 . what was the number i chose ?
Options: a ) 2976 , b ) 2989 , c ) 2789 , d ) 2888 , e ) 2098
Rationale: "let x be the number i chose , then x / 12 − 240 = 8 x / 12 = 248 x = 2976 answer is a ."
Answer: a
Problem: at 1 : 00 pm , a truck left city p and headed toward city q at a constant speed of 36 km / h . one hour later , a car left city q and headed toward city p along the same road at a constant speed of 48 km / h . if the distance between city p and city q is 330 km , at what time will the truck and the car meet each other ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: at 2 : 00 pm , the truck and the car are 294 km apart . the truck and the car complete a distance of 84 km each hour . the time it takes to meet is 294 / 84 = 3.5 hours . they will meet at 5 : 30 pm . the answer is e .
Answer: e
Problem: if x = 27 ^ 324 and y = 3 ^ 134 , what is the units digit of x / y ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "basically it tests pattern : ( 3,9 , 7,1 ) if we take write 27 in terms of 3 and take the dr to the top , it will result in 3 ^ 838 since pattern = 4 divide 838 / 4 and reminder = 2 - - - - - - - this points to 9 in the pattern ( 3,9 , 7,1 ) answer : e"
Answer: e
Problem: in what time will a train 100 meters long cross an electric pole , if its speed is 72 km / hr
Options: a ) 5 seconds , b ) 2.8 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 72 * ( 5 / 18 ) = 20 m / sec time = distance / speed = 100 / 20 = 5 seconds answer : a"
Answer: a
Problem: at joel ’ s bookstore , the current inventory is 30 % historical fiction . of the historical fiction books , 40 % are new releases , while 50 % of the other books are new releases . what fraction of all new releases are the historical fiction new releases ?
Options: a ) 4 / 25 , b ) 12 / 47 , c ) 2 / 5 , d ) 8 / 15 , e ) 2 / 3
Rationale: let there be 100 books in all historic fiction books = 30 % of total = 30 other books = 70 new historic fiction = 40 % of 30 = 12 other new books = 50 % of 70 = 35 total new books = 35 + 12 = 47 fraction = 12 / 47 ans : b
Answer: b
Problem: if 45 % of a class averages 95 % on a test , 50 % of the class averages 78 % on the test , and the remainder of the class averages 60 % on the test , what is the overall class average ? ( round final answer to the nearest percent ) .
Options: a ) 83 % , b ) 84 % , c ) 85 % , d ) 86 % , e ) 87 %
Rationale: "this question is a weighted average question with a series of dependent variables . the remaining portion of the class represents 100 % - 45 % - 50 % = 5 % of the class converting the portions of the class population to decimal weights , we find : class average = 0.45 x 95 + 0.50 x 78 + 0.05 x 60 = 84.75 the class average ( rounded ) is 85 % final answer c ) 85 %"
Answer: c
Problem: on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.30 per glass on the first day , what was the price per glass on the second day ?
Options: a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
Rationale: "on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.3 = 3 * x - - > x = $ 0.2 . answer : b ."
Answer: b
Problem: calculate the effect changes in dimension of a rectangle will have on its area , if length is increased by 40 % and its breadth is decreased by 25 % ?
Options: a ) 5 % increase , b ) 7 % increase , c ) 6 % increase , d ) 4 % increase , e ) 3 % increase
Rationale: "let l and b be 100 each 100 * 100 = 10000 l increase by 40 % = 140 b decrease by 25 % = 75 140 * 75 = 10500 5 % increase answer : a"
Answer: a
Problem: if 3 / w + 3 / x = 3 / y and wx = y , then the average ( arithmetic mean ) of w and x is
Options: a ) 1 / 2 , b ) 1 , c ) 2 , d ) 4 , e ) 8
Rationale: "given : 3 / w + 3 / x = 3 / ywx = y find : ( w + x ) / 2 = ? 3 ( 1 / w + 1 / x ) = 3 ( 1 / y ) - divide both sides by 3 ( 1 / w + 1 / x ) = 1 / y ( x + w ) / wx = 1 / wx - sub ' d in y = wx x + w - 1 = 0 x + w = 1 therefore ( w + x ) / 2 = 1 / 2 ans : a"
Answer: a
Problem: - - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure , and the numbers of students who gave these answers are listed in the table above . if 140 students answered yes only for subject m , how many of the students did not answer yes for either subject ?
Options: a ) 100 , b ) 260 , c ) 360 , d ) 400 , e ) 500
Rationale: "since 140 students answered yes only for subject m , then the remaining 360 students who answered yes for subject m , also answered yes for subject r . so , 360 students answered yes for both subjects . if 360 students answered yes for both subjects , then 400 - 360 = 40 students answered yes only for subject r . so , we have that : 200 students answered yes only for subject m ; 40 students answered yes only for subject r ; 300 students answered yes for both subjects ; therefore 800 - ( 200 + 40 + 300 ) = 260 students did not answer yes for either subject . answer : b ."
Answer: b
Problem: the area of a square field is 7201 sq m . how long will a lady take to cross the field diagonally at the rate of 2.4 km / hr ?
Options: a ) 2 min
b ) 3 min
c ) 4 min
d ) 5 min
e ) 6 min
Rationale: area of a square field = 7201 sq m let the side of square = a a ^ 2 = 7201 = > a = 84.86 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 84.86 = 120 speed of lady = 2.4 km / hour = 2400 m / hour = 40 m / min time taken by lady to cross the field diagonally = 120 / 40 = 3 min answer b
Answer: b
Problem: a man can do a piece of work in 7 days , but with the help of his son , he can finish it in 3 days . in what time can the son do it alone ?
Options: a ) 5 , b ) 4 1 / 5 , c ) 7 1 / 2 , d ) 6 , e ) 9 1 / 2
Rationale: "son ' s 1 day work = 1 / 3 - 1 / 7 = 5 / 21 son alone can do the work in 21 / 5 days = 4 1 / 5 days answer is b"
Answer: b
Problem: 30 liters of a mixture contains milk and water in the ratio 2 : 1 . if 5 liters of this mixture be replaced by 5 liters of milk , the ratio of milk to water in the new mixture would be ?
Options: a ) 3 : 2 , b ) 3 : 1 , c ) 4 : 1 , d ) 5 : 2 , e ) 2 : 1
Rationale: "quantity of milk in 30 liters if mix = 30 * 2 / 3 = 20 liters quantity of milk in 35 liters of new mix = 20 + 5 = 25 liters quantity of water in it = 35 - 25 = 10 liters ratio of milk and water in new mix = 25 : 10 = 5 : 2 answer is d"
Answer: d
Problem: if | 5 x - 25 | = 100 , then find the sum of the values of x ?
Options: a ) 1 , b ) - 2 , c ) 10 , d ) - 3 , e ) 4
Rationale: "| 5 x - 25 | = 100 5 x - 25 = 100 or 5 x - 25 = - 100 5 x = 125 or 5 x = - 75 x = 25 or x = - 15 sum = 25 - 15 = 10 answer is c"
Answer: c
Problem: running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 8 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 1440 , e ) none of these
Rationale: "solution let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) â ˆ ´ 6 ã — 1 ã — x = 8 ã — 4 ã — 270 â ‡ ” x = 8 x 4 x 270 / 6 = 1440 . answer d"
Answer: d
Problem: how many zeroes are there at the end of the number n , if n = 100 ! + 200 ! ?
Options: a ) 73 , b ) 49 , c ) 20 , d ) 48 , e ) 24
Rationale: "the number of zeroes at the end of 100 ! will be less than the number of zeroes at the end of 200 ! hence it would be sufficient to calculate the number of zeroes at the end of 100 ! number of zeroes = [ 100 / 5 ] + [ 100 / 25 ] + [ 100 / 125 ] = 20 + 4 + 0 = 24 correct option : e"
Answer: e
Problem: a number when divided b the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder . the number is :
Options: a ) 1220 , b ) 1250 , c ) 2030 , d ) 22030 , e ) 1350
Rationale: required number = ( 555 + 445 ) * 2 * 110 + 30 = 220000 + 30 = 220030 . answer : d
Answer: d
Problem: if two dice are thrown together , the probability of getting an even prime number on the dice is
Options: a ) 1 / 36 , b ) 1 / 18 , c ) 1 / 13 , d ) 1 / 9 , e ) 5 / 36
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number prime number on the dice . p ( e ) = 1 / 36 a )"
Answer: a
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 108 grams of compound x ?
Options: a ) 90 , b ) 162 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 108 gms of x have 108 * 10 / 12 = 90 gms of b and 108 - 90 = 18 gms of a . cross check : - a / b = 18 / 90 = 2 / 10 ( as given ) ans a"
Answer: a
Problem: find the greatest number that will divide 205 , 626 and 588 leaving 5 , 6 and 8 as remainders respectively
Options: a ) 19 , b ) 17 , c ) 13 , d ) 9 , e ) 20
Rationale: "explanation : answer will be hcf of ( 205 - 5 , 626 - 6 , 588 - 8 ) hcf of ( 200 , 626 , 580 ) = 20 option e"
Answer: e
Problem: tough and tricky questions : ratios 4 / 5 of a certain class left on a field trip . 1 / 3 of the students who stayed behind did not want to go on the field trip ( all the others did want to go ) . when another vehicle was located , 1 / 2 of the students who did want to go on the field trip but had been left behind were able to join . what fraction of the class ended up going on the field trip ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 13 / 15 , d ) 23 / 30 , e ) 4 / 5
Rationale: let total no . of students be 30 students left on a field trip = 4 / 5 ( 30 ) = 24 thus 6 students left behind 1 / 3 ( 6 ) = 2 students did not want to go . thus 4 students want to go on the trip 1 / 2 ( 4 ) = 2 were able to join the other students on the field trip . thus total number of students that went on a field trip = 24 + 2 = 26 thus required fraction = 26 / 30 = 13 / 15 c
Answer: c
Problem: if x ^ 2 + 9 / x ^ 2 = 10 , what is the value of x - 3 / x
Options: a ) 36 , b ) 25 , c ) 2 , d ) 5 , e ) 3
Rationale: to find : x - 3 / x . let it be t . = > x - 3 / x = t = > ( x ^ 2 + 9 / x ^ 2 ) - 2 * x * 3 / x = t ^ 2 ( squaring both sides ) . = > ( 10 ) - 2 * 3 = 4 = > t ^ 2 = 4 . thus t = 2 or t = - 2 . answer c
Answer: c
Problem: the average salary / head of all the workers in a workshop is rs . 1100 , if the average salary / head of 9 technician is rs . 1300 and the average salary / head of the rest is rs . 880 , the total no . of workers in the work - shop is ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 17 , e ) 26
Rationale: let the total number of workers be y . so sum of salary for all workers = sum of salary of 9 technician + sum of salary for other y - 9 workers . 9 x 1300 + 880 ( y - 9 ) = 1100 y ⇒ 11700 + 880 y - 7920 = 1100 y ⇒ 220 y = 3780 ∴ y = 17 so total number of workers = 17 d
Answer: d
Problem: in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 10 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 62 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 10 = 62 answer c"
Answer: c
Problem: joe invested a certain sum of money in a simple interest bond whose value grew to $ 310 at the end of 3 years and to $ 410 at the end of another 5 years . what was the rate of interest in which he invested his sum ?
Options: a ) 6 % , b ) 7 % , c ) 8 % , d ) 9 % , e ) 10 %
Rationale: "in 5 years , the value grew $ 100 , so the simple interest was $ 20 per year . in 3 years , the total interest was 3 * $ 20 = $ 60 the principal is $ 310 - $ 60 = 250 . the interest rate is $ 20 / $ 250 = 8 % the answer is c ."
Answer: c
Problem: a rhombus has area 432 sq m , one diagonal is 36 cm . find other diagonal ?
Options: a ) 2400 m
b ) 2500 m
c ) 2600 m
d ) 2700 m
e ) 2900 m
Rationale: area of rhombus = 1 / 2 * d 1 * d 2 432 = 1 / 2 * d 1 * . 36 d 1 = 2400 m answer : a
Answer: a
Problem: if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 12 } + { 10 } ?
Options: a ) 23 , b ) 20 , c ) 13 , d ) 5 , e ) 2
Rationale: "soln : { 12 } + { 10 } = 12 * { 10 } + { 10 } = 13 * { 10 } answer : c"
Answer: c
Problem: a , b and c invested rs . 2400 , rs . 7200 and rs . 9600 respectively , in a partnership business . find the share of a in profit of rs . 9000 after a year ?
Options: a ) 1125 , b ) 2400 , c ) 7200 , d ) 2500 , e ) 2511
Rationale: "explanation : 2400 : 7200 : 9600 1 : 3 : 4 1 / 8 * 9000 = 1125 answer : a"
Answer: a
Problem: a women purchased 3 towels @ rs . 100 each , 5 towels @ rs . 150 each and two towels at a certain rate which is now slipped off from his memory . but she remembers that the average price of the towels was rs . 165 . find the unknown rate of two towels ?
Options: a ) a ) 400 , b ) b ) 450 , c ) c ) 500 , d ) d ) 550 , e ) e ) 600
Rationale: "10 * 150 = 1650 3 * 100 + 5 * 150 = 1050 1650 – 1050 = 600 e"
Answer: e
Problem: aaron will jog from home at 2 miles per hour and then walk back home by the same route at 4 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 5 , b ) 7 , c ) 3 , d ) 9 , e ) 10
Rationale: xyt / ( x + y ) x = 2 , y = 4 t = 3 2 * 4 * 3 / 2 + 4 = 18 / 6 = 3 answer : c
Answer: c
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 . 57600 ?
Options: a ) 81000 , b ) 81028 , c ) 27772 , d ) 72900 , e ) 22312
Rationale: 57600 * 9 / 8 * 9 / 8 = 72900 . answer : d
Answer: d
Problem: for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 35 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 % , c ) 25 % , d ) 26 % , e ) 28 %
Rationale: "total sales = 800 comission = ( 20 / 100 ) * 500 + ( 35 / 100 ) * 300 = 100 + 105 = 205 % comission = ( 205 / 800 ) * 100 = 25.6 ~ 26 % answer is d"
Answer: d
Problem: a boat can travel with a speed of 22 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 135 km downstream
Options: a ) 5 hours , b ) 4 hours , c ) 3 hours , d ) 2 hours , e ) none of these
Rationale: "explanation : speed of the boat in still water = 22 km / hr speed of the stream = 5 km / hr speed downstream = ( 22 + 5 ) = 27 km / hr distance travelled downstream = 135 km time taken = distance / speed = 135 / 27 = 5 hours . answer : option a"
Answer: a
Problem: a bag contains 5 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 2 / 5 , c ) 3 / 5 , d ) 11 / 15 , e ) 19 / 39
Rationale: "drawing two balls of same color from five green balls can be done in 5 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 5 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 19 / 39 answer : e"
Answer: e
Problem: find the 10 th term of an arithmetic progression whose first term is 8 and the common difference is 2 .
Options: a ) 45 , b ) 26 , c ) 44 , d ) 40 , e ) 46
Rationale: "n th term of a . p = a + ( n - 1 ) * d = 8 + ( 10 - 1 ) * 2 , = 8 + 18 = 26 . answer : b"
Answer: b
Problem: if ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 , then what is the value of x ?
Options: a ) 3 , b ) - 3 , c ) 10 / 3 , d ) 3 / 10 , e ) - 10 / 3
Rationale: ( 10 x + 2 ) / 4 - ( 3 x - 6 ) / 18 = ( 2 x + 4 ) / 3 = > 18 ( 10 x + 2 ) / 4 - ( 3 x - 6 ) = 18 ( 2 x + 4 ) / 3 = > 4.5 ( 10 x + 2 ) - 3 x + 6 = 6 ( 2 x + 4 ) = > 45 x + 9 - 3 x + 6 = 12 x + 24 = > 45 x - 3 x - 12 x = 24 - 9 - 6 = > 30 x = 9 = > x = 9 / 30 = > x = 3 / 10 answer : d
Answer: d
Problem: the cross - section of a cannel is a trapezium in shape . if the cannel is 8 m wide at the top and 6 m wide at the bottom and the area of cross - section is 700 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 100 , c ) 27 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 8 + 6 ) = 700 d = 100 answer : b"
Answer: b
Problem: the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.80 per metre .
Options: a ) 2399 , b ) 6336 , c ) 2999 , d ) 5808 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.80 ) = rs . 6336 . answer : b ) 6336"
Answer: b
Problem: a man bought 20 shares of rs . 50 at 5 discount , the rate of dividend being 4 % . the rate of interest obtained is
Options: a ) 5 % , b ) 5.28 % , c ) 5.30 % , d ) 5.50 % , e ) 6 %
Rationale: "shares = 20 shares 50 at 5 discount rate divident 4 % req = = = > 5.28 % answer b"
Answer: b
Problem: a train 150 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 ) 2 sec , b ) 6 sec , c ) 8 sec , d ) 9 sec , e ) 5 sec
Rationale: "d 9 sec 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 150 m at 50 / 3 m / sec = 150 * 3 / 50 sec = 9 sec"
Answer: d
Problem: convert the 13 / 54 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 0.86 , d ) 1.1 , e ) 1.2
Rationale: "13 / 54 m / s = 13 / 54 * 18 / 5 = 13 / 15 = 0.86 kmph . answer : c"
Answer: c
Problem: in a 300 m race a beats b by 22.5 m or 6 seconds . b ' s time over the course is :
Options: a ) 86 sec , b ) 80 sec , c ) 76 sec , d ) 96 sec , e ) none of these
Rationale: "runs 45 / 2 m in 6 sec . b covers 300 m in 6 x 2 / 45 x 300 sec = 80 sec . answer : b"
Answer: b
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 30 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 30 minutes , sam rides 6 km so sam will be 4 km ahead . it will take annie 80 minutes to catch sam . the answer is d .
Answer: d
Problem: john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.60 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 37.8 , d ) 40 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.60 - - > 15 p - 13.5 p = 60 - - > p = 40 . answer : d ."
Answer: d
Problem: a certain industrial loom weaves 0.126 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 119
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.126 : 15 : : 1 : x = > 0.126 * x = 15 = > x = 15 / 0.126 = > x = 119 answer : e"
Answer: e
Problem: a cistern is normally filled in 8 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 10 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: if leakage / hour = 1 / x , then 1 / 8 - 1 / x = 1 / 10 , solving 1 / x = 1 / 40 so in 40 hours full cistern will be empty . answer : d
Answer: d
Problem: oil cans x and y are right circular cylinders and the height and radius of y are each 4 times those of x . if the oil in can x filled to capacity sells for $ 2 , how much does the oil in y sell for if y is only half filled ?
Options: a ) $ 60 , b ) $ 52 , c ) $ 63 , d ) $ 64 , e ) $ 68
Rationale: formula for vol of a cyl is pi * r ^ 2 * h so vy = 64 * vy y when half filled will cost 32 times x so ans is d
Answer: d
Problem: a searchlight on top of the watch - tower makes 6 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
Rationale: "6 revolutions per minute = 1 revolution every 10 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 10 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 10 seconds ) = 1 - p ( man in dark for max of 10 seconds ) = 1 - 10 / 10 = 1 - 1 = 0 or the other way would be : p ( man in dark for at least 10 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 10 seconds because that is the max . in this approach it would be 10 / 10 seconds = 1 . answer is e"
Answer: e
Problem: jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 4000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 12,000 , d ) 14,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 4000 ) solving for x , we get the shares as 14000 . ans : ( option d )"
Answer: d
Problem: how many distinct integer values of n satisfy the inequality | | n - 3 | + 4 | ≤ 15 ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 13
Rationale: so i can write this as in - 3 i + 4 < = 15 or in - 3 i < = 11 so n can have - 8 to 14 = 13 true values . . . . e
Answer: e
Problem: a man rows his boat 75 km downstream and 45 km upstream , taking 5 hours each time . find the speed of the stream ?
Options: a ) 6 kmph , b ) 5 kmph , c ) 2 kmph , d ) 3 kmph , e ) 1 kmph
Rationale: "speed downstream = d / t = 75 / ( 5 ) = 15 kmph speed upstream = d / t = 45 / ( 5 ) = 9 kmph the speed of the stream = ( 15 - 9 ) / 2 = 3 kmph answer : d"
Answer: d
Problem: an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metre of cloth ?
Options: a ) 194 seconds , b ) 195 seconds , c ) 196 seconds , d ) 197 seconds , e ) none of these
Rationale: "explanation : let the time required by x seconds . then , more cloth means more time ( direct proportion ) so , 0.128 : 1 : : 25 : x = > x = 25 ∗ 1 / 0.128 = > x = 195.31 so time will be approx 195 seconds option b"
Answer: b
Problem: at what time between 5 and 6 o ' clock are the hands of a 3 minutes apart ?
Options: a ) 24 , b ) 55 , c ) 66 , d ) 88 , e ) 21
Rationale: in this type of problems the formuae is ( 5 * x + or - t ) * 12 / 11 here x is replaced by the first interval of given time . here x is 5 . t is spaces apart case 1 : ( 5 * x + t ) * 12 / 11 ( 5 * 5 + 3 ) * 12 / 11 28 * 12 / 11 = 336 / 11 = min therefore the hands will be 3 min apart at 31 5 / 11 min past 5 . case 2 : ( 5 * x - t ) * 12 / 11 ( 5 * 5 - 3 ) * 12 / 11 22 * 12 / 11 = 24 min therefore the hands will be 3 min apart at 24 min past 5 answer : a ) 24 min
Answer: a
Problem: the probability is 1 / 2 that a certain coin turns up heads on any given toss . if the coin is tossed 6 times , what is the probability that the coin turns up tails on at least one of the tosses ?
Options: a ) 15 / 16 , b ) 21 / 32 , c ) 31 / 32 , d ) 63 / 64 , e ) 51 / 64
Rationale: p ( 6 heads ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 . p ( at least one tail ) = 1 - 1 / 64 = 63 / 64 . the answer is d .
Answer: d
Problem: a football field is 8400 square yards . if 1200 pounds of fertilizer are spread evenly across the entire field , how many pounds of fertilizer were spread over an area of the field totaling 3500 square yards ?
Options: a ) 450 , b ) 600 , c ) 500 , d ) 2400 , e ) 3200
Rationale: "answer a ) 4800 yards need 1200 lbs 1 yard will need 1200 / 8400 = 1 / 7 lbs 3600 yards will need 1 / 7 * 3500 yards = 500 lbs c"
Answer: c
Problem: the lowest number which should be added to 11390 so that the sum is exactly divisible by 7 , 9 , 10 and 12 is :
Options: a ) 1010 , b ) 2210 , c ) 1250 , d ) 1210 , e ) 1110
Rationale: l . c . m . of 7 , 9 , 10 and 12 = 1260 . on dividing 11390 by 1260 , the remainder is 50 . number to be added = ( 1260 - 50 ) = 1210 . answer : option ' d '
Answer: d
Problem: a telephone company needs to create a set of 3 - digit area codes . the company is entitled to use only digits 2 , 4 and 3 , which can be repeated . if the product of the digits in the area code must be even , how many different codes can be created ?
Options: a ) 20 , b ) 26 , c ) 24 , d ) 22 , e ) 30
Rationale: "total # of codes possible is 3 * 3 * 3 = 27 . oit of those 27 codes only the product of 333 will be odd , the remaining 26 will have either 2 or 4 in them , which ensures that their product will be even . therefore the number of codes where the product of the digits is even = ( total ) - ( restriction ) = 27 - 1 = 26 . answer : b"
Answer: b
Problem: 120 students represent x percent of the boys at a school . if the boys at the school make up 30 % of the total school population of x students , what is x ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 200 , e ) 250
Rationale: "let b be the number of boys in the school . 120 = xb / 100 b = 0.3 x 12000 = 0.3 x ^ 2 x ^ 2 = 40000 x = 200 the answer is d ."
Answer: d
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has rs . 1400 left with him , find his expenditure on food and conveyance .
Options: a ) 1000 , b ) 2000 , c ) 3000 , d ) 4000 , e ) 5000
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) let the monthly salary be rs . x then , 7 / 40 of x = 1400 x = ( 1400 * 40 / 7 ) = 8600 expenditure on food = rs . ( 3 / 10 * 800 ) = rs . 2400 expenditure on conveyence = rs . ( 1 / 8 * 8000 ) = rs . 1000 answer is a ."
Answer: a
Problem: find the average of all prime numbers between 10 and 30 .
Options: a ) 30 , b ) 33.6 , c ) 39.8 , d ) 18.6 , e ) none
Rationale: "sol . there are six prime numbers between 10 and 30 . they are 11 , 13 , 17 , 19 , 23 , 29 â ˆ ´ required average = [ 11 + 13 + 17 + 19 + 23 + 29 / 6 ] = 112 / 6 = 18.6 answer d"
Answer: d
Problem: of the diplomats attending a summit conference , 17 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 17 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 150 . answer : e ."
Answer: e
Problem: in a recent election , geoff received 15 percent of the 6,000 votes cast . to win the election , a candidate needed to receive more than x % of the vote . if geoff needed exactly 3,571 more votes to win the election , what is the value of x ?
Options: a ) 74.5 , b ) 54 , c ) 56 , d ) 60 , e ) 63
Rationale: "word problems are tricky in somehow more than other problem because you have the additional step to translate . breaking the problem : geoff how many votes he receives ? ? 900 votes he needs 3571 more votes so : 900 + 3571 = 4471 now what ' s the problem wants ? ? a x % . . . . . . . . 4471 is what % of total votes 6000 . . . . . . . . translating : 4471 = x / 100 * 6000 - - - x = 74.5 % . . . . . . . . . . a"
Answer: a
Problem: in a can , there is a mixture of milk and water in the ratio 4 : 5 . if it is filled with an additional 6 litres of milk the can would be full and ratio of milk and water would become 6 : 5 . find the capacity of the can ?
Options: a ) 33 , b ) 44 , c ) 48 , d ) 52 , e ) none of these
Rationale: "let the capacity of the can be t litres . quantity of milk in the mixture before adding milk = 4 / 9 ( t - 6 ) after adding milk , quantity of milk in the mixture = 6 / 11 t . 6 t / 11 - 6 = 4 / 9 ( t - 6 ) 10 t = 594 - 264 = > t = 33 . answer : a"
Answer: a