regisss/math_qa huggingface dataset:
Problem: the ratio of money with ram and gopal is 7 : 17 and that with gopal and krishan is 7 : 17 . if ram has rs . 686 , krishan has ?
Options: a ) s . 2890 , b ) s . 4046 , c ) s . 1190 , d ) s . 1620 , e ) s . 2680
Rationale: "ram : gopal = 7 : 17 = 49 : 119 gopal : krishan = 7 : 17 = 119 : 289 ram : gopal : krishan = 49 : 119 : 289 ram : krishan = 49 : 289 thus , 49 : 289 = 686 : n & there n = 289 x 686 / 49 = rs . 4046 answer : b"
Answer: b
Problem: a no . when divided by 220 gives a remainder 43 , what remainder will be obtainedby dividingthe same no . 17 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 11 , e ) 15
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Problem: two stations a and b are 110 km apart on a straight line . one train starts from a at 8 a . m . and travels towards b at 20 kmph . another train starts from b at 8 a . m . and travels towards a at a speed of 25 kmph . at what time will they meet ?
Options: a ) 11 , b ) 10 , c ) 8 , d ) 12 , e ) 15
Rationale: "suppose they meet x hours after 8 a . m . distance covered by a in x hours = 20 x km . distance covered by b in ( x - 1 ) hours = 25 ( x - 1 ) km . therefore 20 x + 25 ( x - 1 ) = 110 45 x = 135 x = 3 . so , they meet at 11 a . m . answer : a"
Answer: a
Problem: it takes joey the postman 1 hours to run a 2 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 5 mile / hour , what is the speed with which joey returns ?
Options: a ) 10 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "let his speed for one half of the journey be 2 miles an hour let the other half be x miles an hour now , avg speed = 5 mile an hour 2 * 2 * x / 2 + x = 5 4 x = 5 x + 10 = > x = 10 a"
Answer: a
Problem: a contractor undertakes to do a job within 100 days and hires 10 people to do it . after 20 days , he realizes that one fourth of the work is done so he fires 2 people . in how many more days w will the work get over ?
Options: a ) 60 , b ) w = 70 , c ) w = 75 , d ) w = 80 , e ) w = 100
Rationale: "we can also use the concept of man - days here 100 days - - > 10 men so the job includes 100 * 10 = 1000 man - days after 20 days 1 / 4 of job is completed so 1 / 4 x 1000 man - days = 250 man - days job is done now the balance job = 1000 - 250 = 750 man - days worth of job since 2 men are fired so b / l men = 8 therefore total no . of days of job = 750 man - day / 8 days = 375 / 4 = 94 days ( approx . ) now since this is total and ques . is asking for additional no . of days , so 94 - 20 = 74 days the nearest approx . to answer is 75 ans : c ( 75 days )"
Answer: c
Problem: ravi can do a piece of work in 24 days while prakash can do it in 40 days . in how many days will they finish it together ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 10
Rationale: "1 / 24 + 1 / 40 = 1 / 15 15 days answer : a"
Answer: a
Problem: the tax on a commodity is diminished by 30 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 32 % , d ) 16 % , e ) 52 %
Rationale: 100 * 100 = 10000 70 * 120 = 8400 10000 - - - - - - - 1600 100 - - - - - - - ? = 16 % answer : d
Answer: d
Problem: when throwing 2 dices , and looking at the sum of numbers on the dices - what is the probability to have a sum which is smaller than 5 ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 1 / 2 , d ) 1 / 3 , e ) 32 / 36
Rationale: a dice is composed of 6 numbers - 12 , 34 , 56 . when trowing 2 dices - there are 36 options ( 6 x 6 = 36 ) . if we want the sum of two dices to be < 5 there are those options : ( 11 ) , ( 12 ) , ( 21 ) , ( 13 ) , ( 31 ) , ( 22 ) - total of 6 options . therefore - the probability to have a sum which is smaller than 5 is 6 / 36 = 1 / 6 . answer : b
Answer: b
Problem: a man is 24 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is :
Options: a ) 22 , b ) 28 , c ) 32 , d ) 48 , e ) 92
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 24 ) + 2 = 2 ( x + 2 ) x + 26 = 2 x + 4 = > x = 22 . answer is a ."
Answer: a
Problem: in a mixed college 160 students are there in one class . out of this 160 students 1 / 4 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: total number of students : 160 total girls : 160 * 1 / 4 = 40 total boys : 160 - 40 = 120 answer is d
Answer: d
Problem: a and b put in rs . 300 and rs . 500 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 200 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 15 : 16 , d ) 14 : 18 , e ) 39 : 41
Rationale: explanation : 3 : 5 a = 3 / 8 * 200 = 75 375 : 400 39 : 40 answer : c
Answer: c
Problem: if 42.18 = k ( 14 + m / 50 ) , where k and m are positive integers and m < 50 , then what is the value of k + m ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "42.18 = 14 k + km / 50 . . . we can rewrite the number as follows : 42 + 0.18 = 14 k + km / 50 . . . . . . . . since k is integer , then 42 = 14 k . . . . . . . . . . k = 3 0.18 = km / 50 . . . . . . 18 / 100 = 3 m / 50 . . . . . . m = 3 k + m = 3 + 3 = 6 answer : a"
Answer: a
Problem: it takes joey the postman 1 hours to run a 5 mile long route every day . he delivers packages and then returns to the post office along the same path . if the average speed of the round trip is 8 mile / hour , what is the speed with which joey returns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 20
Rationale: let his speed for one half of the journey be 5 miles an hour let the other half be x miles an hour now , avg speed = 8 mile an hour 2 * 5 * x / 5 + x = 8 10 x = 8 x + 40 = > 2 x = 40 = > x = 20 e
Answer: e
Problem: a ’ s speed is 20 / 16 times that of b . if a and b run a race , what part of the length of the race should a give b as a head start , so that the race ends in a dead heat ?
Options: a ) 1 / 17 , b ) 3 / 17 , c ) 1 / 10 , d ) 4 / 20 , e ) 3 / 10
Rationale: "we have the ratio of a ’ s speed and b ’ s speed . this means , we know how much distance a covers compared with b in the same time . this is what the beginning of the race will look like : ( start ) a _________ b ______________________________ if a covers 20 meters , b covers 16 meters in that time . so if the race is 20 meters long , when a reaches the finish line , b would be 4 meters behind him . if we want the race to end in a dead heat , we want b to be at the finish line too at the same time . this means b should get a head start of 4 meters so that he doesn ’ t need to cover that . in that case , the time required by a ( to cover 20 meters ) would be the same as the time required by b ( to cover 16 meters ) to reach the finish line . so b should get a head start of 4 / 20 th of the race . answer ( d )"
Answer: d
Problem: for any integer k > 1 , the term “ length of an integer ” refers to the number of positive prime factors , not necessarily distinct , whose product is equal to k . for example , if k = 24 , the length of k is equal to 4 , since 24 = 2 × 2 × 2 × 3 . if x and y are positive integers such that x > 1 , y > 1 , and x + 3 y < 980 , what is the maximum possible sum of the length of x and the length of y ?
Options: a ) 16 , b ) 14 , c ) 18 , d ) 10 , e ) 20
Rationale: "we know that : x > 1 , y > 1 , and x + 3 y < 980 , and it is given that length means no of factors . for any value of x and y , the max no of factors can be obtained only if factor is smallest no all factors are equal . hence , lets start with smallest no 2 . 2 ^ 1 = 2 2 ^ 2 = 4 2 ^ 3 = 8 2 ^ 4 = 16 2 ^ 5 = 32 2 ^ 6 = 64 2 ^ 7 = 128 2 ^ 8 = 256 2 ^ 9 = 512 2 ^ 10 = 1024 ( it exceeds 1000 , so , x ca n ' t be 2 ^ 10 ) so , max value that x can take is 2 ^ 9 , for which has length of integer is 9 . now , since x = 512 , x + 3 y < 980 so , 3 y < 468 = = > y < 156 so , y can take any value which is less than 162 . and to get the maximum no of factors of smallest integer , we can say y = 2 ^ 7 for 2 ^ 7 has length of integer is 7 . so , combined together : 9 + 7 = 16 . a"
Answer: a
Problem: how long will a boy take to run round a square field of side 55 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 88 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 55 * 4 = 220 m time taken = 220 * 2 / 5 = 88 sec answer is a"
Answer: a
Problem: a contractor undertook to do a piece of work in 15 days . he employed certain number of laboures but 5 of them were absent from the very first day and the rest could finish the work in only 20 days . find the number of men originally employed ?
Options: a ) 25 , b ) 20 , c ) 19 , d ) 23 , e ) 18
Rationale: "let the number of men originally employed be x . 15 x = 20 ( x â € “ 5 ) or x = 20 answer b"
Answer: b
Problem: the temperature of a certain cup of coffee 2 minutes after it was poured was 120 degrees fahrenheit . if the temperature f of the coffee t minutes after it was poured can be determined by the formula f = 120 * 2 ^ ( - at ) + 60 , where f is in degrees fahrenheit and a is a constant . then the temperature of the coffee 30 minutes after it was poured was how many degrees fahrenheit ?
Options: a ) 65 , b ) 60.003662 , c ) 80.2 , d ) 85 , e ) 90
Rationale: "first , we have to find a . we know that after t = 2 minutes the temperature f = 120 degrees . hence : 120 = 120 * ( 2 ^ - 2 a ) + 60 60 = 120 * ( 2 ^ - 2 a ) 60 / 120 = 2 ^ - 2 a 1 / 2 = 2 ^ - 2 a 2 ^ - 1 = 2 ^ - 2 a - 1 = - 2 a 1 / 2 = a now we need to find f after t = 30 minutes : f = 120 * ( 2 ^ - 1 / 2 * 30 ) + 60 f = 120 * ( 2 ^ - 15 ) + 60 f = 120 * ( 1 / 2 ^ 15 ) + 60 f = 120 * 1 / 32768 + 60 f = 0.003662 + 60 = 60.003662 answer b !"
Answer: b
Problem: 10 % of ( 50 % of $ 500 ) is ?
Options: a ) $ 15 , b ) $ 20 , c ) $ 25 , d ) $ 30 , e ) $ 22
Rationale: "10 % of ( 50 % of $ 500 ) = 10 / 100 ( 50 / 100 * 500 ) = $ 25 answer is c"
Answer: c
Problem: a chemical supply company has 60 liters of a 20 % hno 3 solution . how many liters of pure undiluted hno 3 must the chemists add so that the resultant solution is a 50 % solution ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 36
Rationale: "60 liters of a 20 % hno 3 solution means hno 3 = 12 liters in 60 liters of the solution . now , let x be the pure hno 3 added . as per question , 12 + x = 50 % of ( 60 + x ) or x = 36 . hence , e"
Answer: e
Problem: a can finish a piece of work in 5 days . b can do it in 25 days . they work together for four days and then a goes away . in how many days will b finish the work ?
Options: a ) 3 days , b ) 1 day , c ) 2 days , d ) 4 days , e ) 5 days
Rationale: "4 / 5 + ( 4 + x ) / 25 = 1 = > x = 1 day answer : b"
Answer: b
Problem: 4 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 5 women and 10 children take to complete the work ?
Options: a ) 4 days , b ) 6 days , c ) 7 days , d ) 9 days , e ) 1 days
Rationale: "1 women ' s 1 day work = 1 / 28 1 child ' s 1 day work = 1 / 140 ( 5 women + 10 children ) ' s 1 day work = ( 5 / 28 + 10 / 140 ) = 1 / 4 5 women and 10 children will complete the work in 4 days . answer : a"
Answer: a
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 13 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 2 , e ) 7
Rationale: "every prime number greater than 3 can be written 6 n + 1 or 6 n - 1 . if p = 6 n + 1 , then p ^ 2 + 13 = 36 n ^ 2 + 12 n + 1 + 13 = 36 n ^ 2 + 12 n + 12 + 2 if p = 6 n - 1 , then p ^ 2 + 13 = 36 n ^ 2 - 12 n + 1 + 13 = 36 n ^ 2 - 12 n + 12 + 2 when divided by 12 , it must leave a remainder of 2 . the answer is d ."
Answer: d
Problem: yesterday ' s closing prices of 2,640 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,440
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2640 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) ( 2 ) to get h = 1440 . e is my answer ."
Answer: e
Problem: a bag consists of 20 marbles , of which 6 are blue , 9 are red , and the remainder are white . if lisa is to select a marble from the bag at random , what is the probability that the marble will be red or white ?
Options: a ) 7 / 10 , b ) 2 / 4 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
Rationale: "bag consists of 20 marbles , of which 6 are blue , 9 are red remainder are white . so , white = 20 - 6 - 9 = 5 . probability that the marble will be red or white = probability that the marble will be red + probability that the marble will be white probability that the marble will be red or white = 9 / 20 + 5 / 20 = 14 / 20 = 7 / 10 hence , answer will be a ."
Answer: a
Problem: suppose 12 monkeys take 12 minutes to eat 12 bananas . how many monkeys would it take to eat 72 bananas in 72 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "one monkey takes 12 min to eat 1 banana , so in 72 mins 1 monkey will eat 6 bananas , so for 72 bananas in 72 min we need 72 / 6 = 12 monkeys answer : d"
Answer: d
Problem: a farmer with 1,350 acres of land had planted his fields with corn , sugar cane , and tobacco in the ratio of 5 : 2 : 2 , respectively , but he wanted to make more money , so he shifted the ratio to 2 : 2 : 5 , respectively . how many more acres of land were planted with tobacco under the new system ?
Options: a ) 90 , b ) 150 , c ) 270 , d ) 300 , e ) 450
Rationale: originally ( 2 / 9 ) * 1350 = 300 acres were planted with tobacco . in the new system ( 5 / 9 ) * 1350 = 750 acres were planted with tobacco . thus 750 - 300 = 450 more acres were planted with tobacco . the answer is e .
Answer: e
Problem: the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of charlie 9 years from now ?
Options: a ) 44 , b ) 52 , c ) 57 , d ) 65 , e ) 80
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of charlie = 7 * 5 = 35 charlie ' s age 9 years hence = 35 + 9 = 44 answer = a"
Answer: a
Problem: the radius of a semi circle is 6.4 cm then its perimeter is ?
Options: a ) 32.9
b ) 32.4
c ) 22.4
d ) 32.8
e ) 32.1
Rationale: 36 / 7 r = 6.4 = 32.9 answer : a
Answer: a
Problem: the grade point average of the entire class is 87 . if the average of one third of the class is 95 , what is the average of the rest of the class ?
Options: a ) 81 , b ) 82 , c ) 83 , d ) 84 , e ) 85
Rationale: "let x be the number of students in the class . let p be the average of the rest of the class . 87 x = ( 1 / 3 ) 95 x + ( 2 / 3 ) ( p ) x 261 = 95 + 2 p 2 p = 166 p = 83 . the answer is c ."
Answer: c
Problem: an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 30 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 300 cm
Rationale: "we have 30 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 15 and continues . so we have 30,15 , 7.5 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 30 / 1 - ( 1 / 2 ) = 60 equilateral triangle perimeter is 3 a = 3 * 60 = 180 . so option a ."
Answer: a
Problem: john and amanda stand at opposite ends of a straight road and start running towards each other at the same moment . their rates are randomly selected in advance so that john runs at a constant rate of 2 , 3 , 4 , 5 , or 6 miles per hour and amanda runs at a constant rate of 3 , 4 , 5 , 6 , or 7 miles per hour . what is the probability that john has traveled farther than amanda by the time they meet ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 25 , e ) 6 / 25
Rationale: "john will run farther if he runs at 6 mph and amanda runs at 5 mph , 4 mph , or 3 mph . in this case , p ( john runs farther ) = 1 / 5 * 3 / 5 = 3 / 25 john will run farther if he runs at 5 mph and amanda runs at 4 mph or 3 mph . in this case , p ( john runs farther ) = 1 / 5 * 2 / 5 = 2 / 25 john will run farther if he runs at 4 mph and amanda runs at 3 mph . in this case , p ( john runs farther ) = 1 / 5 * 1 / 5 = 1 / 25 overall , p ( john runs farther ) = 3 / 25 + 2 / 25 + 1 / 25 = 6 / 25 the answer is e ."
Answer: e
Problem: the sum of four consecutive even numbers is 292 . what would be the largest number ?
Options: a ) 33 , b ) 88 , c ) 76 , d ) 123 , e ) 12
Rationale: "let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 292 = > x = 37 smallest number is : 2 ( x + 1 ) = 76 . answer : c"
Answer: c
Problem: on dividing 127 by a number , the quotient is 5 and the remainder is 2 . find the divisor .
Options: a ) 25 , b ) 30 , c ) 35 , d ) 40 , e ) 45
Rationale: "d = ( d - r ) / q = ( 127 - 2 ) / 5 = 125 / 5 = 25 a"
Answer: a
Problem: two pipes a and b can separately fill a cistern in 80 minutes and 160 minutes respectively . there is a third pipe in the bottom of the cistern to empty it . if all the three pipes are simultaneously opened , then the cistern is full in 40 minutes . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 90 min , b ) 160 min , c ) 110 min , d ) 120 min , e ) 130 min
Rationale: "1 / 40 - ( 1 / 80 + 1 / 160 ) = - 1 / 160 third pipe can empty in 160 minutes answer : b"
Answer: b
Problem: if 15 students in a class average 70 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 %
Rationale: "( 15 * 70 + 10 * 95 ) / 25 = 80 % the answer is d ."
Answer: d
Problem: a reduction of 30 % in the price of oil enables a house wife to obtain 9 kgs more for rs . 1800 , what is the reduced price for kg ?
Options: a ) rs . 55 , b ) rs . 60 , c ) rs . 65 , d ) rs . 70 , e ) rs . 75
Rationale: "explanation : 1800 * ( 30 / 100 ) = 540 - - - - 9 ? - - - - 1 = > rs . 60 answer : b"
Answer: b
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 273 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 182 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 273 + l ) / 20 = l / 8 2184 + 8 l = 20 l l = 2184 / 12 = 182 m answer a"
Answer: a
Problem: a certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $ 130000 and variables costs averaging $ 10 per item . if the manufacturer ’ s selling price per item is $ 15 , how many items the manufacturer produce and sell to earn an annual profit of $ 150000 ?
Options: a ) 2,858 , b ) 18,667 , c ) 21,429 , d ) 35,000 , e ) 56,000
Rationale: let the items manufactured or sold bex 130000 + 10 x = 15 x - 150000 5 x = 280000 x = 56000 ans : e
Answer: e
Problem: robert is travelling on his cycle and has calculated to reach point a at 2 p . m . if he travels at 10 km / hr ; he will reach there at 12 noon if he travels at 15 km / hr . at what speed must he travel to reach a at 1 p . m . ?
Options: a ) 17 kmph , b ) 19 kmph , c ) 15 kmph , d ) 12 kmph , e ) 16 kmph
Rationale: d 12 kmph let the distance traveled be x km . then , x / 10 - x / 15 = 2 3 x - 2 x = 60 = > x = 60 km . time taken to travel 60 km at 10 km / hr = 60 / 10 = 6 hrs . so , robert started 6 hours before 2 . p . m . i . e . , at 8 a . m . required speed = 60 / 5 = 12 kmph .
Answer: d
Problem: seed mixture x is 40 percent ryegrass and 60 percent bluegrass by weight ; seed mixture y is 25 percent ryegrass and 75 percent fescue . if a mixture of x and y contains 32 percent ryegrass , what percent of the weight of this mixture is x ?
Options: a ) 10 % , b ) 33.33 % , c ) 46.66 % , d ) 50 % , e ) 66.66 %
Rationale: "- - - - - - - - - - - - - - - - > ryegrass x - - - - - - - - - - - - - - > 40 % y - - - - - - - - - - - - - - > 25 % m ( mixture ) - - - - > 32 % 0.4 x + ( m - x ) 0.25 = 0.32 m 0.15 x = 0.07 m x = 0.4666 m x = 46.66 % of m c"
Answer: c
Problem: during 2003 , a company produced an average of 2000 products per month . how many products will the company need to produce from 2004 through 2007 in order to increase its monthly average for the period from 2003 through 2007 by 150 % over its 2003 average ?
Options: a ) 287,000 , b ) 290,000 , c ) 284,000 , d ) 285,000 , e ) 286,000
Rationale: company produced 12 * 2000 = 24,000 products in 2003 . if company produces x products from 2004 to 2007 , then total amount of product produced in 4 years ( 2003 through 2007 ) is x + 24,000 . the gives the average of ( x + 24,000 ) / 4 . this average needs to be 300 % higher than that in 2003 . in math terms , 36,000 + 150 % ( 36,000 ) = 80,000 . so : ( x + 36,000 ) / 4 = 80,000 x + 36,000 = 320,000 x = 284,000 the answer is c .
Answer: c
Problem: in how many ways can a 5 - letter password be chosen , using the letters a , b , c , d , e , f , g , and / or h such that at least one letter is repeated within the password ?
Options: a ) 720 , b ) 864 , c ) 900 , d ) 936 , e ) 26048
Rationale: total number of four letter passwords = 8 * 8 * 8 * 8 * 8 = 32768 - - - - - - ( 1 ) total number of passwords in which no letter repeats = 8 c 5 * 5 ! = 56 * 120 = 6720 - - - - - - ( 2 ) therefore required value = ( 1 ) - ( 2 ) = 32768 - 6720 = 26048 e
Answer: e
Problem: how many seconds will a 700 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 42 , d ) 45 , e ) 50
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 700 * 3 / 50 = 42 sec answer : c"
Answer: c
Problem: a man walking at a constant rate of 5 miles per hour is passed by a woman traveling in the same direction along the same path at a constant rate of 15 miles per hour . the woman stops to wait for the man 2 minutes after passing him , while the man continues to walk at his constant rate . how many minutes must the woman wait until the man catches up ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: "when the woman passes the man , they are aligned ( m and w ) . they are moving in the same direction . after 5 minutes , the woman ( w ) will be ahead the man ( m ) : m - - - - - - m - - - - - - - - - - - - - - - w w in the 5 minutes , after passing the man , the woman walks the distance mw = ww , which is 2 * 15 / 60 = 1 / 2 miles and the man walks the distance mm , which is 2 * 5 / 60 = 1 / 6 mile . the difference of 1 / 2 - 1 / 6 = 1 / 3 miles ( mw ) will be covered by the man in ( 1 / 3 ) / 5 = 1 / 15 of an hour , which is 4 minutes . answer e ."
Answer: e
Problem: a certain galaxy is known to comprise approximately 2 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 4,000 , e ) 80,000
Rationale: total no . of stars on galaxy = 2 * 10 ^ 11 of every 50 million stars , 1 is larger than sun . 1 million = 10 ^ 6 therofore , 50 million = 50 * 10 ^ 6 total no . of stars larger than sun = 2 * 10 ^ 11 / 50 * 10 ^ 6 = 20 * 10 ^ 3 / 5 = 4000 therefore answer is d
Answer: d
Problem: a side of beef lost 35 percent of its weight in processing . if the side of beef weighed 550 pounds after processing , how many pounds did it weigh before processing ?
Options: a ) 191 , b ) 355 , c ) 737 , d ) 846 , e ) 1,560
Rationale: "let weight of side of beef before processing = x ( 65 / 100 ) * x = 550 = > x = ( 550 * 100 ) / 65 = 846 answer d"
Answer: d
Problem: right triangle abc is to be drawn in the xy - plane so that the right angle is at a and ab is parallel to the y - axis . if the x - and y - coordinates of a , b , and c are to be integers that are consistent with the inequalities - 5 ≤ x ≤ 2 and 4 ≤ y ≤ 9 , then how many different triangles can be drawn that will meet these conditions ?
Options: a ) 54 , b ) 1440 , c ) 2,160 , d ) 2,916 , e ) 148,824
Rationale: "we have the rectangle with dimensions 9 * 5 ( 9 horizontal dots and 5 vertical ) . ab is parallel to y - axis and ac is parallel to x - axis . choose the ( x , y ) coordinates for vertex a : 9 c 1 * 5 c 1 ; choose the x coordinate for vertex c ( as y coordinate is fixed by a ) : 8 c 1 , ( 9 - 1 = 8 as 1 horizontal dot is already occupied by a ) ; choose the y coordinate for vertex b ( as x coordinate is fixed by a ) : 4 c 1 , ( 5 - 1 = 4 as 1 vertical dot is already occupied by a ) . 9 c 1 * 5 c * 8 c 1 * 4 c 1 = 1440 . answer : b ."
Answer: b
Problem: one half of a two digit number exceeds its one third by 5 . what is the sum of the digits of the number ?
Options: a ) a ) 3 , b ) b ) 5 , c ) c ) 7 , d ) d ) 9 , e ) e ) 11
Rationale: "x / 2 – x / 3 = 5 = > x = 30 3 + 0 = 3 answer : a"
Answer: a
Problem: the triplicate ratio of 1 : 8 is ?
Options: a ) 1 : 0 , b ) 1 : 8 , c ) 1 : 7 , d ) 1 : 512 , e ) 1 : 1
Rationale: "13 : 83 = 1 : 512 answer : d"
Answer: d
Problem: a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches . what is the area of the white paper , in square inches ?
Options: a ) 96
b ) 196
c ) 128
d ) 144
e ) 168
Rationale: this question is an example of a ' punch out ' question - we have to find the area of everything , then ' punch out ' the part that we do n ' t want . we ' re told that a white paper 2 inches wide is placed around a rectangular black paper with dimensions 8 inches by 12 inches . we ' re asked for the area of the frame , in square inches . area of a rectangle = ( length ) ( width ) so the area of the black paper is . . . ( 8 ) ( 12 ) = 96 the white paper ' adds ' 2 inches to the top , bottom , left and right ' sides ' of the picture , so the area of everything is . . . ( 8 + 2 + 2 ) ( 12 + 2 + 2 ) = ( 12 ) ( 16 ) = 196 when we ' punch out ' the area of the black paper , we ' ll be left with the area of the white paper : 192 - 96 = 96 final answer : b
Answer: b
Problem: find the greatest number which on dividing 4351 and 5161 , leaves a reminder of 8 and 10 respectively
Options: a ) 125 , b ) 111 , c ) 129 , d ) 101 , e ) 141
Rationale: "explanation : in this type of question , its obvious we need to calculate the hcf , trick is hcf of ( 4351 - 8 ) and ( 5161 - 10 ) = hcf ( 4343 , 5151 ) = 101 option d"
Answer: d
Problem: the difference of two numbers is 1340 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 265 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: "let the smaller number be x . then larger number = ( x + 1340 ) . x + 1340 = 6 x + 15 5 x = 1325 x = 265 smaller number = 265 . a )"
Answer: a
Problem: a jar contains only red , yellow , and orange marbles . if there are 1 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: "i started by finding the 2 probabilities , without calculation , like this : p ( yyr ) p ( yry ) p ( ryy ) i calculated the first one and ended in 1 / 22 . i looked at the answer choices at this point and saw answer d : 1 / 45 . this helped me realise that for the 3 possible orderings the probabbility is the same . so , it should be ( 1 / 45 ) * ( 1 ) , which indeed is 1 / 45 . b"
Answer: b
Problem: a scale 6 ft . 8 inches long is divided into 4 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 97 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 6 * 12 ) + 8 = 80 inches length of each of the 4 parts = 80 / 4 = 20 inches answer : a"
Answer: a
Problem: if w is the set of all the integers between 59 and 99 , inclusive , that are either multiples of 3 or multiples of 2 or multiples of both , then w contains how many numbers ?
Options: a ) 27 , b ) 32 , c ) 33 , d ) 34 , e ) 35
Rationale: multiples of 2 from 59 to 99 = multiples of 2 from 1 to 99 - multiples of 2 from 1 to 58 = [ 99 / 2 ] - [ 58 / 2 ] = 49 - 29 = 20 multiples of 3 from 59 to 99 = multiples of 3 from 1 to 99 - multiples of 3 from 1 to 58 = [ 99 / 3 ] - [ 58 / 3 ] = 33 - 169 = 14 multiples of 2 and 3 bothi . e . 6 from 59 to 99 = multiples of 6 from 1 to 99 - multiples of 6 from 1 to 58 = [ 99 / 6 ] - [ 58 / 6 ] = 16 - 9 = 7 these 8 numbers have been counted twice in both the above calculation while calculating multiples of 2 and 3 i . e . total numbers in w = 20 + 14 - 7 = 27 answer option a
Answer: a
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 4 x + 2 = 0 ?
Options: a ) 8 , b ) 10 , c ) 2 , d ) 16 , e ) 24
Rationale: "a / b + b / a = ( a 2 + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab ] / ab a + b = - 4 / 1 = - 4 ab = 2 / 1 = 2 hence a / b + b / a = [ ( - 4 ) 2 - 2 ( 2 ) ] / 2 = 4 / 2 = 2 . c )"
Answer: c
Problem: what least no . must be subtracted from 50248 so that remaining no . is divisible by 20 ?
Options: a ) 3 , b ) 2 , c ) 4 , d ) 8 , e ) 6
Rationale: "explanation : on dividing 50248 by 20 we get the remainder 8 , so 8 should be subtracted option d"
Answer: d
Problem: find the area of a parallelogram with base 32 cm and height 15 cm .
Options: a ) 200 , b ) 384 , c ) 345 , d ) 480 , e ) 242
Rationale: "area of a parallelogram = base * height = 32 * 15 = 480 cm 2 answer : option d"
Answer: d
Problem: a clock shows the time as 10 a . m . if the minute hand gains 5 minutes every hour , how many minutes will the clock gain by 4 p . m . ?
Options: a ) 30 min , b ) 35 min , c ) 45 min , d ) 50 min , e ) 55 min
Rationale: "there are 6 hours in between 10 a . m . to 4 p . m . 6 * 5 = 30 minutes . answer : a"
Answer: a
Problem: a space shuttle orbits the earth at about 6 kilometers per second . this speed is equal to how many kilometers per hour ?
Options: a ) 480 , b ) 2,880 , c ) 21,600 , d ) 28,800 , e ) 48,000
Rationale: seconds in 1 hours : 60 s in 1 min 60 min in 1 hr 60 * 60 = 3600 sec in 1 hr 6 * 3600 = 21,600 answer : c
Answer: c
Problem: a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose there own dress ?
Options: a ) 1 / 3 , b ) 2 / 3 , c ) 1 / 2 , d ) 3 / 4 , e ) 3 / 7
Rationale: explanation : let 1 st girl come and she choose wrong dress so probability of that girl to choose wrong dress out of 3 is = 2 / 3 . now 2 nd girl come nd she choose wrong dress so probability of that girl to choose wrong dress out of 2 is 1 / 2 . now for 3 rd girl probability is 1 to choose wrong dress . so probability tht all the 3 wil not choose der own dress is = 2 / 3 * 1 / 2 * 1 = 1 / 3 . hence ( a ) is the correct answer . answer : a
Answer: a
Problem: a man has some hens and cows . if the number of heads be 48 and the number of feet equals 144 , then the number of hens will be :
Options: a ) 22 , b ) 23 , c ) 24 , d ) 26 , e ) 28
Rationale: "let hens be x and cows be y now , feet : x * 2 + y * 4 = 144 heads : x * 1 + y * 1 = 48 implies , 2 x + 4 y = 144 and x + y = 48 solving these two equations , we get x = 24 and y = 24 therefore , hens are 26 . answer : c"
Answer: c
Problem: a batsman in his 10 th innings makes a score of 60 , and thereby increases his average by 3 . what is his average after the 10 th innings ? he had never been ’ not out ’ .
Options: a ) 47 , b ) 37 , c ) 39 , d ) 43 , e ) 33
Rationale: "average score before 10 th innings = 60 - 3 × 10 = 30 average score after 10 th innings = > 30 + 3 = 33 answer : e"
Answer: e
Problem: the radius of a cylinder is 10 m , height 14 m . the volume of the cylinder is :
Options: a ) 2200 , b ) 5500 , c ) 3300 , d ) 1100 , e ) 4400
Rationale: "cylinder volume = π r ( power 2 ) h = 22 / 7 × 10 × 10 × 14 = 4400 m ( power 3 ) answer is e ."
Answer: e
Problem: at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 30 % on the cost price ?
Options: a ) 62.5 , b ) 62.3 , c ) 65 , d ) 62.2 , e ) 62.9
Rationale: "cp = 47.50 sp = 47.50 * ( 130 / 100 ) = 61.75 mp * ( 95 / 100 ) = 61.75 mp = 65 answer : c"
Answer: c
Problem: income and expenditure of a person are in the ratio 5 : 3 . if the income of the person is rs . 10000 , then find his savings ?
Options: a ) rs . 4000 , b ) rs . 3603 , c ) rs . 3639 , d ) rs . 3632 , e ) rs . 3602
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 3 x respectively . income , 5 x = 10000 = > x = 2000 savings = income - expenditure = 5 x - 3 x = 2 x so , savings = rs . 2 * 2000 = rs . 4000 answer : a"
Answer: a
Problem: in a triangle , one side is 6 cm and another side is 8 cm . which of the following can be the perimeter of the triangle ?
Options: a ) 22 .
b ) 25 .
c ) 30 .
d ) 32 .
e ) 34 .
Rationale: given : one side is 6 cm and another side is 8 cm . so the 3 rd side will be > 3 and < 15 . thus the perimeter will be : 18 < perimeter < 30 . only option satisfying this condition is 22 . hence a .
Answer: a
Problem: in 50 l can , milk and water in the ratio of 3 : 1 . if the ratio has made 1 : 3 then the quantity of water that has to be added further is ?
Options: a ) 100 , b ) 120 , c ) 90 , d ) 80 , e ) 70
Rationale: 100 litre water is to be added . let ' x ' liter water is to be added more . then 1 / 3 = 37.5 / ( 12.5 + x ) x = 100 answer : a
Answer: a
Problem: find the sum of all 4 digit numbers formed using digits 1,2 , 5,6 .
Options: a ) 93324 , b ) 92324 , c ) 93424 , d ) 93424 , e ) 93824
Rationale: "( n - 1 ) ! * ( 111 . . . n ) * ( sum of the digits ) = ( 4 - 1 ) ! * 1111 * ( 1 + 2 + 5 + 6 ) = 93324 answer : a"
Answer: a
Problem: 8.036 divided by 0.04 gives :
Options: a ) 200.9 , b ) 2.06 , c ) 20.06 , d ) 100.9 , e ) 200.6
Rationale: "= 8.036 / 0.04 = 803.6 / 4 = 200.9 answer is a ."
Answer: a
Problem: the simple interest on rs . 20 for 6 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 1.4 , c ) 6 , d ) 7 , e ) none
Rationale: "sol . s . i . = rs . [ 20 * 5 / 100 * 6 ] = rs . 6 answer c"
Answer: c
Problem: tom has travelling to 7 cities . gasoline prices varied from city to city . what is the median gasoline price ?
Options: a ) $ 1 , b ) $ 1.84 , c ) $ 1.98 , d ) $ 2.34 , e ) $ 2.56
Rationale: ordering the data from least to greatest , we get : $ 1.61 , $ 1.75 , $ 1.79 , $ 1.84 , $ 1.96 , $ 2.09 , $ 2.11 the median gasoline price is $ 1.84 . ( there were 3 states with higher gasoline prices and 3 with lower prices . ) b
Answer: b
Problem: if n is an integer and 102 n ^ 2 is less than or equal to 8100 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "102 * n ^ 2 < = 8100 n ^ 2 < = 8100 / 102 which will be less than 81 since 8100 / 100 = 81 which is the square of 9 next closest value of n where n ^ 2 < = 81 is 8 ans b"
Answer: b
Problem: 4 mat - weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 12 mat - weavers in 12 days ?
Options: a ) 25 , b ) 19 , c ) 39 , d ) 61 , e ) 36
Rationale: "let the required number of bottles be x . more weavers , more mats ( direct proportion ) more days , more mats ( direct proportion ) wavers 4 : 12 : : 4 : x days 4 : 12 4 * 4 * x = 12 * 12 * 4 x = ( 12 * 12 * 4 ) / ( 4 x 4 ) x = 36 . answer is e ."
Answer: e
Problem: if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 6 people to do 6 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 6 , e ) 9
Rationale: "3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 6 people can do 6 / 3 of the work in one day . 6 people can do 6 times the work in 3 days . the answer is c ."
Answer: c
Problem: if 4 xz + yw = 7 and xw + yz = 14 , what is the value of the expression ( 2 x + y ) ( 2 z + w ) ?
Options: a ) 9 . , b ) 12 . , c ) 35 . , d ) 16 . , e ) 18 .
Rationale: "( 2 x + y ) * ( 2 z + w ) = 7 + 2 ( 14 ) = 35 answer : c"
Answer: c
Problem: a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 120 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 2 hours to travel 240 km , so c leaves 6 hours after a . the answer is c ."
Answer: c
Problem: a river 3 m deep and 55 m wide is flowing at the rate of 1 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 2338.9 , b ) 2748.9 , c ) 2148.9 , d ) 2745.9 , e ) 2718.9
Rationale: "rate of water flow - 1 kmph - - 1000 / 60 - - 16.66 m / min depth of river - - 3 m width of river - - 55 m vol of water per min - - 16.66 * 3 * 55 - - - 2748.9 answer b"
Answer: b
Problem: in x - y plane , there is a right triangle abc ( ∠ b = 90 o ) . if the length of ac is 100 and the slope of line segment ac is 4 / 3 , what is the length of ab ?
Options: a ) 12 , b ) 18 , c ) 24 , d ) 28 , e ) 80
Rationale: slope = change in vertical direction / change in horizontal direction = 4 / 3 change in vertical direction = 4 x = ab change in horizontal direction = 3 x = bc ab ^ 2 + bc ^ 2 = 100 ^ 2 16 x ^ 2 + 9 x ^ 2 = 10000 25 x ^ 2 = 400 x ^ 2 = 400 x = 20 therefore ab = 20 * 4 = 80 answer : e
Answer: e
Problem: what is the remainder when 14,451 × 15,651 × 16,788 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 3 , e ) 5
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 5 . hence , 1 * 1 * 8 = will give units digit as 8 so , whatever be the number , if it ends in 8 , the remainder after dividing with 5 will be 3 . optiond"
Answer: d
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 850 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 17 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "850 - - - 150 100 - - - ? = > 17.64 % answer : b"
Answer: b
Problem: a bag contains 7 red , 9 blue and 5 green balls . if 3 balls are picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 5 / 26 , d ) 1 / 38 , e ) 5 / 32
Rationale: "p ( both are red ) , = 7 c 3 / 21 c 3 = ( 7 * 6 * 5 ) / 21 * 20 * 19 = 1 / 38 d"
Answer: d
Problem: 40 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 13.2 , b ) 17.5 , c ) 12.8 , d ) 34.25 , e ) 31.25
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 40 = 17.5 answer : b"
Answer: b
Problem: hammers and wrenches are manufactured at a uniform weight per hammer and a uniform weight per wrench . if the total weight of two hammers and three wrenches is one - third that of 8 hammers and 4 wrenches , then the total weight of one wrench is how many times that of one hammer ?
Options: a ) 1 / 2 , b ) 2 / 5 , c ) 1 , d ) 3 / 2 , e ) 2
Rationale: "x b é the weight of a hammer and y be the weight of a wrench . ( 2 x + 3 y ) = 1 / 3 * ( 8 x + 4 y ) 3 ( 2 x + 3 y ) = ( 8 x + 4 y ) 6 x + 9 y = 8 x + 4 y 5 y = 2 x y = 2 x / 5 ans - b"
Answer: b
Problem: a man can row at 5 kmph in still water . if the velocity of the current is 1 kmph and it takes him 1 hour to row to a place and come back . how far is that place .
Options: a ) . 4 km , b ) 1.4 km , c ) 2.4 km , d ) 3.4 km , e ) none of these
Rationale: "explanation : let the distance is x km rate downstream = 5 + 1 = 6 kmph rate upstream = 5 - 1 = 4 kmph then x / 6 + x / 4 = 1 [ because distance / speed = time ] = > 2 x + 3 x = 12 = > x = 12 / 5 = 2.4 km option c"
Answer: c
Problem: in a certain school , the ratio of boys to girls is 5 to 13 . if there are 80 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 50 , e ) 117
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 80 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 80 . so 1 part corresponds to 80 / 8 = 10 and so 5 parts correspond to 5 * 10 = 50 . d"
Answer: d
Problem: a reduction in the price of petrol by 10 % enables a motorist to buy 5 gallons more for $ 300 . find the original price of petrol ?
Options: a ) $ 11 , b ) $ 5 , c ) $ 45 , d ) $ 400 , e ) $ 6.6
Rationale: "price decreased by 10 % , so 9 / 10 times , which means that original gallons bought increased 10 / 9 times . since this increase equals to 5 gallons then 45 gallons were bought originally ( 45 * 10 / 9 = 50 - - > increase 5 gallons ) . hence original price was 300 / 45 = $ 6.6 answer : e ."
Answer: e
Problem: it costs a publishing company 50000 dollars to make books . the 50000 is a fixed cost or a cost that can not change . to help the publishing company sell the books , a marketing company charges 4 dollars for each book sold . if the company charges 9 dollars per book , how many books should they sell to break even ?
Options: a ) 100 , b ) 1000 , c ) 10000 , d ) 100000 , e ) none
Rationale: let c be the cost of producing and selling x books let r be the revenue made for selling x books r = selling price of 1 book × number of books sold r = 9 x c = fixed cost + variable cost variable cost = fee charged for 1 book × number of books sold variable cost = 4 x c = 50000 + 4 x r = c 9 x = 50000 + 4 x 9 x - 4 x = 50000 + 4 x - 4 x 5 x = 50000 x = 10000 since 5 × 10000 = 50000 the break even point is to sell 10000 books . answer c
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 68 % of the distribution lies one standard deviation s of the mean , what percent of the distribution is less than m + s ?
Options: a ) 16 % , b ) 32 % , c ) 48 % , d ) 84 % , e ) 92 %
Rationale: "16 % ________________________________________________ m + s 34 % ________________________________________________ m 34 % ________________________________________________ m - s 16 % since 68 % lies one standard deviation from mean m , = > 50 % of 68 % lies on either side as it is symmetric about m . thus 16 % lie below m - s and 16 % lie above m + s now below m + s = 16 + 34 + 34 = 84 % hence d"
Answer: d
Problem: sam invested rs . 6000 @ 10 % per annum for one year . if the interest is compounded half - yearly , then the amount received by sam at the end of the year will be ?
Options: a ) 5300.0 , b ) 24580.0 , c ) 16537.5 , d ) 7120.0 , e ) 6615.0
Rationale: p = rs . 6000 ; r = 10 % p . a . = 5 % per half - year ; t = 1 year = 2 half - year amount = [ 6000 * ( 1 + 5 / 100 ) 2 ] = ( 6000 * 21 / 20 * 21 / 20 ) = rs . 6615.00 answer : e
Answer: e
Problem: 30 men can do a work in 40 days . when should 20 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 22 days , b ) 10 days , c ) 77 days , d ) 88 days , e ) 55 days
Rationale: "total work to be done = 30 * 40 = 1200 let 20 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 20 * 40 ) = 1200 40 p = 400 = > p = 10 days answer : b"
Answer: b
Problem: find the area of the quadrilateral of one of its diagonals is 50 cm and its off sets 10 cm and 8 cm ?
Options: a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 450 cm 2 , e ) 187 cm 2
Rationale: "1 / 2 * 50 ( 10 + 8 ) = 450 cm 2 answer : d"
Answer: d
Problem: for any real number x , the operatoris defined as : ( x ) = x ( 2 − x ) if p + 1 = ( p + 1 ) , then p =
Options: a ) - 2 , b ) 0 , c ) 1 , d ) 2 , e ) 3
Rationale: ( x ) = x ( 2 − x ) ( p + 1 ) = ( p + 1 ) ( 2 - p - 1 ) = ( 1 - p ) ( p + 1 ) we are given that p + 1 = ( p + 1 ) therefore ( 1 - p ) ( p + 1 ) = ( p + 1 ) or ( p + 1 ) + ( p - 1 ) ( p + 1 ) = 0 ( p + 1 ) ( p - 1 ) = 0 p = - 1 , p = 1 option c
Answer: c
Problem: sachin borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends money to rahul at 25 / 4 % p . a . for 2 years . find the gain of one year by sachin .
Options: a ) 110.5 , b ) 111.5 , c ) 112.5 , d ) 113.5 , e ) none of these
Rationale: explanation : two things need to give attention in this question , first we need to calculate gain for 1 year only . gain in 2 year = [ ( 5000 × 254 × 2100 ) − ( 5000 × 4 × 2100 ) ] = ( 625 − 400 ) = 225 so gain for 1 year = 2252 = 112.50 answer : c
Answer: c
Problem: this year , mbb consulting fired 8 % of its employees and left remaining employee salaries unchanged . sally , a first - year post - mba consultant , noticed that that the average ( arithmetic mean ) of employee salaries at mbb was 10 % more after the employee headcount reduction than before . the total salary pool allocated to employees after headcount reduction is what percent of that before the headcount reduction ?
Options: a ) 98.5 % , b ) 101.2 % , c ) 102.8 % , d ) 104.5 % , e ) 105.0 %
Rationale: "100 employees getting 1000 $ avg , so total salary for 100 ppl = 100000 8 % reduction in employees lead to 92 employees and a salary increase of 10 % of previous avg salary thus the new avg salary is = 10 % ( 1000 ) + 1000 = 1100 so total salary of 92 employees is 92 * 1100 = 101200 now the new salary is more than previous salary by x % . x = ( 101200 / 100000 ) * 100 = 101.2 % so the answer is b"
Answer: b
Problem: on average , the bottle - nosed dolphin comes up for air once every 3 minutes ; the beluga whale , a close relative , comes up for air on average once every 6 minutes . the number of times a bottle - nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period ?
Options: a ) 25 % , b ) 50 % , c ) 75 % , d ) 100 % , e ) 150 %
Rationale: dolphin once in 3 min ; beluga once in 6 min ; so , dolphin comes up 2 times frequently than beluga , which is 150 % ( 6 - 3 ) / 2 * 100 . answer : e .
Answer: e
Problem: the circumference of a circle is equal to 72 pi . find the radius of this circle .
Options: a ) 35
b ) 36
c ) 37
d ) 38
e ) 39
Rationale: the circumference of a circle is given by c = 2 pi r , where r is the radius of the circle . substitute c by 72 pi to obtain the equation 72 pi = 2 pi r simplify and solve for r to obtain r = 36 answer b
Answer: b
Problem: the average of 25 results is 50 . the average of first 12 of those is 14 and the average of last 12 is 17 . what is the 13 th result ?
Options: a ) 741 , b ) 752 , c ) 878 , d ) 785 , e ) 458
Rationale: "solution : sum of 1 st 12 results = 12 * 14 sum of last 12 results = 12 * 17 13 th result = x ( let ) now , 12 * 14 + 12 * 17 + x = 25 * 50 or , x = 878 . answer : option c"
Answer: c
Problem: two trains each 475 m long are running in opposite directions on parallel tracks . their speeds are 55 km / hr and 40 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 77 sec , b ) 66 sec , c ) 48 sec , d ) 36 sec , e ) 45 sec
Rationale: relative speed = 55 + 40 = 95 km / hr . 95 * 5 / 18 = 475 / 18 m / sec . distance covered = 475 + 475 = 950 m . required time = 950 * 18 / 475 = 36 sec . answer : d
Answer: d
Problem: mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65
Rationale: "if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d"
Answer: d