regisss/math_qa huggingface dataset:
Problem: the average of the marks of 12 students in a class is 50 . if the marks of each student are doubled , find the new average ?
Options: a ) 160 , b ) 120 , c ) 100 , d ) 150 , e ) 170
Rationale: "sum of the marks for the 12 students = 12 * 50 = 600 . the marks of each student are doubled , the sum also will be doubled . the new sum = 600 * 2 = 1200 . so , the new average = 1200 / 12 = 100 . answer : c"
Answer: c
Problem: if 75 percent of a class answered the first question on a certain test correctly , 25 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 ) 20 % , c ) 30 % , d ) 50 % , e ) 65 %
Rationale: "{ total } = { first } + { second } - { both } + { neither } 100 % = 75 % + 25 % - { both } + 20 % - - > { both } = 20 % . answer : b ."
Answer: b
Problem: pipe a can fill a tank in 6 hours . due to a leak at the bottom , it takes 8 hours for the pipe a to fill the tank . in what time can the leak alone empty the full tank ?
Options: a ) 13 , b ) 24 , c ) 18 , d ) 19 , e ) 12
Rationale: "let the leak can empty the full tank in x hours 1 / 6 - 1 / x = 1 / 8 = > 1 / x = 1 / 6 - 1 / 8 = ( 4 - 3 ) / 24 = 1 / 24 = > x = 24 . answer : b"
Answer: b
Problem: if the sum of two numbers is 55 and the h . c . f . and l . c . m . of these numbers are 5 and 120 respectively , then the sum of the reciprocals of the numbers is equal to :
Options: a ) 11 / 122 , b ) 11 / 120 , c ) 11 / 121 , d ) 11 / 140 , e ) 11 / 111
Rationale: explanation : let the numbers be a and b . then , a + b = 55 and ab = 5 x 120 = 600 . the required sum answer : b ) 11 / 120
Answer: b
Problem: in a factory , there are 60 % technicians and 100 % non - technicians . if the 60 % of the technicians and 100 % of non - technicians are permanent employees , then the percentage of workers who are temporary is ?
Options: a ) 62 % , b ) 57 % , c ) 52 % , d ) 85 % , e ) 42 %
Rationale: "total = 160 t = 60 nt = 100 60 * ( 100 / 100 ) = 37.5 100 * ( 60 / 100 ) = 37.5 37.5 + 37.5 = 75 = > 160 - 75 = 85 % answer : d"
Answer: d
Problem: the average salary of a person for the months of january , february , march and april is rs . 8000 and that for the months february , march , april and may is rs . 8200 . if his salary for the month of may is rs . 6500 , find his salary for the month of january ?
Options: a ) 2177 , b ) 2876 , c ) 4500 , d ) 5700 , e ) 6711
Rationale: "sum of the salaries of the person for the months of january , february , march and april = 4 * 8000 = 32000 - - - - ( 1 ) sum of the salaries of the person for the months of february , march , april and may = 4 * 8200 = 32800 - - - - ( 2 ) ( 2 ) - ( 1 ) i . e . may - jan = 800 salary of may is rs . 6500 salary of january = rs . 5700 . answer : d"
Answer: d
Problem: the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 12 years and that of the other 9 students is 16 years . the age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 21 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 12 * 5 + 16 * 9 ) ] = ( 225 - 204 ) = 21 years . answer : c"
Answer: c
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 800 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 20 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 800 = x * 1 x / 2 x ² = 1600 x = 40 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 40 / 2 = 20 m answer : d"
Answer: d
Problem: what decimal fraction is 20 ml of a litre ?
Options: a ) . 2 , b ) 0.002 , c ) . 05 , d ) . 02 , e ) none of these
Rationale: "answer required fraction = 20 / 1000 = 2 / 100 = . 02 correct option : d"
Answer: d
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 210 , what is the least possible value of n ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 14
Rationale: "210 = 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is a ."
Answer: a
Problem: a man covers a distance on scooter . had he moved 3 kmph faster he would have taken 40 min less . if he had moved 2 kmph slower , he would have taken 40 min more . the distance is .
Options: a ) 30 km , b ) 60 km , c ) 80 km , d ) 20 km , e ) 40 km
Rationale: e 40 km let distance = x m usual rate = y kmph x / y – x / y + 3 = 40 / 60 hr 2 y ( y + 3 ) = 9 x - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ( 1 ) x / y - 2 – x / y = 40 / 60 hr y ( y - 2 ) = 3 x - - - - - - - - - - - ( 2 ) divide 1 & 2 equations by solving we get x = 40 km
Answer: e
Problem: p is 50 % more efficient than q . p can complete a work in 25 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "the work done by p in 1 day = 1 / 25 let work done by q in 1 day = q q × ( 150 / 100 ) = 1 / 25 q = 100 / ( 25 × 150 ) = 10 / ( 25 × 15 ) the work done by p and q in 1 day = 1 / 25 + 10 / ( 25 × 15 ) = 25 / ( 25 × 15 ) = 1 / 15 p and q together can do the work in 15 days . the answer is c ."
Answer: c
Problem: a can do a piece of work in 4 hours . a and c together can do it in just 2 hours , while b and c together need 3 hours to finish the same work . b alone can complete the work in - - - hours .
Options: a ) 65 , b ) 85 , c ) 48 , d ) 12 , e ) 25
Rationale: explanation : work done by a in 1 hour = 1 / 4 work done by b and c in 1 hour = 1 / 3 work done by a and c in 1 hour = 1 / 2 work done by a , b and c in 1 hour = 1 / 4 + 1 / 3 = 7 / 12 work done by b in 1 hour = 7 / 12 – 1 / 2 = 1 / 12 = > b alone can complete the work in 12 hours answer : d
Answer: d
Problem: beginning in town a , biker bob rides his bike 12 miles west , 6 miles north , 4 miles east , and then 12 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 18.97 miles , b ) 20 miles , c ) 22 miles , d ) 23 miles , e ) 25 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 12 + 6 = 18 m other being the base ie distance traveled west - distance traveled eat = 12 - 6 = 6 m now this third side or the distance between town a and town b = 18 ^ 2 + 6 ^ 2 = sq root 360 = 18.97 mile answer : a"
Answer: a
Problem: the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 60.5 . when one student dropped the class , the average of the remaining scores increased to 64.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 8 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 60.50 = 968 total score of 15 students is 15 * 64 = 960 so , the score of the person who left is 8 ( 968 - 960 ) answer will be ( a"
Answer: a
Problem: median w of price of the car is 52000 . which could be the median of the other two . 35000 , 44000 , x , y , 57000 .
Options: a ) 38000 , b ) 47000 , c ) 48000 , d ) 51000 , e ) 56000
Rationale: median of the car is 52000 therefore 52000 is the middle number . assuming y > = x , x will have to be the median value i . e . 52000 . therefore the remaining value would have to be between 52000 and 57000 inclusive . the only answer choice that fits is w = 56000 . e
Answer: e
Problem: each man in a gang of 100 investors has investments ineither equities or securities or both . exactly 2525 of the investors in equities haveinvestments in securities , exactly 4040 of the investorsin securities have investments inequities . how many have investmentsin equities ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: the investors can be categorized into three groups : ( 1 ) those who have investments in equities only . ( 2 ) those who have investments in securities only . ( 3 ) those who have investments in both equities and securities . let xx , yy , and zz denote the number of people in the respective categories . since the total number of investors is 110 , we have x + y + z = 110 x + y + z = 110 - - - - - - - - - - - - - ( 1 ) also , the number of people with investments in equities is x + zx + z and the number of people with investments in securities is y + zy + z . since exactly 25 % 25 % of the investors in equities have investments in securities , we have the equation 25100 × ( x + z ) = z 25100 × ( x + z ) = z 25100 × x = 25100 × z 25100 × x = 25100 × z x = 3 zx = 3 z - - - - - - - - - - - - - - - - - - - ( 2 ) since exactly 40 % 40 % of the investors in securities have investments in equities , we have the equation 40100 × ( y + z ) = z 40100 × ( y + z ) = z ( y + z ) = 5 z 2 ( y + z ) = 5 z 2 y = 3 z 2 y = 3 z 2 substituting equations ( 2 ) and ( 3 ) into equation ( 1 ) yields 3 z + 3 z 2 + z = 1103 z + 3 z 2 + z = 110 11 z 2 = 11011 z 2 = 110 z = 110 × 211 = 20 z = 110 × 211 = 20 hence , the number of people with investments in equities is : x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 x + z = 3 z + z = 3 × 20 + 20 = 60 + 20 = 80 b
Answer: b
Problem: a certain country had a total annual expenditure of $ 9.6 x 10 ^ 11 last year . if the population of the country was 240 million last year , what was the per capita expenditure ?
Options: a ) $ 500 , b ) $ 1,000 , c ) $ 2,000 , d ) $ 3,000 , e ) $ 4,000
Rationale: total expenditure / population = per capita expenditure hence , ( 9,6 x 10 ^ 11 ) / 240 000 000 = ( 9,6 x 10 ^ 11 ) / ( 2,4 x 10 ^ 8 ) = 4 x 10 ^ ( 11 - 8 ) = 4 x 10 ^ 3 = 4000 . answer is e .
Answer: e
Problem: in the manufacture of a certain product , 6 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.24 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 6 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 6 / 100 ) * 100 % = ( 24 / 10000 ) * 100 % = ( 24 / 100 ) % = . 24 % answer b"
Answer: b
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.10 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 732.6 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.1 = 732.6 answer : c"
Answer: c
Problem: the distance between 2 cities a and b is 1000 km . a train starts from a at 8 a . m . and travels towards b at 100 km / hr . another starts from b at 9 a . m . and travels towards a at 150 km / hr . at what time do they meet ?
Options: a ) 11 am . , b ) 12 p . m . , c ) 3 pm . , d ) 2 p . m . , e ) 1 p . m .
Rationale: "suppose they meet x hrs after 8 a . m . distance moved by first in x hrs + distance moved by second in ( x - 1 ) hrs = 1000 100 x + 150 ( x - 1 ) = 1000 x = 4.60 = 5 hrs they meet at 8 + 5 = 1 p . m . answer is e"
Answer: e
Problem: 445 , 221 , 109 , 53 , . . .
Options: a ) 8 , b ) 7 , c ) 42 , d ) 25 , e ) 63
Rationale: "explanation : to obtain next number , subtract 3 from the previous number and divide the result by 2 445 ( 445 - 3 ) / 2 = 221 ( 221 - 3 ) / 2 = 109 ( 109 - 3 ) / 2 = 53 ( 53 - 3 ) / 2 = 25 answer : d"
Answer: d
Problem: car a runs at the speed of 65 km / hr & reaches its destination in 8 hr . car b runs at the speed of 70 km / h & reaches its destination in 5 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 6 , b ) 52 : 35 , c ) 13 : 7 , d ) 15 : 6 , e ) 13 : 6
Rationale: "sol . distance travelled by car a = 65 ã — 8 = 520 km distance travelled by car b = 70 ã — 5 = 350 km ratio = 520 / 350 = 52 : 35 b"
Answer: b
Problem: find the least number must be subtracted from 568219 so that remaining no . is divisible by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "on dividing 568219 by 5 we get the remainder 4 , so 4 should be subtracted e"
Answer: e
Problem: if the cost price of 40 articles is equal to the selling price of 25 articles , what is the % profit or loss made by the merchant ?
Options: a ) 25 % loss , b ) 25 % profit , c ) 20 % loss , d ) 60 % profit , e ) 75 % profit
Rationale: "let the cost price of 1 article be $ 1 . therefore , cost price of 40 articles = 40 * 1 = $ 40 the selling price of 25 articles = cost price of 40 articles = $ 40 . now , we know the selling price of 25 articles . let us find the cost price of 25 articles . cost price of 25 articles = 25 * 1 = $ 25 . therefore , profit made on sale of 25 articles = selling price of 25 articles - cost price of 25 articles = 40 - 25 = $ 15 . as the profit is in the positive , the merchant has made a profit of $ 15 . therefore , % loss = loss / cp * 100 % loss = 15 / 25 * 100 = 60 % profit . d"
Answer: d
Problem: the numbers 272738 and 232342 , when divided by n , a two digit number , leave a remainder of 13 and 17 respectively . find the sum of the digits of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 4 , e ) 5
Rationale: from the given information , ( 272738 - 13 , 232342 - 17 ) are exactly divisible by that two digit number . we have to find the hcf of the given numbers 272725 , 232325 . hcf = 25 . so sum of the digits = 7 . answer : a
Answer: a
Problem: the area of an isosceles trapezoid with sides of length 5 and bases of length 11 and 17 is ?
Options: a ) 48 , b ) 52 , c ) 54 , d ) 56 , e ) 46
Rationale: "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 17 will be divided into 3 parts = 11 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 28 * 4 = 56 d is the answer"
Answer: d
Problem: find the area of a parallelogram with base 36 cm and height 18 cm ?
Options: a ) 287 cm 2 , b ) 887 cm 2 , c ) 384 cm 2 , d ) 268 cm 2 , e ) 648 cm 2
Rationale: "area of a parallelogram = base * height = 36 * 18 = 648 cm 2 answer : e"
Answer: e
Problem: if the number is divided by 3 , it reduced by 42 . the number is
Options: a ) a ) 51 , b ) b ) 63 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 42 = > 2 x / 3 = 42 = > x = 63 answer : option b"
Answer: b
Problem: when y is divided by 288 , the remainder is 45 . what is the remainder when the same y is divided by 24 ?
Options: a ) 20 , b ) 21 , c ) 23 , d ) 25 , e ) 26
Rationale: "y = 288 * a + 45 = ( 24 * 12 ) * a + 24 + 21 the answer is b ."
Answer: b
Problem: what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 6 ?
Options: a ) 82,650 , b ) 64,850 , c ) 64,749 , d ) 49,700 , e ) 56,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 6 seeing the options after dividing an finding the reminder of 2 my answer was a"
Answer: a
Problem: how many bricks , each measuring 50 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 2400 , c ) 5500 , d ) 7400 , e ) 3200
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 600 x 22.5 ) / ( 50 x 11.25 x 6 ) = 3200 answer : e"
Answer: e
Problem: if teena is driving at 55 miles per hour and is currently 7.5 miles behind yoe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 15 miles ahead of yoe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 105
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . yoe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 15 miles . teena can cover 7.5 miles in 30 mins teena will cover 15 miles in 60 mins so answer 30 + 60 = 90 mins . d"
Answer: d
Problem: at a certain zoo , the ratio of lions to penguins is 3 to 11 . if there are 82 more penguins than lions at the zoo , how many lions are there ?
Options: a ) 24 , b ) 30 , c ) 48 , d ) 72 , e ) 132
Rationale: 3 / 11 = x / x + 82 3 * 82 = 8 x x = 30 b . 30
Answer: b
Problem: a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late . had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late . what is the speed q of the train .
Options: a ) a ) 45 , b ) b ) 33 , c ) c ) 48 , d ) d ) 55 , e ) e ) 61
Rationale: let y be the balance distance to be covered and x be the former speed . a train after traveling for 50 km meets with an accident and then proceeds at 3 / 4 of its former speed and arrives at its destination 35 minutes late so , y / ( 3 x / 4 ) - y / x = 35 / 60 4 y / 3 x - y / x = 7 / 12 y / x ( 4 / 3 - 1 ) = 7 / 12 y / x * 1 / 3 = 7 / 12 y / x = 7 / 4 4 y - 7 x = 0 . . . . . . . . 1 had the accident occurred 24 km farther , it would have reached the destination only 25 minutes late so , ( y - 24 ) / ( 3 x / 4 ) - ( y - 24 ) / x = 25 / 60 4 ( y - 24 ) / 3 x - ( y - 24 ) / x = 5 / 12 ( y - 24 ) / x ( 4 / 3 - 1 ) = 5 / 12 ( y - 24 ) / x * 1 / 3 = 5 / 12 ( y - 24 ) * 12 = 3 x * 5 ( y - 24 ) * 4 = 5 x 4 y - 5 x = 96 . . . . . . . 2 eq 2 - eq 1 2 x = 96 x = 48 = q ans = c
Answer: c
Problem: if 15 % of 30 % of 50 % of a number is 117 , then what is the number ?
Options: a ) 5200 , b ) 3050 , c ) 4400 , d ) 4500 , e ) none of these
Rationale: "let the number be a given , 15 / 100 * 30 / 100 * 50 / 100 * a = 117 = > 3 / 20 * 3 / 10 * 1 / 2 * a = 117 = > a = 10 * 20 * 10 * 2 = 5200 . answer : a"
Answer: a
Problem: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 20 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 8 minutes ?
Options: a ) 100 , b ) 90 , c ) 80 , d ) 30 , e ) 50
Rationale: "machine b produces 100 part in 20 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 20 / 2 = 10 minutes . now , machine a produces 100 parts in 10 minutes which is 100 / 10 = 10 parts / minute . 10 parts x a total of 8 minutes = 80 c"
Answer: c
Problem: during a special promotion , a certain filling station is offering a 10 percent discount on gas purchased after the first 10 gallons . if kim purchased 20 gallons of gas , and isabella purchased 25 gallons of gas , then isabella ‟ s total per - gallon discount is what percent of kim ‟ s total per - gallon discount ?
Options: a ) 80 % , b ) 100 % , c ) 116.7 % , d ) 120 % , e ) 140 %
Rationale: "kim purchased 20 gallons of gas . she paid for 10 + 0.9 * 10 = 19 gallons , so the overall discount she got was 1 / 20 = 5 % . isabella purchased 25 gallons of gas . she paid for 10 + 0.9 * 15 = 23.5 gallons , so the overall discount she got was 1.5 / 25 = 6 % . 6 is 6 / 5 * 100 = 120 % of 5 . answer : d ."
Answer: d
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 4 % sugar by weight . to make a delicious and healthy mixture that is 6 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 2
Rationale: "ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 6 - 4 ) / ( 10 - 6 ) = 2 / 4 = 1 / 2 so they should be mixed in the ratio 1 : 2 answer - e"
Answer: e
Problem: how many numbers between 190 and 580 are divisible by 45 and 6 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: every such number must be divisible by l . c . m of 4 , 5,6 i . e , 60 . such numbers are 240,300 , 360,420 , 480,540 . clearly , there are 6 such numbers answer : a
Answer: a
Problem: if the cost price of 50 articles is equal to the selling price of 28 articles , then the gain or loss percent is ?
Options: a ) 22 , b ) 65 , c ) 78.57 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 28 articles . let cost price of one article = rs . 1 selling price of 28 articles = rs . 50 but cost price of 28 articles = rs . 28 therefore , the trader made profit . \ percentage of profit = 22 / 28 * 100 = 78.57 % answer : c"
Answer: c
Problem: a block of wood has dimensions 10 cm x 10 cm x 100 cm . the block is painted red and then cut evenly at the 50 cm mark , parallel to the sides , to form two rectangular solids of equal volume . what percentage of the surface area of each of the new solids is not painted red ?
Options: a ) 4.5 % , b ) 8.3 % , c ) 10.2 % , d ) 12.5 % , e ) 15.3 %
Rationale: "the area of each half is 100 + 4 ( 500 ) + 100 = 2200 the area that is not painted is 100 . the fraction that is not painted is 100 / 2200 = 1 / 22 = 4.5 % the answer is a ."
Answer: a
Problem: the length of a rectangle is twice its breadth . if its length is decreased by 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq . cm . find the length of the rectangle .
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) none of them
Rationale: "let breadth = x . then , length = 2 x . then , ( 2 x - 5 ) ( x + 5 ) - 2 x * x = 75 < = > 5 x - 25 = 75 < = > x = 20 . therefore , length of the rectangle = 20 cm . answer is d"
Answer: d
Problem: out of 420 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 120 , b ) 150 , c ) 130 , d ) 180 , e ) 220
Rationale: "n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 420 - 50 = 370 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 370 = 130 . answer is c"
Answer: c
Problem: in a certain company , the ratio of the number of managers to the number of non - managers in any department must always be greater than 5 : 24 . in the company , what is the maximum number of non - managers in a department that has 8 managers :
Options: a ) 36 , b ) 37 , c ) 38 , d ) 39 , e ) 40
Rationale: "m / nm > 5 x / 24 x m = 8 8 / nm > 5 x / 24 x 8 / nm - 5 x / 24 x > 0 ( 192 x - 5 x * nm ) / ( 24 x * nm ) > 0 192 x - 5 x * nm > 0 5 x * nm < 192 x nm < 192 x / 5 x nm < 38.4 maximum number of non managers = 38 answer : c"
Answer: c
Problem: the average runs scored by a batsman in 15 matches is 30 . in the next 20 matches the batsman scored an average of 15 runs . find his average in all the 30 matches ?
Options: a ) 31.56 , b ) 25.65 , c ) 21.43 , d ) 28.36 , e ) 27.96
Rationale: total score of the batsman in 15 matches = 450 . total score of the batsman in the next 20 matches = 300 . total score of the batsman in the 35 matches = 750 . average score of the batsman = 750 / 35 = 21.43 . answer : c
Answer: c
Problem: a goes to place x and b goes to place y . after a travelled 180 km more than b they together meet at a point between xy . they together had their lunch for half an hour . after that a took 2 hrs to reach x and b took 4.5 hrs to reach y . find distance between x and y ?
Options: a ) 900 km , b ) 540 km , c ) 720 km , d ) 820 km , e ) 920 km
Rationale: let speed of a be - - - - - - - sa let speed of b be - - - - - - - - sb let the distance covered by b while going to position xy be - - - - - - - - - - - x so distance covered by a in same time while going to xy is - - - - - - - - - - 180 + x ( it ' s given in the question ) so total distance b / w x and y is = x + ( x + 180 ) while going to position xy : - time taken by a = time taken by b ( x + 180 ) / sa = x / sb sa / sb = ( x + 180 ) / x - - - - - - - - - - - - - - - - - - - - - 1 after lunch : - a . c . t ( according to question ) sa = x / 2 sb = ( x + 180 ) / 4.5 dividing sa / sb = ( x * 4.5 ) / ( ( x + 180 ) * 2 ) - - - - - - - - - - - - - - - - - - - - 2 equating equations 1 and 2 9 / 4 = ( x + 180 ) ^ 2 / x ^ 2 now taking square root on both sides we get 3 / 2 = ( x + 180 ) / x x = 360 therefore distance between x and y = x + ( x + 180 ) = 900 km answer : a
Answer: a
Problem: a train 140 m long is running at 60 kmph . in how much time will it pass a platform 260 m long ?
Options: a ) 15 seconds , b ) 24 seconds , c ) 28 seconds , d ) 30 seconds , e ) 35 seconds
Rationale: "distance travelled = 140 + 260 m = 400 m speed = 60 * 5 / 8 = 50 / 3 m time = 400 * 3 / 50 = 24 second answer : b"
Answer: b
Problem: with both valves open , the pool will be filled with water in 48 minutes . the first valve alone would fill the pool in 2 hours . if the second valve emits 50 cubic meters of water more than the first every minute , then what is the capacity r of the pool ?
Options: a ) 9000 cubic meters , b ) 10500 cubic meters , c ) 11750 cubic meters , d ) 12000 cubic meters , e ) 12500 cubic meters
Rationale: "d . 12000 cubic meters . if both hte valves fill the pool in 48 minutes and valve 1 only fills in 120 minutes then valve 2 alone will fill the pool in ( 48 * 120 ) / ( 120 - 48 ) = 80 minutes . now , if valve 1 admits x cubic meter of water per minute then the capacity of pool will be 120 x and also 80 ( x + 50 ) . or , 120 x = 80 ( x + 50 ) . or x = 100 . hence , the capacity of pool = 120 x = 12000 cubic meters ."
Answer: d
Problem: if the ratio of a to b is 2 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
Options: a ) 4 / 15 , b ) 1 / 3 , c ) 2 / 15 , d ) 4 / 5 , e ) 7 / 6
Rationale: "a : b = 2 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 2 : 15 answer c"
Answer: c
Problem: a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 25 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 180,000 , d ) $ 200,000 , e ) $ 192,500
Rationale: "30 % of 1000 = 300 worked for 20 hours payment @ 5 / hr total payment = 300 * 25 * 5 = 37500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 37500 + 100000 + 40000 + 15000 = 192500 hence , answer is e"
Answer: e
Problem: a 290 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
Options: a ) 210 m , b ) 220 m , c ) 230 m , d ) 240 m , e ) 250 m
Rationale: "relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 290 / 9 = 500 / 9 x = 210 ans is 210 m answer : a"
Answer: a
Problem: a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 4 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 25 , e ) 10.93
Rationale: "a : b = 2 : 4 b : c = 2 : 5 a : b : c = 4 : 8 : 20 8 / 32 * 100 = 25 answer : d"
Answer: d
Problem: if f ( x ) = 6 x ^ 4 - 4 x ^ 3 - 3 x ^ 2 + 6 x , then f ( - 1 ) =
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "f ( - 1 ) = 6 ( - 1 ) ^ 4 - 4 ( - 1 ) ^ 3 - 3 ( - 1 ) ^ 2 + 6 ( - 1 ) = 6 + 4 - 3 - 6 = 1 the answer is d ."
Answer: d
Problem: a train 820 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
Options: a ) 510 , b ) 540 , c ) 480 , d ) 520 , e ) 589
Rationale: "speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 820 + x ) / 60 = 65 / 3 x = 480 m . answer : option c"
Answer: c
Problem: if 5 people contributed a total of $ 20.00 toward a gift and each of them contributed at least $ 3.00 , then the maximum possible amount any one person could have contributed is
Options: a ) $ 1.00 , b ) $ 1.25 , c ) $ 5.00 , d ) $ 8.00 , e ) $ 20.00
Rationale: "d for me 4 people with 3 $ each - > maximum = 8"
Answer: d
Problem: a man bought an article and sold it at a gain of 5 % . if he had bought it at 5 % less and sold it for re 8 less , he would have made a profit of 10 % . the c . p . of the article was
Options: a ) 1600 , b ) 1500 , c ) 1200 , d ) 1388 , e ) 1211
Rationale: "explanation : let original cost price is x its selling price = ( 105 / 100 ) * x = 21 x / 20 new cost price = ( 95 / 100 ) * x = 19 x / 20 new selling price = ( 110 / 100 ) * ( 19 x / 20 ) = 209 x / 200 [ ( 21 x / 20 ) - ( 209 x / 200 ) ] = 8 = > x = 1600 answer : a ) rs 1600"
Answer: a
Problem: jacob is now 12 years younger than michael . if 11 years from now michael will be twice as old as jacob , how old will jacob be in 4 years ?
Options: a ) 3 , b ) 7 , c ) 15 , d ) 5 , e ) 25
Rationale: jacob = x years , mike = x + 12 years 11 years from now , 2 ( x + 11 ) = x + 23 2 x + 22 = x + 23 x = 1 x + 4 = 5 years answer d
Answer: d
Problem: the marks obtained by vijay and amith are in the ratio 2 : 5 and those obtained by amith and abhishek in the ratio of 3 : 2 . the marks obtained by vijay and abhishek are in the ratio of ?
Options: a ) 6 : 8 , b ) 3 : 1 , c ) 6 : 5 , d ) 3 : 2 , e ) 3 : 5
Rationale: "2 : 5 3 : 2 - - - - - - - 6 : 15 : 10 6 : 10 3 : 5 answer : e"
Answer: e
Problem: a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent e of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which e is 40 % of 80 hence , d is the answer"
Answer: d
Problem: the area of a rectangular field is 144 m 2 . if the length had been 6 metres more , the area would have been 54 m 2 more . the original length of the field is
Options: a ) 22 metres
b ) 18 metres
c ) 16 metres
d ) 24 metres
e ) none of these
Rationale: let the length and breadth of the original rectangular field be x m and y m respectively . area of the original field = x × y = 144 m 2 ∴ x = 144 ⁄ y . . . . . ( i ) if the length had been 6 m more , then area will be ( x + 6 ) y = 144 + 54 ⇒ ( x + 6 ) y = 198 … ( ii ) putting the value of x from eq ( i ) in eq ( ii ) , we get ( 144 ⁄ y + 6 ) y = 198 ⇒ 144 + 6 y = 198 ⇒ 6 y = 54 ⇒ y = 9 m putting the value of y in eq ( i ) we get x = 16 m answer c
Answer: c
Problem: find a sum for 1 st 6 prime number ' s ?
Options: a ) 41 , b ) 28 , c ) 30 , d ) 34 , e ) 36
Rationale: "required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option a"
Answer: a
Problem: chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 4 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 19
Rationale: "1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 4 4 lbs of nuts = $ 16 total value of mixture = 16 + 3 = 19 fraction of the value of raisin = 3 / 19 ans : e"
Answer: e
Problem: 45 x ? = 45 % of 900
Options: a ) 16.2 , b ) 4 , c ) 5 , d ) 9 , e ) 11
Rationale: "answer let 45 x a = ( 25 x 900 ) / 100 ∴ a = ( 45 x 9 ) / 45 = 9 correct option : d"
Answer: d
Problem: the average of first five multiples of 3 is ?
Options: a ) 2 , b ) 9 , c ) 8 , d ) 6 , e ) 3
Rationale: "average = 3 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 45 / 5 = 9 . answer : b"
Answer: b
Problem: p , q and r together earn rs . 1980 in 9 days . p and r can earn rs . 600 in 5 days . q and r in 7 days can earn rs . 910 . how much amount does r can earn per day ?
Options: a ) s . 30 , b ) s . 70 , c ) s . 90 , d ) s . 100 , e ) s . 120
Rationale: "explanation : amount earned by p , q and r in 1 day = 1980 / 9 = 220 - - - ( 1 ) amount earned by p and r in 1 day = 600 / 5 = 120 - - - ( 2 ) amount earned by q and r in 1 day = 910 / 7 = 130 - - - ( 3 ) ( 2 ) + ( 3 ) - ( 1 ) = > amount earned by p , q and 2 r in 1 day - amount earned by p , q and r in 1 day = 120 + 130 - 220 = 30 = > amount earned by r in 1 day = 30 answer : option a"
Answer: a
Problem: the cost price of a radio is rs . 1390 and it was sold for rs . 890 , find the loss % ?
Options: a ) 18 % , b ) 12 % , c ) 22 % , d ) 35 % , e ) 21 %
Rationale: "1390 - - - - 500 100 - - - - ? = > 35 % answer : d"
Answer: d
Problem: two goods trains each 500 m long are running in opposite directions on parallel tracks . their speeds are 60 km / hr and 90 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 48 , b ) 93 , c ) 24 , d ) 23 , e ) 12
Rationale: "relative speed = 60 + 90 = 150 km / hr . 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 500 + 500 = 1000 m . required time = 1000 * 3 / 125 = 24 sec . answer : c"
Answer: c
Problem: a circular wire of radius 42 cm is cut and bent into the form of a rectangle whose sides are in the ratio of 6 : 5 . the smaller side of the rectangle is :
Options: a ) 30 cm
b ) 60 cm
c ) 72 cm
d ) 132 cm .
e ) 142 cm .
Rationale: length of wire = circumference of circle of radius 42 cm = ( 2 * 22 / 7 * 42 ) = 264 cm . therefore , perimeter of rectangle = 264 cm . let , length = 6 x cm & breadth = 5 x cm . therefore , 2 ( 6 x + 5 x ) = 264 or x = 12 . therefore , smaller side = 60 cm answer : b
Answer: b
Problem: if 6 years are subtracted from the present age of arun and the remainder is divided by 18 , then the present age of his grandson gokul is obtained . if gokul is 2 years younger to madan whose age is 5 years , then what is the age of arun ?
Options: a ) 48 , b ) 60 , c ) 84 , d ) 96 , e ) 69
Rationale: arun age x . ( x - 6 ) / 18 = y y is gokul age which is 3 x = 60 answer : b
Answer: b
Problem: solve for the given equation 121 x 54 = ?
Options: a ) 68225 , b ) 75625 , c ) 76569 , d ) 45854 , e ) 45858
Rationale: explanation : this question can be solved by 2 approaches : = > direct multiplication = > numerical operations direct multiplication is quite time consuming and involves a lot of calculations . an easier approach is based on numerical operations . = > 121 x ( 10 / 2 ) 4 = 121 x 10000 / 16 = 75625 answer : b
Answer: b
Problem: in a ratio which is equal to 7 : 9 , if the antecedent is 42 , then the consequent is ?
Options: a ) 72 , b ) 54 , c ) 64 , d ) 51 , e ) 45
Rationale: "we have 7 / 9 = 42 / x 7 x = 42 * 9 x = 54 consequent = 54 answer is b"
Answer: b
Problem: john has 10 pairs of matched socks . if he loses 11 individual socks , what is the greatest number of pairs of matched socks he can have left ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "because we have to maximize the pair of matched socks , we will remove 5 pairs ( 10 socks ) out of 10 pairs 1 sock from the 6 th pair . thus the no of matching socks pair remaining = 10 - 6 = 4 answer d"
Answer: d
Problem: a meeting has to be conducted with 4 managers . find the number of ways in which the managers may be selected from among 7 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 18 , b ) 21 , c ) 25 , d ) 30 , e ) 35
Rationale: the total number of ways to choose 4 managers is 7 c 4 = 35 we need to subtract the number of groups which include the two managers , which is 5 c 2 = 10 . 35 - 10 = 25 the answer is c .
Answer: c
Problem: convert 100 inches into centimeter ?
Options: a ) 112 cm , b ) 120 cm , c ) 150 cm , d ) 210 cm , e ) 254 cm
Rationale: "1 inch = 2.54 cm 100 inches = 100 * 2.54 = 254 cm answer is e"
Answer: e
Problem: nitin ranks 23 th in a class of 60 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: explanation : number students behind the nitin in rank = ( 60 - 23 ) = 37 nitin is 38 nd from the last answer : b ) 38
Answer: b
Problem: in how many ways 4 boys and 1 girls can be seated in a row so that they are alternate .
Options: a ) 144 , b ) 288 , c ) 24 , d ) 256 , e ) none
Rationale: solution : let the arrangement be , b b b b g 4 boys can be seated in 4 ! ways . girl can be seated in 1 ! ways . required number of ways , = 4 ! * 1 ! = 24 . answer : option c
Answer: c
Problem: { - 10 , - 6 , - 5 , - 4 , - 2.5 , - 1 , 0 , 2.5 , 4 , 6 , 7 , 10 } a number is to be selected at random from the set above . what is the probability that the number will be a solution to the equation ( x 3 ) ( x + 14 ) ( 2 x + 5 ) = 0 ?
Options: a ) 1 / 12 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: x = - 4 prob = 1 / 12 answer - a
Answer: a
Problem: the average of 10 numbers is 40.2 . later it is found that two numbers have been wrongly copied . the first is 19 greater than the actual number and the second number added is 13 instead of 31 . find the correct average .
Options: a ) 40.2 , b ) 40.4 , c ) 40.6 , d ) 40.8 , e ) 40.1
Rationale: "sum of 10 numbers = 402 corrected sum of 10 numbers = 402 – 13 + 31 – 19 = 401 hence , new average = 401 ⁄ 10 = 40.1 answer e"
Answer: e
Problem: the side of a rhombus is 22 m and length of one of its diagonals is 16 m . the area of the rhombus is ?
Options: a ) 327.9 , b ) 325.9 , c ) 347.7 , d ) 357.9 , e ) 327.9
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 22 ; p = 16 a = 1 / 2 * 16 * √ 4 ( 22 ) 2 - ( 16 ) 2 = 1 / 2 * 16 * √ 1936 - 256 = 1 / 2 * 16 * √ 1680 a = 327.9 answer : a"
Answer: a
Problem: sonika bought a v . c . r . at the list price of 18,600 . if the rate of sales tax was 8 % , find the amount she had to pay for purchasing the v . c . r .
Options: a ) 20,088 , b ) 19,780 , c ) 19,680 , d ) 19,380 , e ) none of these
Rationale: "sol . list price of v . c . r . = 18,600 rate of sales tax = 8 % ∴ sales tax = 8 % of 18,600 = 8 ⁄ 100 × 18600 = 1488 so , total amount which sonika had to pay for purchasing the v . c . r . = 18,600 + 1488 = 20,088 . answer a"
Answer: a
Problem: what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 7 , 24 and 25 ?
Options: a ) 2.5 , b ) 6.5 , c ) 12.5 , d ) 14 , e ) 16
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circumraduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 25 / 2 = 12.5 ans . c"
Answer: c
Problem: if 20 machine can finish a job in 36 days , then how many more machines would be needed to finish the job in one - third less time ?
Options: a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
Rationale: "you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 20 machines ( identical ones , i assume ) work simultaneously for 36 days , they will do a total of 20 * 36 machine - days of work . so the job requires 20 * 36 days of machine work in total . we instead want the job done in 1 / 3 less time , so in 24 days . so we ' ll need 20 * 36 / 24 = 30 machines , or 10 additional machines . c"
Answer: c
Problem: suganya and suriya are partners in a business . suganya invests rs . 38,000 for 8 months and suriya invests rs . 40,000 for 10 months . out of a profit of rs . 31,570 . suganya ' s share is
Options: a ) rs . 1435 , b ) rs . 12,628 , c ) rs . 1685 , d ) rs . 18,942 , e ) none
Rationale: "solution ratio of their shares = ( 35000 ã — 8 ) : ( 42000 ã — 10 ) = 2 : 44 . suganya ' s share = rs . ( 31570 ã — 2 / 44 ) = rs . 1435 . answer a"
Answer: a
Problem: suresh started a business , investing rs . 18000 . after 3 months and 4 months respectively , rohan and sudhir joined him with capitals of 12000 and 9000 . at the end of the year the total profit was rs . 3795 . what is the difference between rohan ’ s and sudhir ’ s share in the profit ?
Options: a ) s . 345 , b ) s . 350 , c ) s . 352 , d ) s . 362 , e ) s . 368
Rationale: "suresh : rohan : sudhir ratio of their investments = 18000 × 12 : 12000 × 9 : 9000 × 8 = 6 : 3 : 2 the difference between rohan ’ s and sudhir ’ s share = 1 share : . i . e . = rs . 3795 × 1 / 11 = rs . 345 . a"
Answer: a
Problem: for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 1 / 3 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 3 , d ) 4 / 9 , e ) 2 / 3
Rationale: "probability of not burning out during the first 6 months 1 - 1 / 3 = 2 / 3 probability of not burning out during the next 6 months 2 / 3 / 2 = 1 / 3 , hence probability of burning out 1 - 1 / 3 = 2 / 3 . probability of burning out during the period from 6 months to 1 year = probability of not burning out in first 6 months * probability of burning out in next 6 months = 2 / 3 * 2 / 3 = 4 / 9 answer : d ."
Answer: d
Problem: a grocer has a sale of rs . 5921 , rs . 5468 , rs . 5568 , rs . 6088 and rs . 6433 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 5900 ?
Options: a ) 4902 , b ) 4922 , c ) 5922 , d ) 5924 , e ) 5928
Rationale: "total sale for 5 months = rs . ( 5921 + 5468 + 5568 + 6088 + 6433 ) = rs . 29478 . required sale = rs . [ ( 5900 x 6 ) - 29478 ] = rs . ( 35400 - 29478 ) = rs . 5922 . answer : c"
Answer: c
Problem: if x is real , find the maximum value of the expression - 2 x ^ 2 + 3 x + 5 .
Options: a ) 2.145 , b ) 6.125 , c ) 8.725 , d ) 11.885 , e ) 13.485
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 3 x + 5 = ( - 2 x + 5 ) ( x + 1 ) the roots are 5 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 0.75 the maximum value is - 2 ( 0.75 ) ^ 2 + 3 ( 0.75 ) + 5 = 6.125 the answer is b ."
Answer: b
Problem: nelly made a part payment of $ 875 toward buying a brand new refrigerator , which represents 25 % of the total cost of the refrigerator , how much remains to be paid ?
Options: a ) $ 2225 , b ) $ 2782 , c ) $ 1625 , d ) $ 2629 , e ) $ 2625
Rationale: explanation : let ' s start with what the total price of the refrigerator would be . if 25 % is equal to $ 875 then 100 % equals $ x . we just have to multiply $ 875 by 4 to get total amount = $ 3500 . out of this amount we then need to deduct the amount already paid which was $ 875 so we have $ 3500 - $ 875 = $ 2625 answer : option e
Answer: e
Problem: 16 is what % of 90 ?
Options: a ) 16 , b ) 17.78 , c ) 17 , d ) 18.5 , e ) 18.23
Rationale: we assume that 90 is 100 % assume ' x ' is value we looking for here , 90 = 100 % and x % = 16 therefore , 100 / x = 90 / 16 100 / x = 5.625 x = 17.78 b
Answer: b
Problem: amar takes as much time in running 12 meters as a car takes in covering 45 meters . what will be the distance covered by amar during the time the car covers 1.4 km ?
Options: a ) 700 m , b ) 500 m , c ) 373 m , d ) 356 m , e ) 640 m
Rationale: "distance covered by amar = 12 / 45 ( 1.4 km ) = 4 / 15 ( 1400 ) = 373 m answer : c"
Answer: c
Problem: how many 2 digit number contain number 3 ?
Options: a ) 18 , b ) 28 , c ) 38 , d ) 68 , e ) 58
Rationale: "total 2 digit no . = 9 * 10 * = 90 not containing 3 = 8 * 9 = 72 total 2 digit number contain 3 = 90 - 72 = 18 answer : a"
Answer: a
Problem: the side of a square is increased by 15 % then how much % does its area increases ?
Options: a ) 52.65
b ) 56.25
c ) 50.75
d ) 32.25
e ) 52.75
Rationale: a = 100 a 2 = 10000 a = 115 a 2 = 13225 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 3225 100 - - - - - - - ? = > 32.25 % answer : d
Answer: d
Problem: marla starts running around a circular track at the same time nick starts walking around the same circular track . marla completes 28 laps around the track per hour and nick completes 13 laps around the track per hour . how many minutes after marla and nick begin moving will marla have completed 4 more laps around the track than nick ?
Options: a ) 5 , b ) 8 , c ) 12 , d ) 16 , e ) 20
Rationale: "maria ' s rate - 28 laps per hour - - > 28 / 60 laps / min nick ' s rate - 13 laps per hour - - > 13 / 60 laps / min lets set equations : 28 / 60 * t = 4 ( since maria had to run 4 laps before nick would start ) 13 / 60 * t = 0 ( hick has just started and has n ' t run any lap yet ) ( 28 / 60 - 13 / 60 ) * t = 4 - 0 ( since nick was chasing maria ) t = 16 min needed maria to run 4 laps answer : d"
Answer: d
Problem: a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 14200 after a year ?
Options: a ) 3630 , b ) 9232 , c ) 4260 , d ) 2387 , e ) 2813
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 14200 = 4260 answer : c"
Answer: c
Problem: three coins are tossed . find the probability of at most 2 tails ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 2 / 3 , d ) 7 / 8 , e ) 3 / 8
Rationale: "n ( s ) = 2 ^ 3 = 8 let e is the event of getting at most 2 tails n ( e ) = hhh , tth , htt , tht , hht , hth , thh = 7 p ( e ) = n ( e ) / n ( s ) = 7 / 8 ans - d"
Answer: d
Problem: when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ?
Options: a ) 1 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 63 , the remainder is 25 . what is the remainder when x is divided by 8 ? putting a value say x = 255 we get remainder as 25 when divided by 63 . when 25 divided by 8 we get 1 as remainder . a is the answer ."
Answer: a
Problem: the average of 25 results is 8 . the average of first 12 of them is 14 and that of last 12 is 17 . find the 13 result ?
Options: a ) 52 , b ) 68 , c ) 78 , d ) 92 , e ) 65
Rationale: "13 th result = sum of 25 results - sum of 24 results 18 * 25 - 14 * 12 + 17 * 12 = 78 answer is d"
Answer: d
Problem: 5.02 can be expressed in terms of percentage as
Options: a ) 5.02 % , b ) 50.2 % , c ) 209 % , d ) 502 % , e ) none of these
Rationale: "explanation : while calculation in terms of percentage we need to multiply by 100 , so 5.02 * 100 = 502 answer : option d"
Answer: d
Problem: x and y invested in a business . they earned some profit which they divided in the ratio of 1 : 2 . if x invested rs . 20,000 . the amount invested by y is
Options: a ) rs . 45,000 , b ) rs . 40,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 20000 / y = 1 / 2 â € ¹ = â € º y = ( 20000 ã — 2 / 1 ) . â € ¹ = â € º y = 40000 . answer b"
Answer: b