Cheukting/mathqa huggingface dataset:
Question (physics): a student travels from his house to school at 10 km / hr and reaches school 2 hours late . the next day he travels 15 km / hr and reaches school 1 hour early . what is the distance between his house and the school ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "let x be the distance from his house to the school . x / 10 = x / 15 + 3 6 x = 4 x + 180 2 x = 180 x = 90 km the answer is d ."
Answer: d
Question (physics): a train 250 m long , running with a speed of 50 km / hr will pass a tree in ?
Options: a ) 18 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 1 min
Rationale: "speed = 50 * 5 / 18 = 125 / 9 m / sec time taken = 250 * 9 / 125 = 18 sec answer : a"
Answer: a
Question (physics): the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 20 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 30.54 , e ) 30.27
Rationale: "area of circle is pi * r ^ 2 but in 20 minutes area covered is ( 20 / 60 ) * 360 = 120 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 120 / 360 ) = 30.54 cm ^ 2 answer : d"
Answer: d
Question (general): country x imposes a two - tiered tax on imported cars : the first tier imposes a tax of 25 % of the car ' s price up to a certain price level . if the car ' s price is higher than the first tier ' s level , the tax on the portion of the price that exceeds this value is 15 % . if ron imported a $ 30000 imported car and ended up paying $ 5500 in taxes , what is the first tier ' s price level ?
Options: a ) $ 10000 , b ) $ 11000 , c ) $ 12000 , d ) $ 10500 , e ) $ 11500
Rationale: let t be the tier price , p be total price = 30000 per the given conditions : 0.25 t + 0.15 ( p - t ) = 5500 0.25 t + 0.15 * 30000 - 0.15 t = 5500 0.10 t + 4500 = 5500 0.10 t = 5500 - 4500 = 1000 t = 1000 / 0.10 = 10000 answer a
Answer: a
Question (general): in the faculty of reverse - engineering , 230 second year students study numeric methods , 423 second year students study automatic control of airborne vehicles and 134 second year students study them both . how many students are there in the faculty if the second year students are approximately 80 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 618 . , d ) 649 . , e ) 666 .
Rationale: "answer is d : 649 solution : total number of students studying both are 423 + 230 - 134 = 519 ( subtracting the 134 since they were included in the both the other numbers already ) . so 80 % of total is 519 , so 100 % is approx . 649 ."
Answer: d
Question (general): the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 48 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 55 , e ) 50
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 48 : { mean } - 3 * { sd } > 48 ; { mean } - 6 > 48 ; { mean } > 54 . answer : d ."
Answer: d
Question (other): a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 9 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 3 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 9 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 9 ) = 0.08 t - - > 60 + 6 ( t - 9 ) = 8 t - - > t = 3 . answer : a ."
Answer: a
Question (general): zachary is helping his younger brother , sterling , learn his multiplication tables . for every question that sterling answers correctly , zachary gives him 3 pieces of candy . for every question that sterling answers incorrectly , zachary takes away two pieces of candy . after 9 questions , if sterling had answered 2 more questions correctly , he would have earned 31 pieces of candy . how many of the 9 questions did zachary answer correctly ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "i got two equations : 3 x - 2 y = 25 x + y = 9 3 x - 2 ( 9 - x ) = 25 3 x - 18 + 2 x = 25 5 x = 43 x = 8.6 or between 8 and 9 . ( ans c )"
Answer: c
Question (general): if the average of 5 positive integers is 60 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 52 , c ) 49 , d ) 68 , e ) 74
Rationale: "sum of 5 integer ( a , b , c , d , e ) = 5 * 60 = 300 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 300 i . e . 5 a = 290 i . e . a = 58 i . e . largest e = 58 + 10 = 68 answer : option d"
Answer: d
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 160 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 140
Rationale: "set up equation : x = total number of workers 160 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 160 = 16 / 30 x x = 300 300 - 160 = 140 answer e"
Answer: e
Question (general): the cost of a one - family home was $ 120,000 in 1980 . in 1988 , the price had increased to $ 180,000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: "percentage increase = increase in price / original price * 100 = ( 180000 - 120000 ) / 120000 * 100 = 50 % answer : b"
Answer: b
Question (general): sum of 53 odd numbers is ?
Options: a ) 2709 , b ) 2809 , c ) 2909 , d ) 3009 , e ) 3109
Rationale: "sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 53 odd numbers = 53 ^ 2 = 2809 answer : b"
Answer: b
Question (general): find the value of 5 + 2 â € ¢ ( 8 â € “ 3 )
Options: a ) 25 , b ) 13 , c ) 17 , d ) 24 , e ) 15
Rationale: 5 + 2 â € ¢ ( 8 â € “ 3 ) = 5 + 2 ( 5 ) = 5 + 2 * 5 = 5 + 10 = 15 correct answer e
Answer: e
Question (geometry): the mass of 1 cubic meter of a substance is 500 kilograms under certain conditions . what is the volume , in cubic centimeters , of 1 gram of this substance under these conditions ? ( 1 kilogram = 1,000 grams and 1 cubic meter = 1 , 000,000 cubic centimeters )
Options: a ) 0.8 , b ) 1.25 , c ) 2.0 , d ) 2.5 , e ) 80.0
Rationale: "density is mass divided by volume . so density of the given substance will be mass / volume = 500 kg / 1 m ^ 3 = 800 kg / m ^ 3 or 1 g / 1.5 cm ^ 3 = 0.5 g / cm ^ 3 . next , ask yourself if 500,000 g is equivalent to 1 , 000,000 cubic centimeters then 1 g is equivalent to how many cubic centimeters ? - - > 1 g - 1 , 000,000 / 500,000 = 10 / 5 = 2.0 cubic centimeters . answer is c"
Answer: c
Question (general): what least number should be added to 1057 , so that the sum is completely divisible by 23
Options: a ) a ) 4 , b ) b ) 1 , c ) c ) 2 , d ) d ) 3 , e ) e ) 5
Rationale: "explanation : ( 1057 / 23 ) gives remainder 22 22 + 1 = 23 , so we need to add 1 answer : option b"
Answer: b
Question (other): he ratio between the sale price and the cost price of an article is 5 : 6 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 6 , b ) 1 : 8 , c ) 1 : 6 , d ) 2 : 1 , e ) 2 : 5
Rationale: "let c . p . = rs . 6 x and s . p . = rs . 5 x . then , gain = rs . x required ratio = x : 6 x = 1 : 6 . answer : c"
Answer: c
Question (general): . in digging a pond 20 m * 10 m * 5 m the volumes of the soil extracted will be ?
Options: a ) 3323 , b ) 1000 , c ) 2877 , d ) 2992 , e ) 7111
Rationale: 20 * 10 * 5 = 1000 answer : b
Answer: b
Question (general): when 1 / 20 % of 8,000 is subtracted from 1 / 10 of 8,000 , the difference is
Options: a ) 50 , b ) 200 , c ) 380 , d ) 798 , e ) 400
Rationale: 1 / 20 % of 8000 = 4 1 / 10 of 8000 = 800 800 - 2 = 798 ans : d
Answer: d
Question (gain): 35 % of the employees of a company are men . 60 % of the men in the company speak french and 40 % of the employees of the company speak french . what is % of the women in the company who do not speak french ?
Options: a ) 4 % , b ) 10 % , c ) 96 % , d ) 90.12 % , e ) 70.77 %
Rationale: no of employees = 100 ( say ) men = 35 women = 65 men speaking french = 0.6 * 35 = 21 employees speaking french = 0.4 * 100 = 40 therefore women speaking french = 40 - 21 = 19 and women not speaking french = 65 - 19 = 46 % of women speaking french = 46 / 65 * 100 = 70.77 % answer e
Answer: e
Question (general): how many integers k greater than 100 and less than 700 are there such that if the hundreds and the unit digits of k are reversed , the resulting integer is k + 99 ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "not sure if this is the shortest . . but this is how i did this there are 5 sets of integers with hundreds and units digits exchanged that satisfies k + 99 . 1 . 102 | 201 ( satisfies k + 99 , where k = 102 ) 2 . 203 | 302 ( satisfies k + 99 , where k = 203 ) 3 . . . . 4 . . . . 5 . 506 | 607 each set has 10 such numbers . 1 . 102 | 201 ( still k + 99 holds good ) 2 . 112 | 211 3 . 122 | 221 4 . 132 | 231 5 . . . . 6 . . . . 7 . . . . 8 . . . . 9 . 182 | 281 10 . 192 | 291 therefore , 5 sets with 10 such number in each set will give 5 x 10 = 50 integers . a"
Answer: a
Question (physics): a motorcyclist started riding at highway marker a , drove 120 miles to highway marker b , and then , without pausing , continued to highway marker c , where she stopped . the average speed of the motorcyclist , over the course of the entire trip , was 45 miles per hour . if the ride from marker a to marker b lasted 3 times as many hours as the rest of the ride , and the distance from marker b to marker c was half of the distance from marker a to marker b , what was the average speed , in miles per hour , of the motorcyclist while driving from marker b to marker c ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "a - b = 120 miles b - c = 60 miles avg speed = 45 miles time taken for a - b 3 t and b - c be t avg speed = ( 120 + 60 ) / total time 45 = 180 / 4 t t = 60 b - c = 60 mph answer e"
Answer: e
Question (physics): which greatest possible length can be used to measure exactly 15 meter 20 cm , 12 meter 20 cm and 14 meter 20 cm
Options: a ) 20 cm , b ) 25 cm , c ) 24 cm , d ) 55 cm , e ) 30 cm
Rationale: "explanation : convert first all terms into cm . i . e . 1520 cm , 1220 cm , 1420 cm . now whenever we need to calculate this type of question , we need to find the hcf . hcf of above terms is 20 . option a"
Answer: a
Question (general): dick and jane each saved $ 5,000 in 1989 . in 1990 dick saved 10 percent more than in 1989 , and together he and jane saved a total of $ 10,000 . approximately what percent less did jane save in 1990 than in 1989 ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "1990 dick saved = $ 5500 jane saved = $ 4500 ( jane saved $ 500 less than she did the prior year ) jane saved approximately $ 500 / 5000 $ ( 10 % ) less in 1990 answer : a"
Answer: a
Question (general): robert ate 7 chocolates , nickel ate 5 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) a ) 4 , b ) b ) 7 , c ) c ) 9 , d ) d ) 5 , e ) e ) 2
Rationale: 7 - 5 = 2 . answer is e
Answer: e
Question (geometry): a small , rectangular park has a perimeter of 560 feet and a diagonal measurement of 600 feet . what is its area , in square feet ?
Options: a ) 172,800
b ) 19,600
c ) 20,000
d ) 20,400
e ) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that , with the info provided , the diagonal forms a triangle inside the rectangle with sides that have a 3 : 4 : 5 ratio . diagonal = 200 2 x + 2 y = 560 , or x + y = 280 a ^ 2 + b ^ 2 = c ^ 2 for each the sides of the triangle using the ratio 3 : 4 : 5 for sides , and knowing c = 600 , you can deduce the following a = 360 b = 480 360 x 480 = 172,800 a is the answer .
Answer: a
Question (general): on dividing 109 by a number , the quotient is 9 and the remainder is 1 . find the divisor
Options: a ) 12 , b ) 14 , c ) 18 , d ) 22 , e ) 24
Rationale: "d = ( d - r ) / q = ( 109 - 1 ) / 9 = 108 / 9 = 12 a )"
Answer: a
Question (gain): find compound interest on $ 10000 at 15 % per annum for 2 years 4 months , compounded annually .
Options: a ) 3886.25 , b ) 3286.25 , c ) 3186.25 , d ) 3386.25 , e ) 3586.25
Rationale: "time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 10000 x ( 1 + ­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 10000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 13886.25 . : . c . i . = rs . ( 13886.25 - 10000 ) = $ 3886.25 answer a ."
Answer: a
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 1.28 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.40 , b ) $ 3.00 , c ) $ 3.20 , d ) $ 3.60 , e ) $ 4.80
Rationale: "total allowance = x amount spent at the arcade = 3 / 5 x amount remaining = 2 / 5 x amount spent at the toy store = 2 / 5 * 1 / 3 x = 2 / 15 x amount remaining = 2 / 5 x - 2 / 15 x = 4 / 15 x now , 4 / 15 x = $ 1.28 therefore , x = $ 4.80 . answer e"
Answer: e
Question (general): what is the range of all the roots of | x ^ 2 - 4 | = x ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 4 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 4 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 4 or x = 1 i guess range is 4 - 1 = 3 b"
Answer: b
Question (physics): sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 60 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 150 , d ) 279 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.60 = rs . 150 answer : c"
Answer: c
Question (gain): the cost price of a radio is rs . 1680 and it was sold for rs . 1450 , find the loss % ?
Options: a ) 18 , b ) 13 , c ) 15 , d ) 18 , e ) 41
Rationale: "1680 - - - - 230 100 - - - - ? = > 13 % answer : b"
Answer: b
Question (general): when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 3 ) , the quotient is 15 and the remainder is 1 . what is the value of n ?
Options: a ) 151 , b ) 331 , c ) 511 , d ) 691 , e ) 205
Rationale: "n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 15 1 / ( p + 3 ) = 15 p + 45 + 1 solving these two equations we get p = 11 n = 205 answer is e ."
Answer: e
Question (general): if a person walks at 25 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 56 km , c ) 13.3 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 25 25 x = 10 x + 200 15 x = 200 x = 13.3 km . answer : c"
Answer: c
Question (general): a big container is 30 % full with water . if 45 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container ?
Options: a ) 36 liters , b ) 40 liters , c ) 45 liters , d ) 54 liters , e ) 100 liters
Rationale: "a big container is 30 % full with water and after 45 liters of water is added , the container becomes 75 % full . hence these 45 liters account for 45 % of the container , which means that the capacity of it is 45 / 0.45 = 100 liters . or : if the capacity of the container is x liters then : 0.3 x + 45 = 0.75 x - - > x = 100 liters . answer : e ."
Answer: e
Question (gain): 32 % of 1500 is
Options: a ) 480 , b ) 440 , c ) 370 , d ) 415 , e ) 435
Rationale: 1 % of 1500 is = 15 32 % of 1500 is = 32 * 15 = 480 answer : a
Answer: a
Question (geometry): find the smallest number that should be multiplied with 54000 to make it a perfect cube .
Options: a ) 4
b ) 5
c ) 6
d ) 3
e ) 7
Rationale: 54000 = 2 ^ 1 * 3 ^ 3 * 10 ^ 3 to make it ps * 2 ^ 2 or 4 answer : a
Answer: a
Question (general): a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 500000 ?
Options: a ) 160 , b ) 200 , c ) 240 , d ) 300 , e ) 480
Rationale: the first digit and last digit are the same so the 2 possibilities are 6 or 8 . the second and third digits can be any number from 0 to 9 . the total number of palindromic integers is 2 * 10 * 10 = 200 the answer is b .
Answer: b
Question (general): the average of 7 numbers is 25 . if each number be multiplied by 5 . find the average of new set of numbers ?
Options: a ) a ) 110 , b ) b ) 122 , c ) c ) 120 , d ) d ) 125 , e ) e ) 145
Rationale: "explanation : average of new numbers = 25 * 5 = 125 answer : option d"
Answer: d
Question (physics): a 90 cm long wire is to be cut into two pieces so that one piece will be 2 / 5 th of the other , how many centimeters will the shorter piece be ?
Options: a ) 25 , b ) 20 , c ) 47 , d ) 36 , e ) 30
Rationale: "1 : 2 / 5 = 5 : 2 2 / 7 * 90 = 25 answer : a"
Answer: a
Question (general): there are cats got together and decided to kill the mice of 999964 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
Options: a ) 941,1009 , b ) 991,1001 , c ) 991,1009 , d ) 791,1009 , e ) 994,1006
Rationale: "999964 can be written as 1000000 â € “ 36 = 10002 â € “ 62 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 6 ) * ( 1000 - 6 ) = ( 1006 ) * ( 994 ) given that number of cats is less than number if mice . so number of cats is 994 and number of mice were 1006 answer e"
Answer: e
Question (general): what is the remainder when you divide 2 ^ 200 - 1 by 7 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: answer is c . this is very similar to the 32 ^ 32 ^ 32 - 1 divided by 7 question .
Answer: c
Question (physics): a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is :
Options: a ) 16000 , b ) 18000 , c ) 20000 , d ) 22000 , e ) none of these
Rationale: "explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 option c"
Answer: c
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 1008 ?
Options: a ) 900 , b ) 2217 , c ) 2889 , d ) 2777 , e ) 2991
Rationale: "1008 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 900 answer : a"
Answer: a
Question (gain): if a sum of money doubles itself in 20 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 13 , d ) 5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 20 ) = 5 option d"
Answer: d
Question (general): what is the greatest integer m for which the number 50 ! / 10 ^ m is an integer ?
Options: a ) 5 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: "as for 50 ! / 10 ^ m , the greatest value of m will be obtained by finding the maximum number of 5 s in 50 ! the quick process for that ( discussed in the link above ) is 50 / 5 = 10 10 / 5 = 2 total number of 5 s is 12 . so maximum value of m will also be 12 . answer ( e )"
Answer: e
Question (general): at joes steakhouse the hourly wage for a chef is 20 % greater than that of a dishwasher , and the hourly wage of a dishwasher is half as much as the hourly wage of a manager . if a managers wage is $ 7.50 per hour , how much less than a manager does a chef earn each hour ?
Options: a ) $ 1.40 , b ) $ 3 , c ) $ 3.40 , d ) $ 4.40 , e ) $ 5.40
Rationale: "manager wages per hour = $ 7.50 dishwasher wages per hour = half of manager ' s wages . = 1 / 2 ( $ 7.50 ) = = > $ 3.75 chef wages per hour = 20 % greater than dishwasher wages - - > 20 % of $ 3.75 = ( 20 * ( $ 3.75 ) ) / 100 - - > ( $ 75 ) / 100 - - > $ 0.75 therefore , chef wages per hour = $ 3.75 + $ 0.75 = = > $ 4.5 difference of wages between manager and chef = $ 7.50 - $ 4.5 = = > $ 3 answer : b"
Answer: b
Question (gain): a person incurs a loss of 5 % be selling a watch for rs . 1140 . at what price should the watch be sold to earn 5 % profit
Options: a ) rs . 1200 , b ) rs . 1230 , c ) rs . 1260 , d ) rs . 1290 , e ) none of these
Rationale: "explanation : let the new s . p . be x , then . ( 100 - loss % ) : ( 1 st s . p . ) = ( 100 + gain % ) : ( 2 nd s . p . ) = > ( 95 / 1140 = 105 / x ) = > x = 1260 option c"
Answer: c
Question (physics): a train is 400 meter long is running at a speed of 60 km / hour . in what time will it pass a signal post ?
Options: a ) 28 seconds , b ) 30 seconds , c ) 40 seconds , d ) 24 seconds , e ) 18 seconds
Rationale: speed = 60 km / hr = 60 * ( 5 / 18 ) m / sec = 150 / 9 m / sec total distance = 400 meter time = distance / speed = 400 * ( 9 / 150 ) = 24 seconds answer : d
Answer: d
Question (general): the average of first 10 natural numbers is ?
Options: a ) 5.6 , b ) 5.5 , c ) 5.1 , d ) 5.8 , e ) 5.2
Rationale: "sum of 10 natural no . = 110 / 2 = 55 average = 55 / 10 = 5.5 answer : b"
Answer: b
Question (general): if a / b = 4 / 5 , then ( 5 a - 3 b ) / ( 5 a + 3 b ) = ?
Options: a ) 4 , b ) 2 / 3 , c ) 3 , d ) 1 , e ) 1 / 7
Rationale: "answer dividing numerator as well as denominator by b , we get given exp . = ( 5 a - 3 b ) / ( 5 a + 3 b ) = ( 5 a / b - 3 ) / ( 5 a / b + 3 ) since a / b = 4 / 5 this implies that = [ ( 5 * 4 ) / 5 - 3 ] / [ ( 5 * 4 ) / 5 + 3 ) ] = ( 4 - 3 ) / ( 4 + 3 ) = 1 / 7 option : e"
Answer: e
Question (physics): how long does a train 105 m long running at the speed of 68 km / hr takes to cross a bridge 90 m length ?
Options: a ) 13.9 sec , b ) 10.7 sec , c ) 17.9 sec , d ) 61.9 sec , e ) 47.98 sec
Rationale: "speed = 68 * 5 / 18 = 19 m / sec total distance covered = 105 + 90 = 205 m . required time = 205 / 19 = 10.7 sec . answer : b"
Answer: b
Question (general): there are 6 people in the elevator . their average weight is 152 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
Options: a ) 145 , b ) 168 , c ) 189 , d ) 190 , e ) 200
Rationale: "solution average of 7 people after the last one enters = 151 . â ˆ ´ required weight = ( 7 x 151 ) - ( 6 x 152 ) = 1057 - 912 = 145 . answer a"
Answer: a
Question (gain): ms . lopez deposits $ 150 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 181.15 , d ) $ 122.00 , e ) $ 140.00
Rationale: "using formula - a = p ( 1 + r / n ) ^ nt given p = 150 n = 2 t = 1 r = 0.2 substituting value in formula a = 150 ( 1 + 0.2 / 2 ) ^ 2 a = 181.15 $ = c"
Answer: c
Question (physics): a , b , c can complete a piece of work in 25 , 5,10 days . working together , they complete the same work in how many days ?
Options: a ) 2 , b ) 4 / 5 , c ) 50 / 17 , d ) 10 , e ) 24 / 7
Rationale: "a + b + c 1 day work = 1 / 25 + 1 / 5 + 1 / 10 = 17 / 50 a , b , c together will complete the job in 50 / 17 days answer is c"
Answer: c
Question (general): how much is 70 % of 40 is greater than 4 / 5 of 25 ?
Options: a ) 22 , b ) 67 , c ) 88 , d ) 12 , e ) 8
Rationale: "( 70 / 100 ) * 40 – ( 4 / 5 ) * 25 = 8 answer : e"
Answer: e