Cheukting/mathqa huggingface dataset:
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 18.75 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 23 % , c ) 25 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 118.75 let marked price be rs . x . then , 95 / 100 x = 118.75 x = 11875 / 95 = rs . 125 now , s . p . = rs . 125 , c . p . = rs . 100 profit % = 25 % . answer : c"
Answer: c
Question (gain): a sum of 15,600 amounts to 21,200 in 5 years at the rate of simple interest . what is the rate of interest ?
Options: a ) 2 % , b ) 1 % , c ) 7 % , d ) 5 % , e ) 8 %
Rationale: "c 7 % s . i . = ( 21200 - 15600 ) = 5600 . rate = ( 100 x 5600 ) / ( 15600 x 5 ) % = 7 %"
Answer: c
Question (general): a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 8 gallons of water and 16 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?
Options: a ) 120 , b ) 75 , c ) 100 , d ) 150 , e ) 175
Rationale: "nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 16 gallons salt is added and 8 gallons of water is added . so salt now becomes - > ( 0.2 x + 16 ) and water - - > ( 0.6 x + 8 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 16 ) = ( 0.6 x + 8 ) / 2 = > 0.2 x = 24 solving , x = 120 answer : a"
Answer: a
Question (gain): rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 8 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 8 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 8 / 100 ( 6000 - x ) = 480 - x / 100 = > 480 - 1 / 100 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b"
Answer: b
Question (gain): we invested a total of $ 1,000 . we invested one part of the money at 4 % and the rest of the money at 6 % . the total investment with interest at the end of the year was $ 1,046 . how much money did we invest at 4 % ?
Options: a ) $ 600 , b ) $ 650 , c ) $ 700 , d ) $ 750 , e ) $ 800
Rationale: let x be the money invested at 4 % . 1.04 x + 1.06 ( 1000 - x ) = 1046 . 0.02 x = 1060 - 1046 . 0.02 x = 14 . 2 x = 1400 . x = 700 . the answer is c .
Answer: c
Question (physics): steve traveled the first 2 hours of his journey at 40 mph and the last 3 hours of his journey at 60 mph . what is his average speed of travel for the entire journey ?
Options: a ) 52 mph , b ) 56.67 mph , c ) 53.33 mph , d ) 64 mph , e ) 66.67 mph
Rationale: "answer average speed of travel = total distance travelled / total time taken total distance traveled by steve = distance covered in the first 2 hours + distance covered in the next 3 hours . distance covered in the first 2 hours = speed * time = 40 * 2 = 80 miles . distance covered in the next 3 hours = speed * time = 60 * 3 = 180 miles . therefore , total distance covered = 80 + 180 = 260 miles . total time taken = 2 + 3 = 5 hours . hence , average speed = total distance travelled / total time taken = 260 / 5 = 52 miles per hour . choice a"
Answer: a
Question (geometry): the volume of a box with a square base is 128 cubic cm . the area of the base of the box is 8 inches more than the height . what is the length of the base of the box ?
Options: a ) 4 cm
b ) 8 cm
c ) 16 cm
d ) 24 cm
e ) none of the above
Rationale: l x w x h = 64 l x w - 8 = h l = w solving the 3 equations we get area of base = 16 square cm and height = 8 cm , which means length = 4 cm and width = 4 cm correct answer : a
Answer: a
Question (general): subtracting 6 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.94 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 6 % of a = ab . ⇒ ( 94 x a ) / 100 = ab ∴ b = 0.94 correct option : a"
Answer: a
Question (general): how many 3 digit numbers are completely divisible 6 ?
Options: a ) 146 , b ) 148 , c ) 150 , d ) 152 , e ) none of these
Rationale: "explanation : 100 / 6 = 16 , remainder = 4 . hence 2 more should be added to 100 to get the minimum 3 digit number divisible by 6 . = > minimum 3 digit number divisible by 6 = 100 + 2 = 102 999 / 6 = 166 , remainder = 3 . hence 3 should be decreased from 999 to get the maximum 3 digit number divisible by 6 . = > maximum 3 digit number divisible by 6 = 999 - 3 = 996 hence , the 3 digit numbers divisible by 6 are 102 , 108 , 114 , . . . 996 this is arithmetic progression with a = 102 , d = 6 , l = 996 number of terms = ( l − a ) / d + 1 = ( 996 − 102 ) / 6 + 1 = 894 / 6 + 1 = 149 + 1 = 150 . answer : option c"
Answer: c
Question (general): what is the remainder if 7 ^ 3 is divided by 100 ?
Options: a ) 52 , b ) 35 , c ) 42 , d ) 41 , e ) 43
Rationale: "7 * 7 * 7 / 100 = 343 / 100 remainder 43 answer : e"
Answer: e
Question (physics): in 140 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 28 m , c ) 22.5 m , d ) 9 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 140 / 45 x 9 m = 28 m . a beats b by 28 metres . answer : option b"
Answer: b
Question (physics): how many times in a day , the hands of a clock are straight ?
Options: a ) 22 , b ) 24 , c ) 44 , d ) 48 , e ) 52
Rationale: "in 12 hours , the hands coincide or are in opposite direction 22 times . in 24 hours , the hands coincide or are in opposite direction 44 times a day . answer : option c"
Answer: c
Question (geometry): a right circular cylinder has a height of 22 and a radius of 5 . a rectangular solid with a height of 15 and a square base , is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall . liquid is then poured into the cylinder such that it reaches the rim . what is the volume of the liquid ?
Options: a ) 500 ( π – 3 )
b ) 500 ( π – 2.5 )
c ) 500 ( π – 2 )
d ) 550 ( π – 1.5 )
e ) 500 ( π – 1 )
Rationale: [ quote = bunuel ] a right circular cylinder has a height of 20 and a radius of 5 . a rectangular solid with a height of 15 and a square base , is placed in the cylinder such that each of the corners of the solid is tangent to the cylinder wall . liquid is then poured into the cylinder such that it reaches the rim . what is the volume of the liquid ? the square base has sides of sqrt ( 50 ) due to the 45 - 45 - 90 triangle 22 * 25 * pi - 15 * sqrt ( 50 ) ^ 2 = 550 ( π – 1.5 ) d . 500 ( π – 1.5 )
Answer: d
Question (general): the visitors of a modern art museum who watched a certain picasso painting were asked to fill in a short questionnaire indicating whether they had enjoyed looking at the picture and whether they felt they had understood it . according to the results of the survey , all 140 visitors who did not enjoy the painting also did not feel they had understood the painting , and the number of visitors who enjoyed the painting was equal to the number of visitors who felt they had understood the painting . if 3 / 4 of the visitors who answered the questionnaire both enjoyed the painting and felt they had understood the painting , then how many visitors answered the questionnaire ?
Options: a ) 90 , b ) 120 , c ) 160 , d ) 360 , e ) 560
Rationale: "if we exclude those cases and take the question at face value , then it seems straightforward . group # 1 = ( did n ' t like , did n ' t understand ) = 120 group # 2 = ( likeunderstood ) = 3 / 4 ( 1 / 4 ) n = 560 n = 480 answer = ( e )"
Answer: e
Question (general): the average monthly salary of 8 workers and one supervisor in a factory was 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . @ sswhen @ ssthe @ sssupervisor @ cc @ sswhose @ sssalary @ sswas @ ss 430 . whenthesupervisor , whosesalarywas 430 . when the supervisor , whose salary was 870 per month , retired , a new person was appointed and then the average salary of 9 people was $ $ 430 per month . the salary of the new supervisor is :
Options: a ) 870 , b ) 600 , c ) 287 , d ) 771 , e ) 191
Rationale: "explanation : total salary of 8 workers and supervisor together = 9 ã — 430 = 3870 now total salary of 8 workers = 3870 â ˆ ’ 870 = 3000 total salary of 9 workers including the new supervisor = 9 ã — 430 = 3870 salary of the new supervisor = 3870 â ˆ ’ 3000 = 870 answer : a"
Answer: a
Question (general): 3 men and 2 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24
Rationale: the list should be wmwmw . hence , from women 2 ! and men 3 ! , we get ( 2 ! ) ( 3 ! ) = 12 . therefore , the correct answer is a .
Answer: a
Question (general): what is the greatest integer m for which the number 40 ! / 10 ^ m is an integer ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 40 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 , 35 , 40 . thus 5 ^ 9 will divide 40 ! but 5 ^ 10 will not . clearly 2 ^ 9 will divide 40 ! so m = 9 is the largest possible integer . the answer is c ."
Answer: c
Question (physics): 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: "explanation : total volume of water displaced = ( 4 x 50 ) m 3 = 200 m 3 rise in water level = 200 / 40 × 20 = 0.25 m = 25 cm answer : b"
Answer: b
Question (physics): darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 25 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 10.5 , b ) 0.5 , c ) 25.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 25 x = 0.5 minutes answer : b"
Answer: b
Question (general): if 5 ^ 21 x 8 ^ 7 = 10 ^ n what is the value of n ?
Options: a ) 26 , b ) 24 , c ) 21 , d ) 28 , e ) 20
Rationale: 5 ^ 21 * ( 2 ^ 3 ) ^ 7 = 10 ^ n or 5 ^ 21 * 2 ^ 21 = 10 ^ n or 10 ^ 21 = 10 ^ n n = 21 c
Answer: c
Question (general): at a certain supplier , a machine of type a costs $ 20000 and a machine of type b costs $ 60000 . each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time . if the finance charges are equal to 40 percent of the remainder of the cost , how much less would 2 machines of type a cost than 1 machine of type b under this arrangement ?
Options: a ) $ 10,000 , b ) $ 11,200 , c ) $ 12,000 , d ) $ 12,800 , e ) $ 26,400
Rationale: total cost of 2 machines of type a = 20 % of ( cost of 2 machine a ) + remainder + 40 % remainder = 20 % of 40000 + ( 40000 - 20 % of 40000 ) + 40 % of ( 40000 - 20 % of 40000 ) = 52800 total cost of 1 machine of type b = 20 % of ( cost of 1 machine b ) + remainder + 40 % remainder = 20 % of 60000 + ( 60000 - 20 % of 60000 ) + 40 % of ( 60000 - 20 % of 60000 ) = 79200 diff = 79200 - 52800 = 26400 hence , e .
Answer: e
Question (physics): the wages of 24 men and 16 women amounts to rs . 11600 per day . half the number of men and 37 women earn the same amount per day . what is the daily wage of a man ?
Options: a ) 2378 , b ) 277 , c ) 208 , d ) 270 , e ) 350
Rationale: let the wage of a man is m and woman be w . 24 m + 16 w = 11600 12 m + 37 w = 11600 solving we get m = 350 answer : e
Answer: e
Question (gain): a library branch originally contained 18360 volumes , 30 % of which were fiction novels . 1 / 3 of the volumes were transferred to another location and 1 / 2 of the volumes transferred were fiction novels . what percent of the remaining collection was fiction novels ?
Options: a ) 2.5 % , b ) 20 % , c ) 28.3 % , d ) 45.2 % , e ) 73.6 %
Rationale: "fiction novels = 5,508 transferred to another location = 6,120 transferred fiction novels = 3,060 non transferred fiction novels = 2,448 percent of the remaining collection was fiction novels = 2,448 / ( 18360 - 6120 ) * 100 = > 20 % hence answer will be ( b )"
Answer: b
Question (physics): find the expenditure on digging a well 14 m deep and of 3 m diameter at rs . 18 per cubic meter ?
Options: a ) 2998
b ) 2799
c ) 1782
d ) 1485
e ) 2780
Rationale: 22 / 7 * 14 * 3 / 2 * 3 / 2 = 99 m 2 99 * 18 = 1782 answer : c
Answer: c
Question (gain): what is the compound interest on rs . 7000 at 8.5 % p . a . compounded half - yearly for 5 years .
Options: a ) 3616.5 , b ) 3613.5 , c ) 3313.5 , d ) 3616.5 , e ) 3113.5
Rationale: "compound interest : a = p ( 1 + r / n ) nt a = 10 , 613.50 c . i . > > 10 , 613.50 - 7000 > > rs . 3613.5 answer : b"
Answer: b
Question (general): the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 14 years . the ratio of their ages after 8 years will be
Options: a ) 5 : 3 , b ) 8 : 11 , c ) 8 : 7 , d ) 6 : 5 , e ) 3 : 11
Rationale: "let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 14 x = 2 mini ’ s age = 8 years and minakshi ’ s age = 6 years ratio of their ages after 8 years = ( 8 + 8 ) : ( 6 + 8 ) = 16 : 14 = 8 : 7 answer : c"
Answer: c
Question (general): a large field of 700700 hectares is divided into two parts . the difference of the areas of the two parts is one - fifth of the average of the two areas . what is the area of the smaller part in hectares ?
Options: a ) 400 , b ) 365 , c ) 385 , d ) 315 , e ) 355
Rationale: "explanation : average of the two areas = 700 / 2 = 350 one - fifth of the average of the two areas = 350 / 5 = 70 ⇒ difference of the two areas = 70 = 70 let area of the smaller part = x hectares . then , area of the larger part = x + 70 hectares . x + ( x + 70 ) = 700 ⇒ 2 x = 630 ⇒ x = 315 answer : option d"
Answer: d
Question (gain): the purchase price of an article is $ 48 . in order to include 30 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 55 %
Rationale: "cost price of article = 48 $ % of overhead cost = 30 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 30 = 55 % answer e"
Answer: e
Question (geometry): how many diagonals does a polygon with 23 sides have , if one of its vertices does not connect to any diagonal ?
Options: a ) 201 , b ) 159 , c ) 179 , d ) 189 , e ) 209
Rationale: "if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 23 - 1 then 22 * ( 22 - 3 ) / 2 = 209 correct option : e"
Answer: e
Question (gain): mary invested a certain sum of money in a bank that paid simple interest . the amount grew to $ 260 at the end of 2 years . she waited for another 3 years and got a final amount of $ 350 . what was the principal amount that she invested at the beginning ?
Options: a ) $ 220 , b ) $ 230 , c ) $ 240 , d ) $ 200 , e ) $ 250
Rationale: what shall be the rate of interest . ? does that is not required for the calculation ? not really ! keep in mind that the interest earned each year will be the same in simple interest . at the end of 2 years , amount = $ 260 at the end of 5 years , amount = $ 350 this means she earned an interest of $ 90 in 3 years . or $ 30 in each year . we know that the interest earned each year will be the same . therefore she must have earned $ 60 in 2 years . hence principal amount = $ 260 - $ 60 = $ 200 option d
Answer: d
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 50 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 6.25 liters . , e ) 2.1 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 50 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 6.25 liters . answer : d"
Answer: d
Question (physics): laxmi and prasanna set on a journey . laxmi moves northwards at a speed of 22 kmph and prasanna moves southward at a speed of 24 kmph . how far will be prasanna from laxmi after 60 minutes ?
Options: a ) 44 , b ) 50 , c ) 28 , d ) 27 , e ) 18
Rationale: "explanation : we know 60 min = 1 hr total northward laxmi ' s distance = 22 kmph x 1 hr = 22 km total southward prasanna ' s distance = 24 kmph x 1 hr = 24 km total distance between prasanna and laxmi is = 22 + 24 = 44 km . answer : a"
Answer: a
Question (physics): a good train and a passenger train are running on parallel tracks in the same direction . the driver of the goods train observes that the passenger train coming from behind overtakes and crosses his train completely in 60 sec . whereas a passenger on the passenger train marks that he crosses the goods train in 40 sec . if the speeds of the trains be in the ratio 1 : 2 . find the ratio of their lengths .
Options: a ) 2 : 1 , b ) 3 : 1 , c ) 5 : 2 , d ) 1 : 1 , e ) none of these
Rationale: explanation : let , the speeds of the two trains be s and 2 s m / s respectively . also , suppose that the lengths of the two trains are p and q metres respectively . then , = > ( p + q ) / ( 2 s − s ) = 60 . - - - - - - - - - - - - - - ( 1 ) and , = > p / ( 2 s − s ) = 40 . - - - - - - - - - - - - - - ( 2 ) on dividing ( 1 ) by ( 2 ) , we get : - = > ( p + q ) / p = 60 / 40 . the required ratio is p : q = 2 : 1 . answer : a
Answer: a
Question (general): ( 3164 + 6160 ) / 28
Options: a ) 380 , b ) 350 , c ) 333 , d ) 310 , e ) none of these
Rationale: "explanation : as per bodmas rule , first we will solve the equation in bracket then we will go for division = ( 9324 ) / 28 = 333 option c"
Answer: c
Question (general): a prize of $ 600 is to be distributed among 15 winners , each of whom must be awarded at least $ 15 . if 2 / 5 of the prize will be distributed to 3 / 5 of the winners , what is the greatest possible individual award ?
Options: a ) $ 200 , b ) $ 220 , c ) $ 285 , d ) $ 300 , e ) $ 360
Rationale: "total value of the prize = $ 600 number of people = 15 2 / 5 of 600 ( = $ 240 ) should be distributed among 3 / 5 of 15 ( = 9 people ) with each getting $ 15 each . remaining money = 600 - 240 = $ 360 . now in order to ' maximize ' 1 prize , we need to minimise the others and we have been given that each should get $ 15 . thus , minimising the remaining 5 people ( = 15 - 9 - 1 . ' - 1 ' to exclude 1 that needs to be maximised ) = 5 * 15 = 75 . thus the maximum award can be = 360 - 75 = $ 285 , hence c is the correct answer ."
Answer: c
Question (geometry): a rectangular grass field is 75 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 3 per sq m ?
Options: a ) 675 , rs . 2025 , b ) 575 , rs . 1350 , c ) 1350 , rs . 675 , d ) 1450 , rs . 775 , e ) 1550 , rs . 875
Rationale: "area = ( l + b + 2 d ) 2 d = ( 75 + 55 + 2.5 * 2 ) 2 * 2.5 = > 675 675 * 3 = rs . 2025 answer : a"
Answer: a
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 8.30 , is :
Options: a ) 10 º , b ) 75 º , c ) 180 º , d ) 270 º , e ) 360 º
Rationale: "angle traced by hour hand in 17 / 2 hrs = ( 360 / 12 x 17 / 2 ) º = 255 . angle traced by min . hand in 30 min . = ( 360 / 60 x 30 ) º = 180 . required angle = ( 255 - 180 ) º = 75 º . answer b"
Answer: b
Question (general): evaluate ( 51 + 52 + 53 + . . . + 100 )
Options: a ) 3775 , b ) 3665 , c ) 3456 , d ) 3459 , e ) 3569
Rationale: sn = ( 1 + 2 + 3 + . . . + 50 + 51 + 52 + . . . + 100 ) - ( 1 + 2 + 3 + . . . + 50 ) = ( 50 x 101 ) - ( 25 x 51 ) = ( 5050 - 1275 ) = 3775 . option a
Answer: a
Question (other): 90 people are attending a newspaper conference . 45 of them are writers and more than 38 are editors . of the people at the conference , x are both writers and editors and 2 x are neither . what is the largest possible number of people who are both writers and editors ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 10 , e ) 6
Rationale: { total } = { writers } + { editors } - { both } + { neither } . { total } = 90 ; { writers } = 45 ; { editors } > 38 ; { both } = x ; { neither } = 2 x ; 90 = 45 + { editors } - x + 2 x - - > x = 45 - { editors } . we want to maximize x , thus we should minimize { editors } , minimum possible value of { editors } is 39 , thus x = { both } = 45 - 39 = 6 . answer : e .
Answer: e
Question (general): in an examination , 34 % of total students failed in hindi , 44 % failed in english and 22 % in both . the percentage of these who passed in both the subjects is :
Options: a ) 23 , b ) 37 , c ) 28 , d ) 44 , e ) 81
Rationale: explanation : formula n ( a â ˆ ª b ) = n ( a ) + n ( b ) â ˆ ’ n ( a â ˆ © b ) fail in hindi or english = 34 + 44 â € “ 22 = 56 therefore students who passed = 100 â € “ 56 = 44 . answer : d
Answer: d
Question (physics): nicky and cristina are running a 500 meter race . since cristina is faster than nicky , she gives him a 12 second head start . if cristina runs at a pace of 5 meters per second and nicky runs at a pace of only 3 meters per second , how many seconds will nicky have run before cristina catches up to him ?
Options: a ) 50 , b ) 45 , c ) 40 , d ) 35 , e ) 30
Rationale: "the distance traveled by both of them is the same at the time of overtaking . 3 ( t + 12 ) = 5 t t = 18 . cristina will catch up nicky in 18 seconds . so in 18 seconds cristina would cover = 18 * 5 = 90 meter . now time taken my nicky to cover 90 meter = 90 / 3 = 30 seconds . e"
Answer: e
Question (general): in 1990 the budgets for projects q and v were $ 540,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?
Options: a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996
Rationale: let the no of years it takes is x . 540 + 30 x = 780 - 10 x - - > 40 x = 240 and x = 6 . thus , it happens in 1996 . e .
Answer: e
Question (physics): there is a train and car . the ratio between the speed of a train & a car is 24 : 19 respectively . also , a bus covered a distance of 320 km in 5 hours . the speed of the bus is 2 / 3 rd of the speed of the train . how many kilometers will the car cover in 5 hours ?
Options: a ) 320 , b ) 340 , c ) 360 , d ) 380 , e ) 400
Rationale: "the speed of the bus is 320 / 5 = 64 km / hr the speed of the train is ( 64 * 3 ) / 2 = 96 km / hr the speed of the car is 96 / 24 * 19 = 76 km / hr the distance covered by the car in 5 hours is 76 × 5 = 380 km the answer is d ."
Answer: d