Cheukting/mathqa huggingface dataset:
Question (general): how many times digit 20 is used while writing numbers from 100 to 500 ?
Options: a ) 20 , b ) 30 , c ) 15 , d ) 25 , e ) 20
Rationale: "in 100 to 200 there are 5 20 ' s in 200 to 300 there are 5 20 ' s in 300 to 400 there are 5 20 ' s in 400 to 500 there are 5 20 ' s so , total 20 is 20 ' s correct option : a"
Answer: a
Question (general): the average of first 6 natural numbers is ?
Options: a ) 5.2 , b ) 3.5 , c ) 5.3 , d ) 5.9 , e ) 5.1
Rationale: "sum of 6 natural no . = 42 / 2 = 21 average = 21 / 6 = 3.5 answer : b"
Answer: b
Question (general): a part - time employee ’ s hourly wage was increased by 20 % . she decided to decrease the number of hours worked per week so that her total income did not change . by approximately what percent should the number of hours worked be decreased ?
Options: a ) 9 % , b ) 17 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "let ' s plug in somenicenumbers and see what ' s needed . let ' s say the employee used to make $ 1 / hour and worked 100 hours / week so , the total weekly income was $ 100 / week after the 20 % wage increase , the employee makes $ 1.20 / hour we want the employee ' s income to remain at $ 100 / week . so , we want ( $ 1.20 / hour ) ( new # of hours ) = $ 100 divide both sides by 1.20 to get : new # of hours = 100 / 1.20 ≈ 83 hours so , the number of hours decreases from 100 hours to ( approximately ) 83 hours . this represents a 17 % decrease ( approximately ) . answer : b"
Answer: b
Question (other): the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 4725 . the sum of the numbers is ?
Options: a ) a ) 10
b ) b ) 12
c ) c ) 15
d ) d ) 14
e ) e ) 9
Rationale: let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 4725 21 x ^ 2 = 4725 x ^ 2 = 225 x = 15 answer is c
Answer: c
Question (other): madhav ranks seventeenth in a class of thirtyone . what is his rank from the last ?
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: ( rank from top ) + ( rank from bottom ) - 1 = total students 17 + x - 1 = 31 x = 15 answer : c
Answer: c
Question (geometry): what positive number , when squared , is equal to the cube of the positive square root of 17 ?
Options: a ) 64
b ) 32
c ) 8
d ) 4
e ) 2
Rationale: let the positive number be x x ^ 2 = ( ( 17 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 64 = > x = 8 answer c
Answer: c
Question (gain): the cost of an article was rs . 75 . the cost was first increased by 20 % and later on it was reduced by 20 % . the present cost of the article is :
Options: a ) rs . 72 , b ) rs . 60 , c ) rs . 75 , d ) rs . 76 , e ) none
Rationale: solution : initial cost = rs . 75 after 20 % increase in the cost , it becomes , ( 75 + 20 % of 75 ) = rs . 90 now , cost is decreased by 20 % , so cost will become , ( 90 - 20 % of 90 ) = rs . 72 . so , present cost is rs . 72 . mind calculation method : 75 - - - - - 20 % ↑ - - → 90 - - - - - 20 % ↓ - - - - - → 72 . answer : option a
Answer: a
Question (physics): two trains 111 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 100 km and the other at the rate of 120 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 4.85 , b ) 7.85 , c ) 4.51 , d ) 5.85 , e ) 6.15
Rationale: "t = ( 111 + 165 ) / ( 100 + 120 ) * 18 / 5 t = 4.51 answer : c"
Answer: c
Question (gain): in how many years will a sum of money be doubled given that the annual interest on it is 10 % ?
Options: a ) 11 , b ) 14 , c ) 13 , d ) 15 , e ) 10
Rationale: p = ( p * 10 * r ) / 100 r = 10 % answer : e
Answer: e
Question (geometry): rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 2 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 2 / 5 , b ) 2 / 25 , c ) 5 / 2 , d ) 5 / 4 , e ) 4 / 25
Rationale: "the area of rectangle a is ab . c = 5 a / 2 and d = 5 b / 2 . the area of rectangle b is cd = 25 ab / 4 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 4 ) = 4 / 25 . the answer is e ."
Answer: e
Question (physics): if a boat is rowed downstream for 600 km in 20 hours and upstream for 48 km in 4 hours , what is the speed of the boat and the river ?
Options: a ) 21 , 21 , b ) 9 , 21 , c ) 21 , 9 , d ) 9 , 9 , e ) 20 , 8
Rationale: "explanation : if x : speed of boats man in still water y : speed of the river downstream speed ( ds ) = x + y upstream speed ( us ) = x â € “ y x = ( ds + us ) / 2 y = ( ds â € “ us ) / 2 in the above problem ds = 30 ; us = 12 x = ( 30 + 12 ) / 2 = 42 / 2 = 21 km / hr y = ( 30 - 12 ) / 2 = 18 / 2 = 9 km / hr answer : c"
Answer: c
Question (physics): a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 700 m long ?
Options: a ) 333 sec , b ) 190 sec , c ) 176 sec , d ) 2687 sec , e ) 1876 sec
Rationale: "l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 1900 m t = d / s t = 1900 / 10 t = 190 sec answer : b"
Answer: b
Question (gain): each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 4 of the slips are the drawn , without replacement , what is the probability that all 4 have a even number written on it ?
Options: a ) 1 / 12 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 42 , e ) 5 / 9
Rationale: key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 = 1 / 42 d
Answer: d
Question (general): two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 70 km more than the other . what is the distance between the two stations ?
Options: a ) 630 km , b ) 540 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 70 km more than the other , 25 x â € “ 20 x = 70 5 x = 70 x = 14 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 14 = 630 km . answer : a"
Answer: a
Question (general): the average age of 10 men increases by 2 years when two women are included in place of two men of ages 10 and 12 years . find the average age of the women ?
Options: a ) 21 , b ) 32 , c ) 30 , d ) 41 , e ) 37
Rationale: "10 + 12 + 10 * 2 = 42 / 2 = 21 answer : a"
Answer: a
Question (general): a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 , c receives :
Options: a ) 8400 , b ) 14703 , c ) 37798 , d ) 13777 , e ) 14778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . c ' s share = rs . ( 35000 * 12 / 50 ) = rs . 8,400 . answer : a )
Answer: a
Question (physics): due to construction , the speed limit along an 6 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 4 , b ) 8 , c ) 10 , d ) 15 , e ) 24
Rationale: 6 / 35 - 6 / 55 = 6 / 5 * ( 11 - 7 ) / 77 = 6 / 5 * 4 / 77 * 60 min = 6 * 12 * 4 / 77 = 288 / 77 ~ 3.7 answer - a
Answer: a
Question (gain): a , b and c invested rs . 600 , rs . 800 and rs . 1200 respectively , in a partnership business . find the share of b in profit of rs . 900 after a year ?
Options: a ) 276.92 , b ) 267.92 , c ) 266.27 , d ) 900 , e ) 237.8
Rationale: "explanation : 600 : 800 : 1200 3 : 4 : 6 4 / 13 * 900 = 276.92 answer : a"
Answer: a
Question (general): a driver would have reduced the time it took to drive from home to the store by 1 / 3 if the average speed had been increased by 21 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 36 , b ) 42 , c ) 45 , d ) 48 , e ) 51
Rationale: "let r be the original speed and let t be the original time . since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 3 would give us : d = ( r ) ( t ) = ( 2 t / 3 ) ( x * r ) x = 3 / 2 since ( 2 t / 3 ) ( 3 r / 2 ) = ( r ) ( t ) = d 3 r / 2 = r + 21 r / 2 = 21 r = 42 the answer is b ."
Answer: b
Question (physics): p works 25 % more efficiently than q and q works 50 % more efficiently than r . to complete a certain project , p alone takes 50 days less than q alone . if , in this project p alone works for 60 days and then q alone works for 135 days , in how many days can r alone complete the remaining work ?
Options: a ) 50 days , b ) 92.4 days , c ) 100 days , d ) 150 days , e ) 80 days
Rationale: "p works 25 % more efficiently than q : something that takes q 5 days , takes p 4 days q works 50 % more efficiently than r : something that takes r 7.5 days , takes q 5 days p alone takes 50 days less than q : for every 4 days p works , q has to work an extra day . hence p alone can do it in 200 days and q alone in 250 days and hence r alone in 385 days p works for 60 days - - > 60 / 200 work done = > 30 % q works for 135 days - - > 135 / 250 work done = > 54 % 24 % work left . . . r alone will take 24 % * 385 = 92.4 days answer is ( b )"
Answer: b
Question (general): find a number such that when 15 is subtracted from 7 times the number , the result is 10 more than twice the number .
Options: a ) 1 , b ) 4 , c ) 5 , d ) 0 , e ) 3
Rationale: let the number be x . then , 7 x - 15 = 2 x + 10 = > 5 x = 25 = > x = 5 . hence , the required number is 5 . answer is c .
Answer: c
Question (gain): harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 45 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1055 , c ) c ) 965 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 8 kg grapes = 70 × 8 = 560 . cost of 9 kg of mangoes = 45 × 9 = 405 . total cost he has to pay = 560 + 405 = 965 . c )"
Answer: c
Question (general): the average monthly income of a and b is rs . 4050 . the average monthly income of b and c is rs . 5250 and the average monthly income of a and c is rs . 4200 . what is the monthly income of a ?
Options: a ) 2000 , b ) 2500 , c ) 3000 , d ) 3500 , e ) 4000
Rationale: let monthly income of a = x monthly income of b = y monthly income of c = z x + y = 2 × 4050 . . . . ( equation 1 ) y + z = 2 × 5250 . . . . ( equation 2 ) z + x = 2 × 4200 . . . . ( equation 3 ) ( equation 1 ) + ( equation 3 ) - ( equation 2 ) = > x + y + x + z - ( y + z ) = ( 2 × 4050 ) + ( 2 × 4200 ) - ( 2 × 5250 ) = > 2 x = 2 ( 4050 + 4200 - 5250 ) = > x = 3000 i . e . , monthly income of a = 3000 answer : c
Answer: c
Question (gain): a merchant marks his goods up by 40 % and then offers a discount of 15 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 19 %
Rationale: let the original price be 100 . after 40 % markup , price = 140 after 15 % discount on this marked - up price , price = 140 - ( 15 % of 140 ) = 140 - 21 = 119 final profit = ( ( 119 - 100 ) / 100 ) * 100 = 19 % option e
Answer: e
Question (physics): a rectangular grassy plot 100 m . by 70 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 90 paise per sq . metre .
Options: a ) rs . 700 , b ) rs . 708.50 , c ) rs . 732.50 , d ) rs . 742.50 , e ) none of these
Rationale: "explanation : area of the plot = ( 100 x 70 ) m 2 = 7000 m 2 area of the plot excluding the path = [ ( 100 - 5 ) * ( 70 - 5 ) ] m 2 = 6175 m 2 . area of the path = ( 7000 - 6175 ) m 2 = 825 m 2 . cost of gravelling the path = rs . 825 * ( 90 / 100 ) = rs . 742.50 answer : option d"
Answer: d
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 4 : 3 and b : c = 4 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ?
Options: a ) 20.23 , b ) 20.13 , c ) 30.93 , d ) 20.93 , e ) 10.93
Rationale: "a : b = 4 : 3 b : c = 4 : 5 a : b : c = 16 : 12 : 15 12 / 43 * 75 = 20.93 answer : d"
Answer: d
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre .
Options: a ) rs . 15500 , b ) rs . 16500 , c ) rs . 17500 , d ) rs . 18500 , e ) rs . 19500
Rationale: "area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b"
Answer: b
Question (general): the ages of 2 persons differ by 38 years . if 12 years ago the elder one be 6 times as old as the younger one , find the present age of elder person .
Options: a ) 30.5 , b ) 48.5 , c ) 50.4 , d ) 62.6 , e ) 57.6
Rationale: "age of the younger person = x age of the elder person = x + 38 6 ( x - 12 ) = x + 38 - 12 x = 19.6 age of elder person = 19.6 + 38 = 57.6 answer is e"
Answer: e
Question (general): the product x of two prime numbers is between 15 and 70 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 69
Rationale: option bc can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 69 = 3 * 23 > > answer answer = e
Answer: e
Question (general): we define that k @ j is the product of j number from k in increasing order for positive integers k , j . for example , 6 @ 4 = 6 * 7 * 8 * 9 . if a = 2020 and b = 2120 , what is the value r of the ratio a / b ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 2 / 3 , d ) 1 / 4 , e ) 1 / 5
Rationale: "r - > a / b = 20 * 21 * … … * 39 / 21 * 22 * … . * 39 * 40 = 20 / 40 = 1 / 2 . therefore , the answer is a ."
Answer: a
Question (gain): a candidate got 40 % of the votes polled and he lost to his rival by 5000 votes . how many votes were cast ?
Options: a ) 25000 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 5000 100 % - - - - - - - - - ? = > 25000 answer : a"
Answer: a
Question (general): two employees a and b are paid a total of rs . 560 per week by their employer . if a is paid 150 percent of the sum paid to b , how much is b paid per week ?
Options: a ) s . 130 , b ) s . 140 , c ) s . 150 , d ) s . 224 , e ) s . 280
Rationale: "let the amount paid to a per week = x and the amount paid to b per week = y then x + y = 560 but x = 150 % of y = 150 y / 100 = 15 y / 10 ∴ 15 y / 10 + y = 560 ⇒ y [ 15 / 10 + 1 ] = 560 ⇒ 25 y / 10 = 560 ⇒ 25 y = 5600 ⇒ y = 5600 / 25 = rs . 224 d )"
Answer: d
Question (general): what is the units digit of 17 ^ 83 × 13 ^ 82 × 11 ^ 87 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "cyclicity of 7 is 4 - - > 7 , 9 , 3 , 1 cyclicity of 3 is 4 - - > 3 , 9 , 7 , 1 11 raised to any positive power has a units digit 1 17 ^ 83 × 13 ^ 82 × 11 ^ 87 = units digit of 3 * 9 * 1 = 7 answer : d"
Answer: d
Question (general): find the lowest common multiple of 10 , 14 and 20 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 140
Rationale: "lcm = 2 * 2 * 5 * 7 = 140 . answer is e"
Answer: e
Question (general): 3034 - ( 1002 / 200.4 ) = ?
Options: a ) 2984 , b ) 3029 , c ) 2982 , d ) 2981 , e ) none of these
Rationale: "3034 - 5 = 3029 answer : b"
Answer: b
Question (general): if 2 x = 3 y = 10 , then 6 xy = ?
Options: a ) 100 , b ) 200 , c ) 120 , d ) 40 , e ) 20
Rationale: "2 x = 10 ; x = 5 3 y = 10 ; y = 10 / 3 multiply : 6 xy = 6 * 5 * 10 / 3 = 100 answer : a ."
Answer: a
Question (physics): a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.6 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 6 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 160 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 160 - x ) = 8000 × 1000 = > ( 160 - x ) = 8000 × 1000 / 320 = 100 = > x = 60 cm = 6 dm . answer : b
Answer: b
Question (physics): the length of minute hand of a clock is 5.5 cm . what is the area covered by this in 10 minutes
Options: a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 19.27 , e ) 15.83
Rationale: "area of circle is pi * r ^ 2 but in 10 minutes area covered is ( 10 / 60 ) * 360 = 60 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.5 ^ 2 ) * ( 60 / 360 ) = 15.83 cm ^ 2 answer : e"
Answer: e
Question (general): if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 290 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 180 , b ) 184 , c ) 188 , d ) 192 , e ) 196
Rationale: "j + k = 290 and so k = 290 - j j - 8 = 2 k j - 8 = 2 ( 290 - j ) 3 j = 588 j = 196 the answer is e ."
Answer: e
Question (physics): a , b , k start from the same place and travel in the same direction at speeds of 30 km / hr , 40 km / hr , 80 km / hr respectively . b starts two hours after a . if b and k overtake a at the same instant , how many hours after a did k start ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "in 2 hours , a travels 60 km . b can catch a at a rate of 10 km / hr , so b catches a 6 hours after b starts . so a and b both travel a distance of 240 km . c needs 3 hours to travel 240 km , so c leaves 5 hours after a . the answer is d ."
Answer: d
Question (general): in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent x of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march x = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Question (other): at a garage sale , all of the items were sold at different prices . if the price of a radio sold at the garage sale was both the 16 th highest price and the 23 rd lowest price among the prices of the items sold , how many items were sold at the garage sale ?
Options: a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
Rationale: "there were 15 items sold at a higher price than the radio and 22 items sold at a lower price than the radio . including the radio , there were 15 + 22 + 1 = 38 items sold . the answer is d ."
Answer: d
Question (physics): one hour after yolanda started walking from x to y , a distance of 52 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 28 , b ) 23 , c ) 22 , d ) 21 , e ) 19.5
Rationale: "when b started walking y already has covered 3 miles out of 52 , hence the distance at that time between them was 52 - 3 = 49 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 49 / 7 = 7 hours . in 6 hours b walked 7 * 4 = 28 miles . answer : a ."
Answer: a
Question (general): find the sum the difference between the compound and s . i . on a certain sum of money for 2 years at 10 % per annum is rs . 13 of money ?
Options: a ) 1300 , b ) 1992 , c ) 9921 , d ) 2798 , e ) 2789
Rationale: "p = 13 ( 100 / 10 ) 2 = > p = 1300 answer : a"
Answer: a
Question (physics): 30 men can do a work in 40 days . when should 10 men leave the work so that the entire work is completed in 40 days after they leave the work ?
Options: a ) 87 days , b ) 10 days , c ) 55 days , d ) 44 days , e ) 20 days
Rationale: "total work to be done = 30 * 40 = 1200 let 10 men leave the work after ' p ' days , so that the remaining work is completed in 40 days after they leave the work . 40 p + ( 10 * 40 ) = 1200 40 p = 800 = > p = 20 days answer : e"
Answer: e
Question (physics): two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?
Options: a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec
Rationale: "speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 120 + 120 ) / 20 = 12 sec . answer : b"
Answer: b
Question (general): what is 990 * 990 ?
Options: a ) 974,169 , b ) 974,219 , c ) 974,549 , d ) 980,100 , e ) 985,369
Rationale: "if you take a base of 1000 then 990 is 10 less than 1000 to get the product of 990 x 990 write like this 990 - 10 ( as 10 less than base 1000 ) 990 - 10 now 10 x 10 = 100 and 990 - 10 = 980 so 990 x 990 = 980100 . . . ( bingo the answer is d . you can even have a shortcut . . . . . . 10 x 10 = 100 . . . only answer choice has last three digits as 100 . . so no need to calculate 990 - 10 . after you get 10 x 10 you can straight way pick answer choice d ."
Answer: d
Question (other): jill ' s favorite number is even and has some repeating prime factors . john is guessing jills favorite number , and the only hint she gives is that 7 is a prime factor . what is johns best guess ?
Options: a ) 84 , b ) 105 , c ) 54 , d ) 42 , e ) 70
Rationale: a 84 = 2 * 2 * 2 * 7 b 105 is odd c 54 = 2 * 3 * 3 d 42 = 2 * 3 * 7 e 70 = 2 * 5 * 7 the answer must meet three criteria : odd , have repeating prime factors , and 7 is a prime factor . a is the only answer that meets all criteria
Answer: a
Question (general): kamal obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 72 , d ) 75 , e ) none
Rationale: "sol . average = 76 + 65 + 82 + 67 + 85 / 5 ) = ( 375 / 5 ) = 75 . answer d"
Answer: d
Question (general): find the number of factors of 180 that are in the form ( 4 * k + 2 ) , where k is a non - negative integer ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 6
Rationale: make sure to follow posting guidelines ( link in my signatures ) . title of the thread must mention the first few words of the question itself . as for the question , the most straightforward way is to list out the factors ( this is fine for this question as 180 is a relatively small number ) . number of factors of 180 ( = 2 ^ 2 * 3 ^ 2 * 5 ) = 18 . so listing the factors gives us : 1 , 180 2 , 90 3 , 60 4 , 45 5 , 36 6 , 30 9 , 20 10 , 18 12 , 15 as the question asks us about the factors of the form 4 k + 2 - - - > eliminate all odd factors . you are now left with 24 , 610 , 1218 , 2030 , 3660 , 90180 for the form 4 k + 2 , the first few values are 2 , 6 , 10 , 14 , 18 , 22 , 26 , 30 . . . already giving you 5 factors ( = 2 , 610 , 1830 ) . you can stop here and mark 6 ( 6 th one = 90 ) as the correct answer as 5 is not given . for checking any particular factor whether they conform to the form 4 k + 2 - - - > do the following 4 k + 2 = 36 - - - > 4 k = 34 - - > this will not give you an integer value for k - - - > reject . proceed with others until you find all the values asked . e is thus the correct answer .
Answer: e