Cheukting/mathqa huggingface dataset:
Question (general): if the price of a certain bond on may 1 st was 1 / 2 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 160 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 2 * 12 = 6 ; the price on july 1 st = 6 * 1.5 = 9 . the average price of the bond on may 1 st and july 1 st = ( 6 + 9 ) / 2 = 7.5 . the price of the bond on june 1 st ( 12 ) is 8 / 5 times ( 160 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
Answer: e
Question (gain): an investment compounds annually at an interest rate of 33.34 % what is the smallest investment period by which time the investment will more than triple in value ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 4
Rationale: "assume initial amount is x annual interest is 34.1 % so after 1 year the amount will become x * ( 100 + 33.34 ) / 100 = > x * 4 / 3 now we need to find n for x * ( 4 / 3 ) ^ n = 3 x or in other words n = 4 e"
Answer: e
Question (general): a no . when divided by 220 gives a remainder 43 , what remainder will beobtained by dividingthe same no . 67 ?
Options: a ) 4 , b ) 6 , c ) 9 , d ) 11 , e ) 14
Rationale: "221 + 43 = 264 / 17 = 9 ( remainder ) c"
Answer: c
Question (gain): a and b ’ s salaries together amount to rs . 3,000 . a spends 95 % of his salary and b spends 85 % of his . if now their savings are the same , what is b ’ s salary ?
Options: a ) 777 , b ) 750 , c ) 789 , d ) 776 , e ) 881
Rationale: "( 5 / 100 ) a = ( 15 / 100 ) b a = 3 b a + b = 3000 4 b = 3000 = > b = 750 answer b"
Answer: b
Question (gain): ritesh and co . generated revenue of rs . 1,700 in 2006 . this was 12.5 % of its gross revenue . in 2007 , the gross revenue grew by rs . 2,500 . what is the percentage increase in the revenue in 2007 ?
Options: a ) 18.38 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) none of these
Rationale: "explanation : given , ritesh and co . generated revenue of rs . 1,700 in 2006 and that this was 12.5 % of the gross revenue . hence , if 1700 is 12.5 % of the revenue , then 100 % ( gross revenue ) is : = > ( 100 / 12.5 ) × 1700 . = > 13,600 . hence , the total revenue by end of 2007 is rs . 13,600 . in 2006 , revenue grew by rs . 2500 . this is a growth of : = > ( 2500 / 13600 ) × 100 . = > 18.38 % . answer : a"
Answer: a
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 . 1120 ?
Options: a ) 1000 , b ) 3889 , c ) 8908 , d ) 3780 , e ) 2709
Rationale: "1120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1000 answer : a"
Answer: a
Question (geometry): the radius of a cylindrical vessel is 7 cm and height is 5 cm . find the whole surface of the cylinder ?
Options: a ) 281 , b ) 528 , c ) 440 , d ) 767 , e ) 1981
Rationale: "r = 7 h = 5 2 π r ( h + r ) = 2 * 22 / 7 * 7 ( 12 ) = 528 answer : b"
Answer: b
Question (gain): a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 5400 interest . the principal amount borrowed by him was .
Options: a ) rs 14000 , b ) rs 15000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
Rationale: "explanation : s . i . = p ∗ r ∗ t / 100 = > p = s . i . ∗ 100 / r ∗ t = > p = 5400 ∗ 100 / 12 ∗ 3 = rs 15000 option b"
Answer: b
Question (general): in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 12 % . what is population of after 2 year .
Options: a ) 139 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: "next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 11 % so total man = 150 * . 88 = 132 women will be = 175 - 132 = 43 so population after two years = [ 135 ^ 2 + 43 ^ 2 ] ^ . 5 = 138.8 = 139 so population after two year = 139 answer : a"
Answer: a
Question (general): evaluate : 58 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 50 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 58 - 12 * 3 * 2 = 58 - 8 = 50 correct answer b"
Answer: b
Question (physics): jenny has recently moved house and is working out her optimal commute . she can take an indirect route which involves taking a bus for 1 mile and then walk 0.75 miles . or she can take a direct route and walk for 1.5 miles and this takes her 30 minutes . what is the most amount time that the bus journey can take for jenny to be indifferent between the two routes assuming travel time is her only concern ?
Options: a ) 5 minutes , b ) 10 minutes , c ) 15 minutes , d ) 20 minutes , e ) 25 minutes
Rationale: if jenny can walk 1.5 miles in 30 minutes , then she can talk 0.75 miles in half the time i . e . 15 minutes . for jenny to be indifferent between the two routes , the two journeys must have the same travel time . the direct route has a travel time of 30 minutes ( walking ) . the indirect route has a travel time of 15 minutes ( walking ) plus the bus journey . for the two routes to be the same the bus journey must take 15 minutes ( 30 - 15 ) . answer : c
Answer: c
Question (general): seller selling an apple for rs . 15 , a seller loses 1 / 6 th of what it costs him . the cp of the apple is ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 18 , e ) 20
Rationale: "sp = 15 loss = cp 16 loss = cp − sp = cp − 15 ⇒ cp 16 = cp − 15 ⇒ 15 cp 16 = 15 ⇒ cp 16 = 1 ⇒ cp = 16 c"
Answer: c
Question (geometry): if the volume of a cube is x ^ 3 cubic units , what is the number of square units in the surface area of the cube ?
Options: a ) x ^ 2
b ) x ^ 3
c ) x ^ 6
d ) 6 x ^ 2
e ) 6 x ^ 3
Rationale: the question basically asks you to calculate the surface area of the cube . volume of the cube = x ^ 3 this means each side of the cube = x hence area of each side = x ^ 2 total surfaces in a cube = 6 total surface area = 6 * x 2 correct option : d
Answer: d
Question (geometry): the area of a square field is 28808 sq m . how long will a lady take to cross the field diagonally at the rate of 7.2 km / hr ?
Options: a ) 2.5 min , b ) 3 min , c ) 2 min , d ) 4 min , e ) 4.5 min
Rationale: "area of a square field = 28808 sq m let the side of square = a a ^ 2 = 28808 = > a = 169.73 diagonal = ( 2 ) ^ ( 1 / 2 ) * a = 1.414 * 169.73 = 240 speed of lady = 7.2 km / hour = 7200 m / hour = 120 m / min time taken by lady to cross the field diagonally = 240 / 120 = 2 min answer c"
Answer: c
Question (gain): if a town of 35,000 people is growing at a rate of approx . 1 % per year , the population of the town in 5 years will be closest to ?
Options: a ) a . 36000 , b ) b . 37000 , c ) c . 38000 , d ) d . 39000 , e ) e . 40000
Rationale: 1 % is quite small and hence the answer is a )
Answer: a
Question (other): there are 12 slate rocks , 17 pumice rocks , and 8 granite rocks randomly distributed in a certain field . if 2 rocks are chosen at random and without replacement , what is the probability that both rocks will be slate rocks ?
Options: a ) 5 / 36 , b ) 7 / 64 , c ) 9 / 83 , d ) 11 / 111 , e ) 13 / 135
Rationale: "12 / 37 * 11 / 36 = 11 / 111 the answer is d ."
Answer: d
Question (general): one day a car rental agency rented 3 / 4 of its cars , including 5 / 6 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 13 / 20 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 7 , e ) 2 / 5
Rationale: "the cars with cd players which were not rented is ( 1 / 6 ) ( 3 / 5 ) = 1 / 10 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 1 / 10 ) / ( 1 / 4 ) = 2 / 5 the answer is e ."
Answer: e
Question (general): how many words , with or without meaning , can be formed using all letters of the word red using each letter exactly once ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: the word red has exactly 3 letters which are all different . therefore the number of words that can be formed = number of permutations of 3 letters taken all at a time . = p ( 3 , 3 ) = 3 ! = 3 x 2 × 1 = 6 answer : a
Answer: a
Question (other): of the 65 cars on a car lot , 30 have air - conditioning , 45 have air bag , and 12 have both air - conditioning and air bag . how many of the cars on the lot have neither air - conditioning nor air bag ?
Options: a ) 2 , b ) 8 , c ) 10 , d ) 15 , e ) 18
Rationale: "total - neither = all air conditioning + all air bags - both or 65 - neither = 30 + 45 - 12 = 63 . = > neither = 2 , hence c . answer : c"
Answer: c
Question (physics): a and b can do a piece of work in 2 days . with the help of c they finish the work in 1 days . c alone can do that piece of work in ?
Options: a ) 1.5 days , b ) 4 days , c ) 3 days , d ) 1 day , e ) 2 days
Rationale: c = 1 / 1 – 1 / 2 = 1 / 2 = > 2 days answer : e
Answer: e
Question (physics): four machines , each working at the same constant rate , together can complete a certain job in 20 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 10 days ?
Options: a ) 5 , b ) 3 , c ) 4 , d ) 6 , e ) 1
Rationale: "rate of one machine = 1 job / ( 20 * 4 ) days let x = number of machines needed to complete the job in 10 days 1 / ( 4 * 20 ) * 10 * x = 1 job x = 8 8 - 4 = 4 answer : c"
Answer: c
Question (physics): a car gets 32 miles to the gallon . if it is modified to use a solar panel , it will use only 80 percent as much fuel as it does now . if the fuel tank holds 12 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 84 , b ) 88 , c ) 92 , d ) 96 , e ) 100
Rationale: originally , the distance the car could go on a full tank was 12 * 32 = 384 miles . after it has been modified , the car can go 32 / 0.8 = 40 miles per gallon . on a full tank , the car can go 12 * 40 = 480 miles , thus 96 miles more . the answer is d .
Answer: d
Question (physics): john bought 9.25 m of cloth for $ 434.75 . find the cost price per metre .
Options: a ) 46 , b ) 47 , c ) 58 , d ) 56 , e ) 54
Rationale: "cloth bought by john = 9.25 m cost of 9.25 m = $ 434.75 cost per metre = 434.75 ÷ 9.25 the cost of the cloth per metre = $ 47 answers : b"
Answer: b
Question (general): the average of 60 results is 40 and the average of other 40 results is 60 . what is the average of all the results ?
Options: a ) 24 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: "answer sum of 100 result = sum of 60 result + sum of 40 result . = 60 x 40 + 40 x 60 = 4800 / 100 correct option : c"
Answer: c
Question (general): 3 , 7,12 , 18,25 , . . . . . . . . . . . . . . 6 th terms
Options: a ) 43 , b ) 53 , c ) 63 , d ) 33 , e ) 78
Rationale: "3 + 4 = 7 7 + 5 = 12 12 + 6 = 18 18 + 7 = 25 25 + 8 = 33 answer : d"
Answer: d
Question (general): a person was asked to state his age in years . his reply was , ` ` take my age 3 years hence , multiply it by 4 and subtract 4 times my age 3 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 24 , e ) 19
Rationale: explanation : let the present age of person be x years . then , 4 ( x + 3 ) - 4 ( x - 3 ) = x < = > ( 4 x + 12 ) - ( 4 x - 12 ) = x < = > x = 24 . . answer : d
Answer: d
Question (general): there are cats got together and decided to kill the mice of 999984 . 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 ) 996,1004 , d ) 791,1009 , e ) 931,1009
Rationale: "999984 can be written as 1000000 â € “ 16 = 10002 â € “ 42 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 4 ) * ( 1000 - 4 ) = ( 1004 ) * ( 996 ) given that number of cats is less than number if mice . so number of cats is 996 and number of mice were 1004 answer c"
Answer: c
Question (other): 100 kg of an alloy a is mixed with 200 kg of alloy b . if alloy a has lead and tin in the ratio 5 : 3 and alloy b has tin and copper in the ratio 2 : 3 , then the amount of tin in the new alloy is ?
Options: a ) 100.6 kg , b ) 120.3 kg , c ) 117.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 100 kg of a = 100 * 3 / 8 = 37.5 kg quantity of tin in 200 kg of b = 200 * 2 / 5 = 80 kg quantity of tin in the new alloy = 37.5 + 80 = 117.5 kg answer is c"
Answer: c
Question (physics): a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 1 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 30 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 13 , b ) 18 , c ) 12 , d ) 15 , e ) 17
Rationale: "total vehicle = 1 / 3 of speedster + 2 / 3 of others . speedster convertibles = 1 / 3 total vehicle * 4 / 5 given : 2 / 3 constitutes 30 vehicles . hence 1 / 3 constitutes 15 speedster convertibls = 15 * 4 / 5 = 12 c"
Answer: c
Question (general): a group of 55 adults and 70 children go for trekking . if there is meal for either 70 adults or 90 children and if 35 adults have their meal , find the total number of children that can be catered with the remaining food .
Options: a ) 33 , b ) 54 , c ) 18 , d ) 45 , e ) 01
Rationale: "explanation : as there is meal for 70 adults and 35 have their meal , the meal left can be catered to 35 adults . now , 70 adults = 90 children 7 adults = 9 children therefore , 35 adults = 45 children hence , the meal can be catered to 45 children . answer : d"
Answer: d
Question (geometry): the monthly rent of a shop of dimension 10 feet × 10 feet is rs . 1300 . what is the annual rent per square foot of the shop ?
Options: a ) 43 , b ) 156 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 1300 / ( 10 * 10 ) = 13 & annual rent per square feet = 12 * 13 = 156 answer : b"
Answer: b
Question (gain): a candidate got 35 % of the votes polled and he lost to his rival by 2280 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 2888 , e ) 7600
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2280 100 % - - - - - - - - - ? = > 7600 answer : e"
Answer: e
Question (general): it takes 3 workers a total of 9 hours to build a giant machine with each worker working at the same rate . if 3 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 2 : 00 pm , at what time will the machine be complete ?
Options: a ) 5 : 15 , b ) 5 : 26 , c ) 5 : 37 , d ) 5 : 48 , e ) 5 : 59
Rationale: "3 workers build 1 / 9 of a machine in one hour . 1 worker builds 1 / 27 of a machine in one hour . in the first 3 hours , 3 workers build 3 * ( 1 / 27 ) * 3 = 9 / 27 of a machine from 2 : 00 to 3 : 00 , 4 workers build another 4 / 27 . the total is 13 / 27 . from 3 : 00 to 4 : 00 , 5 workers build another 5 / 27 . the total is 18 / 27 . from 4 : 00 to 5 : 00 , 6 workers build another 6 / 27 . the total is 24 / 27 . to build another 3 / 27 , 7 workers need ( 3 / 7 ) * 60 minutes which is about 26 minutes . the machine is complete at about 5 : 26 . the answer is b ."
Answer: b
Question (geometry): the ratio of the volumes of a cube to that of the sphere which will fit inside the cube is ?
Options: a ) 6.862 kg
b ) 6.838 kg
c ) 6.632 kg
d ) 6.832 kg
e ) 6.834 kg
Rationale: 52 * 40 * 29 = 60320 48 * 36 * 27 = 46650 - - - - - - - - - - - - 13664 13664 * 1 / 2 = 6832 = > 6.832 kg answer : d
Answer: d
Question (physics): a and b start walking towards each other at 1 pm at speed of 5 kmph and 7 kmph . they were initially 24 km apart . at what time do they meet ?
Options: a ) 4 pm , b ) 6 pm , c ) 3 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 24 / 7 + 5 = 24 / 12 = 2 hrs after 1 pm = 3 pm answer is c"
Answer: c
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 27 seconds . what is the length of the train ?
Options: a ) 186 m , b ) 176 m , c ) 450 m , d ) 150 m , e ) 765 m
Rationale: "speed = ( 60 * 5 / 18 ) m / sec = ( 50 / 3 ) m / sec length of the train = ( speed x time ) = ( 50 / 3 * 27 ) m = 450 m . answer : c"
Answer: c
Question (gain): fresh grapes contain 75 % by weight while dried grapes contain 25 % water by weight . what is the weight of dry grapes available from 200 kg of fresh grapes ?
Options: a ) 40.00 kg , b ) 45.50 kg , c ) 66.67 kg , d ) 80.56 kg , e ) 90.00 kg
Rationale: "from the question we know : 200 kg * 75 % = 150 kg of water in the fresh grapes 200 kg - 150 kg of water = 50 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 25 % of the weight of the dry graps is water and we know that 50 kg is non - water mass we can set up the following equation : x = 1 / 4 ( x ) + 50 kg 3 / 4 ( x ) = 50 kg x = 66.67 kg answer - c"
Answer: c
Question (geometry): the ratio of the volumes of two cubes is 1000 : 3375 . what is the ratio of their total surface areas ?
Options: a ) 81 : 121 , b ) 4 : 9 , c ) 729 : 1331 , d ) 27 : 121 , e ) none of these
Rationale: "ratio of the sides = â ³ â ˆ š 1000 : â ³ â ˆ š 3375 = 10 : 15 ratio of surface areas = 10 ^ 2 : 15 ^ 2 = 100 : 225 = 4 : 9 answer : b"
Answer: b
Question (general): a man goes into a barbershop and gets a $ 15 haircut . he pays the barber with a $ 20 bill , but the barber does n ' t have change because it is an especially slow day . the barber goes to the flower shop next to his own and trades the $ 20 bill for a $ 10 dollar bill and two $ 5 bills . then he gives the man his $ 5 in change . later the lady from the flower shop confronts the barber and tells him that the $ 20 bill he gave her was counterfeit . the barber agrees and he gives the lady a different $ 20 bill . later that day he tries to figure out how much money he lost . what did he lose ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 12 , d ) $ 15 , e ) $ 20
Rationale: he lost $ 5 . the lady from the flower shop gave him $ 20 in change , but eventually got $ 20 back . she broke even . the man who got the haircut gave the barber nothing ( except counterfeit money ) but got $ 5 back from the barber . so the barber lost only $ 5 , and gave a free haircut .
Answer: a
Question (gain): if the cost price of 72 articles is equal to the selling price of 60 articles , then what is the percent profit ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "let x be the cost price of one article . let y be the selling price of one article . 60 y = 72 x y = 1.2 x the answer is c ."
Answer: c
Question (general): of all the homes on gotham street , 1 / 3 are termite - ridden , and 5 / 8 of these are collapsing . what fraction of the homes are termite - ridden , but not collapsing ?
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 6 , e ) 1 / 8
Rationale: "the fraction of homes which are termite - infested but not collapsing is 3 / 8 * 1 / 3 = 1 / 8 the answer is e ."
Answer: e
Question (gain): what will be the compound interest on a sum of rs . 22,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8908.42 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 22000 * ( 1 + 12 / 100 ) 3 ] = 22000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 30908.42 c . i . = ( 30908.42 - 22000 ) = rs . 8908.42 answer : a"
Answer: a
Question (gain): of the votes cast on a certain proposal , 68 more were in favor of the proposal than were against it . if the number of votes against the proposal was 40 percent of the total vote , what was the total number of votes cast ? ( each vote cast was either in favor of the proposal or against it . )
Options: a ) 300 , b ) 340 , c ) 380 , d ) 420 , e ) 460
Rationale: "let x be the total number of votes cast . 0.6 x = 0.4 x + 68 0.2 x = 68 x = 340 the answer is b ."
Answer: b
Question (geometry): a box is in the shape of a semicircle with a radius of 12 . what is the approximate perimeter of the semicircle ?
Options: a ) 54
b ) 62
c ) 25
d ) 34
e ) 60
Rationale: perimeter of a circle = 2 pi * r perimeter of a semicircle = pi * r + 2 r aprox perimiter = 3.14 * 12 + 2 * 12 = 61.68 approximately 62 answer b
Answer: b
Question (physics): a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates x apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: "number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates x / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c"
Answer: c
Question (physics): in traveling from a dormitory to a certain city , a student went 1 / 5 of the way by foot , 2 / 3 of the way by bus , and the remaining 4 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 45 , c ) 60 , d ) 90 , e ) 120
Rationale: "whole trip = distance by foot + distance by bus + distance by car x = 1 / 5 x + 2 / 3 x + 4 x - 13 / 15 x = 4 2 / 15 x = 4 = > so x = ( 15 / 2 ) * 4 = 30 km answer a"
Answer: a
Question (physics): a tree of height 36 m is on one edge of a road broke at a certain height . it fell in such a way that the top of the tree touches the other edge of the road . if the breadth of the road is 12 m , then what is the height at which the tree broke ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: let the tree was broken at x meters height from the ground and 36 - x be the length of other part of the tree . from the diagram , ( 36 − x ) 2 = x 2 + 122 ( 36 − x ) 2 = x 2 + 122 ⇒ 1296 − 72 x + x 2 = x 2 + 144 ⇒ 1296 − 72 x + x 2 = x 2 + 144 ⇒ 72 x = 1296 − 144 ⇒ 72 x = 1296 − 144 ⇒ x = 16 answer : a
Answer: a
Question (geometry): if y is the smallest positive integer such that 3,675 multiplied by y is the square of an integer , then y must be
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 12
Rationale: "i just tried plugging in the numbers and found out that 12 * 3675 = 44 , 100 , which is a square of 210 e"
Answer: e
Question (general): if a person walks at 16 km / hr instead of 12 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 , b ) 65 , c ) 70 , d ) 61 , e ) 60
Rationale: "let the actual distance traveled be x km . then , x / 12 = ( x + 20 ) / 16 x - 60 = > x = 60 km . answer : e"
Answer: e
Question (general): a man is 29 years older than his son . in two years , his age will be twice the age of his son . the present age of his son is :
Options: a ) 14 years , b ) 18 years , c ) 20 years , d ) 27 years , e ) 16 years
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 24 ) years . ( x + 29 ) + 2 = 2 ( x + 2 ) x + 31 = 2 x + 4 x = 27 . answer : d"
Answer: d
Question (general): the average of 25 results is 18 . the average of first 12 of them is 10 and that of last 12 is 20 . find the 13 th result ?
Options: a ) 60 , b ) 75 , c ) 90 , d ) 100 , e ) 110
Rationale: 13 th result = sum of 25 results - sum of 24 results = 18 * 25 - 12 * 10 - 12 * 20 = 450 - 120 - 240 = 90 answer is c
Answer: c
Question (general): the average weight of a group of boys is 30 kg . after a boy of weight 36 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) a ) 5 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 36 kg joins the group , total weight of boys = 30 x + 36 so 30 x + 36 = 31 ( x + 1 ) = > x = 5 . answer : a"
Answer: a