Cheukting/mathqa huggingface dataset:
Question (general): a boat crossed a lake from north to west at the speed of 5 km / h , entered a river and covered twice as much distance going upstream at 4 km / h . it then turned around and stopped at the south shore of the lake . if it averaged 3.6 km / h that day , what was its approximate downstream speed ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 7 , e ) 8
Rationale: one way of solving this is : speed of boat on still water ( lake ) = 5 kmph speed upstream = 4 kmph = speed in still water - speed of river = > speed of river = 1 kmph = > speed downstream = speed in still water + speed of river = 5 + 1 = 6 kmph ans is c
Answer: c
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 9 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discounts rates is 50 percent , what is the discount rate on pony jeans ?
Options: a ) 9 % , b ) 10 % , c ) 110 % , d ) 120 % , e ) 150 %
Rationale: "x discount on pony jeans , ( 0.5 - x ) discount on fox jeans . set the equation : 3 * 15 ( 0.5 - x ) + 2 * 18 x = 9 - - > x = 1.5 = 150 % answer : e ."
Answer: e
Question (gain): a shopkeeper forced to sell at cost price , uses a 750 grams weight for a kilogram . what is his gain percent ?
Options: a ) 10 % , b ) 9 % , c ) 33.33 % , d ) 12 % , e ) none of these
Rationale: shopkeeper sells 750 g instead of 1000 g . so , his gain = 1000 - 750 = 250 g . thus , % gain = ( 250 * 100 ) / 750 = 33.33 % . answer : option c
Answer: c
Question (other): uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought more of toyota than honda at the ratio of 9 : 1 . if 90 % of the toyota bought and 10 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 82 % , b ) 64 % , c ) 28 % , d ) 69 % , e ) 80 %
Rationale: "let total no of vehicles bought be 100 , toyota 90 and honda 10 , so total number of suv ' s bought for toyota and honda respectively 90 * 90 / 100 = 81 and 10 * 10 / 100 = 1 so total 82 suv ' s were bought out of 100 vehicles bought . . so required % is 82 % answer : a"
Answer: a
Question (general): if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 171 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "let p be the number of participants . pc 2 = 171 ( p ) ( p - 1 ) = 342 = 19 * 18 p = 19 the answer is e ."
Answer: e
Question (general): a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 10 that a person who randomly guesses the answer to each question will be a winner ?
Options: a ) 5 , b ) 10 , c ) 50 , d ) 100 , e ) 1000
Rationale: a contest will consist of n questions , each of which is to be answered eithertrueorfalse . anyone who answers all n questions correctly will be a winner . what is the least value of n for which the probability is less than 1 / 1000 that a person who randomly guesses the answer to each question will be a winner ? a . 5 b . 10 c . 50 d . 100 e . 1000 soln : ans is b probability that one question is answered right is 1 / 2 . now for minimum number of questions needed to take probability less than 1 / 1000 is = > ( 1 / 2 ) ^ n < 1 / 1000 n = 10 satisfies this . d
Answer: d
Question (physics): a pipe takes a hours to fill the tank . but because of a leakage it took 3 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 70 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 180 x = 90 min answer : c"
Answer: c
Question (general): the average of 13 numbers is 60 . average of the first 7 of them is 56 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 39 , b ) 83 , c ) 45 , d ) 53 , e ) 64
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 56 = 392 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 392 - 780 = 39 . answer : a"
Answer: a
Question (general): a student got twice as many sums wrong as he got right . if he attempted 75 sums in all , how many did he solve correctly ?
Options: a ) 25 , b ) 16 , c ) 18 , d ) 24 , e ) 26
Rationale: "explanation : suppose the boy got x sums right and 2 x sums wrong . then , x + 2 x = 75 3 x = 75 x = 25 . answer : a"
Answer: a
Question (general): how much water should be added to 12 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 28 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 12 + x ) ) ) 2 = 5 % * ( 12 + x ) - - - - - - - - > x = 28 ans a
Answer: a
Question (general): a sum of money lent out at s . i . amounts to rs . 710 after 2 years and to rs . 1020 after a further period of 5 years . the sum is ?
Options: a ) s . 440 , b ) s . 586 , c ) s . 540 , d ) s . 740 , e ) s . 840
Rationale: "s . i for 5 years = ( 1020 - 710 ) = rs . 310 . s . i . for 2 years = 310 / 5 * 2 = rs . 124 . principal = ( 710 - 124 ) = rs . 586 . answer : b"
Answer: b
Question (gain): there is 60 % increase in an amount in 6 years at si . what will be the ci of rs . 15,000 after 3 years at the same rate ?
Options: a ) 2372 , b ) 2572 , c ) 4542 , d ) 4965 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 15000 . t = 3 years and r = 10 % p . a . c . i . = rs . 15000 x 1 + 10 3 - 1 100 = rs . 15000 x 331 1000 = 4965 . d"
Answer: d
Question (general): the overall age of x and y is 10 year greater than the overall age of y and z . z is how many decades younger that x ?
Options: a ) 11 , b ) 10 , c ) 12 , d ) 17 , e ) 19
Rationale: "b 10 ( x + y ) â € “ ( y + z ) = 10 x â € “ z = 10"
Answer: b
Question (probability): a bag contains 15 red jellybeans and 15 blue jellybeans . if 3 jellybeans are removed one at a time , at random and are not replaced , what is the probability that all 3 jellybeans removed from the bag are blue ?
Options: a ) 9 / 100 , b ) 2 / 19 , c ) 1 / 8 , d ) 3 / 20 , e ) 3 / 10
Rationale: "method - 1 10 red jellybeans and 10 blue jellybeans total outcomes = no . of ways to choose 3 jelly bean at random out of a total 20 jellybeans = 20 c 3 = 1140 favourable outcomes = no . of ways to choose 3 jelly bean such that they are all blue out of 10 blue = 10 c 3 = 120 probability = favourable outcomes / total outcomes = 10 c 3 / 20 c 3 probability = 120 / 1140 = 2 / 19 answer : option b method - 2 probability of first jelly bean to be blue = 10 / 20 [ total 10 blue out of total 20 jellybeans ] probability of second jelly bean to be blue = 9 / 19 [ total 9 blue remaining out of total 19 jellybeans remaining ] probability of third jelly bean to be blue = 8 / 18 [ total 8 blue remaining out of total 18 jellybeans remaining ] required probability = ( 10 / 20 ) * ( 9 / 19 ) * ( 8 / 18 ) = 3 / 10 answer : option e"
Answer: e
Question (gain): if the simple interest on a sum of money for 6 years at 12 % per annum is rs . 700 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) 746.77 , b ) 945.77 , c ) 946.77 , d ) 246.77 , e ) 926.77
Rationale: "sum = ( 700 * 100 ) / ( 6 * 12 ) = rs . 972.22 c . i . on rs . rs . 972.22 for 6 years at 12 % = rs . 1 , 918.99 . = rs . 1 , 918.99 - 972.22 = rs . 946.77 answer : c"
Answer: c
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 52 , then how old is b ?
Options: a ) 17 years , b ) 20 years , c ) 29 years , d ) 10 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 52 5 x = 50 = > x = 10 hence , b ' s age = 2 x = 20 years . answer : b"
Answer: b
Question (general): a man ' s age is 125 % of what it was 10 years ago , but 83 x 1 / 3 % of what it will be after 10 years . what is his present age ?
Options: a ) 20 , b ) 60 , c ) 50 , d ) 70 , e ) 80
Rationale: c 50 let the age before 10 years = x then , 125 x / 100 = x + 10 ⇒ 125 x = 100 x + 1000 ⇒ x = 1000 / 25 = 40 present age = x + 10 = 40 + 10 = 50
Answer: c
Question (general): when average age of 20 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 20 numbers = 0 . sum of 20 numbers ( 0 x 20 ) = 0 . it is quite possible that 19 of these numbers may be positive and if their sum is a then 20 th number is ( - a ) answer is 19 ( b )"
Answer: b
Question (general): 5301 x 13 = ?
Options: a ) 89136 , b ) 31986 , c ) 68910 , d ) 53113 , e ) 68913
Rationale: "append 0 before and after : 053010 calculation : 1 x 3 + 0 = 3 ( take 3 as ones digit of the product ) 0 x 3 + 1 = 1 ( take 1 tens digit of the product ) 3 x 3 + 0 = 9 ( take 9 hundreds digit of the product ) 5 x 3 + 3 = 18 ( take 8 as thousands digit of the product , carry over 1 ) 0 x 3 + 5 = 5 ; 5 + 1 = 6 ( take 6 as ten thousands digits of the product ) so , 5301 x 13 = 68913 answer is e ."
Answer: e
Question (physics): a cistern can be filled by a tap in 3 hours while it can be emptied by another tap in 9 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 4.5 hrs , b ) 5 hrs , c ) 6.5 hrs , d ) 7.2 hrs , e ) 9.2 hrs
Rationale: "net part filled in 1 hour = 1 / 3 - 1 / 9 = 2 / 9 therefore the cistern will be filled in 9 / 2 hours or 4.5 hours . answer : a"
Answer: a
Question (physics): a river 8 m deep and 25 m wide is flowing at the rate of 8 kmph the amount of water that runs into the sea per minute is ?
Options: a ) 26666 , b ) 26166 , c ) 29666 , d ) 22666 , e ) 26699
Rationale: "rate of water flow - 8 kmph - - 8000 / 60 - - 133.33 m / min depth of river - - 8 m width of river - - 25 m vol of water per min - - 133.33 * 8 * 25 - - - 26666 answer a"
Answer: a
Question (other): among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188
Rationale: "i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 168 using your analysis : we see that the total number of students who study either maths or sociology = 176 + 224 - 168 = 232 so , in the image we know that the number of students in the zone with the black boundary = 232 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 232 + b + w = 400 or , b + w = 400 - 232 = 168 that is , b = 168 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 168 d"
Answer: d
Question (general): each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 12 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 12 , the ratio of 10 - pound boxes : 20 - pound boxes should be 4 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 4 : 1 , the number of 20 - pound boxes must be 1 . we need to remove 15 of the 20 - pound boxes . the answer is e ."
Answer: e
Question (general): if n is a positive integer and n ^ 2 is divisible by 264 , then the largest positive integer that must divide n is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "the question asks aboutthe largest positive integer that must divide n , not could divide n . since the least value of n for which n ^ 2 is a multiple of 72 is 12 then the largest positive integer that must divide n is 12 . complete solution of this question is given above . please ask if anything remains unclear . i spent a few hours on this one alone and i ' m still not clear . i chose 12 at first , but then changed to 48 . i ' m not a native speaker , so here is how i interpreted this question : the largest positive integer that must divide n = the largest positive factor of n . since n is a variable ( i . e . n is moving ) , so is its largest factor . please correct if i ' m wrong here . i know that if n = 12 , n ^ 2 = 144 = 2 * 72 ( satisfy the condition ) . when n = 12 , the largest factor of n is n itself , which is 12 . check : 12 is the largest positive number that must divide 12 - - > true however if n = 48 , n ^ 2 = 48 * 48 = 32 * 72 ( satisfy the condition too ) . when n = 48 , the largest factor of n is n itself , which is 48 . check : 48 is the largest positive number that must divide 48 - - > true so , i also notice that the keyword ismust , notcould . the question is , why is 48 notmust divide 48 , but instead onlycould divide 48 ? i ' m not clear right here . why is 12 must divide 12 ? what ' s the difference between them ? only restriction we have on positive integer n is that n ^ 2 is divisible by 72 . the least value of n for which n ^ 2 is divisible by 72 is 12 , thus nmustbe divisible by 12 ( n is in any case divisible by 12 ) . for all other values of n , for which n ^ 2 is divisible by 72 , n will still be divisible by 12 . this means that n is always divisible by 12 if n ^ 2 is divisible by 72 . now , ask yourself : if n = 48 , is n divisible by 48 ? no . so , n is not always divisible by 48 . e"
Answer: e
Question (gain): ramesh purchased a refrigerator for rs . 17500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 10 % if no discount was offered ?
Options: a ) 34778 , b ) 26888 , c ) 24475 , d ) 17600 , e ) 12778
Rationale: "price at which the tv set is bought = rs . 17,500 discount offered = 20 % marked price = 17500 * 100 / 80 = rs . 21875 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 21875 + 375 = rs . 22250 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 22250 * 110 / 100 = rs . 24475 answer : c"
Answer: c
Question (gain): harkamal purchased 3 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 700 , b ) b ) 1065 , c ) c ) 1070 , d ) d ) 1075 , e ) e ) 1080
Rationale: "cost of 3 kg grapes = 70 × 3 = 210 . cost of 9 kg of mangoes = 55 × 9 = 490 . total cost he has to pay = 210 + 490 = 700 a"
Answer: a
Question (general): the wages earned by robin is 35 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much % is the wages earned by charles more than that earned by robin ?
Options: a ) 25.92 % , b ) 18.75 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: "explanatory answer let the wages earned by erica be $ 100 then , wages earned by robin and charles will be $ 135 and $ 160 respectively . charles earns $ 35 more than robin who earns $ 135 . therefore , charles ' wage is 35 / 135 * 100 = 25.92 % . the correct choice is ( a )"
Answer: a
Question (other): if log 1087.5 = 4.9421 , then the number of digits in ( 875 ) 10 is ?
Options: a ) 60 , b ) 28 , c ) 27 , d ) 26 , e ) 25
Rationale: "x = ( 875 ) 10 = ( 87.5 x 10 ) 10 therefore , log 10 x = 10 ( log 4087.5 + 1 ) = 10 ( 4.9421 + 1 ) = 10 ( 5.9421 ) = 59.421 x = antilog ( 59.421 ) therefore , number of digits in x = 60 . answer : a"
Answer: a
Question (general): a soccer store typically sells replica jerseys at a discount of 30 percent to 70 percent off list price . during the annual summer sale , everything in the store is an additional 20 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 70 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 40 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , d is the answer"
Answer: d
Question (physics): speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph . a man rows to place at a distance of 210 km and comes back to the starting point . the total time taken by him is :
Options: a ) 12 hours , b ) 24 hours , c ) 36 hours , d ) 48 hours , e ) none
Rationale: "sol . speed upstream = 7.5 kmph ; speed downstream = 10.5 kmph . ∴ total time taken = [ 210 / 7.5 + 210 / 10.5 ] hours = 48 hours . answer d"
Answer: d
Question (general): q ' = 3 q - 3 , what is the value of ( 4 ' ) ' ?
Options: a ) 48 , b ) 57 , c ) 66 , d ) 72 , e ) 81
Rationale: "( 4 ' ) ' = ( 3 * 4 - 3 ) ' = 9 ' = 9 * 9 - 9 = 72 answer d"
Answer: d
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is $ 50 , what is the compound interest on the same at the same rate and for the same time ?
Options: a ) $ 50 , b ) $ 51.5 , c ) $ 52 , d ) $ 52.5 , e ) $ 51.25
Rationale: "sum = 50 x 100 / ( 2 x 5 ) = 500 = 500 x ( 1 + 5 / 100 ) ^ 2 = 500 x 21 / 20 x 21 / 20 = 551.25 . c . i = 551.25 - 500 = 51.25 . answer e ) $ 51.25"
Answer: e
Question (physics): a train running at the speed of 180 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 288 meter , e ) 450 meter
Rationale: "speed = 180 * ( 5 / 18 ) m / sec = 50 m / sec length of train ( distance ) = speed * time ( 50 ) * 9 = 450 meter answer : e"
Answer: e
Question (general): the cost of 2 chairs and 3 tables is rs . 1700 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 500
Rationale: "explanation : 2 c + 3 t = 1700 - - - ( 1 ) 3 c + 2 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 500 = > t - c = 500 answer : e"
Answer: e
Question (physics): the speed of a subway train is represented by the equation z = s ^ 2 + 2 s for all situations where 0 ≤ s ≤ 7 , where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving . in kilometers per hour , how much faster is the subway train moving after 5 seconds than it was moving after 3 seconds ?
Options: a ) 4 , b ) 9 , c ) 15 , d ) 20 , e ) 63
Rationale: "given : z = s ^ 2 + 2 s for 0 ≤ s ≤ 7 z ( 3 ) = 3 ^ 2 + 2 * 3 = 15 z ( 5 ) = 5 ^ 2 + 2 * 5 = 35 therefore z ( 7 ) - z ( 3 ) = 35 - 15 = 20 km / hr option d"
Answer: d
Question (general): consider the word rotor . whichever way you read it , from left to right or from right to left , you get the same word . such a word is known as palindrome . find the maximum possible number of 5 - letter palindromes ?
Options: a ) 56678 , b ) 16789 , c ) 17576 , d ) 35142 , e ) none of these
Rationale: "explanation : the first letter from the right can be chosen in 26 ways because there are 26 alphabets . having chosen this , the second letter can be chosen in 26 ways . = > the first two letters can be chosen in 26 * 26 = 676 wayshaving chosen the first two letters , the third letter can be chosen in 26 ways . = > all the three letters can be chosen in 676 * 26 = 17576 ways . it implies that the maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter . answer : c"
Answer: c
Question (other): the present ages of reena and usha are 24 and 36 yr . respectively . what was the ratio between the ages of usha and reena respectively 8 yr ago ?
Options: a ) 7 : 4 , b ) 4 : 7 , c ) 11 : 8 , d ) 8 : 11 , e ) 9 : 12
Rationale: required ratio = ( 36 - 8 ) / ( 24 - 8 ) = 28 / 16 = 7 : 4 answer : a
Answer: a
Question (general): a type of extra - large suv averages 12.2 miles per gallon ( mpg ) on the highway , but only 7.6 mpg in the city . what is the maximum distance , in miles , that this suv could be driven on 24 gallons of gasoline ?
Options: a ) 190 , b ) 284.6 , c ) 300 , d ) 292 , e ) 312
Rationale: so 12.2 * 24 = 292 . . imo option d is correct answer . .
Answer: d
Question (physics): a train traveling at 72 kmph crosses a platform in 30 seconds and a man standing on the platform in 20 seconds . what is the length of the platform in meters ?
Options: a ) 200 meters , b ) 360 meters , c ) 420 meters , d ) 600 meters , e ) can not be determined
Rationale: "speed of the train in metres / sec = 72000 / 3600 = 20 distance travelled by train to cross the platform = 30 * 20 = 600 = length of train + length of platform distance travelled by train to cross the man = 20 * 20 = 400 = length of train length of platform = 600 - 400 = 200 answer : a"
Answer: a
Question (general): what is the 20 - fourth decimal to the right in the fraction 35 / 36 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: 35 / 36 = 0.97222222222 . . . the answer is b .
Answer: b
Question (physics): a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 10 : 00 a . m . ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 5 , e ) 10
Rationale: sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour and 5 times in next hour . hence , they cross each other 10 times before 10 : 00 a . m . answer e
Answer: e
Question (general): a regular hexagon is there . the mid points of the sides were joined and formed another hexagon . then what is the percentage reduction in area .
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 55 % , e ) 65 %
Rationale: let abcdef be the regular hexagon with sides ab and ed parallel . p and q are mid points of af and ef resp . ae = root ( 3 ) * s ( s is side of hexagon ) then pq = ( root ( 3 ) * s ) / 2 mid point theorem now u know side of inner hexagon use formula area of hexagon = ( 3 * root ( 3 ) ) 2 * s ^ 2 and find diff in area of two hexagon multiply by 100 and divide the product by area of bigger hexagon ans 25 % answer : a
Answer: a
Question (general): in the faculty of reverse - engineering , 226 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 85 % of the total ?
Options: a ) 515 . , b ) 545 . , c ) 606 . , d ) 644 . , e ) 666 .
Rationale: "answer is c : 606 solution : total number of students studying both are 423 + 226 - 134 = 515 ( subtracting the 134 since they were included in the both the other numbers already ) . so 85 % of total is 515 , so 100 % is approx . 606 ."
Answer: c