Cheukting/mathqa huggingface dataset:
Question (general): in a class of 20 students , 2 students did not borrow any books from the library , 8 students each borrowed 1 book , 5 students each borrowed 2 books , and the rest of the students each borrowed at least 3 books . if the average ( arithmetic mean ) number of books borrowed per student was 2 , what is the maximum number of books that any single student could have borrowed ?
Options: a ) 3 , b ) 5 , c ) 10 , d ) 13 , e ) 15
Rationale: "the average number of books per student was 2 means that total of 2 * 20 = 40 books were borrowed ; 2 + 8 + 5 = 15 students borrowed total of 2 * 0 + 8 * 1 + 5 * 2 = 18 books ; so 40 - 18 = 22 books are left to distribute among 20 - 15 = 5 students , these 5 arethe rest who borrowed at least 3 books ; tomaximizethe number of books one student from above 5 could have borrowed we shouldminimizethe number of books other 4 students from 5 could have borrowed . minimum these 4 students could have borrowed is 3 books per student , so total number of books they could have borrowed is 4 * 3 = 12 books . so the 5 th student could have borrowed is 22 - 12 = 10 books . answer : c ."
Answer: c
Question (general): mukesh borrowed a sum of rs . 10000 at simple interest from a bank . after two years he takes rs . 12000 more as loan and discharge all the debt at the end of next 3 years depositing rs . 27160 to the bank . what is the rate of interest per annum ?
Options: a ) 5 % , b ) 6 % , c ) 8 % , d ) 10 % , e ) none of these
Rationale: si = 27160 - ( principal amount ) = 27160 - 22000 = 5160 . now , ( 10000 * 5 * r / 100 ) + ( 12000 * 3 * r / 100 ) = 5160 . 500 r + 360 r = 5160 . . . . . rate = 6 % . answer : b
Answer: b
Question (probability): a player holds 13 cards of 4 suits , of which 7 are black and 6 are red . there are twice as many diamonds as spades and twice as many hearts as diamonds . how many clubs does he hold
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : clearly , the black cards are either clubs or spades while the red cards are either diamonds or hearts . let the number of spades be x . then , number of clubs = ( 7 - x ) . number of diamonds = 2 x number of spades = 2 x ; number of hearts = 2 x number of diamonds = 4 x . total number of cards = x + 2 x + 4 x + 7 - x = 6 x + 7 . therefore 6 x + 7 = 13 6 x = 6 x - 1 . hence , number of clubs = ( 7 - x ) = 6 . answer : c
Answer: c
Question (physics): a worker can load one truck in 6 hours . a second worker can load the same truck in 8 hours . if both workers load one truck simultaneously while maintaining their constant rates , approximately how long , in hours , will it take them to fill one truck ?
Options: a ) 2.6 , b ) 2.8 , c ) 3.0 , d ) 3.2 , e ) 3.4
Rationale: "the workers fill the truck at a rate of 1 / 6 + 1 / 8 = 14 / 48 = 7 / 24 of the truck per hour . then the time to fill one truck is 24 / 7 which is about 3.4 hours . the answer is e ."
Answer: e
Question (general): here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ?
Options: a ) 11 , b ) 15 , c ) 18 , d ) 17 , e ) 19
Rationale: b 15 the number of bees was 15
Answer: b
Question (general): the largest 5 digit number exactly divisible by 91 is ?
Options: a ) 99918 , b ) 99919 , c ) 99921 , d ) 99923 , e ) 99929
Rationale: "largest 5 - digit number = 99999 91 ) 99999 ( 1098 91 - - - 899 819 - - - - 809 728 - - - 81 - - - required number = ( 99999 - 81 ) = 99918 . option a"
Answer: a
Question (general): if the digits 35 in the decimal 0.00035 repeat indefinitely , what is the value of ( 10 ^ 5 - 10 ^ 3 ) ( 0.00035 ) ?
Options: a ) 37 , b ) 41 , c ) 3.5 e - 05 , d ) 35 , e ) 3.5 e - 07
Rationale: "99 * 0.35 = 34.65 approx . 35 answer : b"
Answer: b
Question (general): product of two co - prime numbers is 117 . their l . c . m should be
Options: a ) 222 , b ) 117 , c ) 278 , d ) 767 , e ) 298
Rationale: h . c . f of co - prime numbers is 1 . so , l . c . m = \ inline \ fn _ jvn \ frac { 117 } { 1 } = 117 answer : b
Answer: b
Question (general): if to a certain number , 720 be added , and the sum be divided by 125 ; the quotient will be equal to 7392 divided by 462 . what is that number ?
Options: a ) 1280 , b ) 1270 , c ) 1260 , d ) 1250 , e ) none
Rationale: solution let x = the number required . a = 720 d = 7392 b = 125 h = 462 then by the conditions of the problem ( x + a ) / b = d / h therefore x = ( bd - ah ) / h restoring the numbers , x = [ ( 125.7392 ) - ( 720.462 ) ] / 462 = 1280 . answer a
Answer: a
Question (physics): 10 women can complete a work in 9 days and 10 children take 12 days to complete the work . how many days will 6 women and 7 children take to complete the work ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 8 , e ) 2
Rationale: "1 women ' s 1 day work = 1 / 90 1 child ' s 1 day work = 1 / 120 ( 6 women + 7 children ) ' s 1 day work = ( 6 / 90 + 7 / 120 ) = 1 / 8 6 women and 7 children will complete the work in 8 days . d"
Answer: d
Question (general): a cricket player whose bowling average was 22.5 runs per wicket , takes 5 wicket for 52 runs in a match . due to this his average decreases by 0.5 . what will be the number of wickets taken by him till the last match ?
Options: a ) 64 , b ) 72 , c ) 121 , d ) 984 , e ) 108
Rationale: average = total runs / total wickets total runs after last match = 22.5 w + 52 total wickets after last match = w + 5 ( 22.5 w + 52 ) / ( w + 5 ) = 22.5 - 0.5 = 22 w = 116 so total wickets aftr last match = w + 5 = 121 answer : c
Answer: c
Question (physics): the radius of the wheel of a bus is 35 cms and the speed of the bus is 66 km / h , then the r . p . m . ( revolutions per minutes ) of the wheel is
Options: a ) 200 , b ) 250 , c ) 300 , d ) 500 , e ) none of these
Rationale: radius of the wheel of bus = 35 cm . then , circumference of wheel = 2 ï € r = 70 ï € = 220 cm distance covered by bus in 1 minute = 66 â  „ 60 ã — 1000 ã — 100 cms distance covered by one revolution of wheel = circumference of wheel = 220 cm â ˆ ´ revolutions per minute = 6600000 / 60 ã — 220 = 500 answer d
Answer: d
Question (physics): a furniture manufacturer has two machines , but only one can be used at a time . machine e is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine e can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: machine e finish the job in 2 * 12 shifts = 24 shifts machine b finish the job in 2 * 15 shifts = 30 shifts lets assume total work require 120 shifts therefore , rate of e = 5 shifts / day rate of b = 4 shifts / day rate of ( e + b ) = 9 shifts / day according to current schedule work complete in a day = 5 + 4 + ( 9 / 2 ) = 13.5 shifts / day therefore , time required to finish 120 shifts = ( 120 / 13.5 ) = 8.88 . . days ~ 9 days = d
Answer: d
Question (physics): a train 110 m long is running with a speed of 84 km / hr . in what time will it pass a man who is running at 6 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 7 sec , b ) 6 sec , c ) 8 sec , d ) 4.4 sec , e ) 2 sec
Rationale: "speed of train relative to man = 84 + 6 = 90 km / hr . = 90 * 5 / 18 = 25 m / sec . time taken to pass the men = 110 / 25 = 4.4 sec . answer : d"
Answer: d
Question (general): a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 25 payments is to be $ 500 ; each of the remaining payments is to be $ 100 more than each of the first 25 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 500 , b ) 450 , c ) 552 , d ) 600 , e ) 400
Rationale: "total = 500 ( 25 ) + 600 ( 27 ) number of installments = 52 average = total / number of installments = 552 approximately answer : c"
Answer: c
Question (general): there are 6 fictions and 6 non - fictions . how many cases are there such that 2 fictions and 2 non - fictions are selected from them ?
Options: a ) 90 , b ) 120 , c ) 225 , d ) 180 , e ) 200
Rationale: "number of ways of selecting 2 fiction books = 6 c 2 number of ways of selecting 2 non fiction books = 6 c 2 6 c 2 * 6 c 2 = 15 * 15 = 225 answer : c"
Answer: c
Question (general): a certain school implemented a reading program for its students , with the goal of getting each student to read 4 books per month year - round . if the school has c classes made up of s students in each class , how many books will the entire student body read in one year ?
Options: a ) 20 cs , b ) cs / 2 , c ) 48 cs , d ) ( 2 cs ) / 12 , e ) ( 24 c ) / s
Rationale: "ans : c solution : simple multiplication s students , c classes , 4 books / month = 48 books a year total number of books = 48 cs"
Answer: c
Question (general): in a certain quiz that consists of 10 questions , each question after the first is worth 4 points more than the preceding question . if the 10 questions on the quiz are worth a total of 340 points , how many points is the third question worth ?
Options: a ) 39 , b ) 24 , c ) 28 , d ) 26 , e ) 30
Rationale: "x x + 4 x + 8 x + 12 x + 16 x + 20 x + 24 x + 28 x + 32 x + 36 10 x + 180 = 340 10 x = 160 x = 16 3 rd question = x + 8 = 16 + 8 = 24 answer b"
Answer: b
Question (general): how many natural numbers are there between 43 and 200 which are exactly divisible by 6 ?
Options: a ) 26 , b ) 25 , c ) 24 , d ) 22 , e ) 23
Rationale: "43 / 6 = 7 , remainder = 1 . hence 5 more should be added to 43 to get the minimum number divisible by 6 between 43 and 200 . = > minimum number divisible by 6 between 43 and 200 = 43 + 5 = 48 200 / 6 = 33 , remainder = 2 . hence 2 should be decreased from 200 to get the maximum number divisible by 6 between 43 and 200 . = > maximum number divisible by 6 between 43 and 200 = 200 - 2 = 198 hence , natural numbers numbers divisible by 6 between 43 and 200 are 48 , 54 , 60 , . . . 198 this is arithmetic progression with a = 48 , d = 6 , l = 198 number of terms = ( l − a ) / d + 1 = ( 198 − 48 ) / 6 + 1 = 150 / 6 + 1 = 25 + 1 = 26 answer is a"
Answer: a
Question (general): right triangle pqr is to be constructed in the xy - plane so that the right angle is at p and pr is parallel to the x - axis . the x - and y - coordinates of p , q , and r are to be integers that satisfy the inequalities - 4 < = x < = 5 and 6 < = y < = 16 . how many different triangles with these properties could be constructed ?
Options: a ) 110 , b ) 1,100 , c ) 9,900 , d ) 10,000 , e ) 12,100
Rationale: "p can take a total of 10 * 11 co - ordinates . for a given p , r can take a total of 9 co - ordinates and q can take a total of 10 co - ordinates . hence , total = 110 * 9 * 10 = 9900 ans : c"
Answer: c
Question (physics): in an examination , a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer . if he attempts all 60 questions and secures 160 marks , the no of questions he attempts correctly is :
Options: a ) 35 , b ) 38 , c ) 40 , d ) 42 , e ) 44
Rationale: "explanation : let the number of correct answers be x . number of incorrect answers = ( 60 – x ) . 4 x – ( 60 – x ) = 160 = > 5 x = 220 = > x = 44 answer : e"
Answer: e
Question (general): in the coordinate plane , points ( x , 1 ) and ( 18 , y ) are on line k . if line k passes through the origin and has slope 1 / 2 , then x + y =
Options: a ) 4.5 , b ) 7 , c ) 8 , d ) 11 , e ) 12
Rationale: "line k passes through the origin and has slope 1 / 2 means that its equation is y = 1 / 2 * x . thus : ( x , 1 ) = ( 2 , 1 ) and ( 18 , y ) = ( 18,9 ) - - > x + y = 2 + 9 = 11 . answer : d ."
Answer: d
Question (gain): find the simple interest on $ 1200 for 5 years at 20 % per annum ?
Options: a ) $ 1200 , b ) $ 1000 , c ) $ 500 , d ) $ 1100 , e ) $ 1500
Rationale: "si = ptr / 100 = 1200 * 5 * 20 / 100 = $ 1200 answer is a"
Answer: a
Question (general): a batsman makes a score of 50 runs in the 17 th inning and thus increases his averages by 2 . what is his average after 17 th inning ?
Options: a ) 39 , b ) 18 , c ) 42 , d ) 40.5 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 50 then average run after 17 th inning = ( 16 x + 50 ) / 17 ( 16 x + 50 ) / 17 = x + 2 = > 16 x + 50 = 17 x + 34 = > x = 16 x = 16 ; average after 17 th inning = 16 + 2 = 18 answer : b"
Answer: b
Question (gain): to produce an annual income of rs . 800 from a 8 % stock at 90 , what is the amount of stock needed ?
Options: a ) 10000 , b ) 11000 , c ) 12000 , d ) 13000 , e ) 14000
Rationale: "since face value is not given , take it as rs . 100 . as it is an 8 % stock , income ( dividend ) per stock = rs . 8 ie , for an income of rs . 8 , amount of stock needed = rs . 100 for an income of rs . 800 , amount of stock needed = 100 × 800 / 8 = 10000 answer is a ."
Answer: a
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 7.5 ) , ( 8 , 0 ) , ( 0 , - 7.5 ) , ( - 8 , 0 ) ?
Options: a ) 56 , b ) 88 , c ) 112 , d ) 116 , e ) 120
Rationale: "ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 7.5 + 7.5 = 15 area = 1 / 2 * 16 * 15 = 120 e is the answer"
Answer: e
Question (gain): ramu bought an old car for rs . 40000 . he spent rs . 13000 on repairs and sold it for rs . 64900 . what is his profit percent ?
Options: a ) a ) 14 % , b ) b ) 16 % , c ) c ) 18 % , d ) d ) 21.6 % , e ) of these
Rationale: "total cp = rs . 40000 + rs . 13000 = rs . 53000 and sp = rs . 64900 profit ( % ) = ( 64900 - 53000 ) / 55000 * 100 = 21.6 % answer : d"
Answer: d
Question (physics): on a map , 1.5 inches represent 24 miles . how many miles approximately is the distance if you measured 44 centimeters assuming that 1 - inch is 2.54 centimeters ?
Options: a ) 174.2 , b ) 277 , c ) 288.1 , d ) 296 , e ) 282.4
Rationale: "1.5 inch = 2.54 * 1.5 cm . so , 2.54 * 1.5 represents 24 miles . so for 44 cm . : 44 / ( 2.54 * 1.5 ) = x / 24 - - - > x = 24 * 44 / ( 3.81 ) = 277 answer will be b ."
Answer: b
Question (general): if 0.12 ÷ x 2 = 12 , than x = ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 1 , e ) 0
Rationale: explanation : 0.12 ÷ x 2 = 12 = > 0.12 / x 2 = 12 = > x 2 = 0.12 / 12 = 0.01 = > x = 0.1 answer : option c
Answer: c
Question (physics): a woman complete a journey in 30 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
Options: a ) 334 km . , b ) 216 km . , c ) 314 km . , d ) 224 km . , e ) 672 km .
Rationale: "0.5 x / 21 + 0.5 x / 24 = 30 - - > x / 21 + x / 24 = 60 - - > x = 672 km . e"
Answer: e
Question (other): in a class of 35 students 26 play football and play 20 long tennis , if 17 play above , many play neither ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "26 + 20 - 17 = 29 35 - 29 = 6 play neither answer is a"
Answer: a
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 488 , c ) 882 , d ) 269 , e ) 298
Rationale: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a
Answer: a
Question (other): the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ratio less than 16 : 21 , is ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: let x be subtracted . then , 6 - x 7 - x < 16 21 21 ( 6 - x ) < 16 ( 7 - x ) 5 x > 14 x > 2.8 least such whole number is 3 . answer : a
Answer: a
Question (general): a part - time employee whose hourly wage was decreased by 20 percent decided to increase the number of hours worked per week so that the employee ' s total income did not change . by what percent should the number of hours worked be increased ?
Options: a ) 12.5 % , b ) 20 % , c ) 25 % , d ) 50 % , e ) 100 %
Rationale: "assume hours worked : 10 hours hourly wage : 10 $ weekly wage : 100 $ after decrease of 20 % in hourly wage would become 8 $ hours worked would have to be 12.5 hours in order to maintain weekly wage of 100 $ % increase in number of hours worked = ( 12.5 - 10 ) / 10 = 0.25 * 100 = 25 % answer is c"
Answer: c
Question (physics): a and b can do a piece of work in 8 days . with the help of c they finish the work in 4 days . c alone can do that piece of work in ?
Options: a ) 40 days , b ) 20 days , c ) 8 days , d ) 60 days , e ) 40 days
Rationale: "c 8 days c = 1 / 4 – 1 / 8 = 1 / 8 = > 8 days"
Answer: c
Question (general): patrick purchased 60 pencils and sold them at a loss equal to the selling price of 20 pencils . the cost of 60 pencils is how many times the selling price of 60 pencils ?
Options: a ) 0.75 , b ) 0.8 , c ) 1 , d ) 1.33 , e ) 1.75
Rationale: "say the cost price of 60 pencils was $ 60 ( $ 1 per pencil ) and the selling price of 1 pencil was p . selling at a loss : 60 - 60 p = 20 p - - > p = 3 / 4 . ( cost price ) / ( selling price ) = 1 / ( 3 / 4 ) = 4 / 3 = 1.33 . answer : d ."
Answer: d
Question (physics): the distance between two cities a and b is 600 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 am , b ) 07 am , c ) 01 pm , d ) 05 pm , e ) 03 pm
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 600 . therefore , 60 x + 75 ( x - 1 ) = 600 . = > x = 5 . so , they meet at ( 8 + 5 ) i . e , 1 p . m . answer : c )"
Answer: c
Question (general): in a group of 800 people , 1 / 5 play at least one instrument , 128 play two or more . what is the probability that one student play exactly one instrument ?
Options: a ) 2 / 125 , b ) 3 / 125 , c ) c ) 2 / 25 , d ) 3 / 25 , e ) 1 / 25
Rationale: "p ( playing 2 or more instruments ) = 128 / 800 = 4 / 25 . then , the probability of playing exactly one instrument is given by : p ( playing 1 or more instruments ) - p ( playing 2 or more instruments ) = 1 / 5 - 4 / 25 = 1 / 25 . answer e ."
Answer: e
Question (gain): the present worth of a sum due sometime hence is rs . 576 and the banker ’ s gain is rs . 16 . the true discount is :
Options: a ) 36 , b ) 52 , c ) 66 , d ) 96 , e ) none
Rationale: "sol . t . d . = √ p . w . * b . g . = √ 576 * 16 = 96 . answer d"
Answer: d
Question (physics): car a runs at the speed of 52 km / hr & reaches its destination in 10 hr . car b runs at the speed of 46 km / h & reaches its destination in 8 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 62 : 25 , b ) 66 : 52 , c ) 68 : 15 , d ) 65 : 41 , e ) 23 : 59
Rationale: "sol . distance travelled by car a = 52 × 10 = 520 km distance travelled by car b = 46 × 8 = 368 km ratio = 520 / 368 = 65 : 41 d"
Answer: d
Question (physics): the distance from city a to city b is 60 miles . while driving from city a to city b , bob drives at a constant speed of 40 miles per hour . alice leaves city a 30 minutes after bob . what is the minimum constant speed in miles per hour that alice must exceed in order to arrive in city b before bob ?
Options: a ) 45 , b ) 48 , c ) 50 , d ) 52 , e ) 60
Rationale: "the time it takes bob to drive to city b is 60 / 40 = 1.5 hours . alice needs to take less than 1 hour for the trip . alice needs to exceed a constant speed of 60 / 1 = 60 miles per hour . the answer is e ."
Answer: e
Question (physics): if 18 persons can build a wall 140 m long in 42 days , the number of days that 30 persons will take to complete a similar wall 100 m long , is ?
Options: a ) 28 , b ) 18 , c ) 24 , d ) 21 , e ) 16
Rationale: "explanation : ( length 140 : 100 ) : ( persons 30 : 18 ) : : 42 : x 140 x 30 x x = 100 x 18 x 42 or x = 18 answer : b"
Answer: b
Question (general): a pharmaceutical company received $ 7 million in royalties on the first $ 20 million in sales of the generic equivalent of one of its products and then $ 9 million in royalties on the next $ 108 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 20 million in sales to the next $ 108 million in sales ?
Options: a ) 8 % , b ) 15 % , c ) 45 % , d ) 52 % , e ) 76 %
Rationale: "solution : this is a percent decrease problem . we will use the formula : percent change = ( new – old ) / old x 100 to calculate the final answer . we first set up the ratios of royalties to sales . the first ratio will be for the first 20 million in sales , and the second ratio will be for the next 108 million in sales . because all of the sales are in millions , we do not have to express all the trailing zeros in our ratios . first 20 million royalties / sales = 7 / 20 next 108 million royalties / sales = 9 / 108 = 1 / 12 because each ratio is not an easy number to use , we can simplify each one by multiplying each by the lcm of the two denominators , which is 60 . keep in mind that we are able to do this only because our answer choices are expressed in percents . first 20 million royalties / sales = ( 7 / 20 ) x 60 = 21 next 108 million royalties / sales = 9 / 108 = ( 1 / 12 ) x 60 = 5 we can plug 9 and 5 into our percent change formula : ( new – old ) / old x 100 [ ( 5 – 21 ) / 21 ] x 100 - 1600 / 21 x 100 at this point we can stop and consider the answer choices . since we know that 1600 / 21 is just a bit less than ½ , we know that - 1600 / 21 x 100 is about a 76 % decrease . answer e ."
Answer: e
Question (physics): the sum of three consecutive even numbers is 93 . find the middle number of the three ?
Options: a ) 14 , b ) 35 , c ) 39 , d ) 31 , e ) 12
Rationale: "middle value = 93 / 3 = 31 ans d"
Answer: d
Question (gain): an error 6 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 12.36 , b ) 8.36 , c ) 9.36 , d ) 10.36 , e ) 11.36
Rationale: "explanation : 100 cm is read as 106 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 106 × 106 ) cm 2 = 11236 ( a 2 - a 1 ) = 11236 - 10000 = 1236 = > 1236 / 10000 * 100 = 12.36 answer : a"
Answer: a
Question (physics): 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height . find the diameter of each sphere .
Options: a ) 4 cm , b ) 6 cm , c ) 8 cm , d ) 10 cm , e ) 12 cm
Rationale: "explanation : in this type of question , just equate the two volumes to get the answer as , volume of cylinder = π r 2 h volume of sphere = 43 π r 3 = > 12 ∗ 4 / 3 π r 3 = π r 2 h = > 12 ∗ 4 / 3 π r 3 = π ∗ 8 ∗ 8 ∗ 2 = > r 3 = 8 ∗ 8 ∗ 2 ∗ 3 / 12 ∗ 4 = > r 3 = 8 = > r = 2 cm = > diameter = 2 ∗ 2 = 4 cm option a"
Answer: a
Question (general): what is the decimal equivalent of ( 1 / 9 ) ^ 2 ?
Options: a ) 0.0123 , b ) 0.0625 , c ) 0.16 , d ) 0.25 , e ) 0.5
Rationale: "( 1 / 9 ) ² = ( 1 / 9 ) ( 1 / 9 ) = 1 / 81 approach # 1 : use long division to divide 81 into 1 to get 1 / 81 = 0.0123 a"
Answer: a
Question (general): 7589 - ? = 3434
Options: a ) 4242 , b ) 4155 , c ) 1123 , d ) 11023 , e ) none of them
Rationale: "let 7589 - x = 3434 then x = 7589 - 3434 = 4155 answer is b"
Answer: b
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.2 . what should be the run rate in the remaining 30 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 5.5 , c ) 7.4 , d ) 8.3 , e ) 6.2
Rationale: "explanation : runs scored in the first 10 overs = 10 × 3.2 = 32 total runs = 282 remaining runs to be scored = 282 - 32 = 250 remaining overs = 30 run rate needed = 250 / 30 = 8.3 answer : option d"
Answer: d