Cheukting/mathqa huggingface dataset:
Question (geometry): what is the perimeter , in meters , of a rectangular garden 24 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 24 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 8 meters . perimeter of garden = 2 * ( 8 + 24 ) = 64 meter . answer is c"
Answer: c
Question (physics): a can do a work in 12 days . when he had worked for 3 days , b joinedhim . if they complete the work in 3 more days , in how manydays can balone finish the work ?
Options: a ) 2 days , b ) 4 days , c ) 5 days , d ) 6 days , e ) 9 days
Rationale: sax work done by afar 3 days : i j . . remzming war — 1 . work done by ( a + b ) for 1 day : . work done by a for 1 day 6 days d
Answer: d
Question (general): if k is an integer and 0.0010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "0.0010101 * 10 ^ k > 100 we need to move the decimal point to the right 5 places to get 101.01 this is equivalent to multiplying by 10 ^ 5 . the answer is d ."
Answer: d
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 18 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 2 , c ) 9 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 18 w 19 + 9 x = 18 ( x + 1 ) x = 1 / 9 ratio of gold with copper = 1 : 1 / 9 = 9 : 1 answer is c"
Answer: c
Question (general): find the ones digit of 73 ^ 350
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "3,9 , 7,1 repeats after every four times therefore 350 / 4 = 87 + 2 remainder 9 is the ones digit so e is correct"
Answer: e
Question (general): a man engaged a servant on the condition that he would pay him rs . 900 and a uniform after 1 year service . he served onlyfor 9 months and received uniform & rs . 650 , find the price of the uniform ?
Options: a ) rs . 90 , b ) rs . 100 , c ) rs . 150 , d ) rs . 190 , e ) rs . 200
Rationale: "9 / 12 = 3 / 4 * 900 = 675 650 - - - - - - - - - - - - - 25 1 / 4 - - - - - - - - 25 1 - - - - - - - - - ? = > rs . 100 b"
Answer: b
Question (physics): a 600 meter long train crosses a signal post in 20 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 5 min
Rationale: "s = 600 / 20 = 1530 mps s = 3600 / 30 = 120 sec = 2 min answer : b"
Answer: b
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 3 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 2 : 3 , e ) 10 : 9
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 3 - - > e : s = 5 : 3 = 15 : 9 . thus , l : s = 10 : 9 . answer : e ."
Answer: e
Question (general): in the coordinate plane a slope of the line k is 0.5 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 2 , d ) 1 / 2 , e ) - 2
Rationale: as y = 0.5 mx + m , from 0 = 1 / 2 mx + m we get x = - 2 . hence , the correct answer choice is e .
Answer: e
Question (geometry): a metallic sheet is of rectangular shape with dimensions 48 m x 36 m . from each of its corner , a square is cut off so as to make an open box . if the length of the square is 8 m , the volume of the box ( in m 3 ) is
Options: a ) 6420 , b ) 8960 , c ) 5120 , d ) 4830 , e ) none
Rationale: "sol . clearly , l = ( 48 - 16 ) m = 32 m , b = ( 36 - 16 ) m = 20 m , h = 8 m . ∴ volume of the box = ( 32 x 20 x 8 ) m 3 = 5120 m 3 answer c"
Answer: c
Question (physics): a motorboat can go at 21 kmph and still water . it takes 7 hours to row from a to b and back . what is the distance between a and b if the speed of the stream is 3 kmph ?
Options: a ) 65 km , b ) 85 km , c ) 55 km , d ) 72 km , e ) 40 km
Rationale: let the distance between a and b be x km . total time = x / ( 21 + 3 ) + x / ( 21 - 3 ) = 7 = > x / 24 + x / 18 = 7 = > ( 4 x + 3 x ) / 72 = 7 = > x = 72 km . answer : d
Answer: d
Question (general): the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum r of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: "we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just r = 900 : the answer is c ."
Answer: c
Question (gain): a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 4 percent and 8 percent , respectively . if the total interest on the two certificates was $ 1,440 at the end of one year , what fractional part of the $ 20.000 was invested at the higher rate ?
Options: a ) 3 / 8 , b ) 4 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "x * 4 / 100 * 1 + ( 20000 - x ) * 8 / 100 * 1 = 1440 4 x - 8 x = 144000 - 160000 = > - 4 x = - 16000 = > x = 4000 / 4 so 16000 / 20000 = 4 / 5 answer - b"
Answer: b
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 6 kilometers by car . what is the distance , in kilometers , from the dormitory to the city ?
Options: a ) 30 , b ) 58 , c ) 60 , d ) 90 , e ) 120
Rationale: "i believe there is a better way to do it . basically one of the options should satisfy the given criteria . 60 did 1 / 5 * 60 = 12 2 / 3 * 60 = 40 so total distance 52 + remaining 6 = 58 answer b"
Answer: b
Question (general): when positive integer x is divided by positive integer y , the remainder is 9 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "x = qy + 9 , where q is the quotient x / y = ( q y + 9 ) / y = q + ( 9 / y ) = 96.12 = 96 + 0.12 = > q = 96 9 / y = 0.12 = > y = 75 answer is b ."
Answer: b
Question (general): tom read a book containing 1000 pages by reading the same number of pages each day . if he would have finished the book 5 days earlier by reading 15 pages a day more , how many days did tom spend reading the book ?
Options: a ) 20 , b ) 18 , c ) 16 , d ) 15 , e ) 15.39
Rationale: "actually u can set up 2 equation p - - stands for the pages d - - stands for the days 1 ) p * d = 480 ( we want to find the days , sop = 480 / d ) 2 ) ( p + 15 ) ( d - 5 ) = 1000 = > pd - 5 p + 15 d - 75 = 1000 as the 1 ) stated u can put 1 ) into 2 ) = > 1000 - 5 p + 15 d - 75 = 1000 = > 15 d - 5 p = 75 put the bold one into it = > 15 d - 5 ( 480 / d ) = 75 the we get the final equation 16 d ^ 2 - 2400 = 80 d ( divide 16 ) = > d ^ 2 - 5 d - 160 = 0 so d = 15.39 days . ans : ( e )"
Answer: e
Question (gain): find the compound interest on $ 16,000 at 20 % per annum for 9 months , compounded quarterly
Options: a ) 2532 , b ) 2552 , c ) 2524 , d ) 2522 , e ) 2512
Rationale: "principal = $ 16000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 16000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 18522 . ci . = $ ( 18522 - 16000 ) = $ 2522 . answer d ."
Answer: d
Question (physics): the number of students in each section of a school is 24 . after admitting new students , three new sections were started . now , the total number of sections is 16 and there are 21 students in each section . the number of new students admitted is :
Options: a ) 12
b ) 42
c ) 24
d ) 28
e ) 26
Rationale: original number of sections = 16 - 3 = 13 original number of students = 24 x 13 = 312 present number of students = 21 x 16 = 336 number of new students admitted = 336 - 312 = 24 so the answer is option c ) 24 .
Answer: c
Question (physics): a man crosses a 600 m long street in 5 minutes . what is his speed in km per hour ?
Options: a ) 7 km / hr , b ) 7.2 km / hr , c ) 5.2 km / hr , d ) 10 km / hr , e ) 5 km / hr
Rationale: speed = 600 / 5 * 60 = 2 m / sec converting m / sec to km / hr . = 2 * 18 / 5 = 7.2 km / hr answer is b
Answer: b
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 24 , what is the sum of the first 15 terms of the progression ?
Options: a ) 300 , b ) 240 , c ) 220 , d ) 200 , e ) 180
Rationale: "4 th term + 12 th term = 24 i . e . , ( a + 3 d ) + ( a + 11 d ) = 24 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 24 - - - - - - - - - - - - - - - from ( 1 ) = 180 answer : e"
Answer: e
Question (general): how many 4 - digit positive integers are there , where each digit is positive , and no 3 adjacent digits are same ?
Options: a ) 1236 , b ) 3528 , c ) 4096 , d ) 4608 , e ) 6561
Rationale: first digit . . 9 posibilities second digit , 8 possibilities third digit , 7 possibilities fourth digit , 7 possibilities . 9 * 8 * 7 * 7 = 3528 . b
Answer: b
Question (general): 15 lts are taken of from a container full of liquid a and replaced with liquid b . again 15 more lts of the mixture is taken and replaced with liquid b . after this process , if the container contains liquid a and b in the ratio 9 : 16 , what is the capacity of the container w ?
Options: a ) a : 45 , b ) b : 25 , c ) c : 37.5 , d ) d : 36 , e ) e : 42
Rationale: "if you have a 37.5 liter capacity , you start with 37.5 l of a and 0 l of b . 1 st replacement after the first replacement you have 37.5 - 15 = 22.5 l of a and 15 l of b . the key is figuring out how many liters of a and b , respectively , are contained in the next 15 liters of mixture to be removed . the current ratio of a to total mixture is 22.5 / 37.5 ; expressed as a fraction this becomes ( 45 / 2 ) / ( 75 / 2 ) , or 45 / 2 * 2 / 75 . canceling the 2 s and factoring out a 5 leaves the ratio as 9 / 15 . note , no need to reduce further as we ' re trying to figure out the amount of a and b in 15 l of solution . 9 / 15 of a means there must be 6 / 15 of b . multiply each respective ratio by 15 to get 9 l of a and 6 l of b in the next 15 l removal . final replacement the next 15 l removal means 9 liters of a and 6 liters of b are removed and replaced with 15 liters of b . 22.5 - 9 = 13.5 liters of a . 15 liters of b - 6 liters + 15 more liters = 24 liters of b . test to the see if the final ratio = 9 / 16 ; 13.5 / 24 = ( 27 / 2 ) * ( 1 / 24 ) = 9 / 16 . choice c is correct ."
Answer: c
Question (general): a number when divided by 45 , gives 30 as quotient and 0 as remainder . what will be the remainder when dividing the same number by 15
Options: a ) a ) 0 , b ) b ) 3 , c ) c ) 4 , d ) d ) 6 , e ) e ) 7
Rationale: explanation : p ÷ 45 = 30 = > p = 30 * 45 = 1350 p / 15 = 1350 / 15 = 90 , remainder = 0 answer : option a
Answer: a
Question (general): a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price s per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average s = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Question (general): of the families in city x in 1904 , 50 percent owned a personal computer . the number of families in city x owning a computer in 1908 was 30 percent greater than it was in 1904 , and the total number of families in city x was 5 percent greater in 1908 than it was in 1904 . what percent of the families in city x owned a personal computer in 1908 ?
Options: a ) 61.90 % , b ) 52.20 % , c ) 56.20 % , d ) 70.45 % , e ) 74.41 %
Rationale: "say a 100 families existed in 1904 then the number of families owning a computer in 1904 - 50 number of families owning computer in 1908 = 50 * 130 / 100 = 65 number of families in 1908 = 105 the percentage = 65 / 105 * 100 = 61.90 % . option : a"
Answer: a
Question (gain): a merchant marks his goods up by 40 % and then offers a discount of 20 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 21 % , b ) 25 % , c ) 69 % , d ) 31 % , e ) 12 %
Rationale: "let the price be 100 . the price becomes 140 after a 40 % markup . now a discount of 20 % on 140 . profit = 112 - 100 12 % answer e"
Answer: e
Question (geometry): the perimeter of a triangle is 36 cm and the in radius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 76 , b ) 88 , c ) 66 , d ) 55 , e ) 45
Rationale: "area of a triangle = r * s where r is the in radius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : e"
Answer: e
Question (general): during a certain two - week period , 70 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 4 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
Options: a ) 16 a , b ) 13 a , c ) 14 a , d ) 11 2 / 3 a , e ) 12 a
Rationale: "total movies = 100 . comedies = 70 . action + drama = 30 . since there were 5 times as many dramas as action movies , then action + 4 * action = 30 - - > action = a = 6 . comedies = 70 = 14 a . answer : d ."
Answer: d
Question (gain): there were two candidates in an election . winner candidate received 58 % of votes and won the election by 288 votes . find the number of votes casted to the winning candidate ?
Options: a ) 776 , b ) 1044 , c ) 299 , d ) 257 , e ) 125
Rationale: "w = 58 % l = 42 % 58 % - 42 % = 16 % 16 % - - - - - - - - 288 58 % - - - - - - - - ? = > 1044 answer : b"
Answer: b
Question (general): 4 / 15 of 5 / 7 of a number is greater than 4 / 9 of 2 / 5 of the same number by 8 . what is half of that number ?
Options: a ) 305 , b ) 315 , c ) 345 , d ) 325 , e ) 335
Rationale: let the number be x . then 4 / 15 of 5 / 7 of x - 4 / 9 of 2 / 5 of x = 8  4 / 21 x - 8 / 45 x = 8 ( 4 / 21 - 8 / 45 ) x = 8  ( 60 - 56 ) / 315 x = 8  4 / 315 x = 8 x = ( 8 * 315 ) / 4 = 630  1 / 2 x = 315 hence required number = 315 answer is b .
Answer: b
Question (gain): a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 20 per kg , then his gain percent is
Options: a ) 7 % , b ) 13 % , c ) 14 % , d ) 15 % , e ) 16 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 20 ) = rs . 160 . profit = 160 - 150 = 10 so , profit % = ( 10 / 150 ) * 100 = 7 % option a"
Answer: a
Question (general): what is the total number of y integers between 100 and 200 that are divisible by 3 ?
Options: a ) 33 , b ) 32 , c ) 31 , d ) 30 , e ) 29
Rationale: yes there is a different way of arriving at that answer . . . . u can also use airthmetic progression to get the answer since the first term to be divisble by 3 is 102 . . take that as a . . the starting no and since 198 is the last digit to be divisible by 3 take that as n . . . since the difference is 3 take that as d no u have to find what term is 198 take that as nth term the formula for that is n = a + ( n - 1 ) * d 198 = 102 + ( n - 1 ) * 3 from this u get n = 33
Answer: a
Question (general): if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 136 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 = 136 ( p ) ( p - 1 ) = 272 = 17 * 16 p = 17 the answer is c .
Answer: c
Question (physics): a , b and c can do a piece of work in 4 days , 8 days and 20 days respectively . how long will they taken , if all the three work together ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 67 , e ) 2 6 / 17
Rationale: "1 / 4 + 1 / 8 + 1 / 20 = 17 / 40 = > 40 / 17 = > 2 6 / 17 days answer : e"
Answer: e
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 40 units . if today ' s production of 90 units raises the average to 45 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 7
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 40 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 40 n + 90 = 45 * ( n + 1 ) - - > n = 9 answer : d ."
Answer: d
Question (general): in the johnsons ' monthly budget , the dollar amounts allocated to household expenses , food , and miscellaneous items are in the ratio 5 : 4 : 1 , respectively . if the total amount allocated to these 3 categories is $ 1800 , what is the amount allocated to food ?
Options: a ) $ 900 , b ) $ 720 , c ) $ 675 , d ) $ 450 , e ) $ 225
Rationale: to solve this question , it will be best to first express the given ratio using variable multipliers . thus , we have : household expenses : food : miscellaneous = 5 x : 4 x : x since we are told that the total amount allocated to these categories is $ 1,800 we can set up the equation : 5 x + 4 x + x = 1,800 10 x = 1,800 x = 180 thus , the total amount allocated to food is 4 x 180 = $ 720 . answer b .
Answer: b
Question (general): one ton has 2600 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 2080 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: "16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2600 pound = 13 * 2600 * 16 ounces . hence the answer is ( 13 * 2600 * 16 ) / 260 = 2080 . answer : a ."
Answer: a
Question (general): what is the remainder when 8 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 3 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? d
Answer: d
Question (general): the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.4 years , the ratio of the number of boys to the number of girls in the class is
Options: a ) 7 : 3 , b ) 2 : 3 , c ) 9 : 3 , d ) 6 : 3 , e ) 2 : 5
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.4 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.4 ) < = > k = 0.4 / 0.6 = 2 / 3 . required ratio = 2 / 3 : 1 = 2 : 3 . answer : b"
Answer: b
Question (gain): in a certain boys camp , 20 % of the total boys are from school a and 30 % of those study science . if there are 35 boys in the camp that are from school a but do not study science then what is the total number of boys in the camp ?
Options: a ) 70 , b ) 245 , c ) 150 , d ) 35 , e ) 250
Rationale: "since 30 % of the boys from school a study science , then 70 % of the boys from school a do not study science and since 20 % of the total number of boys are from school a , then 0.2 * 0.7 = 0.14 , or 14 % of the boys in the camp are from school a and do not study science . we are told that this number equals to 35 , so 0.14 * { total } = 35 - - > { total } = 250 . answer : e ."
Answer: e
Question (general): of the female students at barkely university , 5 / 6 are on the honor roll . of the male students , 2 / 3 are on the honor roll . if 2 / 5 of the students are female , what fraction of all the students are on the honor roll ?
Options: a ) 5 / 9 , b ) 3 / 15 , c ) 23 / 30 , d ) 22 / 30 , e ) 53 / 90
Rationale: let the total students be 30 given 2 / 5 of the students are females = 12 then males = 3 / 5 = 18 5 / 6 of the females are on honor roll = 10 males on the honor roll = 2 / 3 = 12 total students on honor roll = 12 + 10 = 22 fraction = 22 / 30 d
Answer: d
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 18 seconds . find the length of the train .
Options: a ) 150 , b ) 278 , c ) 179 , d ) 300 , e ) 191
Rationale: ": speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 18 = 300 meter answer : d"
Answer: d
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 88 m , find the area of the rectangle ?
Options: a ) 432 sq m
b ) 363 sq m
c ) 452 sq m
d ) 428 sq m
e ) 525 sq m
Rationale: 2 ( 3 x + x ) = 88 l = 33 b = 11 lb = 33 * 11 = 363 answer : b
Answer: b
Question (geometry): the ratio of the volumes of two cubes is 729 : 2197 . what is the ratio of their total surface areas ?
Options: a ) 81 : 169 , b ) 81 : 122 , c ) 81 : 124 , d ) 81 : 126 , e ) 81 : 129
Rationale: "ratio of the sides = 3 √ 729 : 3 √ 2197 = 9 : 13 ratio of surface areas = 9 ^ 2 : 13 ^ 2 = 81 : 169 answer : option a"
Answer: a
Question (physics): a monkey ascends a greased pole 22 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 40 th minute , b ) 41 st minute , c ) 43 rd minute , d ) 42 nd minute , e ) 45 th minute
Rationale: "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 20 meters . i mean this will continue for first 20 * 2 = 40 mins . he would have reached 20 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 40 + 1 = 41 mins . so , asnwer will be b"
Answer: b
Question (physics): a can run 256 metre in 28 seconds and b in 32 seconds . by what distance a beat b ?
Options: a ) 32 metre , b ) 28 metre , c ) 23 metre , d ) 15 metre , e ) 28 metre
Rationale: "clearly , a beats b by 4 seconds now find out how much b will run in these 4 seconds speed of b = distance / time taken by b = 256 / 32 = 8 m / s distance covered by b in 4 seconds = speed ã — time = 8 ã — 4 = 32 metre i . e . , a beat b by 32 metre answer is a"
Answer: a
Question (general): if | x | = 4 x - 2 , then x = ?
Options: a ) 1 , b ) 2 , c ) 1 and 1 / 2 , d ) - 1 / 2 , e ) - 1
Rationale: "answer : approach : substituted option a i . e x = 2 . inequality satisfied . b"
Answer: b