Cheukting/mathqa huggingface dataset:
Question (geometry): a triangle has sides 10 , 17 , and 21 . a square is inscribed in the triangle . one side of the square lies on the longest side of the triangle . the other two vertices of the square touch the two shorter sides of the triangle . what is the length of the side of the square ?
Options: a ) 148 / 29
b ) 168 / 29
c ) 168 / 26
d ) 158 / 29
e ) 198 / 29
Rationale: by heron ' s formula , the area , a , of a triangle with sides a , b , c is given by a = square root [ s ( s − a ) ( s − b ) ( s − c ) ] , where s = ½ ( a + b + c ) is the semi - perimeter of the triangle . then s = ½ ( 10 + 17 + 21 ) = 24 , and a = 84 . a square inscribed in a 10 by 17 by 21 triangle , with perpendicular dropped onto the side of length 21 . now drop a perpendicular of length h onto the side of length 21 . we also have a = ½ × base × perpendicular height . hence a = 21 h / 2 = 84 , from which h = 8 . notice that the triangle above the square is similar to the whole triangle . ( this follows because its base , the top of the square , is parallel to the base of the whole triangle . ) let the square have side of length d . considering the ratio of altitude to base in each triangle , we have 8 / 21 = ( 8 − d ) / d = 8 / d − 1 . therefore the length of the side of the square is 168 / 29 . answer : b
Answer: b
Question (physics): if a train , travelling at a speed of 160 kmph , crosses a pole in 9 sec , then the length of train is ?
Options: a ) 281 , b ) 125 , c ) 288 , d ) 266 , e ) 400
Rationale: "d = 160 * 5 / 18 * 9 = 400 m answer : e"
Answer: e
Question (general): when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 63 , the remainder is 11 . what is the remainder when x is divided by 9 ? putting a value say x = 11 we get remainder as 11 when divided by 63 . when 11 divided by 9 we get 2 as remainder . a is the answer ."
Answer: a
Question (physics): due to construction , the speed limit along an 15 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 8 , c ) 9.36 , d ) 15 , e ) 24
Rationale: "old time in minutes to cross 15 miles stretch = 15 * 60 / 55 = 15 * 12 / 11 = 16.36 new time in minutes to cross 15 miles stretch = 15 * 60 / 35 = 15 * 12 / 7 = 25.71 time difference = 9.36 answer c )"
Answer: c
Question (general): [ ( 3.242 x 12 ) / 100 ] = ?
Options: a ) 0.045388 , b ) 4.5388 , c ) 453.88 , d ) 473.88 , e ) 0.038904
Rationale: answer multiplying 3.242 x 12 = 3.8904 now divide 3.8904 by 100 so , 3.8904 ÷ 100 = 0.038904 ∴ shift the decimal two places to the left as 100 correct option : e
Answer: e
Question (general): for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 5 ] * [ 6 ] equivalent to ?
Options: a ) [ 45 ] , b ) [ 30 ] , c ) [ 15 ] , d ) [ 5 ] , e ) [ 50 ]
Rationale: "[ 5 ] * [ 6 ] = 15 * 3 = 45 = [ 15 ] the answer is c ."
Answer: c
Question (gain): find the c . i . on a sum of rs . 10000 for 9 months at 20 % per annum , interest being compounded quarterly ?
Options: a ) 2000 , b ) 10025 , c ) 1025 , d ) 2015 , e ) 2025
Rationale: "c . i . = 10000 ( 21 / 20 ) ^ 3 - 10000 = 1025 answer : c"
Answer: c
Question (physics): a person crosses a 720 m long street in 12 minutes . what is his speed in km per hour ?
Options: a ) 3.6 , b ) 4.5 , c ) 4.8 , d ) 5.4 , e ) 5.5
Rationale: "speed = 720 / ( 12 x 60 ) m / sec = 1 m / sec . converting m / sec to km / hr = 1 x ( 18 / 5 ) km / hr = 3.6 km / hr . answer : a"
Answer: a
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 28 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 ) 200 , e ) 350
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 28 , so 0.14 * { total } = 28 - - > { total } = 200 . answer : d ."
Answer: d
Question (physics): if 22 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 125 , b ) 187 , c ) 231 , d ) 375 , e ) 460
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 22 lines is 22 c 2 = 231 the answer is c ."
Answer: c
Question (general): the population of a town increased from 1 , 75,000 to 2 , 45,000 in a decade . the average percent increase of population per year is
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none
Rationale: "solution increase in 10 years = ( 245000 - 175000 ) = 87500 . increase % = ( 70000 / 175000 ã — 100 ) % = 40 % . required average = ( 40 / 10 ) % = 4 % . answer a"
Answer: a
Question (general): how many integers between 1 and 10 ^ 20 are such that the sum of their digits is 2 ?
Options: a ) 190 , b ) 210 , c ) 211 , d ) 230 , e ) 231
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 19 and there are 20 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 19 thus , the total number of integers is 1 + 2 + . . . + 19 + 20 = 20 * 21 / 2 = 210 the answer is b ."
Answer: b
Question (general): the price of commodity x increases by 40 paise every year , while the price of commodity y increases by 15 paise every year . if in 1988 , the price of commodity x was 4.20 and that of y was 6.30 , in which year will commodity x cost 40 paise more than commodity y ?
Options: a ) 1997 , b ) 1998 , c ) 1999 , d ) 2000 , e ) none of these
Rationale: suppose in ‘ n ’ years the price of comodity x will be more by 40 paise than that of commodity y . ∴ 420 + 40 n – 630 – 15 n = 40 or , 25 n – 210 = 40 or , 25 n = 250 or , n = 250 ⁄ 25 = 10 years . answer b
Answer: b
Question (physics): when tom works alone he chops 4 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 4 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? .
Options: a ) 125 % , b ) 100 % , c ) 25 % , d ) 225 % , e ) 400 %
Rationale: "tom chops 8 lbs in 12 minutes tammy chopswhen tom works alone he chops 2 lb . salad in 3 minutes , and when tammy works alone she chops 3 lb . salad in 2 minutes . they start working together , and after some time finish chopping 65 lb . of salad . of those 80 lb . , the salad quantity chopped by tammy is what percent greater than the quantifying chopped by tom ? . 9 lbs in 6 minutes so in the same amount of time , tammy chops 125 % more than tom , since 9 is 125 % greater than 4 . so 125 % is the answer . note that the actual time does n ' t matter . if you multiply the time each work by x , you ' ll multiply the work each does by x , and 9 x is still 125 % greater than 4 x . ans : a"
Answer: a
Question (general): of the total amount that jill spent on a shopping trip , excluding taxes , she spent 45 percent on clothing , 45 percent on food , and 10 percent on other items . if jill paid a 5 percent tax on the clothing , no tax on the food , and an 10 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
Options: a ) 3.5 , b ) 3.35 , c ) 3.45 , d ) 3.25 , e ) 3.55
Rationale: "assume she has $ 200 to spend . tax clothing = 45 % = $ 90 = $ 4.5 food = 45 % = $ 90 = $ 0.00 items = 10 % = $ 20 = $ 2.00 total tax = $ 6.50 % of total amount = 6.5 / 200 * 100 = 3.25 % answer d"
Answer: d
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 10 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 2.9 hrs , b ) 8.9 hrs , c ) 2.9 hrs , d ) 6.7 hrs , e ) 8.6 hrs
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 10 ) = 3 / 20 the cistern will be filled in 20 / 3 hrs i . e . , 6.7 hrs . answer : d"
Answer: d
Question (gain): j is 25 % less than p and 20 % less than t . t is t % less than p . what is the value of t ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( t / 100 ) ] * p i . e . 100 - t = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . t = 6.25 answer : option d
Answer: d
Question (physics): the speed of a car is 90 km in the first hour and 80 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 85 , d ) 54 , e ) 15
Rationale: "s = ( 90 + 80 ) / 2 = 85 kmph answer : c"
Answer: c
Question (general): if the price of gasoline increases by 25 % and ron intends to spend only 15 % more on gasoline , by how much % should he reduce the quantity of gasoline that he buys ?
Options: a ) 10 % , b ) 12.5 % , c ) 8 % , d ) 12 % , e ) 6.66 %
Rationale: explanatory answer let the price of 1 litre of gasoline be $ x and let ron initially buy ' y ' litres of gasoline . therefore , he would have spent $ xy on gasoline . when the price of gasoline increases by 25 % , the new price per litre of gasoline is 1.25 x . ron intends to increase the amount he spends on gasoline by 15 % . i . e . , he is willing to spend xy + 15 % of xy = 1.15 xy let the new quantity of gasoline that he can get be ' q ' . then , 1.25 x * q = 1.15 xy or q = 1.15 xy / 1.25 x = 0.92 y . as the new quantity that he can buy is 0.92 y , he gets 0.08 y lesser than what he used to get earlier . or a reduction of 8 % . the correct choice is ( c )
Answer: c
Question (gain): in how many years will a sum of money doubles itself at 10 % per annum on simple interest ?
Options: a ) 70 % , b ) 20 % , c ) 10 % , d ) 28 % , e ) 20 %
Rationale: "p = ( p * 10 * r ) / 100 r = 10 % answer : c"
Answer: c
Question (general): if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 925 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 250 , d ) rs . 350 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 925 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 925 3.7 z = 925 , z = 250 answer : . c"
Answer: c
Question (gain): what will be the compound interest on a sum of rs . 45,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) s : 10123.19 , b ) s : 10123.29 , c ) s : 10123.20 , d ) s : 18221.76 , e ) s : 10123.12
Rationale: "amount = [ 45000 * ( 1 + 12 / 100 ) 3 ] = 45000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 63221.76 c . i . = ( 63221.76 - 45000 ) = rs : 18221.76 answer : d"
Answer: d
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 60 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 60 rs . 5 m + 5 m + 5 m - - - - - 60 rs . 15 m - - - - - - 60 rs . = > 1 m = 4 rs . answer : c"
Answer: c
Question (general): 3034 - ( 1002 / 20.04 ) = ?
Options: a ) 2984 , b ) 2983 , c ) 2982 , d ) 2981 , e ) none of these
Rationale: option a
Answer: a
Question (general): the tax on a commodity is diminished by 12 % and its consumption increased by 10 % . the effect on revenue is ?
Options: a ) 8 , b ) 6 , c ) 3 , d ) 5 , e ) 4
Rationale: "100 * 100 = 10000 88 * 110 = 9680 - - - - - - - - - - - 10000 - - - - - - - - - - - 320 100 - - - - - - - - - - - ? = > 3 % decrease answer : c"
Answer: c
Question (gain): last year a worker saved 15 % of her annual salary . this year , she made 20 % more money than last year and she saved 25 % of her salary . the amount she saved this year was what percent of the amount she saved last year ?
Options: a ) 120 % , b ) 140 % , c ) 160 % , d ) 180 % , e ) 200 %
Rationale: "let x be the worker ' s salary last year . last year , she saved 0.15 x . this year , she saved 0.25 ( 1.2 x ) = 0.3 x 0.3 x / 0.15 x = 200 % the answer is e ."
Answer: e
Question (physics): one pipe can fill a pool 1.25 times faster than a second pipe . when both pipes are opened , they fill the pool in 4 hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 1.25 , d ) 9 , e ) 7.2
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.25 r = 5 r / 4 . since when both pipes are opened , they fill the pool in four hours , then their combined rate is 1 / 4 pool / hour . thus we have that r + 5 r / 4 = 1 / 4 - - > r = 1 / 9 pool / hour - - > time is reciprocal of rate thus it ' s 9 / 1 = 9 hours . answer : d ."
Answer: d
Question (general): what will be the reminder when ( 27 ^ 27 + 27 ) is divided by 28 ?
Options: a ) 92 , b ) 43 , c ) 71 , d ) 26 , e ) 31
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 27 ^ 27 + 1 ) will be divisible by ( 27 + 1 ) ; ( 27 ^ 27 + 1 ) + 26 when divided by 28 will give 26 as remainder . correct option : d"
Answer: d
Question (general): ram ' s salary is 25 % more than raja ' s . how much percent is raja ' s salary less than ram ' s ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 50 %
Rationale: raja ' s salary less than ram ' s by 25 / ( 100 + 25 ) * 100 % = 20 % answer is c
Answer: c
Question (general): what is the tens digit of 6 ^ 20 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the tens digit of 6 in integer power starting from 2 ( 6 ^ 1 has no tens digit ) repeats in a pattern of 5 : { 3 , 1 , 9 , 7 , 5 } : the tens digit of 6 ^ 2 = 36 is 3 . the tens digit of 6 ^ 3 = 216 is 1 . the tens digit of 6 ^ 4 = . . . 96 is 9 . the tens digit of 6 ^ 5 = . . . 76 is 7 . the tens digit of 6 ^ 6 = . . . 56 is 5 . the tens digit of 6 ^ 7 = . . . 36 is 3 again . etc . . . 20 has the form 5 n , so the tens digit of 6 ^ 20 is 7 . the answer is d ."
Answer: d
Question (geometry): a 25 cm wide path is to be made around a circular garden having a diameter of 4 meters . approximate area of the path is square meters is
Options: a ) 3.34
b ) 3.36
c ) 3.34
d ) 6.32
e ) 3.31
Rationale: area of the path = area of the outer circle - area of the inner circle = ∏ { 4 / 2 + 25 / 100 } 2 - ∏ [ 4 / 2 ] 2 = ∏ [ 2.252 - 22 ] = ∏ ( 0.25 ) ( 4.25 ) { ( a 2 - b 2 = ( a - b ) ( a + b ) } = ( 3.14 ) ( 1 / 4 ) ( 17 / 4 ) = 53.38 / 16 = 3.34 sq m . answer : a
Answer: a
Question (gain): x and y invested in a business . they earned some profit which they divided in the ratio of 1 : 3 . if x invested rs . 10,000 . the amount invested by y is
Options: a ) rs . 30,000 , b ) rs . 50,000 , c ) rs . 60,000 , d ) rs . 80,000 , e ) none
Rationale: "solution suppose y invested rs . y then , 10000 / y = 1 / 3 â € ¹ = â € º y = ( 10000 ã — 3 / 1 ) . â € ¹ = â € º y = 30000 . answer a"
Answer: a
Question (gain): in a certain math department , students are required to enroll in either calculus or trigonometry , each of which is offered in beginner and advanced courses . the number of students enrolled in trigonometry is 50 % greater than the number of students enrolled in calculus , and 80 % of calculus students are enrolled in the beginner course . if 4 / 5 of students are in the beginner courses , and one student is selected at random , what is the probability that a beginner trigonometry student is selected ?
Options: a ) 40 % , b ) 44 % , c ) 48 % , d ) 52 % , e ) 56 %
Rationale: let x be the number of students in calculus . then the number of students in trigonometry is 1.5 x the number of students on beginner calculus is 0.8 x the number of students in beginner trigonometry is 4 / 5 * ( 2.5 x ) - 0.8 x = 1.2 x the percentage in beginner trigonometry is 1.2 x / 2.5 x = 48 % the answer is c .
Answer: c
Question (physics): a car going at 10 miles per hour set out on an 80 - mile trip at 9 : 00 a . m . exactly 10 minutes later , a second car left from the same place and followed the same route . how fast , in miles per hour , was the second car going if it caught up with the first car at 10 : 30 a . m . ?
Options: a ) 45 , b ) 20 , c ) 53 , d ) 55 , e ) 60
Rationale: "let car a = car that starts at 9 am car b = car that starts at 9 : 10 am time for which car a travels at speed of 10 m per hour = 1.5 hours distance travelled by car a = 10 * 1.5 = 15 miles since car b catches up car a at 10 : 30 , time = 80 mins = 4 / 3 hour speed of car b = 15 / ( 4 / 3 ) = 20 miles per hour answer b"
Answer: b
Question (general): 0.009 / x = 0.1 . find the value of x
Options: a ) 0.0009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: x = 0.009 / 0.1 = 0.09 answer : b
Answer: b
Question (general): the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 4 ?
Options: a ) 10 ^ 5 , b ) 10 ^ 6 , c ) 10 ^ 7 , d ) 10 ^ 8 , e ) 10 ^ 9
Rationale: "0.1 = 10 ^ - 1 ( 0.01 ) ^ 4 = ( 10 ^ - 2 ) ^ 4 = 10 ^ - 8 10 ^ 7 * 10 ^ - 8 = 10 ^ - 1 the answer is c ."
Answer: c
Question (other): in a group of 70 people , 60 like swimming , 50 like wrestling . how many like both swimming and wrestling ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "make a venn diagram , and enter your data . let the number of people who like both swimming and wrestling be x 60 - x + x + 50 - x = 70 x = 40 so number who like both swimming and wrestling = 40 answer c"
Answer: c
Question (general): in the coordinate plane a slope of the line k is 3 times the y - intercept of the line k . what is the x - intercept of the line k ?
Options: a ) - 4 , b ) 4 , c ) - 1 / 4 , d ) - 1 / 3 , e ) 2
Rationale: as y = 3 mx + m , from 0 = 3 mx + m we get x = - 1 / 3 . hence , the correct answer choice is d .
Answer: d
Question (general): a number when divided by 128 gives a remainder 34 , what remainder will be obtained by dividing the same number 19 ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 10 , e ) 3
Rationale: "explanation : 128 + 34 = 162 / 19 = 10 ( remainder ) answer : d"
Answer: d
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 30 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 120 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 210
Rationale: "set up equation : x = total number of workers 120 = 0,4 * 2 / 3 * x + 0,7 * 1 / 3 * x 120 = 15 / 30 x x = 240 240 - 120 = 120 answer d"
Answer: d
Question (general): find the value of x : x ² − 3 x + 2
Options: a ) - 1 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "( x − 1 ) ( x − 2 ) x = 1 or 2 . c"
Answer: c
Question (physics): aarti can do a piece of work in 3 days . in how many days will she complete four time of work of same type ?
Options: a ) 12 days , b ) 18 days , c ) 21 days , d ) 3 days , e ) 13 days
Rationale: "we have the important relation , more work , more time ( days ) a piece of work can be done in 3 days . four times of work of same type can be done in 3 x 4 = 12 days answer a"
Answer: a
Question (geometry): find the area of the quadrilateral of one of its diagonals is 40 cm and its off sets 11 cm and 9 cm ?
Options: a ) 100 cm 2 , b ) 150 cm 2 , c ) 333 cm 2 , d ) 400 cm 2 , e ) 750 cm 2
Rationale: "1 / 2 * 40 ( 11 + 9 ) = 400 cm 2 answer : d"
Answer: d
Question (physics): if 3 taps are opened together a tank is filled in 3 hrs . one of the taps alone can fill it in 10 hrs . and another in 15 hrs . in how many hours will the third tap fill it ?
Options: a ) 7 hrs . , b ) 4 hrs . , c ) 5 hrs . , d ) 6 hrs . , e ) 8 hrs .
Rationale: part filled by three taps together in 1 hr = 1 / 3 part filled by one of the tap in 1 hr = 1 / 10 part filled by another tap in 1 hr = 1 / 15 part filled by third tap in 1 hr = 1 / 3 - ( 1 / 0 + 1 / 15 ) = 5 / 30 therefore the third tap can fill the whole tank in : 30 / 5 hrs . = 6 hrs . answer : d
Answer: d
Question (gain): a man took a loan from a bank at the rate of 10 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,000 , c ) rs . 18,000 , d ) rs . 20,000 , e ) none
Rationale: "solution principal = rs . ( 100 x 5400 / 10 x 3 ) = rs . 18000 . answer c"
Answer: c
Question (general): how many different positive integers exist between 10 ^ 9 and 10 ^ 10 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 10
Rationale: "so , the numbers should be from 1,000 , 000,000 to 10,000 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 1,000 , 000,001 1,000 , 000,010 1,000 , 000,100 1,000 , 001,000 1,000 , 010,000 1,000 , 100,000 1,001 , 000,000 1,010 , 000,000 1,100 , 000,000 9 numbers . 2 . one 2 and the rest are 0 ' s : 2,000 , 000,000 1 number . total = 10 numbers . answer : e"
Answer: e
Question (gain): a pair of articles was bought for $ 50 at a discount of 60 % . what must be the marked price of each of the article ?
Options: a ) $ 25 , b ) $ 10 , c ) $ 29.65 , d ) $ 35.95 , e ) $ 45.62
Rationale: "s . p . of each of the article = 50 / 2 = $ 25 let m . p = $ x 40 % of x = 25 x = 25 * . 4 = $ 10 answer is b"
Answer: b
Question (general): the average runs of a cricket player of 15 innings was 25 . how many runs must he make in his next innings so as to increase his average of runs by 6 ?
Options: a ) 121 , b ) 421 , c ) 143 , d ) 176 , e ) 84
Rationale: "explanation : average after 16 innings = 31 required number of runs = ( 31 * 16 ) – ( 25 * 15 ) = 496 – 375 = 121 answer a"
Answer: a
Question (physics): two airplanes take off from one airfield at noon . one flies due east at 202 miles per hour while the other flies directly northeast at 283 miles per hour . approximately how many miles apart are the airplanes at 2 p . m . ?
Options: a ) 166 , b ) 332 , c ) 400 , d ) 483 , e ) 404
Rationale: "e in two hours : the plane flying east will be 404 miles away from airport . the other plane will be 566 miles away from airport . 566 / 404 = ~ 1.4 = ~ sqrt ( 2 ) this means that planes formed a right isocheles triangle = > sides of such triangles relate as 1 : 1 : sqrt ( 2 ) = > the planes are 404 miles apart . e"
Answer: e
Question (general): ( x ) + 1315 + 9211 - 1569 = 11901 . calculate the value of x
Options: a ) 87801 , b ) 87811 , c ) 87862 , d ) 11803 , e ) 87803
Rationale: x + 1315 + 9211 - 1569 = 11901 = x + 1315 + 9211 = 11901 + 1569 = x + 10526 = 13470 = x = 98329 - 10526 = 87803 answer is e
Answer: e
Question (general): find the product of the local value and absolute value of 8 in 564823
Options: a ) 1600 , b ) 6400 , c ) 16000 , d ) 12000 , e ) 18000
Rationale: "explanation : place value = local value face value = absolute value the place value of 8 in 564823 is 8 x 100 = 800 the face value of 8 in 564823 is nothing but 8 . = > 800 * 8 = 6400 answer : option b"
Answer: b