Cheukting/mathqa huggingface dataset:
Question (physics): two trains a and b are 100 m and 150 m long and are moving at one another at 54 km / hr and 36 km / hr respectively . arun is sitting on coach b 1 of train a . calculate the time taken by arun to completely cross train b .
Options: a ) 10 s , b ) 6 s , c ) 4 s , d ) 8 s , e ) 12 s
Rationale: "detailed solution speed of a = 54 ∗ 1000 / 60 ∗ 60 = 15 m / s speed of b = 36 ∗ 1000 / 60 ∗ 60 = 10 m / s relative speed = s 1 + s 2 = 15 + 10 m / s = 25 m / s the length that needs to be crossed = length of train b = 150 m . therefore time taken = 150 / 25 = 6 s . what is the time taken for trains to completely cross each other ? the length that needs to be crossed = 100 + 150 = 250 m . time taken = 250 / 25 = 10 s . correct answer b ."
Answer: b
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 5,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 7,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 5,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 5,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 400 = 0.10 x combine terms and subtract 0.08 x from both sides : 150 = 0.02 x divide both sides by 0.02 : 7,500 = x your answer is a ."
Answer: a
Question (general): 15 % people of a village in sri lanka died by bombardment , 25 % of the remainder left the village on account of fear . if now the population is reduced to 4555 , how much was it in the beginning ?
Options: a ) 7400 , b ) 7145 , c ) 7200 , d ) 7323 , e ) 6030
Rationale: "x * ( 85 / 100 ) * ( 75 / 100 ) = 4555 x = 7145 answer : b"
Answer: b
Question (general): in a group of cows and hens , the number of legs are 18 more than twice the number of heads . the number of cows is
Options: a ) 5 , b ) 7 , c ) 9 , d ) 12 , e ) 14
Rationale: "explanation : let the number of cows be x and the number of hens be y . then , 4 x + 2 y = 2 ( x + y ) + 18 4 x + 2 y = 2 x + 2 y + 18 2 x = 18 x = 9 . answer : c"
Answer: c
Question (geometry): the area of rectangular field is 460 square metres . if the length is 15 per cent more than the breadth , what is the breadth of the rectangular field ?
Options: a ) 15 metres
b ) 26 metres
c ) 34.5 metres
d ) can not be determined
e ) none of these
Rationale: let the breadth of the rectangular field be ‘ x ’ m . then , length of the field will be x + x × 15 / 100 = 23 x / 20 now , x × 23 x / 20 = 460 or , 23 x 2 = 460 × 20 or , x 2 = 20 × 20 or , x = 20 m answer e
Answer: e
Question (general): sum of the squares of 3 no . is 252 and the sum of their products taken two at a time is 116 . find the sum ?
Options: a ) 24 , b ) 33 , c ) 22 , d ) 20 , e ) 21
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 252 + 2 * 116 a + b + c = â ˆ š 484 = 22 answer c"
Answer: c
Question (physics): a train 120 m long running at 72 kmph crosses a platform in 25 sec . what is the length of the platform ?
Options: a ) 443 m , b ) 354 m , c ) 450 m , d ) 380 m , e ) 250 m
Rationale: "d 350 d = 72 * 5 / 18 = 25 = 500 â € “ 120 = 380"
Answer: d
Question (general): an exam consists of 8 true / false questions . brian forgets to study , so he must guess blindly on each question . if any score above 60 % is a passing grade , what is the probability that brian passes ?
Options: a ) 1 / 16 , b ) 37 / 256 , c ) 1 / 2 , d ) 35 / 256 , e ) 15 / 16
Rationale: "if you have 8 t or f and brian is going to guess then each question he has a 50 % chance of getting correct . if a passing score is 70 % it means brian needs to get 6 / 8 = 75 % , 7 / 8 = 87.5 % , or 8 / 8 = 100 % to pass . each is a possibility . if brian gets a 5 / 8 ( = 62.5 % ) or below he fails . so first figure out the number of ways that brian can get 6 out of 8 , 7 out of 8 , and 8 out of 8 questions correct . which is 8 choose 6 , equals is 28 , 8 choose 7 , equals 8 , and 8 choose 8 , equals 1 . this sums to 37 . the number of possible questions outcomes - the sum of 8 choose 8 , 7 choose 8 , 6 choose 8 … . 2 choose 8 , 1 choose 8 , and 0 choose 8 is 256 , so the chance of him passing is 35 / 256 . d"
Answer: d
Question (general): the positive numbers w , x , y , and z are such that x is 35 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 20 - answer c"
Answer: c
Question (general): evaluate : 22 + sqrt ( - 4 + 6 * 4 * 3 ) = ?
Options: a ) 4 , b ) 14 , c ) 24 , d ) 34 , e ) 44
Rationale: "according to order of operations , inner brackets first where 6 ? 4 ? 3 is first calculated since it has a multiplication and a division . 6 * 4 * 3 = 24 * 3 = 8 hence 22 + sqrt ( - 4 + 6 * 4 * 3 ) = 22 + sqrt ( - 4 + 8 ) = 22 + sqrt ( 4 ) = 22 + 2 = 24 correct answer c"
Answer: c
Question (geometry): the width of a rectangle is 10 mtr and its area is 150 square meter . if length of the rectangle is increased , then its new area is 1 ( 1 / 3 ) times of the original area . what is the new perimeter of the rectangle ?
Options: a ) 45
b ) 54
c ) 67
d ) 60
e ) 69
Rationale: ans . ( d ) sol . length of original rectangle = 150 / 10 = 15 ( 10 * ( 15 + x ) ) / ( 10 * 15 ) = 4 / 3 x = 5 perimeter of new rectangle = 2 ( 10 + 20 ) = 60
Answer: d
Question (gain): how long will a boy take to run round a square field of side 40 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 64 sec , b ) 45 sec , c ) 1 min , d ) 32 sec , e ) 25 sec
Rationale: "speed = 9 km / hr = 9 * 5 / 18 = 5 / 2 m / sec distance = 40 * 4 = 160 m time taken = 160 * 2 / 5 = 64 sec answer is a"
Answer: a
Question (geometry): the side of a square is increased by 40 % then how much % does its area increases ?
Options: a ) 96 , b ) 56.25 , c ) 50.75 , d ) 42.75 , e ) 52.75
Rationale: "a = 100 a 2 = 10000 a = 140 a 2 = 19600 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 9600 100 - - - - - - - ? = > 96 % answer : a"
Answer: a
Question (physics): a runs twice as fast as b and gives b a start of 83 m . how long should the racecourse be so that a and b might reach in the same time ?
Options: a ) 75 m . , b ) 80 m . , c ) 150 m . , d ) 100 m . , e ) none of the above
Rationale: "ratio of speeds of a and b is 2 : 1 b is 83 m away from a but we know that a covers 1 meter ( 2 - 1 ) more in every second than b the time taken for a to cover 83 m is 83 / 1 = 83 m so the total time taken by a and b to reach = 2 * 83 = 166 m answer : e"
Answer: e
Question (physics): two trains 190 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.7 , b ) 10.9 , c ) 10.6 , d ) 12.6 , e ) 18.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 190 + 160 = 350 m . required time = 350 * 9 / 250 = 12.6 sec . answer : d"
Answer: d
Question (geometry): if a square mirror has a 20 - inch diagonal , what is the approximate perimeter w of the mirror , in inches ?
Options: a ) 40 , b ) 60 , c ) 80 , d ) 100 , e ) 120
Rationale: "if you draw the square and diagonal inside the square . u can see square becomes part of two triangles opposite to each other . and we know the property of the triangle , addition of two sides of triangle must be greater than its diagonal in order to complete the triangle . and each side must be less than 20 and perimeter w must be less than 80 , so we can eliminate answer choice c , d and e . so side 1 + side 2 > 20 , that means side 1 or side 2 must be > 10 . so we can eliminate the answer choice a . now we are left with is b"
Answer: b
Question (physics): 10 litres of water are poured into an aquarium of dimensions 50 cm length , 20 cm breadth , and 40 cm height . how high ( in cm ) will the water rise ? ( 1 litre = 1000 cm ³ )
Options: a ) 6 , b ) 8 , c ) 10 , d ) 20 , e ) 40
Rationale: lxbxh = 10000 h = 10000 / 50 * 20 = 10 cm ' c ' is the answer .
Answer: c
Question (general): a retailer sells 10 shirts . the first 3 he sells for $ 82 , $ 100 and $ 90 . if the retailer wishes to sell the 10 shirts for an overall average price of over $ 100 , what must be the minimum average price of the remaining 7 shirts ?
Options: a ) $ 100.00 , b ) $ 104.00 , c ) $ 110.00 , d ) $ 115.00 , e ) $ 119.00
Rationale: first 3 shirts are sold for $ 82 , $ 100 and $ 90 = $ 272 . to get average price of $ 100 , total sale should be 10 * $ 100 = $ 1000 so remaining 7 shirts to be sold for $ 1000 - $ 272 = $ 728 answer should be 728 / 7 = $ 104.00 that is b
Answer: b
Question (physics): a train running at the speed of 90 km / hr crosses a pole in 9 seconds . find the length of the train .
Options: a ) 225 meter , b ) 200 meter , c ) 250 meter , d ) 210 meter , e ) 230 meter
Rationale: "speed = 90 * ( 5 / 18 ) m / sec = 25 m / sec length of train ( distance ) = speed * time ( 25 ) * 9 = 225 meter answer : a"
Answer: a
Question (general): what is the total number of integers between 20 and 80 ( exclusive ) that are divisible by 10 ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 9 , e ) 3
Rationale: "30 , 40,50 , 60,70 total 5 answer is a"
Answer: a
Question (general): a mixture of 85 kg contains milk and water in the ratio 27 : 7 . how much more water is to be added to get a new mixture containing milk and water in the ratio 3 : 1 ?
Options: a ) 5 kg , b ) 6.5 kg , c ) 7.5 kg , d ) 8 kg , e ) 9 kg
Rationale: explanation : expl : milk in 85 kg of mix = 85 * ( 27 / 34 ) = 135 / 2 kg . water in it = 85 - 135 / 2 = 35 / 2 kg . let x kg of water be added to it . then , ( 135 / 2 ) / ( 35 / 2 + x ) = 3 / 1 ; 135 / ( 35 + 2 x ) = 3 / 1 ; 105 + 6 x = 135 ; 6 x = 30 ; x = 5 the quantity of water to be added = 5 kg answer : a
Answer: a
Question (general): what is the sum of all the multiples of 25 between 30 and 100 ?
Options: a ) 800 , b ) 625 , c ) 600 , d ) 250 , e ) 200
Rationale: "you first have to know all the multiples of 25 between 30 and 100 . they are 25 , 50,75 and 100 . if you add all these numbers together , you get 250 . final answer : d"
Answer: d
Question (general): the product of a and b is equal to 12 more than twice the sum of a and b . if b = 10 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 6 , e ) 35
Rationale: ab = 12 + 2 ( a + b ) 10 a = 12 + 2 a + 20 8 a = 32 a = 4 b - a = 10 - 4 = 6 d is the answer
Answer: d
Question (physics): a 600 meter long train crosses a signal post in 40 seconds . how long will it take to cross a 5.4 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 6 min , e ) 3 min
Rationale: "s = 600 / 40 = 15 mps s = 5400 / 15 = 360 sec = 6 min . answer : d"
Answer: d
Question (general): there are 7 stores in town that had a total of 21 visitors on a particular day . however , only 11 people went shopping that day ; some people visited more than one store . if 7 people visited exactly two stores each , and everyone visited at least one store , what is the largest number of stores anyone could have visited ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 9 , e ) 2
Rationale: "7 people visited 2 stores each for 14 visits . to maximize the number of stores that one person visited , let ' s assume that 3 people visited 1 store each . the number of remaining visits is 21 - 14 - 3 = 4 , which is the maximum that one person could have visited . the answer is c ."
Answer: c
Question (general): what is the largest 4 digit number exactly divisible by 12 ?
Options: a ) 4676 , b ) 4678 , c ) 8888 , d ) 9504 , e ) 9996
Rationale: "largest 4 digit number = 9999 9999 ÷ 12 = 833 , remainder = 3 hence largest 4 digit number exactly divisible by 12 = 9999 - 3 = 9996 answer : e"
Answer: e
Question (physics): the length of a rectangulat plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 5300 , what is the length of the plot in metres ?
Options: a ) 40 , b ) 50 , c ) 200 , d ) 120 , e ) none
Rationale: solution let breadth = x metres then , length = ( x + 20 ) metres . perimeter = ( 5300 / 26.50 ) m = 200 m answer c
Answer: c
Question (general): if two positive numbers are in the ratio 1 / 8 : 1 / 7 , then by what percent is the second number more than the first ?
Options: a ) 14.3 % . , b ) 70 % . , c ) 60 % . , d ) 68 % . , e ) 80 % .
Rationale: given ratio = 1 / 8 : 1 / 7 = 7 : 8 let first number be 7 x and the second number be 8 x . the second number is more than first number by 1 x . required percentage = 1 x / 7 x * 100 = 14.3 % . answer : a
Answer: a
Question (general): ashok secured average of 79 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
Options: a ) 104 , b ) 27 , c ) 99 , d ) 17 , e ) 80
Rationale: "explanation : number of subjects = 6 average of marks in 6 subjects = 79 therefore total marks in 6 subjects = 79 * 6 = 474 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 474 – 370 = 104 answer : a"
Answer: a
Question (physics): johnny makes $ 4.75 per hour at his work . if he works 6 hours , how much money will he earn ?
Options: a ) $ 30 , b ) $ 54 , c ) $ 28.50 , d ) $ 12 , e ) $ 9.60
Rationale: 4.75 * 6 = 28.50 . answer is c .
Answer: c
Question (gain): the sale price sarees listed for rs . 150 after successive discount is 20 % and 10 % is ?
Options: a ) 187 , b ) 120 , c ) 108 , d ) 178 , e ) 175
Rationale: "150 * ( 80 / 100 ) * ( 90 / 100 ) = 108 answer : c"
Answer: c
Question (general): the difference between a number and its three fifth is 50 . what is the number ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 180 , e ) none
Rationale: "solution let the number be x . then , x - 3 / 5 x = 50 ‹ = › 2 / 5 x = 50 ‹ = › x = ( 50 x 5 / 2 ) ‹ = › 125 . answer c"
Answer: c
Question (physics): a rectangular plot measuring 90 metres by 50 metres is to be enclosed by wire fencing . if the poles of the fence are kept 20 metres apart , how many poles will be needed ?
Options: a ) 55 , b ) 56 , c ) 14 , d ) 58 , e ) none of these
Rationale: "solution perimeter of the plot = 2 ( 90 + 50 ) = 280 m . ∴ number of poles = [ 280 / 20 ] = 14 m answer c"
Answer: c
Question (gain): how many liters of water must be added to 14 liters of milk and water containing 10 % water to make it 30 % water ?
Options: a ) 1 liter , b ) 2 liters , c ) 3 liters , d ) 4 liters , e ) 5 liters
Rationale: by rule of alligation : 30 % - 10 % = 20 % 100 % - 30 % = 70 % quantity of pure water : quantity of the mixture = 2 : 7 there are 14 liters of mixture , so we need to add 4 liters of pure water . the answer is d .
Answer: d
Question (general): in the x - y plane , there are 4 points ( 0,0 ) , ( 0,4 ) , ( 4,4 ) , and ( 4,0 ) . if these 4 points makes a rectangle , what is the probability that x + y < 4 ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 5 , e ) 1 / 6
Rationale: "if x + y < 4 , then y < - x + 4 . the line y = - x + 4 intersects the rectangle and these three points of intersection ( 0,0 ) , ( 0,4 ) and ( 4,0 ) form a triangle . the points below the line y = - x + 4 satisfy x + y < 4 . the area of this triangle is ( 1 / 2 ) ( 4 ) ( 4 ) = 8 the area of the rectangle is 16 . p ( x + y < 4 ) = 8 / 16 = 1 / 2 the answer is a ."
Answer: a
Question (gain): the population of a town is 10000 . it increases annually at the rate of 20 % p . a . what will be its population after 6 years ?
Options: a ) 14300 , b ) 29859 , c ) 14500 , d ) 14600 , e ) 15400
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 10000 × 120 / 100 ^ 6 = 29859 b )"
Answer: b
Question (gain): john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 58000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 37.4 %
Rationale: ( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 130000 = 36 / 65 . 36 / 65 is a little above 36 / 72 = 1 / 2 . thus , our answer is just a little above 35 . answer : d
Answer: d
Question (general): a basketball player is shooting hoops . he shoots a free throw , a high school 3 - pointer , and then a professional 3 - pointer . the probability that he makes the free throw is 4 / 5 , the probability that he makes the high school 3 - pointer is 1 / 2 , and the probability that he makes the professional 3 - pointer is 1 / 3 . what is the probability that he makes at least one of the 3 shots ?
Options: a ) 14 / 15 , b ) 15 / 16 , c ) 17 / 18 , d ) 9 / 10 , e ) 5 / 6
Rationale: the probability that he makes at least one of the three shots = 1 - ( the probability that he misses all of the shots ) the probability that he misses all shots = ( prob that he misses free throw ) * ( prob that he misses 3 - pointer ) * ( prob that he misses the professional 3 - pointer ) prob that he misses the free throw = 1 - 4 / 5 = 1 / 5 ; prob that he misses the 3 - pointer = 1 - 1 / 2 = 1 / 2 ; prob that he misses the professional 3 - pointer = 1 - 1 / 3 = 2 / 3 thus the probability that he misses all shots = ( 1 / 5 ) * ( 1 / 2 ) * ( 2 / 3 ) = 1 / 15 answer : 1 - 1 / 15 = 14 / 15 a
Answer: a
Question (general): a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 28 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 392 , b ) 412 . , c ) 432 . , d ) 502 , e ) 522
Rationale: "solution 1 : given that number of pastries are equally divided in to 28 groups , so the answer should be a multiple of 28 . and in the given choices , only 392 is divisible by 28 with remainder 0 ( make sure others are no multiples of 28 ) . so this is good enough to stop here , but to verify , 392 / 28 = 14 and 392 / 49 = 8 , which confirms the second part of question , 14 - 8 , 6 pastry short of each customer . solution 2 : going mathematical , expressing in the equation form , let x be the number of pastries and , n be the number of customers in 28 groups . so , x = 28 * n , as per second statement , x = 49 * ( n - 6 ) solve the above 2 for n and then we get x as 392 . answer is a : 392 ."
Answer: a
Question (physics): what decimal of an hour is a second
Options: a ) . 0028 , b ) . 0027 , c ) . 0026 , d ) . 0025 , e ) none of these
Rationale: explanation : 1 / ( 60 * 60 ) = 1 / 3600 = . 0027 option b
Answer: b
Question (physics): a train of 24 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.5 km long ?
Options: a ) 6 , b ) 3 , c ) 4 , d ) 9 , e ) 2
Rationale: "d = 25 * 60 + 1500 = 3000 m t = 3000 / 60 * 18 / 5 = 180 sec = 3 mins answer : b"
Answer: b
Question (gain): the total cost of 100 paper plates and 200 paper cups is $ 7.50 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 7.50 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.50 therefore oa is d"
Answer: d
Question (general): the average age of 20 students in a class is 15 years . if the age of teacher is also included , the average becomes 16 years , find the age of the teacher .
Options: a ) 35 , b ) 38 , c ) 45 , d ) 36 , e ) 60
Rationale: "explanation : if teacher ' s age is 15 years , there is no change in the average . but teacher has contributed 1 year to all the students along with maintaining his age at 16 . age of teacher = average age of all + total increase in age = 16 + ( 1 x 20 ) = 36 years answer : d"
Answer: d
Question (general): in how many t ways can 4 white and 3 black chess pieces be arranged in a row such that they occupy alternate places ? assume that the pieces are distinct .
Options: a ) t = 288 , b ) t = 144 , c ) t = 12 , d ) 48 , e ) 96
Rationale: 4 white chess pieces can be arranged in 4 ! ways and 4 black pieces can be arranged in 3 ! ways . w _ w _ w _ w number of ways = 4 ! * 3 ! = 24 * 6 = 144 answer b
Answer: b
Question (gain): a baseball card decreased in value 20 % in its first year and 10 % in its second year . what was the total percent decrease of the card ' s value over the two years ?
Options: a ) 28 % , b ) 30 % , c ) 32 % , d ) 36 % , e ) 72 %
Rationale: "let the initial value of baseball card = 100 after first year , value of baseball card = ( 1 - 20 / 100 ) * 100 = 80 after second year , value of baseball card = ( 1 - 10 / 100 ) * 80 = 72 total percent decrease of the card ' s value over the two years = ( 100 - 72 ) / 100 * 100 % = 28 % answer a"
Answer: a
Question (general): 1393 x 1393 = ?
Options: a ) a ) 1951609 , b ) b ) 1951601 , c ) c ) 1940449 , d ) d ) 1951603 , e ) e ) 1951604
Rationale: "1393 x 1393 = ( 1393 ) 2 = ( 1400 - 7 ) 2 = ( 1400 ) 2 + ( 7 ) 2 - ( 2 x 1400 x 7 ) = 1960000 + 49 - 19600 = 1960049 - 19600 = 1940449 . answer : c"
Answer: c
Question (other): two alloys a and b are composed of two basic elements . the ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 5 : 1 , respectively . a new alloy x is formed by mixing the two alloys a and b in the ratio 4 : 3 . what is the ratio of the composition of the two basic elements in alloy x ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 5 : 2 , d ) 4 : 3 , e ) 7 : 9
Rationale: "mixture a has a total of 5 + 3 = 8 parts . if in the final mixture this represents 4 parts , then the total number of parts in mixture b should be ( 8 / 4 ) * 3 = 6 . so , we should take of mixture b a quantity with 5 and 1 parts , respectively . this will give us in the final mixture ( 5 + 5 ) : ( 3 + 1 ) , which means 10 : 4 , or 5 : 2 . answer c ."
Answer: c
Question (general): in the rectangular coordinate system , what is the x - intercept of a line passing through ( 10 , 3 ) and ( − 4 , − 4 ) ?
Options: a ) 4 , b ) 2 , c ) 0 , d ) − 2 , e ) − 4
Rationale: "slope = rise / run = 7 / 14 = 1 / 2 the equation of the line is y = ( 1 / 2 ) x + b 3 = ( 1 / 2 ) ( 10 ) + b b = - 2 the equation of the line is y = ( 1 / 2 ) x - 2 to find the x - intercept , let y = 0 : 0 = ( 1 / 2 ) x - 2 x = 4 the answer is a ."
Answer: a
Question (general): how many liters of pure alcohol must be added to a 100 - liter solution that is 20 percent alcohol in order to produce a solution that is 24 percent alcohol ?
Options: a ) 7 / 2 , b ) 5 , c ) 20 / 3 , d ) 100 / 19 , e ) 39 / 4
Rationale: "20 % alcohol solution means ; in the 100 liter solution , 20 liters of solution is alcohol and 80 liters other solvents . if we addxliters of alcohol to the solution , the solution becomes 100 + xliters and alcohol , which was 20 liters , becomes 20 + x liters . according to the statement ; 20 + x = 24 % of ( 100 + x ) or 20 + x = ( 100 + x ) 6 / 25 500 + 25 x = 600 + 6 x 19 x = 100 x = 100 / 19 ans : d"
Answer: d