Cheukting/mathqa huggingface dataset:
Question (gain): rs . 6000 is lent out in two parts . one part is lent at 7 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 480 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 2 : 1 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 7 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 7 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 480 = > x = 5000 amount lent at 10 % = 2000 required ratio = 2000 : 1000 = 2 : 1 answer : a"
Answer: a
Question (gain): the banker ' s gain on a bill due due 1 year hence at 12 % per annum is rs . 7.2 . the true discount is
Options: a ) rs . 72 , b ) rs . 36 , c ) rs . 54 , d ) rs . 60 , e ) none
Rationale: "solution t . d = [ b . g x 100 / r x t ] = rs . ( 7.2 x 100 / 12 x 1 ) = rs . 60 . answer d"
Answer: d
Question (general): n is the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder in each case . what is the sum of the digits in n ?
Options: a ) 23 , b ) 28 , c ) 4 , d ) 1 , e ) 25
Rationale: if the remainder is same in each case and remainder is not given , hcf of the differences of the numbers is the required greatest number 6905 - 1305 = 5600 6905 - 4665 = 2240 4665 - 1305 = 3360 hence , the greatest number which divides 1305 , 4665 and 6905 and gives the same remainder , n = hcf of 5600 , 2240 , 3360 = 1120 sum of digits in n = sum of digits in 1120 = 1 + 1 + 2 + 0 = 4 answer is c
Answer: c
Question (gain): john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 2 % and the mobile phone at a profit of 10 % . overall how much he make a profit .
Options: a ) s . 90 , b ) s . 120 , c ) s . 200 , d ) s . 250 , e ) s . 500
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 2 / 100 ) = 15000 - 300 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 300 + 800 = rs . 500 as this is positive , an overall profit of rs . 200 was made . e"
Answer: e
Question (general): mid intended to type a 7 - digit number , but the two 3 ' s he meant to type did not appear . what appeared instead was the 5 - digit number 52115 . how many different 7 - digit numbers could mid have meant to type ?
Options: a ) 10 , b ) 16 , c ) 21 , d ) 24 , e ) 27
Rationale: should be 21 . mid intended to type a seven - digit number there are two possibilities for placing 2 3 s . case 1 : two 3 s were missed consecutively . i . e . he typed 33 and it came blank on screen . - 5 - 2 - 1 - 1 - 5 - in this arrangement we can fit 33 in 6 ways . ( six dashes , each dash represent one possible place for placing 33 ) case 2 : two 3 s are not together , i . e . they have one or more digits between them . - 5 - 2 - 1 - 1 - 5 - , in this arrangement if we place first 3 at first dash i . e . 35 - 2 - 1 - 1 - 5 - then the other 3 can fit into 5 places . if we place first 3 at second dash i . e . - 532 - 1 - 1 - 5 - then the other 3 can fit into 4 places . if we place first 3 at third dash i . e . - 5 - 231 - 1 - 5 - then the other 3 can fit into 3 places . if we place first 3 at fourth dash i . e . - 5 - 2 - 131 - 5 - then the other 3 can fit into 2 places . if we place first 3 at fifth dash i . e . - 5 - 2 - 1 - 135 - then the other 3 can fit into 1 place . so total 15 ways . case 2 + case 1 = 6 + 15 = 21 ways answer c
Answer: c
Question (general): in a clothing store , there are 6 different colored neckties ( red , orange , yellow , green , blue , and indigo ) and 4 different colored shirts ( red , orange , yellow , green , blue , and indigo ) that must be packed into boxes for gifts . if each box can only fit one necktie and one shirt , what is the probability that all of the boxes will contain a necktie and a shirt of the same color ?
Options: a ) 719 / 720 , b ) 1 / 24 , c ) 2 / 233 , d ) 3 / 543 , e ) 1 / 720
Rationale: 4 ties and 4 shirts . . . red tie can take any of 4 shirts . . orange can take any of the remaining 3 shirts yellow any of remaining 2 . . and so on till last indigo chooses the 1 remaining . . total ways = 4 * 3 * 2 * 1 = 24 out of this 720 , only 1 way will have same colour tie and shirt . . prob = 1 / 720 b
Answer: b
Question (general): a , b , c subscribe rs . 50000 for a business , a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 70000 , a receives :
Options: a ) 14700 , b ) 24703 , c ) 29400 , d ) 33777 , e ) 34778
Rationale: explanation : let c = x . then , b = x + 5000 and a = x + 5000 + 4000 = x + 9000 . so , x + x + 5000 + x + 9000 = 50000 < = > 3 x = 36000 < = > x = 12000 . a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 . a ' s share = rs . ( 70000 * 21 / 50 ) = rs . 29,400 . answer : c )
Answer: c
Question (general): a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability q that you can still row the canoe ?
Options: a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
Rationale: "simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability q of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer : 1 – 4 / 25 = 21 / 25 . answer choice e ."
Answer: e
Question (gain): john purchased a grinder and a mobile for rs . 15000 & rs . 8000 respectively . he sold the grinder at a loss of 4 % and the mobile phone at a profit of 10 % . overall how much he make aprofit .
Options: a ) rs . 90 , b ) rs . 120 , c ) rs . 200 , d ) rs . 250 , e ) rs . 290
Rationale: "let the sp of the refrigerator and the mobile phone be rs . r and rs . m respectively . r = 15000 ( 1 - 4 / 100 ) = 15000 - 600 m = 8000 ( 1 + 10 / 100 ) = 8000 + 800 total sp - total cp = r + m - ( 15000 + 8000 ) = - 600 + 800 = rs . 200 as this is positive , an overall profit of rs . 200 was made . c"
Answer: c
Question (general): 0.03 x 0.5 = ?
Options: a ) 0.0001 , b ) 0.001 , c ) 0.015 , d ) 0.1 , e ) none of these
Rationale: "explanation : 3 x 5 = 15 . sum of decimal places = 3 0.02 x 0.5 = 0.015 answer - c"
Answer: c
Question (gain): how much interest can a person get on rs . 7200 at 17.5 % p . a . simple interest for a period of two years and 6 months ?
Options: a ) rs . 4150 , b ) rs . 3850 , c ) rs . 3770 , d ) rs . 3150 , e ) none of these
Rationale: i = ( 7200 * 2.5 * 17.5 ) / 100 = ( 7200 * 5 * 35 ) / ( 100 * 2 * 2 ) = rs . 3150 answer : d
Answer: d
Question (general): what is the units digit of 13 ^ 4 * 17 ^ 2 * 29 ^ 3 ?
Options: a ) 9 , b ) 7 , c ) 5 , d ) 3 , e ) 1
Rationale: "3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 7 3 ^ 4 = 1 , it is first digit 7 ^ 2 = 9 , it is second digit 9 ^ 3 = 9 , it is third digit 1 * 9 * 9 = 1 answer : e"
Answer: e
Question (gain): donovan took a math test and got 35 correct and 13 incorrect answers . what was the percentage of correct answers ? ( round to the nearest hundredth )
Options: a ) 57.78 % , b ) 67.78 % , c ) 72.92 % , d ) 47.78 % , e ) 97.78 %
Rationale: 35 correct our of 48 total ( 35 + 13 ) 35 / 48 correct answer c
Answer: c
Question (geometry): the slant height of a cone is 14 cm and radius of the base is 12 cm , find the curved surface of the cone .
Options: a ) 150 , b ) 170 , c ) 48 , d ) 528 , e ) 600
Rationale: "π * 12 * 14 = 528 answer : d"
Answer: d
Question (geometry): triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 49 , what is the measure of side xy ?
Options: a ) 4
b ) 4 √ 2
c ) 14
d ) 8 √ 2
e ) can not be determined from the information provided
Rationale: ans c . . 14 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 4 or yz = 7 * \ sqrt { 2 } . . therefore hyp = xy = 14
Answer: c
Question (general): if the price of sugar rises from rs . 6 per kg to rs . 7.50 per kg , a person , to have no increase in his expenditure on sugar , will have to reduce his consumption of sugar by
Options: a ) 10 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) none
Rationale: "solution let the original consumption = 100 kg and new consumption = x kg . so , 100 x 6 = x × 7.50 x = 80 kg . reduction in consumption = 20 % . answer b"
Answer: b
Question (probability): in a lottery there are 10 prizes and 25 blanks . a lottery is drawn at random . what is the probability of getting a blank ?
Options: a ) 2 / 3 , b ) 6 / 7 , c ) 5 / 7 , d ) 8 / 7 , e ) 4 / 3
Rationale: total draws = prizes + blanks = 10 + 25 = 35 probability of getting a blank = 25 / 35 = 5 / 7 correct option is c
Answer: c
Question (geometry): what is the maximum number of pieces that a circular pizza can be cut into with 6 linear cuts ?
Options: a ) 12
b ) 13
c ) 16
d ) 20
e ) 22
Rationale: 1 cut makes 2 pieces a second cut can make 4 pieces by cutting through 2 of the pieces a third cut can make 7 pieces by cutting through 3 of the pieces a fourth cut can make 11 pieces by cutting through 4 of the pieces a fifth cut can make 16 pieces by cutting through 5 of the pieces a sixth cut can make 22 pieces by cutting through 6 of the pieces e
Answer: e
Question (physics): walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min . running at a speed of 16.5 kmph the man will cover the same distance in .
Options: a ) 12 min , b ) 25 min , c ) 40 min , d ) 48 min , e ) 52 min
Rationale: distance = speed * time 4 * 11 / 4 = 11 km new speed = 16.5 kmph therefore time = d / s = 11 / 16.5 = 40 min answer : c
Answer: c
Question (other): how many positive factors do 120 and 96 have in common ?
Options: a ) 8 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 120 and 96 is 24 number of factors of 24 = 8 answer : a"
Answer: a
Question (general): if p and q are positive integers each greater than 1 , and 15 ( p + 1 ) = 29 ( q + 1 ) , what is the least possible value of p + q ?
Options: a ) 36 , b ) 42 , c ) 44 , d ) 46 , e ) none
Rationale: 17 ( p + 1 ) = 29 ( q + 1 ) - - > ( p + 1 ) / ( q + 1 ) = 29 / 17 - - > the least positive value of p + 1 is 29 , so the least value of p is 28 and the least positive value of q + 1 is 15 , so the least value of q is 14 - - > the least value of p + q is 28 + 14 = 42 . answer : b .
Answer: b
Question (general): how many numbers from 10 to 50 are exactly divisible by 3 ?
Options: a ) 13 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits a )"
Answer: a
Question (gain): the percentage profit earned by selling an article for rs . 1820 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 2000 , d ) 5600 , e ) 1937.5
Rationale: "c . p . be rs . x . then , ( 1820 - x ) / x * 100 = ( x - 1280 ) / x * 100 1820 - x = x - 1280 2 x = 3100 = > x = 1550 required s . p . = 125 % of rs . 1550 = 125 / 100 * 1550 = rs . 1937.5 . answer e"
Answer: e
Question (general): if the remainder is 3 when positive integer n is divided by 18 , what is the remainder when n is divided by 6 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: assume x is quotient here , n = 18 x + 3 - - - - - - - - - - ( 1 ) and n = 6 x + ? we can also write first term as n = ( 18 x + 6 ) = 6 ( 3 x + 1 ) + 3 ie 6 ( 3 x + 1 ) + 3 ie the first term is perfectly divisible by 6 . so , the remainder left is 3 . so , answer ( a ) is right choice .
Answer: a
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 7 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 304 , d ) 310 , e ) 320
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 2 ) : 4 * 5 * 4 * 4 = 320 numbers with seven 7 - s , 7 x 7 x 4 * 1 * 1 * 4 = 16 . thus there are 320 - 16 = 304 such numbers . answer : c ."
Answer: c
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: "mixture 1 and 2 having individual profit % of 10 and 20 respectively . individual profits of vodka a for mixture 1 = 1 / 3 * 10 = 3.33 individual profits of vodka b for mixture 1 = 2 / 3 * 10 = 6.77 individual profits for a and b are increased 4 / 3 and 5 / 3 times . means profits of mixtures 1 and 2 will increase too . increased profits of vodka a for mixture 1 = 4 / 3 * 3.33 = 4.44 increased profits of vodka b for mixture 2 = 5 / 3 * 6.77 = 10.55 total increased profits for mixture 1 = 14.99 similarly total increased profits for mixture 2 = 24.42 using allegation formula va : vb = 1 : 1 = [ 24.42 - ( profit of mixture ) ] / [ ( profit of mixture ) - 14.99 ] hence profit of mixture = 19.705 approx = 20 % answer : b"
Answer: b
Question (general): farm tax is levied on the 40 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . willam . mr . willam paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 31.25 % , b ) 25 % , c ) 12.5 % , d ) 0.2083 % , e ) none
Rationale: "only trick n this question is to ignore 40 % information as farm tax is levied uniformly in the village and that includes mr william ' s land . what percentage of tax mr william paid ? this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 40 ) = 31.25 % and the answer is not there in the options . the correct answer is ( a ) ."
Answer: a
Question (geometry): the area of a circular field is 13.86 hectares . find the cost of fencing it at the rate of rs . 4.50 per metre .
Options: a ) 2399 , b ) 3888 , c ) 2999 , d ) 5940 , e ) 2888
Rationale: "explanation : area = ( 13.86 x 10000 ) sq . m = 138600 sq . m circumference = cost of fencing = rs . ( 1320 x 4.50 ) = rs . 5940 . answer : d ) 5940"
Answer: d
Question (general): a mixture contains alcohol and water in the ratio 4 : 3 . if 6 litres of water is added to the mixture , the ratio becomes 4 : 5 . find the quantity of alcohol in the given mixture
Options: a ) 15 litres , b ) 10 litres , c ) 30 litres , d ) 12 litres , e ) 8 litres
Rationale: "let the quantity of alcohol and water be 4 x litres and 3 x litres respectively 4 x / ( 3 x + 6 ) = 4 / 5 20 x = 4 ( 3 x + 6 ) 8 x = 24 x = 3 quantity of alcohol = ( 4 x 3 ) litres = 12 litres . answer is d"
Answer: d
Question (geometry): if the sides of a triangle are 26 cm , 25 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 125
Rationale: "the triangle with sides 26 cm , 25 cm and 10 cm is right angled , where the hypotenuse is 26 cm . area of the triangle = 1 / 2 * 25 * 10 = 125 cm 2 answer : option e"
Answer: e
Question (general): ( 7.5 × 7.5 + 37.5 + 2.5 × 2.5 ) is equal to :
Options: a ) 30 , b ) 60 , c ) 80 , d ) 100 , e ) none of these
Rationale: solution given expression = ( 7.5 × 7.5 + 2 × 7.5 × 2.5 + 2.5 × 2.5 ) = ( a 2 + 2 ab + b 2 ) = ( a + b ) 2 = ( 7.5 + 2.5 ) 2 = 102 = 100 . answer d
Answer: d
Question (general): a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 350 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 350 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 350 = 3320 - 2800 = 520 i . e . a = 130 and b = 350 - 130 = 220 more seats in balcony than orchestra = b - a = 220 - 130 = 90 answer : option a"
Answer: a
Question (general): if a - b = 3 and a 2 + b 2 = 29 , find the value of ab .
Options: a ) 10 , b ) 12 , c ) 13 , d ) 15 , e ) 18
Rationale: "2 ab = ( a 2 + b 2 ) - ( a - b ) 2 = 29 - 9 = 20 ab = 10 . answer : a"
Answer: a
Question (general): each child has 4 pencils and 13 skittles . if there are 8 children , how many pencils are there in total ?
Options: a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 32
Rationale: 4 * 8 = 32 . answer is e .
Answer: e
Question (gain): sandy had $ 140 left after spending 30 % of the money she took for shopping . how much money did sandy take along with her ?
Options: a ) $ 180 , b ) $ 200 , c ) $ 220 , d ) $ 240 , e ) $ 260
Rationale: let the money sandy took for shopping be x . 0.7 x = 140 x = 200 the answer is b .
Answer: b
Question (physics): three pipes , a , b , & c are attached to a tank . a & b can fill it in 20 & 30 minutes respectively while c can empty it in 15 minutes . if a , b & c are kept open successively for 1 minute each , how soon will the tank be filled ?
Options: a ) 2 hours , b ) 4 hours , c ) 3 hours , d ) 5 hours , e ) 6 hours
Rationale: "in three minute 1 / 20 + 1 / 30 - 1 / 15 = 1 / 60 part is filled 3 min - - - - - - - - 1 / 60 parts x min - - - - - - - - - 1 part ( full ) x = 180 min = 3 hours answer : c"
Answer: c
Question (gain): a total of $ 20,000 was invested in two certificates of deposit at simple annual interest rates of 6 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 ) 2 / 5 , c ) 1 / 2 , d ) 3 / 5 , e ) 3 / 4
Rationale: "let ` ` $ x ' ' be invested with the higher rate of 8 % thus , ` ` 20000 - x ' ' must have been invested with lower rate of 6 % simple interest = principal * rate * time for the amount invested at 8 % principal = x rate = 0.08 time = 1 simple interest = x * 0.08 * 1 = 0.08 x for the amount invested at 6 % principal = 20000 - x rate = 0.06 time = 1 simple interest = ( 20000 - x ) * 0.06 * 1 = 1200 - 0.06 x total interest = $ 1440 0.08 x + 1200 - 0.06 x = 1440 0.02 x = 240 x = 240 / 0.02 = 12000 fraction of x per total amount = 12000 / 20000 = 12 / 20 = 3 / 5 ans : ` ` d ' '"
Answer: d
Question (general): the average of 5 quantities is 6 . the average of 3 of them is 4 . what is the average of remaining 2 numbers ?
Options: a ) 9 , b ) 10 , c ) 8 , d ) 9.5 , e ) none of these
Rationale: answer : a
Answer: a
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.40 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 1.50 , b ) $ 2.00 , c ) $ 2.50 , d ) $ 3.00 , e ) $ 3.50
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 40 4 x / 15 = 40 x = 150 = $ 1.50 the answer is a ."
Answer: a
Question (geometry): how much space , in cubic units , is left vacant when maximum number of 2 x 2 x 2 cubes are fitted in a rectangular box measuring 8 x 10 x 9 ?
Options: a ) 60 , b ) 65 , c ) 70 , d ) 75 , e ) 80
Rationale: "no of cubes that can be accommodated in box = ( 8 * 10 * 9 ) / ( 2 * 2 * 2 ) 8 * 10 in numerator can be perfectly divided by 2 * 2 in denominator . side with length 9 ca n ' t be perfectly divided by 2 and hence is the limiting factor . closet multiple of 2 less that 9 is 8 . so vacant area in cube = = 10 * 8 ( 9 - 8 ) = 10 * 8 * 1 = 80 ans - e"
Answer: e
Question (physics): how many 4 digit numbers are there , if it is known that the first digit is even , the second is odd , the third is prime , the fourth ( units digit ) is divisible by 3 , and the digit 3 can be used only once ?
Options: a ) 20 , b ) 150 , c ) 225 , d ) 250 , e ) 316
Rationale: "4 options for the first digit : 2 , 4 , 6 , 8 ; 5 options for the second digit : 1 , 3 , 5 , 7 , 9 ; 4 options for the third digit : 2 , 3 , 5 , 7 ; 4 options for the fourth digit : 0 , 3 , 6 , 9 . four digit # possible without the restriction ( about the digit 6 ) : 4 * 5 * 4 * 4 = 320 numbers with three 3 - s , 3 x 3 x 3 4 * 1 * 1 * 1 = 4 thus there are 320 - 4 = 316 such numbers . answer : e ."
Answer: e
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 32 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.00 % , d ) 69.57 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 32 % of 1100 ) + ( 32 % of 900 ) = 352 + 288 = 640 failed = 2000 - 640 = 1360 failed % = [ ( 1360 / 2000 ) x 100 ] % = 68 % . answer : c"
Answer: c
Question (general): find ( 7 x + 5 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 5 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 5 y ) / ( 3 y - 2 y ) = > 26 y / y = 26 answer : c"
Answer: c
Question (general): when a student weighing 45 kgs left a class , the average weight of the remaining 59 students increased by 200 g . what is the average weight of the remaining 59 students
Options: a ) 55 , b ) 56 , c ) 57 , d ) 58 , e ) 59
Rationale: explanation : let the average weight of the 59 students be a . so the total weight of the 59 of them will be 59 * a . the questions states that when the weight of this student who left is added , the total weight of the class = 59 a + 45 when this student is also included , the average weight decreases by 0.2 kgs 59 a + 45 / 60 = a − 0.2 = > 59 a + 45 = 60 a - 12 = > 45 + 12 = 60 a - 59 a = > a = 57 answer : option c
Answer: c
Question (physics): mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate j in miles per hour for the entire trip ?
Options: a ) 26.7 , b ) j = 30.0 , c ) j = 40.0 , d ) j = 53.3 , e ) 60.0
Rationale: veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct .
Answer: c