Cheukting/mathqa huggingface dataset:
Question (general): at the end of year x , automobile installment credit accounted for 20 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 57 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 171 , b ) 855 , c ) 870 , d ) 788 , e ) 684
Rationale: "system of equations a = ( 20 / 100 ) c ( 1 / 3 ) a = 57 - - > a = 171 substitution 171 = ( 20100 ) c c = ( 100 / 20 ) 171 - calculate 171 / 20 * 100 the correct answer b . the answer is 855 ."
Answer: b
Question (physics): a man can row upstream at 32 kmph and downstream at 48 kmph , and then find the speed of the man in still water ?
Options: a ) 22 , b ) 37 , c ) 30 , d ) 27 , e ) 40
Rationale: "us = 32 ds = 48 m = ( 48 + 32 ) / 2 = 40 answer : e"
Answer: e
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling alongthe oundary of the park at the speed of 12 km / hr completes one round in 8 minutes , then the area of the park ( in sq . m ) is
Options: a ) 124345 m , b ) 233234 m , c ) 153600 m , d ) 123567 m , e ) 168999 m
Rationale: "perimeter = distance covered in 8 min . = 12000 x 8 m = 1600 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 1600 or x = 160 . length = 480 m and breadth = 320 m . area = ( 480 x 320 ) m 2 = 153600 m c"
Answer: c
Question (geometry): the radius of the two circular fields is in the ratio 3 : 10 the area of the first field is what percent less than the area of the second ?
Options: a ) 71 % , b ) 51 % , c ) 91 % , d ) 81 % , e ) 61 %
Rationale: "r = 3 ï € r 2 = 9 r = 10 ï € r 2 = 100 100 ï € â € “ 9 ï € = 91 100 - - - - ? = > 91 % . answer : c"
Answer: c
Question (general): 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 24 days . if 60 more cows and 30 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 24 days . 60 cows + 30 buffaloes = 30 oxen + 20 oxen = 50 oxen the new total is equal to 80 oxen instead of 30 oxen . 30 * 24 / 80 oxen = 9 days the answer is b ."
Answer: b
Question (physics): an woman swims downstream 64 km and upstream 24 km taking 8 hours each time ; what is the speed of the current ?
Options: a ) 1.6 , b ) 1.8 , c ) 3.5 , d ) 1.5 , e ) 2.5
Rationale: "64 - - - 8 ds = 8 ? - - - - 1 24 - - - - 8 us = 3 ? - - - - 1 s = ? s = ( 8 - 3 ) / 2 = 2.5 answer : e"
Answer: e
Question (gain): what is 30 % of 210 ?
Options: a ) 61 , b ) 63 , c ) 65 , d ) 67 , e ) 69
Rationale: "x / 210 = 30 / 100 100 x = 210 x 30 x = ( 210 x 30 ) / 100 x = 6300 / 100 = 63 answer = b = 63"
Answer: b
Question (general): company x provides bottled water to its employees in 1 liter bottles , $ 2 each . at least how many 1 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 10 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 27
Rationale: let the no . of 1 liter bottles be x , so the no . of 10 l bottles will be x / 10 ( to equate the vol . ) since the total cost will be equal , 2 x = 50 + x / 10 so x = 26.31 or 27 . answer is ( e ) .
Answer: e
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 15.3 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 ) 5 : 6
Rationale: "explanation : let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 < = > ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) < = > k = 0.5 / 0.6 = 5 / 6 . required ratio = 5 / 6 : 1 = 5 : 6 . answer : e"
Answer: e
Question (physics): a train can travel 50 % faster than a car . both start from point a at the same time and reach point b 75 kms away from a at the same time . on the way , however , the train lost about 12.5 minutes while stopping at the stations . what is the speed of the car ?
Options: a ) 22 , b ) 28 , c ) 120 , d ) 287 , e ) 278
Rationale: let speed of the car = x kmphthen speed of the train = ( 100 + 50 ) 100 x = 150100 x = 32 x kmphtime taken by the car to travel from a to b = 75 x hourstime taken by the train to travel from a to b = 75 ( 32 x ) + 12.560 hourssince both start from a at the same time and reach point b at the same time 75 x = 75 ( 32 x ) + 12.56025 x = 12.560 x = 25 × 6012.5 = 2 × 60 = 120 answer : c
Answer: c
Question (geometry): if the sides of a triangle are 39 cm , 32 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 772 , c ) 288 , d ) 160 , e ) 2848
Rationale: "the triangle with sides 39 cm , 32 cm and 10 cm is right angled , where the hypotenuse is 39 cm . area of the triangle = 1 / 2 * 32 * 10 = 160 cm 2 answer : d"
Answer: d
Question (general): the remainder when q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . + 3 ^ 200 is divided 13 .
Options: a ) 12 , b ) 7 , c ) 0 , d ) 5 , e ) 3
Rationale: q = 1 + 3 + 3 ^ 2 + 3 ^ 3 + . . . . . . . . . . . . . . . . . . + 3 ^ 200 is a geometric progression having common ratio as ' 3 ' and number of terms as ' 201 ' . since sum to n terms in gp = a ( r ^ n - 1 ) / ( r - 1 ) where a = first term and r = common ration hence , 1 * ( 3 ^ 201 - 1 ) / ( 3 - 1 ) rem of ( 3 ^ 201 - 1 ) / 2 divided by 13 3 ^ 201 - 1 / 26 wkt , 3 ^ 3 = 27 = 26 + 1 { ( 26 + 1 ) ^ 67 - 1 } / 26 { 1 - 1 } / 26 = > 0 . c
Answer: c
Question (gain): p and q invested in a shop . the profits were divided in the ratio of 5 : 2 respectively . if p invested rs . 5600 , the amount invested by q is :
Options: a ) 3500 , b ) 5600 , c ) 2200 , d ) 2400 , e ) none
Rationale: suppose q invested rs . y . then , 5600 / y = 5 / 2 or y = [ 5600 x 2 / 5 ] = 2240 answer e
Answer: e
Question (physics): a car gets 20 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 120 kilometers ?
Options: a ) 8.5 gallons , b ) 5 gallons , c ) 7 gallons , d ) 5.5 gallons , e ) 6 gallons
Rationale: "each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 120 kilometers ? 120 / 20 = 4.5 * 1 gallon = 6 gallons correct answer e"
Answer: e
Question (general): a cuboidal block 6 cm x 9 cm x 12 cm is cut up into an exact number of equal cubes . the least possible number of equal cubes will be
Options: a ) 6 , b ) 9 , c ) 24 , d ) 30 , e ) 35
Rationale: explanation : volume of block = ( 6 x 9 x 12 ) cm 3 = 648 cm 3 side of largest cube = h . c . f of 6 , 912 = 3 cm volume of the cube = ( 3 x 3 x 3 ) = 27 cm 3 number of cubes = ( 648 / 27 ) = 24 answer : c
Answer: c
Question (general): in a class of 25 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 4 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "the total number of books the students borrowed is 25 * 2 = 50 . the students who borrowed zero , one , or two books borrowed 12 * 1 + 4 * 2 = 20 books . the 7 students who borrowed at least three books borrowed 50 - 20 = 30 books . if 6 of these students borrowed exactly 3 books , then the maximum that one student could have borrowed is 30 - 18 = 12 books . the answer is e ."
Answer: e
Question (physics): the sector of a circle has radius of 21 cm and central angle 180 o . find its perimeter ?
Options: a ) 91.5 , b ) 92 , c ) 108 , d ) 94 , e ) 95
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 108 cm answer : option c"
Answer: c
Question (physics): beginning in town a , biker bob rides his bike 30 miles west , 6 miles north , 15 miles east , and then 18 miles north , to town b . how far apart are town a and town b ? ( ignore the curvature of the earth . )
Options: a ) 27 miles , b ) 25 miles , c ) 24 miles , d ) 28.3 miles , e ) 23 miles
Rationale: "using pythagoras we have one side i , e total distance traveled in north direction = 18 + 6 = 24 m other being the base ie distance traveled west - distance traveled eat = 30 - 15 = 15 m now this third side or the distance between town a and town b = 24 ^ 2 + 15 ^ 2 = sq root 801 = 28.3 m answer : d"
Answer: d
Question (general): a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 68 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 28 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 68 - x ounces of q is present in the mixture ( as the total = 68 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 68 - x ) = 15 = > x = 40 = > 68 - 40 = 28 ounces of q is present in the mixture . answer is b ."
Answer: b
Question (physics): two trains 200 m and 300 m long run at the speed of 70 kmph and 50 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 10 sec , b ) 15 sec , c ) 18 sec , d ) 20 sec , e ) 22 sec
Rationale: "relative speed = 70 + 50 = 120 kmph * 5 / 18 = 100 / 3 m / s distance covered in crossing each other = 200 + 300 = 500 m required time = 500 * 3 / 100 = 15 sec answer is b"
Answer: b
Question (geometry): find the area of a parallelogram with base 12 cm and height 10 cm ?
Options: a ) 297 cm 2 , b ) 384 cm 2 , c ) 120 cm 2 , d ) 267 cm 2 , e ) 186 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 10 = 120 cm 2 answer : c"
Answer: c
Question (physics): 6 lights begin to flash together at 12 : 00 noon and flash respectively at intervals of 3 , 4 , 5 , 6 , 7 , and 8 seconds . not including the flash at 12 : 00 noon , how many more times will all 6 lights flash together before 1 : 00 pm ( i . e . one hour later ) ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 10 , e ) 12
Rationale: the least common multiple is 2 * 2 * 2 * 3 * 5 * 7 = 840 . 3600 seconds / 840 = 4 + remainder . the answer is a .
Answer: a
Question (general): a is the hundreds digit of the 3 digit integer x , b is the tens digit of x , and c is the units digit of x . 2 a = b = 4 c , and a > 0 . what is the difference between the two greatest possible values of x ? tip : dont stop till you have exhausted all answer choices to arrive at the correct one .
Options: a ) 124 , b ) 241 , c ) 394 , d ) 421 , e ) 842
Rationale: ratio of a : b : c = 2 : 4 : 1 two possible greatest single digit values for b are 8 and 4 if b is 8 , then x = 482 if b is 4 , then x = 241 difference = 482 - 241 = 241 b is the answer
Answer: b
Question (general): find the slope of the line perpendicular to the line y = ( 1 / 2 ) x - 7
Options: a ) 1 , b ) 2 , c ) - 2 , d ) 4 , e ) 5
Rationale: "two lines are perpendicular if the product of their slopes is equal to - 1 . the slope of the given line is equal to 1 / 2 . if m is the slope of the line perpendicular to the given line , then m × ( 1 / 2 ) = - 1 solve for m m = - 2 correct answer c ) - 2"
Answer: c
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 25 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 222 , d ) 448 , e ) 111
Rationale: "explanation : 110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 100 * 560 ) / 125 = rs . 448 answer : d"
Answer: d
Question (other): the triplicate ratio of 1 : 2 is ?
Options: a ) 1 : 7 , b ) 1 : 8 , c ) 1 : 3 , d ) 1 : 1 , e ) 1 : 2
Rationale: "13 : 23 = 1 : 8 answer : b"
Answer: b
Question (gain): a number with an interesting property : when i divide it by 2 , the remainder is 1 . when i divide it by 3 , the remainder is 2 . when i divide it by 4 , the remainder is 3 . when i divide it by 5 , the remainder is 4 . when i divide it by 6 , the remainder is 5 . when i divide it by 7 , the remainder is 6 . when i divide it by 8 , the remainder is 7 . when i divide it by 9 , the remainder is 8 . when i divide it by 10 , the remainder is 9 . it ' s not a small number , but it ' s not really big , either . when i looked for a smaller number with this property i could n ' t find one . can you find it ?
Options: a ) 2588 , b ) 2474 , c ) 2254 , d ) 2519 , e ) 8725
Rationale: d 2519 the number has to end in 9 . looked brute force for small numbers . 59 and 119 were promising , but no cigar . then looked for agreement among 39 + multiples of 40 , 69 + multiples of 70 and 89 + multiples of 90 smallest one was 2519 .
Answer: d
Question (general): 65 % of a number is 21 less than 4 / 5 th of that number . what is the number ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 130 , e ) 115
Rationale: let the number be x then , 4 x / 5 - ( 65 % of x ) = 21 4 x / 5 - 65 x / 100 = 21 x = 140 answer is c
Answer: c
Question (general): what is the sum of the integers 45 through 175 inclusive ?
Options: a ) 12,295 , b ) 13,000 , c ) 14,300 , d ) 14,410 , e ) 28,820
Rationale: "sum of n consecutive positive integers = n ( n + 1 ) / 2 . . in one case n = 44 and other 175 . . . subtract the sum to get the answer sum of first 175 + ive numbers = 175 * 176 / 2 = 15400 . . sum of first 45 + i ' ve numbers = 45 * 44 / 2 = 990 . . answer = 15400 - 990 = 14410 answer : d"
Answer: d
Question (geometry): the ratio of males to females in a class is 2 : 3 . the career preferences of the students in the class are represented in a circle graph . if the area of the graph allocated to each career preference is proportional to the number of students who have that career preference , how many degrees of the circle should be used to represent a career that is preferred by one - half of the males and one - fourth of the females in the class ?
Options: a ) 120 , b ) 126 , c ) 132 , d ) 138 , e ) 144
Rationale: "1 / 2 * 2 / 5 + 1 / 4 * 3 / 5 = 4 / 20 + 3 / 20 = 7 / 20 the number of degrees is 7 / 20 * 360 = 126 degrees the answer is b ."
Answer: b
Question (general): a vendor sells 60 percent of the apples he had and throws away 40 percent of the remainder . the next day , the vendor sells 50 percent of the remaining apples and throws away the rest . in total , what percent of his apples does the vendor throw away ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "let x be the original number of apples . on day one , the vendor throws away ( 0.4 ) ( 0.4 ) x = 0.16 x . the remaining apples are ( 0.6 ) ( 0.4 ) x = 0.24 x . on day two , the vendor throws away ( 0.5 ) ( 0.24 ) x = 0.12 x . the vendor throws away a total of 0.16 x + 0.12 x = 0.28 x . the vendor throws away 28 percent of the apples . the answer is c ."
Answer: c
Question (general): a vendor sells 80 percent of the pears he had and throws away 50 percent of the remainder . the next day , the vendor sells 80 percent of the remaining pears and throws away the rest . in total , what percent of his pears does the vendor throw away ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: "let x be the original number of pears . on day one , the vendor throws away ( 0.5 ) ( 0.2 ) x = 0.1 x . the remaining pears are ( 0.5 ) ( 0.2 ) x = 0.1 x . on day two , the vendor throws away ( 0.2 ) ( 0.1 ) x = 0.02 x . the vendor throws away a total of 0.1 x + 0.02 x = 0.12 x . the vendor throws away 12 percent of the pears . the answer is d ."
Answer: d
Question (physics): a train 700 m long can cross an electric pole in 20 sec and then find the speed of the train ?
Options: a ) 117 kmph , b ) 178 kmph , c ) 126 kmph , d ) 118 kmph , e ) 119 kmph
Rationale: "length = speed * time speed = l / t s = 700 / 20 s = 35 m / sec speed = 35 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 126 kmph answer : c"
Answer: c
Question (general): the average weight of 8 persons increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
Options: a ) 75 kg , b ) 65 kg , c ) 55 kg , d ) 85 kg , e ) 93 kg
Rationale: "total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . answer : e"
Answer: e
Question (physics): an industrial loom weaves 1.14 meters of cloth every second . approximately , how much time will it take to weave 52 meters of cloth ?
Options: a ) 29.32 sec , b ) 42.51 sec , c ) 39.25 sec , d ) 45.61 sec , e ) none of these
Rationale: explanation : given loom weaves 1.14 mts of cloth in one second then 52 mts of cloth can be weaved by loom in , 1.14 - - - - - 1 52.0 - - - - - - ? = > 52 / 1.14 = 45.61 sec answer is d
Answer: d
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill tank in 37 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 229 , b ) 787 , c ) 144 , d ) 148 , e ) 121
Rationale: "let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 37 4 / x = 1 / 37 = > x = 148 min . answer : d"
Answer: d
Question (physics): if 10 machines can produce 20 units in 10 hours , how long would it take 40 machines to produce 100 units ?
Options: a ) 9.5 , b ) 6.4 , c ) 2.3 , d ) 8.9 , e ) 12.5
Rationale: "10 machines would produce 100 units in 50 hours . increasing the amount of machines by 4 would mean dividing 50 hours by 4 . 50 / 4 = 12.5 answer : e"
Answer: e
Question (general): when positive integer n is divided by positive integer j , the remainder is 14 . if n / j = 134.07 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 200 , e ) 175
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.07 , the decimal part of the decimal quotient , must equal the remainder , 14 , divided by the divisor j . 0.07 = 14 / j 0.07 * j = 14 j = 14 / 0.07 = 1400 / 7 = 200 so j = 200 , answer = d ."
Answer: d
Question (physics): if m : n is 2 : 9 and n : p is 9 : 4 then m : p is equal to
Options: a ) 1 : 4 , b ) 1 : 3 , c ) 5 : 2 , d ) 3 : 2 , e ) 1 : 2
Rationale: the two ratios given are having the same number 9 for n in both the ratios . hence - m : n = 2 : 9 n : p = 9 : 4 = > m : p = 2 : 4 = > 1 : 2 answer e
Answer: e
Question (physics): the product of two numbers is 1320 and their h . c . f is 6 . the l . c . m of the numbers is
Options: a ) 220 , b ) 1314 , c ) 1326 , d ) 7920 , e ) none
Rationale: "solution l . c . m = product of numbers / h . c . f ‹ = › 1320 / 6 ‹ = › 220 . answer a"
Answer: a
Question (general): a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ?
Options: a ) 15.6 , b ) 16.0 , c ) 18.4 , d ) 18.7 , e ) 19.1
Rationale: "a certain taxi company charges $ 2.80 for the first 1 / 5 of a mile plus $ 0.40 for each additional 1 / 5 of a mile . what would this company charge for a taxi ride that was 8 miles long ? a . 15.60 b . 16.00 c . 17.50 d . 18.70 e . 19.10 1 / 5 miles = 0.2 miles . the cost of 8 miles long ride would be $ 2.80 for the first 0.2 miles plus ( 8 - 0.2 ) / 0.2 * 0.4 = $ 2.8 + $ 15.6 = $ 18.4 . answer : c ."
Answer: c
Question (general): the average of first five multiples of 4 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "solution average = 4 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 60 / 5 . = 12 answer d"
Answer: d
Question (general): of the 3 - digit integers greater than 200 , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 90 , b ) 82 , c ) 80 , d ) 45 , e ) 36
Rationale: let the three digit number be represented as x y z . there are 3 cases : case i . [ x = y ] z is not equal to xy : xxzoryyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 1 way after xy are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 1 ) [ example numbers : 774,779 , 882,993 etc ] case ii . [ x = z ] y is not equal to xz : xyxorzyz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , z can be chosen in 1 way after xz are chosen , z can be chosen in 9 ways thus , possible no of digits = ( 3 ways ) * ( 9 ways ) * ( 1 way ) = 27 . . . . ( 2 ) [ example numbers : 747,797 , 828,939 etc ] case iii . [ y = z ] x is not equal to yz : xyyorxzz x can be either 7 , 8 or 9 , so digit at x can be chosen in 3 ways after x is chosen , y can be chosen in 9 ways after y is chosen , z can have 1 way thus , possible no of digits = ( 3 ways ) * ( 1 way ) * ( 9 ways ) = 27 . . . . ( 3 ) [ example numbers : 744,799 , 822,933 etc ] therefore , total numbers of possible digits [ sum of case ( 1 ) , ( 2 ) ( 3 ) above ] = 27 + 27 + 27 - 1 = 80 one digit is subtracted from total number of possible digits to eliminate one possibility of xyz = 700 to satisfy the condition that digit > 200 . answer : ( e )
Answer: e
Question (geometry): a rectangular mat has an area of 120 sq . metres and perimeter of 46 m . the length of its diagonal is :
Options: a ) 19 m
b ) 17 m
c ) 15 m
d ) 16 m
e ) 20 m
Rationale: rectangular area = l × b = 120 and perimeter = 2 ( l + b ) = 46 l + b = 23 ( l - b ) power 2 - 4 lb = ( 23 ) power 2 - 4 × 120 = ( 529 - 480 ) = 49 = l - b = 7 l + b = 23 , l - b = 7 , we get l = 15 , b = 8 diagonal = √ 152 + 82 √ 225 + 64 = > √ 289 = 17 m answer is b .
Answer: b
Question (other): a farmer used 1,034 acres of land for beans , wheat , and corn in the ratio of 5 : 2 : 4 , respectively . how many r acres were used for corn ?
Options: a ) 188 , b ) 258 , c ) 376 , d ) 470 , e ) 517
Rationale: "consider 5 x acres of land used for bean consider 2 x acres of land used for wheat consider 4 x acres of land used for corn total given is 1034 acres 11 x = 1034 x = 94 land used for corn r = 4 * 94 = 376 correct option - c"
Answer: c
Question (general): the tax on a commodity is diminished by 40 % but its consumption is increased by 25 % . find the decrease percent in the revenue derived from it ?
Options: a ) 18 % , b ) 72 % , c ) 25 % , d ) 12 % , e ) 52 %
Rationale: "100 * 100 = 10000 60 * 125 = 7500 10000 - - - - - - - 2500 100 - - - - - - - ? = 25 % answer : c"
Answer: c