Cheukting/mathqa huggingface dataset:
Question (general): the sum of all two digit numbers divisible by 8 is
Options: a ) 910 , b ) 510 , c ) 611 , d ) 616 , e ) 810
Rationale: "required numbers are 16,24 . . . . . 96 this is an a . p . in which a = 16 , d = 8 and l = 96 . let the number of terms in it be n . then t = 96 so a + ( n - 1 ) d = 96 . 16 + ( n - 1 ) * 8 = 96 16 + 8 n - 8 = 96 8 + 8 n = 96 8 n = 96 - 8 n = 88 / 8 then n = 11 . required sum = n / 2 ( a + l ) = 11 / 2 ( 16 + 96 ) = 616 answer is d"
Answer: d
Question (general): dropbox charges $ 3.10 for first 1 / 5 of a month for 500 gb storage , plus $ 0.40 for each additional 1 / 5 of a month . what would dropbox charge for a data storage of 500 gb for 8 months ?
Options: a ) $ 15.60 , b ) $ 16.00 , c ) $ 17.80 , d ) $ 18.70 , e ) $ 19.10
Rationale: first 1 / 5 month charge = $ 3.10 rest of the months = 8 - ( 1 / 5 ) = 39 / 5 charge for the rest of the months = 39 * 0.4 = 15.6 total charge = 3.10 + 15.6 = 18.7 answer is d .
Answer: d
Question (gain): find the simple interest on rs . 72,000 at 16 2 / 3 % per year for 9 months .
Options: a ) 7500 , b ) 6500 , c ) 9000 , d ) 9500 , e ) none of them
Rationale: "p = rs . 72000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . simple interest = ( p * r * t ) / 100 = rs . ( 72,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 9000 answer is c ."
Answer: c
Question (physics): if it would take one machine 20 minutes to fill a large production order and another machine 30 minutes to fill the same order , how many minutes would it take both machines working together , at their respective rates , to fill the order ?
Options: a ) 10 min , b ) 12 min , c ) 15 min , d ) 20 min , e ) 18 min
Rationale: this question can be solved using the work formula : work = ( a ) ( b ) / ( a + b ) where a and b are the individual completion rates of the respective entities ( for the same job ) . we ' re told that one machine takes 10 minutes to complete a job and another machine takes 12 minutes to complete the same job . plugging in those values gets us . . . ( 20 ) ( 30 ) / ( 20 + 30 ) = 600 / 50 = 12 minutes answer is b
Answer: b
Question (general): how many digits are required to number a book containing 220 pages ?
Options: a ) 674 , b ) 604 , c ) 552 , d ) 372 , e ) 250
Rationale: "9 pages from 1 to 9 will require 9 digits . 90 pages from 10 to 99 will require 90 * 2 = 180 digits . 220 - ( 90 + 9 ) = 121 pages will require 121 * 3 = 363 digits . the total number of digits is 9 + 180 + 363 = 552 . the answer is c ."
Answer: c
Question (general): a case of 12 rolls of paper towels sells for $ 9 . the cost of one roll sold individually is $ 1 . what is the percent w of savings per roll for the 12 - roll package over the cost of 12 rolls purchased individually ?
Options: a ) 9 % , b ) 11 % , c ) 15 % , d ) 25 % , e ) 90 %
Rationale: "cost of 12 paper towels individually = 1 * 12 = 12 cost of a set of 12 paper towels = 9 cost of one roll = 9 / 12 = 3 / 4 = 0.75 savings per roll = 1 - . 75 = 0.25 % of savings is w = . 25 / 1 * 100 = 25 % d is the answer ."
Answer: d
Question (other): the ratio between the number of sheep and the number of horses at the stewart farm is 5 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 56 , e ) 60
Rationale: "let the number of sheeps and horses be 4 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 5 x = 5 * 8 = 40 . hence c ."
Answer: c
Question (geometry): a rectangular box of volume v has width , depth and height in the ratio of 2 : 1 : 3 ( in that order ) . what is the height as a function of v ?
Options: a ) ( v / 2 ) ^ ( 1 / 3 )
b ) ( 2 v / 6 ) ^ ( 1 / 3 )
c ) ( 9 v / 2 ) ^ ( 1 / 3 )
d ) ( 4 v / 3 ) ^ ( 1 / 3 )
e ) ( 4 v / 2 ) ^ ( 1 / 3 )
Rationale: we are given width = 2 , depth = 1 , height = 3 . then volume v = width x depth x height = 2 * 1 * 3 = 6 i . e . v = 6 the correct option should result in 3 ( the height ) on substituting the value of v = 6 . checking options with v = 6 : a ) ( v / 2 ) ^ ( 1 / 3 ) = ( 6 / 2 ) ^ ( 1 / 3 ) = 3 ^ ( 1 / 3 ) incorrect answer b ) ( 2 v / 6 ) ^ ( 1 / 3 ) = ( 12 / 6 ) ^ ( 1 / 3 ) = 2 ^ ( 1 / 3 ) incorrect answer c ) ( 9 v / 2 ) ^ ( 1 / 3 ) = ( 54 / 2 ) ^ ( 1 / 3 ) = 3 correct answer d ) ( 4 v / 3 ) ^ ( 1 / 3 ) = ( 24 / 3 ) ^ ( 1 / 3 ) = 8 ^ ( 1 / 3 ) = 2 incorrect answer e ) ( 4 v / 2 ) ^ ( 1 / 3 ) = ( 24 / 2 ) ^ ( 1 / 3 ) = 12 ^ ( 1 / 3 ) incorrect answer answer : option c
Answer: c
Question (gain): calculate the amount that an investor needs to be invest to earn $ 1005 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 11 % compounded semi - annually ?
Options: a ) 8000 , b ) 8100 , c ) 8900 , d ) 8600 , e ) 8400
Rationale: "the approach is substitution , our interest requirement is $ 1005 after 12 months , 2 compounding period . calculate the compound interest on each option and find out the one that yields 460 in 12 months 8900 yielded $ 1005 using the formula a = p ( 1 + r / n ) nt hence answer is c"
Answer: c
Question (gain): a reduction of 42 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.15 , b ) 8.15 , c ) 7.15 , d ) 3.15 , e ) 1.15
Rationale: "explanation : 40 * ( 42 / 100 ) = 16.8 - - - 64 ? - - - 12 = > rs . 3.15 answer : d"
Answer: d
Question (physics): a train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds . what is the length of the train in metres ?
Options: a ) 375 m , b ) 750 m , c ) 250 m , d ) 600 m , e ) 300 m
Rationale: "let length of train = l case - 1 : distance = 1500 + l ( while crossing the bridge ) time = 70 seconds i . e . speed = distance / time = ( 1500 + l ) / 70 case - 2 : distance = l ( while passing the lamp post ) time = 20 seconds i . e . speed = distance / time = ( l ) / 20 but since speed has to be same in both cases so ( 1500 + l ) / 70 = ( l ) / 20 i . e . 1500 + l = 3.5 l i . e . 2.5 l = 1500 i . e . l = 600 answer : option d"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 square feet , if the price per foot of building the fence is rs . 58 ?
Options: a ) 3944 , b ) 3932 , c ) 3929 , d ) 3926 , e ) 3902
Rationale: "let the side of the square plot be a foot a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 foot cost of building the fence = 68 * 58 = rs . 3944 . answer : a"
Answer: a
Question (physics): for a race a distance of 224 meters can be covered by p in 28 seconds and q in 56 seconds . by what distance does p defeat q eventually ?
Options: a ) 232 m , b ) 224 m , c ) 244 m , d ) 231 m , e ) 236 m
Rationale: "explanation : this is a simple speed time problem . given conditions : = > speed of p = 224 / 28 = 8 m / s = > speed of q = 224 / 56 = 4 m / s = > difference in time taken = 28 seconds therefore , distance covered by p in that time = 8 m / s x 28 seconds = 224 metres answer : b"
Answer: b
Question (geometry): points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction d of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives d = 1 / 9 . a"
Answer: a
Question (other): the dimensions of a field are 20 m by 10 m . a pit 8 m long , 5 m wide and 2 m deep is dug in one corner of the field and the earth removed has been evenly spread over the remaining area of the field . what will be the rise in the height of field as a result of this operation ?
Options: a ) 1 m
b ) 2 m
c ) 0.5 m
d ) 0.75 m
e ) 1.5 m
Rationale: the volume of the earth removed is 8 * 5 * 2 = 80 m ^ 3 . the remaining area of the field is 20 * 10 - 8 * 5 = 160 m ^ 2 . 80 m ^ 3 of the earth evenly spread over the area of 160 m ^ 2 will rise the height by ( height ) = ( volume ) / ( area ) = 80 / 160 = 0.5 m . answer : c
Answer: c
Question (general): the grade point average of the entire class is 90 . if the average of one third of the class is 96 , what is the average of the rest ?
Options: a ) 92 , b ) 89 , c ) 88 , d ) 87 , e ) 86
Rationale: "let us take number of students on the class as ' x ' . avg grade point = sum of all grade points / x sum of all grade points = avg grade point * x = 90 x average of one third of the class = 96 = sum of one third grade points of the class / ( x / 3 ) sum of one third grade points of the class = 96 * ( x / 3 ) = 32 x sum of rest two third grade points of the class = sum of all grade points - sum of one third grade points of the class sum of rest two third grade points of the class = 90 x - 32 x = 58 x avg of two third of the class = sum of rest two third grade points of the class / ( x * 2 / 3 ) = 58 x / ( 2 x / 3 ) = 29 * 3 = 87 . hence , answer is d"
Answer: d
Question (general): last year department store x had a sales total for december that was 6 times the average ( arithmetic mean ) of the monthly sales totals for january through november . the sales total for december was what fraction of the sales total for the year ?
Options: a ) 6 / 17 , b ) 4 / 15 , c ) 1 / 3 , d ) 4 / 11 , e ) 4 / 5
Rationale: "let avg for 11 mos . = 10 therefore , dec = 60 year total = 11 * 10 + 60 = 170 answer = 60 / 170 = 6 / 17 = a"
Answer: a
Question (geometry): points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction c of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9
b ) 1 / 8
c ) 1 / 6
d ) 1 / 5
e ) 1 / 3
Rationale: if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a
Answer: a
Question (general): if x is the median of the set { 9 / 2 , 11 / 3 , x , 28 / 9 , 21 / 5 } , x could be
Options: a ) 16 / 5 , b ) 17 / 5 , c ) 4 / 7 , d ) 30 / 7 , e ) 4
Rationale: "the median is the middle number once all the numbers are arranged in increasing / decreasing order . we see that 11 / 3 = 3 . something , 28 / 9 = 3 . something 21 / 5 = 4 . something 9 / 2 = 4 . something so x should greater than the smallest two numbers and smaller than the greatest two numbers . we can see that x = 4 is possible . ( first look at the simplest option or the middle option since options are usually arranged in increasing / decreasing order ) answer ( e )"
Answer: e
Question (physics): a can do a piece of work in 4 days . b can do it in 7 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
Options: a ) 22 days , b ) 28 / 3 days , c ) 67 days , d ) 17 / 5 days , e ) 18 days
Rationale: "c = 1 / 2 - 1 / 4 - 1 / 7 = 3 / 28 = > 28 / 3 days answer : b"
Answer: b
Question (general): how many integers from 101 to 200 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 20 , b ) 25 , c ) 28 , d ) 30 , e ) 40
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 101 to 200 , inclusive is ( 189 - 105 ) / 21 + 1 = 5 ; 33 - 5 = 28 . answer : c ."
Answer: c
Question (physics): buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 30 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 50 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 84 , c ) 132 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 84 min b"
Answer: b
Question (general): what is the remainder when 7 ^ 74 - 10 ^ 74 is divided by 24 ?
Options: a ) 3 , b ) 1 , c ) 2 , d ) 0 , e ) none of these
Rationale: "easiest way for me : 7 ^ 74 - 5 ^ 74 = ( 49 ) ^ 37 - 25 ^ 37 = ( 24 * 2 + 1 ) ^ 37 - ( 24 + 1 ) ^ 37 - > remainder is 1 ^ 37 - 1 ^ 37 = 0 ans : d"
Answer: d
Question (general): what least no . must be subtracted from 101054 so that remaining no . is divisible by 10 ?
Options: a ) 6 , b ) 4 , c ) 8 , d ) 5 , e ) 3
Rationale: "explanation : on dividing 101054 by 10 we get the remainder 4 , so 4 should be subtracted option b"
Answer: b
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 8 years ?
Options: a ) 6 % , b ) 2.5 % , c ) 4 % , d ) 5 % , e ) 3.5 %
Rationale: 150 = ( 750 * 8 * r ) / 100 r = 2.5 % answer : b
Answer: b
Question (general): machine – x produces 50 % of the total output and machine - y produces 75 % of the total output . an average of 9 units out of a 1000 goods manufactured by machine - x and two unit of 500 units produced by machine - x prove to be defective . what is the probability that a unit chosen at random from the total daily output of the factory is defective ?
Options: a ) 0.008 , b ) 0.1 , c ) 0.12 , d ) 0.006 , e ) 0.007
Rationale: suppose machine x produce 1000 units total defective = 9 machine y then produces = 1500 units total defective = 6 probability = 15 / 2500 = 0.006 answer : d
Answer: d
Question (general): what is the units digit of ( 5 ! * 4 ! + 6 ! * 5 ! ) / 2 ?
Options: a ) 4 , b ) 3 , c ) 0 , d ) 1 , e ) 2
Rationale: "( 5 ! * 4 ! + 6 ! * 5 ! ) / 2 = 5 ! ( 4 ! + 6 ! ) / 2 = 120 ( 24 + 720 ) / 2 = ( 120 * 744 ) / 2 = 120 * 372 units digit of the above product will be equal to 0 answer c"
Answer: c
Question (physics): find the cost of fencing around a circular field of diameter 22 m at the rate of rs . 2.50 a meter ?
Options: a ) 188 , b ) 172 , c ) 278 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 11 = 69 69 * 2 1 / 2 = rs . 172 answer : b"
Answer: b
Question (general): two cycles are standing side - by - side . one cycle , which is 2.5 feets tall , casts a shadow that is 5 feets long . the other cycle is 2 feets tall . compute , in feets , the length of the shadow that the shorter cycle casts .
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: the ratio of shadow to height is constant , so if x is the length of the shadow , then 2.5 / 5 = 2 / x and x = 4 . correct answer b
Answer: b
Question (physics): stacy has a 12 page history paper due in 12 days . how many pages per day would she have to write to finish on time ?
Options: a ) 9 , b ) 8 , c ) 10 , d ) 1 , e ) 6
Rationale: "12 / 12 = 1 answer : d"
Answer: d
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 10 % while buying and by 20 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 10 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 110 kg ; the owner sells 100 kg but actually gives 80 kg ; profit : ( 110 - 80 ) / 80 * 100 = 10 % answer : d ."
Answer: d
Question (general): on a two - dimensional coordinate plane , the line a = x ^ 2 - x ^ 3 touches the x - axis in how many places ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "apparently it ' s a = x ^ 2 - x ^ 3 instead of a = x ^ 2 - a ^ 3 . in this case : the x - intercept is the value ( s ) of x for a = 0 . 0 = x ^ 2 - x ^ 3 ; 0 = x ^ 2 ( 1 - x ) ; x = 0 or x = 1 . answer : c ."
Answer: c
Question (physics): if the wages of 6 men for 15 days be rs . 2100 , then find the wages of for 12 days .
Options: a ) rs . 2420 , b ) rs . 2500 , c ) rs . 2520 , d ) rs . 2020 , e ) rs . 2650
Rationale: . let the required wages be rs . x . more men , more wages ( direct proportion ) less days , less wages ( direct proportion ) men 6 : 9 : : 2100 : x days 15 : 12 therefore ( 6 x 15 x x ) = ( 9 x 12 x 2100 )  x = ( 9 x 12 x 2100 ) / ( 6 x 15 ) = 2520 hence the required wages are rs . 2520 . answer is c
Answer: c
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 40 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 5 % , b ) 70 % , c ) 25 % , d ) 40 % , e ) 55 %
Rationale: "the complete round trip consists of driving to the service center and then back home again . so , once the technician drives to the service center he / she has already competed 50 % of the entire trip . since the technician completes a portion of the trip back home , the correct answer must be greater than 50 % so 0.5 + 0.5 * 0.4 = 0.70 answer : b"
Answer: b
Question (other): what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 11 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "number divisible by 11 : - 1000 / 11 = 90 numbers divisible by 35 : - 1000 / 35 = 28 numbers divisible by both 11 and 35 = 2 total numbers divisible by both 11 and 28 = 90 + 28 - 2 = 116 ( because we counted 2 in both 90 and 28 ) total numbers not divisible by 11 or 35 = 1000 - 116 = 884 answer : a"
Answer: a
Question (physics): convert the 15 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.2
Rationale: "15 / 36 m / s = 15 / 36 * 18 / 5 = 3 / 2 = 1.5 kmph . answer : b"
Answer: b
Question (general): 3 positive integers a , b , and c are such that their average is 20 and a ≤ b ≤ c . if the median is ( a + 13 ) , what is the least possible value of c ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: solution : we know that the average value is 20 therefore ( a + b + c ) / 3 = 20 so a + b + c = 60 and b = a + 13 therefore a + ( a + 13 ) + c = 60 the least value of c is when c = b so take c = a + 13 hence , a + ( a + 13 ) + ( a + 13 ) = 60 i . e . , a = 34 / 3 a non integer therefore c is not equal to b so take c = b + 1 therefore c = a + 14 a + ( a + 13 ) + ( a + 14 ) = 60 i . e . , a = 33 / 3 = 11 hence , a = 11 , b = 24 , and c = 25 answer : e
Answer: e
Question (probability): if a certain coin is flipped , the probability that the coin will land heads is 1 / 2 . if the coin is flipped 6 times , what is the probability that it will land heads up on the first 4 flips but not on the last 2 flips ?
Options: a ) 1 / 8 , b ) 1 / 16 , c ) 1 / 32 , d ) 1 / 64 , e ) 1 / 128
Rationale: "p ( hhhhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 64 the answer is d ."
Answer: d
Question (general): if n is a positive integer , what is the remainder when ( 6 ^ ( 4 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?
Options: a ) 7 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 6 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 7 . a or j in this problem ."
Answer: a
Question (general): what number is 60 more than two - fourth of itself ?
Options: a ) 180 , b ) 225 , c ) 288 , d ) 324 , e ) 336
Rationale: "2 / 4 x + 60 = x that means 60 = 2 / 4 x x = 60 * 3 = 180 a is the answer"
Answer: a
Question (physics): a man goes downstream at 10 kmph , and upstream 8 kmph . the speed of the stream is
Options: a ) 0 kmph , b ) 4 kmph , c ) 1 kmph , d ) 2.5 kmph , e ) 26 kmph
Rationale: "speed of the stream = 1 / 2 ( 10 - 8 ) kmph = 1 kmph . correct option : c"
Answer: c
Question (other): if shares of two persons in profits are rs . 600 and rs . 1000 then ratio of their capitals is
Options: a ) 3 : 5 , b ) 2 : 3 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 2
Rationale: "profit = time * capital so 600 : 1000 = 3 : 5 answer : a"
Answer: a
Question (general): if a * b * c = ( √ ( a + 2 ) ( b + 3 ) ) / ( c + 1 ) , find the value of 6 * 15 * 1 .
Options: a ) 8 , b ) 5 , c ) 2 , d ) 3 , e ) 4
Rationale: "6 * 15 * 1 = ( √ ( 6 + 2 ) ( 15 + 3 ) ) / ( 1 + 1 ) = ( √ 8 * 18 ) / 2 = ( √ 144 ) / 2 = 12 / 6 = 2 answer is c ."
Answer: c
Question (general): if 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 , then n =
Options: a ) 3 , b ) 6 , c ) 12 , d ) 23 , e ) 21
Rationale: 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 22 = > 4 x 2 ^ 2 n = 4 ^ 22 = 2 ^ 44 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 44 = > 2 ^ ( 2 n + 2 ) = 2 ^ 44 = > 2 n + 2 = 44 = > n = 21 so . answer will be e .
Answer: e
Question (general): a is the average ( arithmetic mean ) of the first 7 positive multiples of 5 and b is the median of the first 3 positive multiples of positive integer n . if the value of a ^ 2 – b ^ 2 is zero , what is the value of n ?
Options: a ) 5 , b ) 6 , c ) 10 , d ) 15 , e ) 20
Rationale: "if a ^ 2 - b ^ 2 = 0 , then let ' s assume that a = b . a must equal the 4 th positive multiple of 4 , thus a = 20 , which also equals b . b is the second positive multiple of n , thus n = 20 / 2 = 10 . the answer is c ."
Answer: c
Question (physics): length of a rectangular plot is 10 mtr more than its breadth . if the cost of fencin g the plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 46 m , b ) 55 m , c ) 58 m , d ) 78 m , e ) 80 m
Rationale: "let breadth = x metres . then , length = ( x + 10 ) metres . perimeter = 5300 / 26.5 = 200 m . 2 [ ( x + 10 ) + x ] = 200 2 x + 10 = 100 2 x = 90 x = 45 . hence , length = x + 10 = 55 m b"
Answer: b
Question (general): 2 men and 4 women are lined up in a row . what is the number of cases where they stand with each other in turn ? ( the number of cases in which men ( or women ) do not stand next to each other )
Options: a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 48
Rationale: the list should be wmwmw . hence , from women 4 ! and men 2 ! , we get ( 4 ! ) ( 2 ! ) = 48 . therefore , the correct answer is e .
Answer: e
Question (gain): the sale price sarees listed for rs . 375 after successive discount is 20 % and 15 % is ?
Options: a ) 227 , b ) 268 , c ) 342 , d ) 787 , e ) 285
Rationale: "375 * ( 80 / 100 ) * ( 85 / 100 ) = 285 answer : e"
Answer: e