choices
dict
answerKey
listlengths
1
1
question
stringlengths
5
967
rationale
stringlengths
1
2.74k
dataset
stringclasses
1 value
{ "text": [ "1 : 1', '", "2 : 1', '", "3 : 1', '", "5 : 3', '", "8 : 3']" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
abcd is a square . e and f are the midpoints of sides cd and bc , respectively . what is the ratio of the shaded region area to the unshaded region ?
let ' s join the midpoints as shown in the figure then we ' ll get four small squares . . . aodx be 1 and similarly all squares . . and we can split the unit 1 into half and half as per the mid points . . . then shaded will be 1 + 1 / 2 + 1 / 2 + 1 / 2 = 5 / 2 and unshaded is 1 / 2 + 1 / 2 + 1 / 2 = 3 / 2 . . shaded : ...
MathQA
{ "text": [ "26", "29", "19", "30", "40" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
a certain clock marks every hour by striking a number of times equal to the hour , and the time require for a stroke is exactly equal to the time interval between strokes . at 6 : 00 the time lapse between the beginning of the first stoke and the end of the last stroke is 22 seconds . at 7 : 00 , how many seconds elaps...
"at 6 ' o clock , there would be 6 strikes . first strike , then a short interval , the second strike , then a short interval and so on till the 6 th strike . so there would be in all 5 intervals between 6 strikes . similarly , between 7 strikes , there would be 6 intervals . according to the question , the time spent ...
MathQA
{ "text": [ "28 %", "66.7 %", "55 %", "28 %", "55 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a dishonest dealer professes to sell goods at the cost price but uses a weight of 600 grams per kg , what is his percent ?
"600 - - - 400 100 - - - ? = > 66.7 % answer : b"
MathQA
{ "text": [ "0", "1", "2", "3", "5" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
if n is a prime number greater than 5 , what is the remainder when n ^ 2 is divided by 23 ?
"there are several algebraic ways to solve this question including the one under the spoiler . but the easiest way is as follows : since we can not have two correct answersjust pick a prime greater than 5 , square it and see what would be the remainder upon division of it by 23 . n = 5 - - > n ^ 2 = 49 - - > remainder ...
MathQA
{ "text": [ "– 7", "7", "10", "12", "18" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
the sum of all solutions for x in the equation x ^ 2 – 8 x + 21 = | x – 2 | + 5 is equal to :
"x ^ 2 - 8 x + 16 = | x - 2 | rhs can be - ve or + ve x ^ 2 - 9 x + 18 = 0 x ^ 2 - 7 x + 14 = 0 x = 7,6 , 3,2 we test all 3 values in original equation , all ok . thus , sum = 7 + 6 + 3 + 2 = 18 ans ( e )"
MathQA
{ "text": [ "35 %", "40 %", "45 %", "50 %", "55 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
80 is what percent of 160 ?
80 / 160 × 100 = 50 % answer : d
MathQA
{ "text": [ "2007", "2008", "2009", "2010", "2011" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
the price of commodity x increases by 30 cents every year , while the price of commodity y increases by 20 cents every year . if in 2001 , the price of commodity x was $ 4.20 and the price of commodity y was $ 4.40 , in which year will commodity x cost 40 cents more than the commodity y ?
"the cost of commodity x increases by 10 cents per year relative to commodity y . the price of x must gain 20 + 40 = 60 cents on commodity y , which will take 6 years . the answer is a ."
MathQA
{ "text": [ "150 m", "350 m", "420 m", "600 m", "700 m" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a 300 metre long train crosses a platform in 39 seconds while it crosses a post in 18 seconds . what is the length of the platform ?
explanation : length of the train = distance covered in crossing the post = speed × time = speed × 18 speed of the train = 300 / 18 m / s = 50 / 3 m / s time taken to cross the platform = 39 s ( 300 + x ) / ( 50 / 3 ) = 39 s where x is the length of the platform 300 + x = ( 39 × 50 ) / 3 = 650 meter x = 650 - 300 = 350...
MathQA
{ "text": [ "0", "27", "30", "21", "18" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
what is the remainder when 1034 * 1047 * 1050 * 1053 is divided by 33 ?
"take the remainder from each of 1034 / 33 , 1047 / 33 and so on . . 1034 / 33 gives remainder = 11 1047 / 33 gives remainder = 24 1050 / 33 gives remainder = 27 1053 / 33 gives remainder = 30 the net remainder is the product of above individual remainders . i . e = 11 * 24 * 27 * 30 break them into pairs 11 * 24 / 33 ...
MathQA
{ "text": [ "10", "13", "14", "15", "26" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
39 persons can repair a road in 24 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
"let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 39 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 39 x 5 x 24 x = ( 39 x 5 x 24 ) / ( 30 x 6 ) x = 26 . answer : e"
MathQA
{ "text": [ "1 / 12", "6 / 15", "1 / 6", "1 / 3", "1 / 5" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
two boats are heading towards each other at constant speeds of 4 miles / hr and 20 miles / hr respectively . they begin at a distance 20 miles from each other . how far are they ( in miles ) one minute before they collide ?
"the question asks : how far apart will they be 1 minute = 1 / 60 hours before they collide ? since the combined rate of the boats is 4 + 20 = 25 mph then 1 / 60 hours before they collide they ' ll be rate * time = distance - - > 24 * 1 / 60 = 6 / 15 miles apart . answer : b ."
MathQA
{ "text": [ "25.5", "2.5", "25", ". 25" ], "label": [ "A", "B", "C", "D" ] }
[ "C" ]
1 / 0.04 is equal to
"explanation : 1 / 0.04 = ( 1 * 100 ) / 4 = 100 / 4 = 25 option c"
MathQA
{ "text": [ "$ 198", "$ 216", "$ 220", "$ 230", "$ 168" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 30 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
"wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 30 emlpoyee paid = . 7 * 240 = 168 $ answer e"
MathQA
{ "text": [ "1 / 4", "3 / 8", "1 / 2", "29 / 46", "3 / 4" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
if an integer n is to be chosen at random from the integers 1 to 92 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
"n ( n + 1 ) ( n + 2 ) will be divisible by 8 when n is a multiple of 2 or when ( n + 1 ) is a multiple of 8 . thus when n is even , this whole expression will be divisible by 8 . from 1 to 96 , there are 46 even integers . now when ( n + 1 ) is multiple by 8 , we have 12 such values for ( n + 1 ) probability that n ( ...
MathQA
{ "text": [ "2", "3", "4", "5", "6" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
on dividing a number by 56 , we get 27 as remainder . on dividing the same number by 8 , what will be the remainder ?
"number = 56 x + 27 ( ∵ since the number gives 27 as remainder on dividing by 56 ) = ( 7 × 8 × x ) + ( 3 × 8 ) + 3 hence , if the number is divided by 8 , we will get 3 as remainder . answer : b"
MathQA
{ "text": [ "263", "500", "367", "642.9", "339" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
what sum of money will produce rs . 90 as simple interest in 4 years at 3 1 / 2 percent ?
"90 = ( p * 4 * 7 / 2 ) / 100 p = 642.9 answer : d"
MathQA
{ "text": [ "rs . 4800", "rs . 2400", "rs . 3600", "rs . 5600" ], "label": [ "A", "B", "C", "D" ] }
[ "A" ]
a and b enter into a partnership . a contributed rs . 5000 for 8 months and b rs . 6000 for 5 months . find a ' s share in a total profit of rs . 8400 .
explanation : ratio of capitals of a and b = ratio of their investments = 5000 × 8 : 6000 × 5 = 40000 : 30000 = 4 : 3 . : a ' s share = rs . [ ( 4 / 7 ) × 8400 ] = rs . 4800 answer : option a
MathQA
{ "text": [ "3 : 4", "4 : 3", "9 : 7", "7 : 9", "8 : 1" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixtures be mixed to obtain a new mixture in vessel c containing spirit and water in the ratio 8 : 5 ?
"explanation : let cost price ( cp ) of 1 litre spirit be rs . 1 quantity of spirit in 1 litre mixture from vessel a = 5 / 7 cost price ( cp ) of 1 litre mixture from vessel a = rs . = 5 / 7 quantity of spirit in 1 litre mixture from vessel b = 7 / 13 cost price ( cp ) of 1 litre mixture from vessel b = rs . = 7 / 13 q...
MathQA
{ "text": [ "420", "840", "800", "1680", "2100" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
company a imported 10,000 widgets made of either brass or aluminum . the widgets are painted blue , red or green . if 20 percent of the widgets are made of brass and of those 20 percent are painted green and 40 percent are painted red how many brass widgets painted blue were imported ?
"answer a . we are told that 10 % of all imported widgets are made of brass and of those , 20 % are green and 40 % are red . since we know that there are only three colors , the remaining 40 % must be blue . 40 % blue of 20 % brass widgets leads to 8 % blue brass widgets out of the total 10,550 widgets . 10,000 / 100 *...
MathQA
{ "text": [ "3", "5", "6", "8", "10" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
a honey bee flies for 10 seconds , from a daisy to a rose . it immediately continues to a poppy , flying for 6 additional seconds . the distance the bee passed , flying from the daisy to the rose is 6 meters longer than the distance it passed flying from the rose to the poppy . the bee flies to the poppy at 3 meters pe...
"let the speed be ' s ' and let the distance between rose and poppy be ' x ' the problem boils down to : rose to poppy : s + 3 = x / 6 - - - - - - - 1 daisy to rose : s = ( x + 6 ) / 10 - - - - - - 2 so from 1 we can re write x as x = 6 s + 18 substitute the value of x in 2 gives us s = 3 m / s a"
MathQA
{ "text": [ "2288", "2779", "3300", "3900", "2781" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
a rectangular lawn of dimensions 80 m * 40 m has two roads each 10 m wide running in the middle of the lawn , one parallel to the length and the other parallel to the breadth . what is the cost of traveling the two roads at rs . 3 per sq m ?
"area = ( l + b â € “ d ) d ( 80 + 40 â € “ 10 ) 10 = > 1100 m 2 1100 * 3 = rs . 3300 answer : c"
MathQA
{ "text": [ "75", "80", "90", "95", "100" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
there is enough provisions for 1200 girls in a hostel for 50 days . if there were 600 girls less , how long will the provision last ?
"we have , m 1 d 1 = m 2 d 2 1200 * 50 = 600 * d 2 d 2 = 1200 * 50 / 600 = 100 days . answer : e"
MathQA
{ "text": [ "1 / 4", "2 / 5", "1 / 2", "3 / 5", "2 / 3" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
a 50 kg metal bar made of alloy of tin and silver lost 5 kg of its weight in the water . 10 kg of tin loses 1.375 kg in the water ; 5 kg of silver loses 0.375 kg . what is the ratio of tin to silver in the bar ?
"you can simply use this formula to avoid confusion : w 1 / w 2 = ( a 2 - aavg ) / ( avg - a 1 ) here is how you will find the values of a 1 an a 2 . we have an overall loss ( average loss ) . the average loss is 5 kg when 50 kg alloy is immersed . this is a loss of ( 5 / 50 ) * 100 = 10 % . this is aavg the loss of ti...
MathQA
{ "text": [ "", "250", "", "249", "", "248", "", "247", "", "246" ], "label": [ "A", "A", "B", "B", "C", "C", "D", "D", "E", "E" ] }
[ "A" ]
a , b and c have rs . 300 between them , a and c together have rs . 200 and b and c rs . 350 . how much does c have ?
"a + b + c = 300 a + c = 200 b + c = 350 - - - - - - - - - - - - - - a + b + 2 c = 550 a + b + c = 300 - - - - - - - - - - - - - - - - c = 250 answer : a"
MathQA
{ "text": [ "43", "36", "28", "129", "44" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
there are 50 students in a class . if 12 % are absent on a particular day , find the number of students present in the class .
"number of students absent on a particular day = 12 % of 50 i . e . , 12 / 100 × 50 = 6 therefore , the number of students present = 50 - 6 = 44 students . answer : e"
MathQA
{ "text": [ "6", "12", "14", "24", "28" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
how many gallons of milk that is 10 percent butter - fat must be added to 8 gallons of milk that is 50 percent butterfat to obtain milk that is 20 percent butterfat ?
"equate the fat : 0.1 x + 0.5 * 8 = 0.2 ( x + 8 ) - - > x = 24 . answer : d ."
MathQA
{ "text": [ "$ 1", "$ 2", "$ 4", "$ 8", "$ 16" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
can c and can в are both right circular cylinders . the radius of can c is twice the radius of can b , while the height of can c is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can c with the same brand of gasoline ?
let x be the radius of b and 2 h be the height of b . therefore , radius of c = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
MathQA
{ "text": [ "11", "10", "12", "14", "16" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
a certain family has 3 sons : richard is 6 years older than david , and david is 8 years older than scott . if in 8 years , richard will be twice as old as scott , then how old was david 3 years ago ?
"let ' s say age of richard is ` ` r ' ' age of david is ` ` d ' ' age of scott is ` ` s ' ' now richard is 6 years older than david , i . e . r = d + 6 david is 8 years older than scott i . e . d = s + 8 if in 8 years , richard will be twice as old as scott i . e . r + 8 = 2 x ( s + 8 ) i . e . r + 8 = 2 s + 16 i . e ...
MathQA
{ "text": [ "12", "14", "16", "18", "15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
6 years ago , the ratio of the ages of vimal and saroj was 6 : 5 . 4 years hence , the ratio of their ages will be 11 : 10 . what is saroj ' s age at present ?
given that , six years ago , the ratio of the ages of vimal and saroj = 6 : 5 hence we can assume that age of vimal six years ago = 6 x age of saroj six years ago = 5 x after 4 years , the ratio of their ages = 11 : 10 ⇒ ( 6 x + 10 ) : ( 5 x + 10 ) = 11 : 10 ⇒ 10 ( 6 x + 10 ) = 11 ( 5 x + 10 ) ⇒ 5 x = 10 ⇒ x = 105 = 2 ...
MathQA
{ "text": [ "4.25 hr", "3.8 hr", "8.25 hr", "2.25 hr", "2.50 hr" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
"speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 ⠁ „ 18 = 3.8 hours answer is b"
MathQA
{ "text": [ "50 %", "44.4 %", "22.2 %", "33.3 %", "25 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
if 60 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
"60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a"
MathQA
{ "text": [ "25", "50", "75", "80" ], "label": [ "A", "B", "C", "D" ] }
[ "C" ]
a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of each .
c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is c
MathQA
{ "text": [ "28", "31", "34", "37", "40" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ?
"the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list . the answer is c ."
MathQA
{ "text": [ "3.9", "4.2", "4.5", "4.8", "5.1" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
the edges of three metal cubes are 1 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm . the answer is c .
MathQA
{ "text": [ "", "100", "", "120", "", "250", "", "200", "", "160" ], "label": [ "A", "A", "B", "B", "C", "C", "D", "D", "E", "E" ] }
[ "B" ]
an inspector rejects 10 % of the meters as defective . how many will he examine to reject 12 ?
"then , 10 % of x = 12 ( 10 / 100 ) x = 12 x = ( 12 * 100 * ) / 10 = 120 answer is b"
MathQA
{ "text": [ "2 %", "7 %", "14 %", "28 %", "63 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 72 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
"rate of first survey = 7 / 60 rate of second survey = 9 / 72 % response rate increase ( 9 / 72 - 7 / 60 ) / ( 7 / 60 ) = 7 % answer is b = 7 %"
MathQA
{ "text": [ "4 %", "25 %", "50 %", "200 %", "400 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
if the sides of a square are multiplied by 5 , the area of the original square is how many times as large as the area of the resultant square ?
"let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 5 x , so the area is 25 x ^ 2 . the area of the original square is 1 / 25 = 4 % times the area of the new square . the answer is a ."
MathQA
{ "text": [ "11 : 5", "3 : 1", "13 : 7", "15 : 7", "16 : 9" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
car a runs at the speed of 50 km / hr & reaches its destination in 6 hr . car b runs at the speed of 100 km / h & reaches its destination in 1 h . what is the respective ratio of distances covered by car a & car b ?
"sol . distance travelled by car a = 50 × 6 = 300 km distance travelled by car b = 100 × 1 = 100 km ratio = 300 / 100 = 3 : 1 answer : b"
MathQA
{ "text": [ "48", "32", "24", "18", "64" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
a cubical block of metal weighs 8 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
"for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach : if we have sides a and b tha...
MathQA
{ "text": [ "80", "110", "160", "200", "400" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . what is the number of students in the course ?
"we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain mat...
MathQA
{ "text": [ "30", "40", "50", "60", "70" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
how many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long
explanation : we need so simple divide 42.5 / 0.85 , = ( 4250 / 85 ) = 50 option c
MathQA
{ "text": [ "14", "15", "8", "22", "24" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
ratio between rahul and deepak is 5 : 2 , after 6 years rahul age will be 26 years . what is deepak present age .
"explanation : present age is 5 x and 2 x , = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c"
MathQA
{ "text": [ "12", "13", "16.6", "16", "23" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
set a consists of all the prime numbers between 62 and 85 . what is the range of set a ?
the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d
MathQA
{ "text": [ "w = 350", "w = 353", "w = 354", "356", "357" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits w are in s ( 99 ) ?
"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square ....
MathQA
{ "text": [ "5000", "5500", "6000", "6500", "7000" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a candidate got 35 % of the votes and lost to the rival by 1650 votes . how many votes were cast ?
"35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1650 10 % = 550 100 % of the votes = 5500 answer : b"
MathQA
{ "text": [ "13", "15.5", "14", "14.5", "15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 8 miles per gallon , and from town b to town c , the car averaged 18 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through t...
"ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 8 ) + ( x / 18 ) ) = 15.5 ( formula avg speed = total distance / total time )"
MathQA
{ "text": [ "16", "12", "10", "20", "10" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a . ?
"( a + b ) - ( b - c ) = 10 a - c = 10 answer is c"
MathQA
{ "text": [ "82", "17", "14", "82", "18" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
excluding stoppages , the speed of a train is 67 kmph and including stoppages it is 51 kmph . of how many minutes does the train stop per hour ?
"explanation : t = 16 / 67 * 60 = 14 answer : option c"
MathQA
{ "text": [ "12", "42", "64", "96", "84" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
the average runs of a cricket player of 8 innings was 24 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?
"explanation : average after 9 innings = 32 required number of runs = ( 32 * 9 ) – ( 24 * 8 ) = 288 – 192 = 96 answer d"
MathQA
{ "text": [ "3.2", "4.5", "6", "6.25", "15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
if jack walked 4 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a
MathQA
{ "text": [ "90", "120", "150", "440", "430" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
yesterday it took robert 6 hours to drive from city a to city b . today it took robert 4.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 90 miles per hour . what is the distance between city a and city b ?
2 d / 90 = 9.5 ( because time = 6 + 4.5 - 1 hrs ) = > d = 430 answer - e
MathQA
{ "text": [ "251", "253", "255", "257", "260" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :
"let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digits is smaller than the unit ' s digit . hence , required number = 253 . option b"
MathQA
{ "text": [ "11 : 9", "13 : 9", "17 : 9", "21 : 9" ], "label": [ "A", "B", "C", "D" ] }
[ "A" ]
2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds
"explanation : we know total distance is 200 km if both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [ 110 + 90 = 200 km ] so ratio of their speed = 110 : 90 = 11 : 9 option a"
MathQA
{ "text": [ "14.4", "180 / 7", "50.4", "64.8", "90" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
50 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
"50 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 50 ) * 100 = 64.8 square feet answer : option d"
MathQA
{ "text": [ "14 : 13", "13 : 15", "12 : 13", "13 : 12", "14 : 15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a work can be finished in 13 days by ten women . the same work can be finished in fifteen days by ten men . the ratio between the capacity of a man and a woman is
work done by 10 women in 1 day = 1 / 13 work done by 1 woman in 1 day = 1 / ( 13 ã — 10 ) work done by 16 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 ã — 10 ) ratio of the capacity of a man and woman = 1 / ( 15 ã — 10 ) : 1 / ( 13 ã — 10 ) = 1 / 15 : 1 / 13 = 1 / 15 : 1 / 13 = 13 : 15 answer is b .
MathQA
{ "text": [ "0.3408", "3.408", "34.08", "340.8" ], "label": [ "A", "B", "C", "D" ] }
[ "D" ]
if 213 × 16 = 3408 , then 1.6 × 213.0 is equal to :
solution 1.6 × 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d
MathQA
{ "text": [ "100", "120", "130", "150", "140" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is
"let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : option d"
MathQA
{ "text": [ "512", "1024", "768", "2048", "4096" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
the population of a bacteria colony doubles every day . if it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days , how large is the colony today ?
"9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 answer : b"
MathQA
{ "text": [ "200", "210", "220", "230", "240" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
the h . c . f of two numbers is 15 and their l . c . m is 3300 . if one of the numbers is 225 , then the other is ?
"other number = ( 15 * 3300 ) / 225 = 220 . answer : c"
MathQA
{ "text": [ "10 %", "15 %", "20 %", "25 %", "30 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a bag marked at $ 80 is sold for $ 68 . the rate of discount is ?
"rate of discount = 12 / 80 * 100 = 15 % answer is b"
MathQA
{ "text": [ "5", "7", "15", "12", "13" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
{ 5 , 6 , 3 , 8 , 4 } if we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values ?
median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 10 . mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6 . to ge...
MathQA
{ "text": [ "4', '", "8', '", "12', '", "16', '", "20']" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
the area of a rhombus is equal to the area of a square whose side length is 8 cm . if one of the diagonals is 16 cm what is the length of other diagonal ?
area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm answer : b
MathQA
{ "text": [ "10 %", "20 %", "30 %", "40 %", "50 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
the cost price of 7 articles is equal to the selling price of 5 articles . what is the profit percent ?
"5 * sp = 7 * cp sp = 1.4 * cp the profit percent is 40 % . the answer is d ."
MathQA
{ "text": [ "3", "5", "7", "9", "12" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is
"sol . let the numbers be x . then , x - 4 = 21 / x ⇔ x 2 - 4 x - 21 = 0 ⇔ ( x - 7 ) ( x + 3 ) = 0 ⇔ x = 7 . answer c"
MathQA
{ "text": [ "72.5", "55.5", "62.5", "82.5", "60.5" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
"c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"
MathQA
{ "text": [ "38", "20", "28", "49", "10" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a car consumes 210 liters of petrol weekly . for how many days will 1470 liters of petrol be sufficient ?
explanation : no explanation is available for this question ! answer : d
MathQA
{ "text": [ "22.15 %", "23.5 %", "24.3 %", "25 %", "29.6 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
one type of liquid contains 20 % of water and the second type of liquid contains 35 % of water . a glass is filled with 10 parts of 1 st liquid and 4 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c
MathQA
{ "text": [ "17 , 18", "30,31", "5 , 6", "1 , 2", "8 , 9" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
the sum of two consecutive integers is 61 . find the numbers .
"n + ( n + 1 ) = 61 2 n + 1 = 61 2 n = 60 n = 30 answer : b"
MathQA
{ "text": [ "5 m', '", "12 m', '", "6 m', '", "8 m', '", "10 m']" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively . find the height of a cuboid ?
height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d
MathQA
{ "text": [ "16", "17", "18", "19", "10" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
how many positive even integers less than 100 contain digits 7 or 9 ?
"two digit numbers : 7 at tens place : 70 , 72,74 , 76,78 9 at tens place : 90 , 92,94 , 96,98 if 7 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
MathQA
{ "text": [ "650", "250", "150", "100", "400" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
in a group of 650 readers who read science fiction or literacy works or both , 250 read science fiction and 550 read literacy works . how many read both science fiction and literacy works ?
"consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 650 = 250 + 550 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 800 - 650 n ( s â ˆ © ...
MathQA
{ "text": [ "0.36", "3.6", "360", "18,000", "36,000" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
if anangletis defined as 1 percent of 1 degree , then how many anglets are there in one half circle ?
"1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 180 degrees = 18,000 anglets answer - d"
MathQA
{ "text": [ "72 kmph", "60 kmph", "30 kmph", "80 kmph", "82 kmph" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
the speed of a car is 80 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
"s = ( 80 + 40 ) / 2 = 60 kmph answer : b"
MathQA
{ "text": [ "7", "9", "11", "13", "15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 3000 ?
"to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 3000 , then the greatest possible length of integer z is 11 . the answer is c ."
MathQA
{ "text": [ "30", "36", "42", "45", "48" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a cistern is filled by a tap in 4 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
"filling rate - leak rate = net rate 1 / 4.5 - leak rate = 1 / 5 leak rate = 2 / 9 - 1 / 5 = 1 / 45 the answer is d ."
MathQA
{ "text": [ "45225766", "46855821", "47045882", "48925947", "49325989" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
what is ( 19 ^ 7 + 19 ) / 19 ?
"( 19 ^ 7 + 19 ) / 19 = 19 * ( 19 ^ 6 + 1 ) / 19 = 19 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is c ."
MathQA
{ "text": [ "800", "1,250", "8,000", "12,000", "80,000" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a certain galaxy is known to comprise approximately 6 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
"6 * 10 ^ 11 50 mln = 5 * 10 ^ 7 we divide 10 ^ 11 by 10 ^ 7 and we get ( 10 ^ 4 ) * 6 = 60,000 and divide by 5 . the result is 12,000 d"
MathQA
{ "text": [ "0", "1", "2", "3", "4" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
what is the remainder when 4 ^ 381 is divided by 5 ?
i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
MathQA
{ "text": [ "800", "1500", "1000", "750", "500" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town before 1 years ?
"p = 1000 r = 25 % required population of town = p / ( 1 + r / 100 ) ^ t = 1000 / ( 1 + 25 / 100 ) = 1000 / ( 5 / 4 ) = 800 answer is a"
MathQA
{ "text": [ "1 / 4", "1 / 3", "2 / 5", "4 / 9", "1 / 2" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
a = { 0 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 2 / 5 * 2 / 4 = 4 / 20 ; p ( negative , negative ) = 2 / 5 * 2 / 4 = 4 / 20 . p = 4 / 20 + 4 / 20 = 8 / 20 = 2 / 5 . answer : c .
MathQA
{ "text": [ "40 %", "45 %", "50 %", "55 %", "60 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
john and david can finish a job together in 1 hours . if john can do the job by himself in 2 hours , what percent of the job does david do ?
you can also plug in numbers . for example , bob and alice work at a donut factory and make 10 donuts which is the job ( i picked this as a smart number ) . john on his own works 10 / 2 = 5 donuts per hour . john and david work 10 / 1 = 10 donuts per hour so david works 5 donuts / hour to find out the percentage , davi...
MathQA
{ "text": [ "0", "1", "2", "4", "7" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
for the positive integers x , x + 2 , x + 4 , x + 7 , and x + 17 , the mean is how much greater than the median ?
"mean = ( x + x + 2 + x + 4 + x + 7 + x + 17 ) / 5 = ( 5 x + 30 ) / 5 = x + 6 median = x + 4 thus mean - median = x + 6 - ( x + 4 ) = 2 answer = c"
MathQA
{ "text": [ "76 kmph", "6 kmph", "14 kmph", "8 kmph", "3 kmph" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "E" ]
a man rows his boat 84 km downstream and 60 km upstream , taking 4 hours each time . find the speed of the stream ?
"speed downstream = d / t = 84 / ( 4 ) = 21 kmph speed upstream = d / t = 60 / ( 4 ) = 15 kmph the speed of the stream = ( 21 - 15 ) / 2 = 3 kmph answer : e"
MathQA
{ "text": [ "2", "3", "4", "5", "8" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
"another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"
MathQA
{ "text": [ "1 / 2", "1 / 5", "3 / 4", "1 / 3", "3 / 5" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
given a bag with 2 red balls and 3 yellow balls , you randomly select one of them , in order . if the second ball you take is yellow , what is the probability that the first one was also yellow ?
this is a conditional probability question . basically we are told that out of 2 balls picked one is yellow and are asked to find the probability of the other one also to be yellow . so , possible options for this other ball would be : w , w , b , b ( as one yellow is already picked ) so the probability for that ball t...
MathQA
{ "text": [ "1520", "2520", "3520", "5140", "7660" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
how many 4 - digit positive integers are multiple of each integer from 1 to 10
"least no which could be divisible by integers [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] is the lcm of the said integers . lcm [ 1,2 , 3,4 , 5,6 , 7,8 , 9,10 ] = 2520 no the nos which are divisible by 2520 will be divisible by [ 1 , 2,3 , 4,5 , 6,7 , 8,9 ] there are 3 values possible between 1000 to 9999 they are 2520 x 1 = 252...
MathQA
{ "text": [ "3", "6", "9", "12", "15" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
a water tank is one - fifth full . pipe a can fill a tank in 10 minutes and pipe b can empty it in 6 minutes . if both the pipes are open , how many minutes will it take to empty or fill the tank completely ?
the combined rate of filling / emptying the tank = 1 / 10 - 1 / 6 = - 1 / 15 since the rate is negative , the tank will be emptied . a full tank would take 15 minutes to empty . since the tank is only one - fifth full , the time is ( 1 / 5 ) * 15 = 3 minutes the answer is a .
MathQA
{ "text": [ "4.54 %", "9.09 %", "10 %", "11 %", "12.25 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
jar y has 10 % more marbles than jar x . what percent of marbles from jar y need to be moved into x so that both jars have equal marbles
no ; the choices will be approximated only when gmat question explicitly mentions that ; here the answer is very close 4.54 , not 5 . jar y has 10 % more marbles than x y = 1.1 x if k marbles are taken out of y . the remaining marbles in jar y = 1.1 x - k if k marbles are added to x . the new marbles ' count in jar x =...
MathQA
{ "text": [ "15 / 56", "41 / 56", "13 / 28", "15 / 28", "5 / 14" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability that out of the two , one is white and one is blue ?
"the required probability = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 ...
MathQA
{ "text": [ "334 km .", "216 km .", "314 km .", "224 km .", "544 km ." ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
a woman complete a journey in 10 hours . she travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km / hr . find the total journey in km .
"d 224 km . 0.5 x / 21 + 0.5 x / 24 = 10 - - > x / 21 + x / 24 = 20 - - > 15 x = 168 x 20 - - > x = ( 168 x 20 ) / 15 = 224 km ."
MathQA
{ "text": [ "15 kmph", "11 kmph", "18 kmph", "8 kmph", "12 kmph" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
the speed of a train is 80 kmph . what is the distance covered by it in 6 minutes ?
"80 * 6 / 60 = 8 kmph answer : d"
MathQA
{ "text": [ "560", "540", "520", "440", "500" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
if 50 % of the 880 students at a certain college are enrolled in biology classes , how many students at the college are not enrolled in a biology class ?
we know 50 % people study biology , therefore the no of people not studying = 100 - 50 = 50 % > therefore the people not studying biology out of a total 880 people are = 50 % of 880 > ( 50 / 100 ) * 880 = 440 people d
MathQA
{ "text": [ "", "7", "", "9", "", "11", "", "13", "", "15" ], "label": [ "A", "A", "B", "B", "C", "C", "D", "D", "E", "E" ] }
[ "A" ]
sum of two numbers is 10 . two times of the first exceeds by 5 from the three times of the other . then the numbers will be ?
"explanation : x + y = 10 2 x – 3 y = 5 x = 7 y = 3 a )"
MathQA
{ "text": [ "3.2 hr", "3.4 hr", "3.6 hr", "3.8 hr", "4.2 hr" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km . how many hours has been driving at 20 kmph ?
let see d / t = v then x / 20 + ( 400 - x ) / 70 = 8 x = 64 kmh t = 64 / 20 = 3.2 hr answer : a
MathQA
{ "text": [ "20000", "16000", "18000", "17000", "15000" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
a shopkeeper sells 10 % of his stock at 20 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 400 . find the total worth of the stock ?
"let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 10 * x * 6 / 5 = 6 x / 50 the sp of 80 % of the stock = 9 / 10 * x * 0.95 = 171 x / 200 total sp = 24 x / 200 + 171 / 200 = 49 x / 50 overall loss = x - 195 / 20050 = 5 x / 200 5 x / 200 = 400 = > x = 16000 answer : b"
MathQA
{ "text": [ "3", "5", "11", "9", "10" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "C" ]
in one hour , a boat goes 13 km along the stream and 9 km against the stream . the speed of the boat in still water ( in km / hr ) is :
"solution speed in still water = 1 / 2 ( 13 + 9 ) kmph . = 11 kmph . answer c"
MathQA
{ "text": [ "10", "15", "30", "20", "16" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "D" ]
if 5 spiders make 2 webs in 8 days , then how many days are needed for 1 spider to make 1 web ?
"explanation : let , 1 spider make 1 web in x days . more spiders , less days ( indirect proportion ) more webs , more days ( direct proportion ) hence we can write as ( spiders ) 5 : 1 ( webs ) 1 : 8 } : : x : 2 â ‡ ’ 5 ã — 1 ã — 8 = 1 ã — 2 ã — x â ‡ ’ x = 20 answer : option d"
MathQA
{ "text": [ "15 %", "80 %", "20 %", "22 %", "24 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
an employee ’ s annual salary was increased $ 5,000 . if her new annual salary now equals $ 25000 what was the percent increase ?
"new annual salary = $ 25000 salary increase = $ 5000 . original salary = $ 25000 - $ 5,000 . = $ 20,000 % increase = ( $ 15,000 / $ 75,000 ) * 100 = 80 % hence b ."
MathQA
{ "text": [ "45 %", "62.5 %", "35 %", "32.5 %", "30 %" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "B" ]
the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 50 per cent . the two reductions together are equal to a single reduction of
"price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 50 percent is reduced which means the new price is merely 50 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 1 / 2 ) p = 3 / 8 p is the new price after both deduction which is 37.5 percent of the original value p . this imp...
MathQA
{ "text": [ "5 : 1", "2 : 3", "1 : 4", "3 : 7", "2 : 5" ], "label": [ "A", "B", "C", "D", "E" ] }
[ "A" ]
in a school 10 % of the boys are same in number as 1 / 2 th of the girls . what is the ratio of boys to the girls in the school ?
"10 % of b = 1 / 2 g 10 b / 100 = g / 2 b = 5 g / 1 b / g = 5 / 1 b : g = 5 : 1 answer is a"
MathQA