Datasets:
Cheukting
/
mathqa

Dataset card Data Studio Files
xet
 Community
1
Problem
stringlengths
5
967
Rationale
stringlengths
1
2.74k
options
stringlengths
37
300
correct
stringclasses
5 values
annotated_formula
stringlengths
7
6.48k
linear_formula
stringlengths
8
925
category
stringclasses
6 values
a train running at the speed of 60 km / hr crosses a pole in 9 seconds . find the length of the train ?
"speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 9 = 150 meter answer : a"
a ) 150 , b ) 872 , c ) 287 , d ) 288 , e ) 212
a
multiply(divide(multiply(60, const_1000), const_3600), 9)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
a rectangular plot measuring 30 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
"perimeter of the plot = 2 ( 30 + 50 ) = 160 m no of poles = 160 / 5 = 32 m answer : e"
a ) 46 m , b ) 66 m , c ) 26 m , d ) 56 m , e ) 32 m
e
divide(multiply(add(30, 50), const_2), 5)
add(n0,n1)|multiply(#0,const_2)|divide(#1,n2)|
physics
a certain list consists of 21 different numbers . if n is in the list and n is 4 times the average ( arithmetic mean ) of the other 20 numbers in the list , then n is what fraction of the sum of the 21 numbers in the list ?
"series : a 1 , a 2 . . . . a 20 , n sum of a 1 + a 2 + . . . + a 20 = 20 * x ( x = average ) so , n = 4 * x hence , a 1 + a 2 + . . + a 20 + n = 24 x so , the fraction asked = 4 x / 24 x = 1 / 6 ; answer : b ."
a ) 1 / 20 , b ) 1 / 6 , c ) 1 / 5 , d ) 4 / 21 , e ) 5 / 21
b
divide(multiply(const_1, const_1), subtract(subtract(multiply(divide(add(divide(20, 4), 21), 4), const_2), 4), const_3))
divide(n2,n1)|multiply(const_1,const_1)|add(n0,#0)|divide(#2,n1)|multiply(#3,const_2)|subtract(#4,n1)|subtract(#5,const_3)|divide(#1,#6)|
general
a batsman in his 12 th innings makes a score of 80 and thereby increases his average by 2 runs . what is his average after the 12 th innings if he had never been ‘ not out ’ ?
"let ‘ x ’ be the average score after 12 th innings ⇒ 12 x = 11 × ( x – 2 ) + 80 ∴ x = 58 answer e"
a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 58
e
add(subtract(80, multiply(12, 2)), 2)
multiply(n0,n2)|subtract(n1,#0)|add(n2,#1)|
general
what is the compound interest on rs . 4500 at 5 % p . a . compounded half - yearly for 3 1 / 2 years .
"compound interest : a = p ( 1 + r / n ) nt a = 5 , 349.09 c . i . > > 5 , 349.09 - 4500 > > rs . 849.09 answer : e"
a ) rs . 859.09 , b ) rs . 349.09 , c ) rs . 449.09 , d ) rs . 749.09 , e ) rs . 849.09
e
multiply(4500, subtract(power(divide(add(divide(5, const_2), const_100), const_100), multiply(3, const_2)), const_1))
divide(n1,const_2)|multiply(n2,const_2)|add(#0,const_100)|divide(#2,const_100)|power(#3,#1)|subtract(#4,const_1)|multiply(n0,#5)|
gain
danny can divide his herd into 5 equal parts and also to 6 equal parts , but not to 9 equal parts . what could be the number of cows danny has in his herd ?
danny can divide his herd into 5 equal parts and also to 6 equal parts = > no of cows = multiple of 5 and 6 = multiple of 30 . only option a and c qualify . now 2 nd condition : but not to 9 equal parts : so it should not be a multiple of 9 . answer : a
a ) 120 , b ) 155 , c ) 180 , d ) 336 , e ) 456
a
add(const_100, multiply(5, const_4))
multiply(n0,const_4)|add(#0,const_100)
general
a and b can do a work in 8 days , b and c can do it in 12 days ; a , b and c together can finish it in 6 days . a and c together will do it in ?
"a + b + c 1 day work = 1 / 6 a + b 1 day work = 1 / 8 b + c 1 day work = 1 / 12 a + c 1 day work = 2 * 1 / 6 - 1 / 8 + 1 / 12 = 1 / 3 - 5 / 24 = 3 / 24 = 1 / 8 a and c together will do the work in 8 days . answer is a"
a ) 8 days , b ) 10 days , c ) 12 days , d ) 7 days , e ) 5 days
a
inverse(add(subtract(divide(const_1, 12), subtract(divide(const_1, 8), divide(const_1, 6))), subtract(divide(const_1, 8), divide(const_1, 6))))
divide(const_1,n1)|divide(const_1,n0)|divide(const_1,n2)|subtract(#1,#2)|subtract(#0,#3)|add(#4,#3)|inverse(#5)|
physics
how much is 90 % of 40 is greater than 4 / 5 of 25 ?
"( 90 / 100 ) * 40 – ( 4 / 5 ) * 25 36 - 20 = 16 answer : d"
a ) 29 , b ) 776 , c ) 66 , d ) 16 , e ) 99
d
subtract(multiply(40, divide(90, const_100)), multiply(divide(4, 5), 25))
divide(n0,const_100)|divide(n2,n3)|multiply(n1,#0)|multiply(n4,#1)|subtract(#2,#3)|
general
a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 6 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
"however the process of dividing the volume of box by the volume of a soap seems flawed but it does work in this case due to the numbers dimensions of the box = 25 * 42 * 60 dimensions of the soap = 6 * 6 * 7 placing the 7 inch side along 42 inch side we get 6 soaps in a line and in a similar way 5 along 25 and 6 along...
a ) 210 , b ) 252 , c ) 250 , d ) 300 , e ) 420
c
divide(multiply(multiply(25, 42), 60), multiply(multiply(7, 6), 6))
multiply(n0,n1)|multiply(n3,n4)|multiply(n2,#0)|multiply(n5,#1)|divide(#2,#3)|
general
suresh and ramesh started a business investing rs . 24,000 and rs . 40,000 respectively . out of total profit of rs . 19,000 , what is ramesh ' s share ?
explanation : ratio of suresh and ramesh ' s share = 24,000 : 40,000 = 3 : 5 ramesh ' s share = rs . ( 19000 x 5 / 8 ) = rs . 11875 answer : e
a ) s . 7375 , b ) s . 8379 , c ) s . 9875 , d ) s . 10875 , e ) s . 11875
e
multiply(multiply(multiply(const_4, multiply(const_2, add(const_2, const_3))), multiply(const_100, multiply(const_2, add(const_2, const_3)))), divide(multiply(subtract(multiply(multiply(const_3, const_4), const_2), add(const_2, const_3)), multiply(const_100, multiply(const_2, add(const_2, const_3)))), add(multiply(mult...
add(const_2,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#1,const_2)|multiply(#2,const_100)|multiply(#2,const_4)|subtract(#3,#0)|multiply(#4,#6)|multiply(#3,#4)|multiply(#5,#4)|add(#8,#9)|divide(#7,#10)|multiply(#11,#9)
gain
if difference between compound interest and simple interest on a sum at 5 % p . a . for 2 years is rs . 60 , then what is the sum ?
"c . i - s . i = 60 si = ( x * 2 * 5 ) / 100 = x / 10 ci = { x * ( 1 + 5 / 100 ) ^ 2 - x } = 41 x / 400 ci - si = 41 x / 400 - x / 10 = 60 x = 24000 answer : e"
a ) rs . 8000 , b ) rs . 4000 , c ) rs . 5000 , d ) rs . 6000 , e ) rs . 24000
e
divide(60, multiply(divide(5, const_100), divide(5, const_100)))
divide(n0,const_100)|multiply(#0,#0)|divide(n2,#1)|
gain
a larger cube has 343 cubic inch as a volume and in the cube there are 343 smaller cubes such that their volume is 1 cubic inch . what is the difference between the surface areas ’ sum of the 343 smaller cubes and the surface area of the larger cube , in square inch ?
"volume of larger cube = 343 = 7 ^ 3 side of larger cube = 7 volume of smaller cube = 1 - - > side of smaller cube = 1 surface area of larger cube = 6 * 7 ^ 2 = 294 surface area of 27 smaller cubes = 343 * 6 * 1 = 2058 difference = 2058 - 294 = 1764 answer : e"
a ) 54 , b ) 64 , c ) 81 , d ) 108 , e ) 1764
e
subtract(multiply(surface_cube(cube_edge_by_volume(1)), 343), surface_cube(cube_edge_by_volume(343)))
cube_edge_by_volume(n2)|cube_edge_by_volume(n0)|surface_cube(#0)|surface_cube(#1)|multiply(n0,#2)|subtract(#4,#3)|
geometry
salesperson a ' s compensation for any week is $ 360 plus 6 percent of the portion of a ' s total sales above $ 1000 for that week . salesperson b ' s compensation for any week is 10 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
sometime , setting up an equation is an easy way to go with : 360 + 0.06 ( x - 1000 ) = 0.1 x x = 15,000 ans : e
a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,00 , d ) $ 4,500 , e ) $ 15,000
e
divide(multiply(divide(subtract(360, multiply(divide(6, const_100), 1000)), subtract(divide(10, const_100), divide(6, const_100))), const_2), const_1000)
divide(n1,const_100)|divide(n3,const_100)|multiply(n2,#0)|subtract(#1,#0)|subtract(n0,#2)|divide(#4,#3)|multiply(#5,const_2)|divide(#6,const_1000)
general
if 1 / 2 of the air in a tank is removed with each stroke of a vacuum pump , what fraction of the original amount of air has been removed after 3 strokes ?
"left after 1 st stroke = 1 / 2 left after 2 nd stroke = 1 / 2 * 1 / 2 = 1 / 4 left after 3 rd stroke = 1 / 2 * 1 / 4 = 1 / 8 so removed = 1 - 1 / 8 = 7 / 8 = b"
a ) 15 / 16 , b ) 7 / 8 , c ) 1 / 4 , d ) 1 / 8 , e ) 1 / 16
b
add(add(add(add(divide(1, 2), divide(divide(1, 2), 2)), divide(divide(divide(1, 2), 2), 2)), divide(divide(divide(divide(1, 2), 2), 2), 2)), divide(divide(divide(divide(divide(1, 2), 2), 2), 2), 2))
divide(n0,n1)|divide(#0,n1)|add(#0,#1)|divide(#1,n1)|add(#2,#3)|divide(#3,n1)|add(#4,#5)|divide(#5,n1)|add(#6,#7)|
physics
if it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 300 responses are needed , what is the minimum number of questionnaires that should be mailed ?
"minimum no of mail to be sent for getting 300 responses at 60 % = 300 / 0.6 = 500 option d"
a ) 400 , b ) 420 , c ) 480 , d ) 500 , e ) 600
d
divide(300, divide(60, const_100))
divide(n0,const_100)|divide(n1,#0)|
gain
a person crosses a 1000 m long street in 10 minutes . what is his speed in km per hour ?
"distance = 1000 meter time = 10 minutes = 10 x 60 seconds = 600 seconds speed = distance / time = 1000 / 600 = 1.67 m / s = 1.67 ã — 18 / 5 km / hr = 6.0 km / hr answer : d"
a ) 7.1 , b ) 8.2 , c ) 4.6 , d ) 6.0 , e ) 12.8
d
divide(divide(1000, const_1000), divide(multiply(10, const_60), const_3600))
divide(n0,const_1000)|multiply(n1,const_60)|divide(#1,const_3600)|divide(#0,#2)|
physics
how long does a train 110 m long travelling at 60 kmph takes to cross a bridge of 170 m in length ?
"d 16.8 sec d = 110 + 170 = 280 m s = 60 * 5 / 18 = 50 / 3 t = 280 * 3 / 50 = 16.8 sec"
a ) 15.8 sec , b ) 14.9 sec , c ) 12.4 sec , d ) 16.8 sec , e ) 11.8 sec
d
divide(add(110, 170), multiply(60, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
physics
two trains from opposite directions are to cross each other . the length of two trains are 100 meter and 200 meter respectively . the speed of first train is 100 km / hour and second train 200 km / hour . in how much time will they cross each other ?
the crossing moment starts when the head of first compartment of two trains meet or touch . the process of crossing each other continues till 100 + 200 meter = 300 meter is covered . the speed will be 100 km / hour + 200 km / hour = 300 km / hour . 300 x 1000 meter covered in 3600 seconds . so , 300 meter covered in 3....
a ) 2 second , b ) 3.6 second , c ) 5 second , d ) 5.5 second , e ) 6 second
b
divide(add(100, 200), divide(multiply(add(100, 200), const_1000), const_3600))
add(n0,n1)|multiply(#0,const_1000)|divide(#1,const_3600)|divide(#0,#2)
physics
let n be the greatest number that will divide 1305 , 4665 and 6905 , leaving the same remainder in each case . then sum of the digits in n is :
"explanation : n = h . c . f . of ( 4665 - 1305 ) , ( 6905 - 4665 ) and ( 6905 - 1305 ) = h . c . f . of 3360 , 2240 and 5600 = 1120 . sum of digits in n = ( 1 + 1 + 2 + 0 ) = 4 answer is a"
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 10
a
add(add(const_1, const_1), const_2)
add(const_1,const_1)|add(#0,const_2)|
general
in a garden , there are 10 rows and 12 columns of mango trees . the distance between the two trees is 2 metres and a distance of five metre is left from all sides of the boundary of the garden . what is the length of the garden ?
between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 5 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 5 + 5 = 32 meter answer is a .
a ) 32 , b ) 24 , c ) 26 , d ) 28 , e ) 30
a
add(add(multiply(subtract(12, const_1), 2), divide(10, 2)), divide(10, 2))
divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)
physics
15.06 * 0.000001 = ?
"explanation : clearly after decimal 8 digits should be there . option d"
a ) 15060000 , b ) 0.001506 , c ) 0.01506 , d ) 1.506 e - 05 , e ) none of these
d
multiply(divide(15.06, 0.000001), const_100)
divide(n0,n1)|multiply(#0,const_100)|
general
darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the ...
"the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 2 x = 23.5 minutes answer : e"
a ) 10.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 23.5
e
subtract(subtract(divide(const_60, const_2), 2), divide(const_60, divide(20, 1.5)))
divide(const_60,const_2)|divide(n2,n0)|divide(const_60,#1)|subtract(#0,n3)|subtract(#3,#2)|
physics
a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 12 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
"since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 12 r / 3...
a ) 24 , b ) 28 , c ) 32 , d ) 36 , e ) 40
d
divide(multiply(subtract(1, divide(1, 4)), 12), subtract(1, subtract(1, divide(1, 4))))
divide(n0,n1)|subtract(n0,#0)|multiply(#1,n2)|subtract(n0,#1)|divide(#2,#3)|
general
a certain company expects quarterly earnings of $ 0.80 per share of stock , half of which will be distributed as dividends to shareholders while the rest will be used for research and development . if earnings are greater than expected , shareholders will receive an additional $ 0.04 per share for each additional $ 0.1...
"eps actual > eps expected . each gets and additional . 12 per share . thus . 52 * 300 - - > $ 156 answer is c"
a ) $ 92 , b ) $ 96 , c ) $ 156 , d ) $ 120 , e ) $ 240
c
multiply(add(divide(0.80, const_2), multiply(multiply(subtract(1.10, 0.80), const_10), 0.04)), 300)
divide(n0,const_2)|subtract(n3,n0)|multiply(#1,const_10)|multiply(n1,#2)|add(#0,#3)|multiply(n4,#4)|
general
can you find the smallest non fractional number such that if the number gets divided by 6 , we get the remainder of 1 ; if the number gets divided by 7 , we get the remainder of 2 if the number gets divided by 8 , we get the remainder of 3 ; if the number gets divided by 9 , we get the remainder of 4 .
a . 1006 as we know lcm of the numbers 6 7 8 & 9 is 1008 so if i divide 1008 by any of the four number , it gives remainder as 0 . now to get reminder as desired , is should be 2 short of 1006 . ( 3 - 1,4 - 2,5 - 3,6 - 4 ) ans : option a
a ) 1006 , b ) 1230 , c ) 1010 , d ) 1200 , e ) 1300
a
power(subtract(6, 1), const_4)
subtract(n0,n1)|power(#0,const_4)
general
which is less than 3 ?
"0.3 less than 3 . answer : b"
a ) 3 , b ) 0.3 , c ) 33 , d ) 3 / 1 , e ) 13
b
divide(divide(divide(divide(divide(divide(3, const_4), const_3), const_4), const_3), const_2), const_2)
divide(n0,const_4)|divide(#0,const_3)|divide(#1,const_4)|divide(#2,const_3)|divide(#3,const_2)|divide(#4,const_2)|
general
the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
"let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 smaller number = 270 . answer e"
a ) 240 , b ) 270 , c ) 295 , d ) 360 , e ) 269
e
divide(add(1360, 15), subtract(6, const_1))
add(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|
general
the average of 10 numbers is 23 . if each number is increased by 2 , what will the new average be ?
"sum of the 10 numbers = 230 if each number is increased by 2 , the total increase = 2 * 10 = 20 the new sum = 230 + 20 = 250 the new average = 250 / 10 = 25 . answer : b"
a ) 36 , b ) 25 , c ) 72 , d ) 29 , e ) 22
b
multiply(23, 2)
multiply(n1,n2)|
general
on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orang...
"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is ...
a ) $ 0.15 , b ) $ 0.20 , c ) $ 0.33 , d ) $ 0.40 , e ) $ 0.45
c
divide(multiply(add(const_1, const_1), 0.50), add(const_1, const_2))
add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)|
general
a polling company surveyed a certain country , and it found that 35 % of that country ’ s registered voters had an unfavorable impression of both of that state ’ s major political parties and that 20 % had a favorable impression only of party t . if one registered voter has a favorable impression of both parties for ev...
"s = 100 not ( t and b ) = 35 only t = 20 ( t and b ) / b = 1 / 2 let ( t and b ) = x only b = 2 x so now , 20 + 35 + x + 2 x = 100 x = 15 a ans"
a ) 15 , b ) 20 , c ) 30 , d ) 35 , e ) 45
a
divide(subtract(const_100, add(35, 20)), const_3)
add(n0,n1)|subtract(const_100,#0)|divide(#1,const_3)|
gain
rs . 1500 is divided into two parts such that if one part is invested at 6 % and the other at 5 % the whole annual interest from both the sum is rs . 85 . how much was lent at 5 % ?
"( x * 5 * 1 ) / 100 + [ ( 1500 - x ) * 6 * 1 ] / 100 = 85 5 x / 100 + 90 – 6 x / 100 = 85 x / 100 = 5 = > x = 500 answer : d"
a ) 399 , b ) 700 , c ) 288 , d ) 500 , e ) 211
d
multiply(add(5, 6), const_100)
add(n1,n2)|multiply(#0,const_100)|
gain
excluding stoppages , the speed of a train is 30 kmph and including stoppages it is 21 kmph . of how many minutes does the train stop per hour ?
"t = 9 / 30 * 60 = 18 answer : e"
a ) 16 , b ) 17 , c ) 12 , d ) 15 , e ) 18
e
subtract(const_60, multiply(const_60, divide(21, 30)))
divide(n1,n0)|multiply(#0,const_60)|subtract(const_60,#1)|
physics
a man took loan from a bank at the rate of 5 % p . a . s . i . after 13 years he had to pay rs . 1300 interest only for the period . the principal amount borrowed by him was ?
"principal = ( 100 * 1300 ) / ( 5 * 13 ) = rs . 2000 answer : d"
a ) 1750 , b ) 4000 , c ) 3500 , d ) 2000 , e ) 1000
d
divide(divide(multiply(1300, const_100), 13), 5)
multiply(n2,const_100)|divide(#0,n1)|divide(#1,n0)|
gain
in a games hour 4 different types of players came to the ground ? cricket 15 , hokey 12 , football 13 , softball 15 . how many players are present in the ground ?
"total number of players = 15 + 12 + 13 + 15 = 55 answer is c"
a ) 70 , b ) 52 , c ) 55 , d ) 49 , e ) 50
c
add(add(15, 12), add(13, 15))
add(n1,n2)|add(n3,n4)|add(#0,#1)|
physics
if 2 / z = 2 / ( z + 1 ) + 2 / ( z + 25 ) which of these integers could be the value of z ?
solving for z algebraically in this problem would not be easy . instead , we can follow the hint in the question ( “ which of these integers … ” ) and test each answer choice : a . 2 / 0 = 2 / 1 + 2 / 25 incorrect ( division by zero ) b . 2 / 1 = 2 / 2 + 2 / 26 incorrect c . 2 / 2 = 2 / 3 + 2 / 27 incorrect d . 2 / 3 =...
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 5
e
divide(25, add(add(2, 2), 1))
add(n0,n0)|add(n2,#0)|divide(n4,#1)
general
the average student age of a certain class which has 45 students is 14 . if one student aged 15 go to another class and the age of the class teacher is included the average changes to 14.66 . what is the age of class teacher ?
sum of ages of class before replacement = 45 x 14 = 630 sum of ages of class without teacher = 630 - 15 = 615 sum of ages of class after replacement = 45 x 14.66 = 660 age of teacher = 660 - 615 = 45 answer : e
a ) 30 , b ) 35 , c ) 38 , d ) 40 , e ) 45
e
subtract(multiply(45, 14.66), subtract(multiply(45, 14), 15))
multiply(n0,n3)|multiply(n0,n1)|subtract(#1,n2)|subtract(#0,#2)
general
41 % of 801 – 150.17 = ? – 57 % of 910
"explanation : 328 – 150 = 178 x – 519 = 178 x = 697 answer : option b"
a ) 797 , b ) 697 , c ) 687 , d ) 699 , e ) 799
b
divide(multiply(41, 801), 150.17)
multiply(n0,n1)|divide(#0,n2)|
gain
the area of a square garden is q square feet and the perimeter is p feet . if q = 2 p + 33 , what is the perimeter of the garden in feet ?
"let x be the length of one side of the square garden . x ^ 2 = 8 x + 33 x ^ 2 - 8 x - 33 = 0 ( x - 11 ) ( x + 3 ) = 0 x = 11 , - 3 p = 4 ( 11 ) = 44 the answer is e ."
a ) 28 , b ) 32 , c ) 36 , d ) 40 , e ) 44
e
multiply(2, 33)
multiply(n1,n0)|
geometry
the mean of 50 observations was 41 . it was found later that an observation 48 was wrongly taken as 23 . the corrected new mean is
"sol . therefore correct sum = ( 41 × 50 + 48 – 23 ) = 2075 . therefore correct mean = 2075 / 50 = 41.5 . answer d"
a ) 35.2 , b ) 36.1 , c ) 36.5 , d ) 41.5 , e ) none
d
divide(add(multiply(41, 50), subtract(subtract(50, const_2), 23)), 50)
multiply(n0,n1)|subtract(n0,const_2)|subtract(#1,n3)|add(#0,#2)|divide(#3,n0)|
general
a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 3 . find his average after 17 th inning ?
"let the average after 7 th inning = x then average after 16 th inning = x - 3 16 ( x - 3 ) + 87 = 17 x x = 87 - 48 = 39 answer = b"
a ) 15 , b ) 88 , c ) 44 , d ) 54 , e ) 23
b
add(subtract(87, multiply(17, 3)), 3)
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
general
in what time will a train 300 meters long cross an electric pole , if its speed is 90 km / hr
"explanation : first convert speed into m / sec speed = 90 * ( 5 / 18 ) = 25 m / sec time = distance / speed = 300 / 25 = 12 seconds answer : b"
a ) 5 seconds , b ) 12 seconds , c ) 3 seconds , d ) 2.5 seconds , e ) none of these
b
divide(300, multiply(90, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
a present value of a machine is $ 1100 . its value depletion rate is 10 % per annum then find the machine value after 2 years ?
p = $ 1100 r = 10 % t = 2 years machine value after 2 years = p [ ( 1 - r / 100 ) ^ t ] = 1100 * 9 / 10 * 9 / 10 = $ 891 answer is b
a ) $ 900 , b ) $ 891 , c ) $ 915 , d ) $ 715 , e ) $ 795
b
multiply(1100, power(subtract(const_1, divide(10, const_100)), 2))
divide(n1,const_100)|subtract(const_1,#0)|power(#1,n2)|multiply(n0,#2)
gain
vanessa , mike and sarah have missed a total of 17 days of school this year . vanessa and mike have missed 14 days total , and mike and sarah have missed 12 days total . how many days of school did vanessa miss alone ?
vanessa + mike + sarah = 17 v + m = 14 m + s = 12 < < use this formula & plug into the original formula , to get vanessa ' s total v + ( m + s ) = 17 v + 12 = 17 subtract 12 from both sides v = 5 answer : c
a ) 9 , b ) 4 , c ) 5 , d ) 2 , e ) 3
c
subtract(17, 12)
subtract(n0,n2)
physics
sandy is younger than molly by 16 years . if the ratio of their ages is 7 : 9 , how old is sandy ?
"let sandy ' s age be 7 x and let molly ' s age be 9 x . 9 x - 7 x = 16 x = 8 sandy is 56 years old . the answer is c ."
a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
c
multiply(divide(7, subtract(9, 7)), 16)
subtract(n2,n1)|divide(n1,#0)|multiply(n0,#1)|
other
if both 7 ^ 2 and 3 ^ 3 are factors of the number a * 4 ^ 3 * 6 ^ 2 * 13 ^ 11 , then what is the smallest possible value of a ?
"the number a must include at least 3 * 7 ^ 2 = 147 the answer is b ."
a ) 99 , b ) 147 , c ) 363 , d ) 1200 , e ) 1625
b
add(add(add(add(add(multiply(multiply(7, 2), 2), multiply(multiply(7, 2), 2)), multiply(multiply(7, 2), 2)), 2), const_4), const_4)
multiply(n0,n7)|multiply(n1,#0)|add(#1,#1)|add(#2,#1)|add(n7,#3)|add(#4,const_4)|add(#5,const_4)|
other
in a village of 2,600 people , 800 people are over 70 years old and 850 people are female . it is known that 40 percent of the females are younger than 70 years old . if no one in the village is 70 years old , what is the probability that a person chosen at random is either a male or younger than 70 years old ?
the number of people younger than 70 years old is 2600 - 800 = 1800 the number of females older than 70 years old is 0.6 * 850 = 510 then the number of males older than 70 years old is 800 - 510 = 290 . the number of people who are either male or younger than 70 is 1800 + 290 = 2090 . p ( a person is younger than 70 or...
a ) 221 / 250 , b ) 199 / 250 , c ) 33 / 50 , d ) 8 / 25 , e ) 209 / 260
e
divide(subtract(multiply(const_26, divide(multiply(const_5, const_5), const_0_25)), multiply(850, subtract(const_1, divide(40, divide(multiply(const_5, const_5), const_0_25))))), multiply(const_26, divide(multiply(const_5, const_5), const_0_25)))
multiply(const_5,const_5)|divide(#0,const_0_25)|divide(n4,#1)|multiply(#1,const_26)|subtract(const_1,#2)|multiply(n3,#4)|subtract(#3,#5)|divide(#6,#3)
gain
a circle graph shows how the budget of a certain company was spent : 60 percent for salaries , 9 percent for research and development , 5 percent for utilities , 4 percent for equipment , 2 percent for supplies , and the remainder for transportation . if the area of each sector of the graph is proportional to the perce...
"the percent of the budget for transportation is 100 - ( 60 + 9 + 5 + 4 + 2 ) = 20 % 100 % of the circle is 360 degrees . then ( 20 % / 100 % ) * 360 = 72 degrees the answer is d ."
a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °
d
divide(multiply(const_360, subtract(const_100, add(add(add(add(60, 9), 5), 4), 2))), const_100)
add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|subtract(const_100,#3)|multiply(#4,const_360)|divide(#5,const_100)|
geometry
two trains 140 m and 160 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
"answer : option d relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 160 = 300 m . required time = 300 * 9 / 250 = 54 / 5 = 10.8 sec"
a ) 7 , b ) 8.2 , c ) 2 , d ) 10.8 , e ) 11.2
d
divide(add(140, 160), multiply(add(60, 40), const_0_2778))
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
physics
working alone , a can complete a certain kind of job in 6 hours . a and d , working together at their respective rates , can complete one of these jobs in 4 hours . in how many hours can d , working alone , complete one of these jobs ?
"let total time taken by d to complete the job = d total time taken by a to complete the job = 6 work done by a in an hour 1 / a = 1 / 6 working together a and d can complete the job in 4 hours 1 / a + 1 / d = 1 / 4 = > 1 / d = 1 / 4 - 1 / a = 1 / 4 - 1 / 6 = 1 / 12 = > d = 12 hours answer c"
a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
c
inverse(subtract(inverse(4), inverse(6)))
inverse(n1)|inverse(n0)|subtract(#0,#1)|inverse(#2)|
physics
ashok secured average of 70 marks in 6 subjects . if the average of marks in 5 subjects is 74 , how many marks did he secure in the 6 th subject ?
"explanation : number of subjects = 6 average of marks in 6 subjects = 70 therefore total marks in 6 subjects = 70 * 6 = 420 now , no . of subjects = 5 total marks in 5 subjects = 74 * 5 = 370 therefore marks in 6 th subject = 420 – 370 = 50 answer a"
a ) 50 , b ) 74 , c ) 78 , d ) 80 , e ) none of these
a
subtract(multiply(70, 6), multiply(74, 5))
multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|
general
population is 23000 . population increases by 10 % every year , then the population after 3 years is ?
"population after 1 st year = 23000 * 10 / 100 = 2300 = = = > 23000 + 2000 = 25300 population after 2 nd year = 25300 * 10 / 100 = 2530 = = = > 25300 + 2530 = 27830 population after 3 rd year = 27830 * 10 / 100 = 2783 = = = > 27830 + 2783 = 30613 answer : d"
a ) 26630 , b ) 26640 , c ) 36623 , d ) 30613 , e ) 26820
d
multiply(23000, add(const_1, divide(multiply(3, 10), const_100)))
multiply(n1,n2)|divide(#0,const_100)|add(#1,const_1)|multiply(n0,#2)|
gain
a train running at the speed of 72 km / hr crosses a pole in 9 seconds . find the length of the train ?
"speed = 72 * ( 5 / 18 ) m / sec = 20 m / sec length of train ( distance ) = speed * time ( 20 ) * 9 = 180 meter answer : e"
a ) 150 meter , b ) 299 meter , c ) 666 meter , d ) 155 meter , e ) 180 meter
e
multiply(divide(multiply(72, const_1000), const_3600), 9)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
two numbers are in the ratio of 5 : 7 . if 33 is subtracted from each number , they are in the ratio of 1 : 2 . what are the two numbers ?
"( 5 x - 33 ) : ( 7 x - 33 ) = 1 y : 2 y 5 x - 33 = y 7 x - 33 = 2 y 231 - 165 = 10 y - 7 y 66 = 3 y y = 22 5 x - 33 = 22 x = 11 the two numbers are 5 x and 7 x which are 55 and 77 . the answer is c ."
a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
c
subtract(multiply(multiply(subtract(multiply(2, const_4.0), multiply(1, 33)), const_2.0), divide(7, 5)), multiply(subtract(multiply(2, 33), multiply(1, 33)), 5))
divide(const_3.0,n0)|multiply(const_4.0,n4)|multiply(n2,n3)|subtract(#1,#2)|multiply(n0,#3)|multiply(#0,#4)|subtract(#5,#4)|
other
x and y are positive integers . when x is divided by 12 , the remainder is 5 , and when x is divided by 13 , the remainder is 3 . when y is divided by 14 , the remainder is 5 , and when y is divided by 7 , the remainder is 5 . what is the least possible value of x + y ?
"when x is divided by 12 , the remainder is 5 : so , the possible values of x are : 5 , 17 , 29 , 41 , etc . when x is divided by 13 , the remainder is 3 : so , the possible values of x are : 3 , 16,29 . . . stop . since both lists include 29 , the smallest possible value of x is 29 . when y is divided by 14 , the rema...
a ) 24 , b ) 12 , c ) 64 , d ) 48 , e ) 25
d
subtract(add(multiply(14, const_2), 5), add(5, 12))
add(n0,n1)|multiply(n4,const_2)|add(n5,#1)|subtract(#2,#0)|
general
a train running at the speed of 180 km / hr crosses a pole in 7 seconds . what is the length of the train ?
"speed = ( 180 * 5 / 18 ) m / sec = ( 50 ) m / sec length of the train = ( speed x time ) = ( 50 * 7 ) m = 350 m . answer : e"
a ) 530 , b ) 305 , c ) 503 , d ) 430 , e ) 350
e
multiply(divide(multiply(180, const_1000), const_3600), 7)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 432 sq m , then what is the breadth of the rectangular plot ?
"let the breadth of the plot be b m . length of the plot = 3 b m ( 3 b ) ( b ) = 432 3 b 2 = 432 b 2 = 144 b = 12 m . answer : option a"
a ) 12 , b ) 17 , c ) 18 , d ) 19 , e ) 14
a
sqrt(divide(432, const_3))
divide(n0,const_3)|sqrt(#0)|
geometry
one side of a rectangle is 3 cm shorter than the other side . if we increase the length of each side by 1 cm , then the area of the rectangle will increase by 16 cm 2 . find the lengths of all sides .
"let x be the length of the longer side x > 3 , then the other side ' s length is x − 3 cm . then the area is s 1 = x ( x - 3 ) cm 2 . after we increase the lengths of the sides they will become ( x + 1 ) and ( x − 3 + 1 ) = ( x − 2 ) cm long . hence the area of the new rectangle will be a 2 = ( x + 1 ) ⋅ ( x − 2 ) cm ...
a ) 10 and 3 , b ) 9 and 6 , c ) 10 and 7 , d ) 3 and 10 , e ) 10 and 10
b
subtract(add(divide(16, 2), 1), 3)
divide(n2,n3)|add(#0,n1)|subtract(#1,n0)|
geometry
the difference between simple interest and compound interest on rs . 1200 for one year at 10 % per annum reckoned half - yearly is :
s . i = ( 1000 * 10 * 4 ) / 100 = rs . 400 c . i = 1200 * 1 + 5 / 100 ) 2 – 1200 = 123 . difference = rs . ( 123 - 120 ) = rs . 3 answer : b
a ) rs . 2.50 , b ) rs . 3 , c ) rs . 3.75 , d ) rs . 4 , e ) rs . 5
b
subtract(subtract(multiply(power(add(divide(divide(10, const_2), const_100), const_1), const_2), 1200), 1200), divide(multiply(1200, 10), const_100))
divide(n1,const_2)|multiply(n0,n1)|divide(#0,const_100)|divide(#1,const_100)|add(#2,const_1)|power(#4,const_2)|multiply(n0,#5)|subtract(#6,n0)|subtract(#7,#3)
gain
a rectangular tank needs to be coated with insulation . the tank has dimensions of 3 feet , 6 feet , and 2 feet . each square foot of insulation costs $ 20 . how much will it cost to cover the surface of the tank with insulation ?
the total surface area is 2 ( 2 * 3 + 3 * 6 + 2 * 6 ) = 72 square feet the total cost is 72 * $ 20 = $ 1440 the answer is d .
['a ) $ 980', 'b ) $ 1060', 'c ) $ 1220', 'd ) $ 1440', 'e ) $ 1650']
d
multiply(surface_rectangular_prism(3, 6, 2), 20)
surface_rectangular_prism(n0,n1,n2)|multiply(n3,#0)
geometry
if a trader sold two cars each at rs . 325475 and gains 13 % on the first and loses 13 % on the second , then his profit or loss percent on the whole is ?
"sp of each car is rs . 325475 , he gains 13 % on first car and losses 13 % on second car . in this case , there will be loss and percentage of loss is given by = [ ( profit % ) ( loss % ) ] / 100 = ( 13 ) ( 13 ) / 100 % = 1.69 % answer : a"
a ) 1.69 % , b ) 1.74 % , c ) 1.84 % , d ) 1.47 % , e ) 1.24 %
a
divide(multiply(13, 13), const_100)
multiply(n1,n1)|divide(#0,const_100)|
gain
p , q and r have rs . 5000 among themselves . r has two - thirds of the total amount with p and q . find the amount with r ?
"let the amount with r be rs . r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 5000 - r ) = > 3 r = 10000 - 2 r = > 5 r = 10000 = > r = 2000 . answer : c"
a ) rs . 3000 , b ) rs . 3600 , c ) rs . 2000 , d ) rs . 4000 , e ) none of these
c
multiply(divide(5000, add(const_1, divide(const_2, const_3))), divide(const_2, const_3))
divide(const_2,const_3)|add(#0,const_1)|divide(n0,#1)|multiply(#2,#0)|
general
a cab driver 5 days income was $ 250 , $ 400 , $ 750 , $ 400 , $ 500 . then his average income is ?
"avg = sum of observations / number of observations avg income = ( 250 + 400 + 750 + 400 + 500 ) / 5 = 460 answer is c"
a ) $ 440 , b ) $ 450 , c ) $ 460 , d ) $ 470 , e ) $ 480
c
divide(add(add(add(add(250, 400), 750), 400), 500), 5)
add(n1,n2)|add(n3,#0)|add(n4,#1)|add(n5,#2)|divide(#3,n0)|
general
1903 x 1903 = ?
"1903 x 1903 = ( 1903 ) 2 = ( 1900 + 3 ) 2 = ( 1900 ) 2 + ( 3 ) 2 + ( 2 x 1900 x 3 ) = 3610000 + 9 + 11400 . = 3621409 . d )"
a ) a ) 3623216 , b ) b ) 3624216 , c ) c ) 3624316 , d ) d ) 3621409 , e ) e ) 3625216
d
multiply(divide(1903, 1903), const_100)
divide(n0,n1)|multiply(#0,const_100)|
general
a man , a woman and a boy can together complete a piece of work in 3 days . if a man alone can do it in 6 days and a boy alone in 9 days , how long will a woman take to complete the work ?
explanation : ( 1 man + 1 woman + 1 boy ) ’ s 1 day ’ s work = 1 / 3 1 man ’ s 1 day work = 1 / 6 1 boy ’ s 1 day ’ s work = 1 / 9 ( 1 man + 1 boy ) ‘ s 1 day ’ s work = 1 / 6 + 1 / 9 = 5 / 18 therefore , 1 woman ’ s 1 day ’ s work = 1 / 3 – 5 / 18 = 1 / 18 therefore , the woman alone can finish the work in 18 days . a...
a ) 12 days , b ) 15 days , c ) 16 days , d ) 24 days , e ) 18 days
e
inverse(subtract(inverse(3), add(inverse(6), inverse(9))))
inverse(n0)|inverse(n1)|inverse(n2)|add(#1,#2)|subtract(#0,#3)|inverse(#4)
physics
a grocer has a sale of rs . 6435 , rs . 6927 , rs . 6855 , rs . 7230 and rs . 6562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6700 ?
"total fr 5 mnths = ( 6435 + 6927 + 6855 + 7230 + 6562 ) = rs 34009 . reqd . sale = rs . [ ( 6700 * 6 ) - 34009 ] = rs . ( 40200 - 34009 ) = rs . 6191 . answer : d"
a ) s . 4991 , b ) s . 5991 , c ) s . 6001 , d ) s . 6191 , e ) s . 7991
d
subtract(multiply(add(5, const_1), 6700), add(add(add(add(6435, 6927), 6855), 7230), 6562))
add(n5,const_1)|add(n0,n1)|add(n2,#1)|multiply(n6,#0)|add(n3,#2)|add(n4,#4)|subtract(#3,#5)|
general
find the cube root of 804357 ?
"unit digit of the answer is 3 . ( cube of 3 = 27 ) . now omit 357 and find after which cube 804 lies . it is 729 . so our tenth place is 9 . answer = c"
a ) 22 , b ) 88 , c ) 93 , d ) 19 , e ) 18
c
circle_area(804357)
circle_area(n0)|
geometry
if p and q are prime numbers , how many divisors does the product p ^ 3 * q ^ 7 have ?
"when a number n = a ^ x * b ^ y , where a and b are prime numbers , and x , y are positive integers , the number of divisors of n = ( x + 1 ) ( y + 1 ) therefore , the answer is c . 4 * 8 = 32"
a ) 25 , b ) 30 , c ) 32 , d ) 35 , e ) 40
c
multiply(add(3, const_1), add(7, const_1))
add(n0,const_1)|add(n1,const_1)|multiply(#0,#1)|
general
a person spends 40 % of his salary on food , 25 % on house rent , 15 % on entertainment and 15 % on conveyance . if his savings at the end of the month is rs . 1200 , then his salary per month in rupees is :
"total expenditure = 40 + 25 + 15 + 15 = 95 % saving = ( 100 - 95 ) = 5 % 5 / 100 × salary = 1200 , salary = 24000 rs . answer : b"
a ) 4000 , b ) 24000 , c ) 8000 , d ) 10000 , e ) none of these
b
divide(multiply(1200, const_100), 15)
multiply(n4,const_100)|divide(#0,n3)|
gain
a train , 135 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
"explanation : assume the length of the bridge = x meter total distance covered = 135 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 135 + x ) / 30 m / s = > 45 ã — ( 10 / 36 ) = ( 135 + x ) / 30 = > 45 ã — 10 ã — 30 / 36 = 135 + x = > 45 ã — 10 ã — 10 / 12 = 135 + x = > 15 ã — ...
a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
e
subtract(multiply(multiply(45, const_0_2778), 30), 135)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
find the ratio between 1 hr 30 minutes and 2 hrs 40 minutes .
solution : the ratio = 1 hr 30 min : 2 hr 40 min . 90 min : 160 min = 9 : 16 . answer is a
a ) 9 : 16 , b ) 5 : 9 , c ) 12 : 17 , d ) 13 : 24 , e ) none of these
a
divide(add(multiply(1, const_60), 30), add(multiply(2, const_60), 40))
multiply(n0,const_60)|multiply(n2,const_60)|add(n1,#0)|add(n3,#1)|divide(#2,#3)
other
a batsman makes a score of 87 runs in the 17 th inning and thus increases his averages by 3 . what is his average after 17 th inning ?
"explanation : let the average after 17 innings = x total runs scored in 17 innings = 17 x average after 16 innings = ( x - 3 ) total runs scored in 16 innings = 16 ( x - 3 ) total runs scored in 16 innings + 87 = total runs scored in 17 innings = > 16 ( x - 3 ) + 87 = 17 x = > 16 x - 48 + 87 = 17 x = > x = 39 answer :...
a ) 39 , b ) 35 , c ) 42 , d ) 40.5 , e ) 41
a
add(subtract(87, multiply(17, 3)), 3)
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
general
mrs . evans gave a test to her freshmen economics class , which has 40 students enrolled and 30 of them answered question 1 correctly . if 29 answered question 2 correctly and 10 did not take the test then how many answered both questions correctly ?
"total number of enrolled students = 40 number of students who did not take test = 10 hence , number of students who took test = 40 - 10 = 30 number of students who answered q 2 correctly = 29 , therefore , all students who took test answered q 2 correctly . so , number of students who answered q 1 correctly , also ans...
a ) 24 , b ) 27 , c ) 29 , d ) 31 , e ) 33
c
subtract(add(add(30, 29), 10), 40)
add(n1,n3)|add(n5,#0)|subtract(#1,n0)|
other
nina has exactly enough money to purchase 5 widgets . if the cost of each widget were reduced by $ 1.25 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
"a its is . let price = x ( x - 1.25 ) 8 = 5 x x = 10 / 3 hence total money = 5 * 10 / 3 = 16.7"
a ) $ 16.7 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
a
multiply(divide(multiply(1.25, 8), subtract(8, 5)), 5)
multiply(n1,n2)|subtract(n2,n0)|divide(#0,#1)|multiply(n0,#2)|
general
if the sales tax reduced from 3 1 / 2 % to 3 1 / 3 % , then what difference does it make to a person who purchases an article with market price of rs . 9000 ?
"required difference = [ 3 ½ % of rs . 9000 ] – [ 3 1 / 3 % of rs . 9000 ] = [ ( 7 / 20 - ( 10 / 3 ) ] % of rs . 9000 = 1 / 6 % of rs . 9000 = rs . [ ( 1 / 6 ) 8 ( 1 / 100 ) * 9000 ] = rs . 15 . answer is c ."
a ) 11 , b ) 13 , c ) 15 , d ) 18 , e ) 10
c
divide(multiply(subtract(add(divide(1, 2), 3), add(divide(1, 3), 3)), 9000), const_100)
divide(n1,n2)|divide(n1,n0)|add(n0,#0)|add(n0,#1)|subtract(#2,#3)|multiply(n6,#4)|divide(#5,const_100)|
general
in a kilometer race , a beats b by 40 meters or 15 seconds . what time does a take to complete the race ?
"time taken by b run 1000 meters = ( 1000 * 15 ) / 50 = 300 sec . time taken by a = 300 - 15 = 285 sec . answer : b"
a ) 277 sec , b ) 285 sec , c ) 267 sec , d ) 167 sec , e ) 276 sec
b
subtract(divide(multiply(const_1, const_1000), divide(40, 15)), 15)
divide(n0,n1)|multiply(const_1,const_1000)|divide(#1,#0)|subtract(#2,n1)|
physics
a reduction of 40 % in the price of bananas would enable a man to obtain 67 more for rs . 40 , what is reduced price per dozen ?
"40 * ( 40 / 100 ) = 16 - - - 67 ? - - - 12 = > rs . 2.86 answer : b"
a ) 1.86 , b ) 2.86 , c ) 4.86 , d ) 3.86 , e ) 5.86
b
multiply(const_12, divide(multiply(40, divide(40, const_100)), 67))
divide(n0,const_100)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_12)|
gain
a waitress ' s income consists of her salary and tips . during one week , her tips were 7 / 4 of her salary . what fraction of her income for the week came from tips ?
"her tips were 7 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 7 / 4 ) ( $ 4 ) = $ 7 so , her total income = $ 4 + $ 7 = $ 11 what fraction of her income for the week came from tips $ 7 / $ 11 = 7 / 11 = e"
a ) 1 / 9 , b ) 1 / 6 , c ) 2 / 3 , d ) 4 / 9 , e ) 7 / 11
e
divide(7, add(7, 4))
add(n0,n1)|divide(n0,#0)|
general
if one cat eats 1.5 rats in 1.5 days , then in howmany days 3 cats will eat 3 rats ? ?
1 cat - - - - - - 3 / 2 rat - - - - - - - - - 3 / 2 days 1 cat - - - - - - ( 3 / 2 ) * 2 rat - - - - - ( 3 / 2 ) * 2 days ( rat doubled , days doubled ) 1 * 3 cat - - - - - 3 rat - - - - - - - - - - - 3 / 3 = 1 day ( cat * 3 , same rat , days / 3 ) answer : a
a ) 1 day , b ) 2 days , c ) 3 days , d ) 4 days , e ) 5 days
a
divide(multiply(divide(1.5, 1.5), 3), 3)
divide(n0,n0)|multiply(n2,#0)|divide(#1,n2)
physics
the distance between two cities a and b is 465 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
"explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 465 therefore , 60 x + 75 ( x - 1 ) = 465 = > x = 3 . so , they meet at ( 8 + 4 ) i . e , 12 noon answer : c )"
a ) 09 , b ) 07 , c ) 12 , d ) 05 , e ) 03
c
add(divide(add(465, 75), add(60, 75)), 8)
add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)|
physics
a train 100 m long crosses a platform 125 m long in 10 sec ; find the speed of the train ?
"d = 100 + 125 = 225 t = 10 s = 225 / 10 * 18 / 5 = 81 kmph answer : a"
a ) 81 , b ) 77 , c ) 54 , d ) 33 , e ) 99
a
subtract(multiply(10, multiply(125, const_0_2778)), 100)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
calculate the largest 3 digit number which is exactly divisible by 89 ?
"largest 4 digit number is 999 after doing 999 ÷ 89 we get remainder 20 hence largest 3 digit number exactly divisible by 89 = 999 - 20 = 979 c"
a ) 911 , b ) 969 , c ) 979 , d ) 977 , e ) 971
c
multiply(add(const_100, const_2), 89)
add(const_100,const_2)|multiply(n1,#0)|
general
on dividing 83 by a number , the quotient is 9 and the remainder is 2 . find the divisor ?
"d = ( d - r ) / q = ( 83 - 2 ) / 9 = 81 / 9 = 9 c )"
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
c
floor(divide(83, 9))
divide(n0,n1)|floor(#0)|
general
albert invested rs . 1000 in a scheme for 3 years at compound interest rate 10 % p . a . how much amount will albert get on maturity of the fixed deposit ?
"amount = [ 1000 * ( 1 + 10 / 100 ) 3 ] = 1000 * 11 / 10 * 11 / 10 * 11 / 10 = rs . 1331 answer : d"
a ) s . 1300 , b ) s . 1005 , c ) s . 1031 , d ) s 1331 , e ) s . 1120
d
multiply(1000, power(add(const_1, divide(10, const_100)), 3))
divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|
gain
if a ' s height is 35 % less than that of b , how much percent b ' s height is more than that of a ?
"excess of b ' s height over a ' s = [ ( 35 / ( 100 - 35 ) ] x 100 % = 53.84 % answer : c )"
a ) 66.66 % , b ) 66.68 % , c ) 53.84 % , d ) 86.66 % , e ) 66.65 %
c
multiply(divide(35, subtract(const_100, 35)), const_100)
subtract(const_100,n0)|divide(n0,#0)|multiply(#1,const_100)|
general
what is 5 / 8 as a percent
"5 / 8 as a percent = ( 5 / 8 ) x 100 = 0.625 x 100 = 62.5 % answer : a i . e . 62.5 %"
a ) 62.5 % , b ) 63 % , c ) 63.5 % , d ) 64.5 % , e ) 65 %
a
divide(multiply(5, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)
add(const_2,const_3)|add(const_3,const_4)|add(const_3,const_3)|multiply(const_3,const_4)|multiply(#0,const_2)|multiply(#3,const_100)|multiply(#1,#0)|multiply(#4,#5)|multiply(#6,#4)|add(#7,#8)|add(#9,#2)|multiply(n0,#10)|divide(#11,const_100)|
gain
a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 77.44 , the number of the member is the group is :
"money collected = ( 77.44 x 100 ) paise = 7744 paise . number of members = square root of 7744 = 88 . answer : option d"
a ) 57 , b ) 67 , c ) 77 , d ) 88 , e ) 97
d
sqrt(multiply(77.44, const_100))
multiply(n0,const_100)|sqrt(#0)|
general
a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is :
"since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
a ) 288 , b ) 278 , c ) 267 , d ) 285 , e ) 231
d
divide(add(multiply(add(const_4, const_1), 510), multiply(multiply(add(const_4, const_1), add(const_4, const_1)), 240)), 30)
add(const_1,const_4)|multiply(n0,#0)|multiply(#0,#0)|multiply(n1,#2)|add(#1,#3)|divide(#4,n2)|
general
some of the 50 % solution of acid was removed and this was replaced with an equal amount of 10 % solution of acid . as a result , a 20 % solution of acid was obtained . what fraction of the original solution was replaced ?
"let x be the fraction of the original solution that was replaced . 0.5 * ( 1 - x ) + 0.1 ( x ) = 0.2 0.4 x = 0.3 x = 3 / 4 the answer is c ."
a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 3 / 5 , e ) 4 / 5
c
divide(20, add(50, 10))
add(n0,n1)|divide(n2,#0)|
gain
in a park there are two ponds with both brown ducks and green ducks . in the smaller pond there are 30 ducks and in the larger pond there are 50 ducks . if 20 % of the ducks in the smaller pond are green and 12 % of the ducks in the larger pond are green , then what percentage of ducks are green ?
number of ducks in small pond = 30 green ducks in small pond = 20 % of 30 = 6 ducks number of ducks in large pond = 50 green ducks in large pond = 12 % of 50 = 6 ducks total number of ducks = 30 + 50 = 80 total number of green ducks = 6 + 6 = 12 ducks percentage of green ducks = 12 / 80 * 100 = 15 % answer : c
a ) 13 % , b ) 14 % , c ) 15 % , d ) 16 % , e ) 17 %
c
multiply(divide(add(multiply(30, divide(20, const_100)), multiply(50, divide(12, const_100))), add(30, 50)), const_100)
add(n0,n1)|divide(n2,const_100)|divide(n3,const_100)|multiply(n0,#1)|multiply(n1,#2)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)
gain
the h . c . f of two numbers is 17 and their l . c . m is 5134 . if one of the numbers is 289 , then the other is ?
"other number = ( 17 * 5134 ) / 289 = 302 . answer : a"
a ) 302 , b ) 304 , c ) 306 , d ) 308 , e ) 310
a
multiply(17, 289)
multiply(n0,n2)|
physics
a fruit drink is made of orange , watermelon , and grape juice , where 15 percent of the drink is orange juice and 60 percent is watermelon juice . if the drink is made with 35 ounces of grape juice , how many ounces is the drink total ?
"let the total number of ounces in the drink be x . % of orange = 15 % % of watermelon = 60 % % of grape = 100 % - 75 % = 25 % 0.25 x = 35 x = 140 therefore there are a total of 140 ounces in the drink . the answer is b ."
a ) 120 , b ) 140 , c ) 160 , d ) 180 , e ) 200
b
add(add(35, divide(multiply(35, 15), subtract(const_100, add(60, 15)))), divide(multiply(35, 60), subtract(const_100, add(60, 15))))
add(n0,n1)|multiply(n0,n2)|multiply(n1,n2)|subtract(const_100,#0)|divide(#1,#3)|divide(#2,#3)|add(n2,#4)|add(#6,#5)|
general
the dimensions of a room are 25 feet * 15 feet * 12 feet . what is the cost of white washing the four walls of the room at rs . 8 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each ?
area of the four walls = 2 h ( l + b ) since there are doors and windows , area of the walls = 2 * 12 ( 15 + 25 ) - ( 6 * 3 ) - 3 ( 4 * 3 ) = 906 sq . ft . total cost = 906 * 8 = rs . 7248 answer : c
['a ) s . 4529', 'b ) s . 4586', 'c ) s . 7248', 'd ) s . 4530', 'e ) s . 4528']
c
multiply(subtract(subtract(multiply(multiply(const_2, 12), add(15, 25)), multiply(6, const_3)), multiply(3, multiply(4, 3))), 8)
add(n0,n1)|multiply(n2,const_2)|multiply(n4,const_3)|multiply(n5,n6)|multiply(#0,#1)|multiply(n5,#3)|subtract(#4,#2)|subtract(#6,#5)|multiply(n3,#7)
geometry
a money lender finds that due to a fall in the annual rate of interest from 8 % to 7 3 / 4 % his yearly income diminishes by rs . 61.50 , his capital is ?
"let the capital be rs . x . then , ( x * 8 * 1 ) / 100 - ( x * 31 / 4 * 1 / 100 ) = 61.50 32 x - 31 x = 6150 * 4 x = 24,600 . answer : c"
a ) 24,607 , b ) 24,609 , c ) 24,600 , d ) 24,602 , e ) 24,604
c
divide(61.50, divide(const_4, 4))
divide(const_4,n3)|divide(n4,#0)|
gain
a 210 m long train running at the speed of 120 km / hr crosses another train running in opposite direction at the speed of 80 km / hr in 9 sec . what is the length of the other train ?
"relative speed = 120 + 80 = 200 km / hr . = 200 * 5 / 18 = 500 / 9 m / sec . let the length of the other train be x m . then , ( x + 210 ) / 9 = 500 / 9 = > x = 290 . answer : option a"
a ) 290 , b ) 280 , c ) 270 , d ) 260 , e ) 250
a
subtract(multiply(multiply(add(120, 80), const_0_2778), 9), 210)
add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)|
physics
walking with 4 / 5 of my usual speed , i miss the bus by 6 minutes . what is my usual time ?
"speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 5 1 - - - - - - - - 6 4 - - - - - - - - - ? è 24 answer : d"
a ) 16 min , b ) 26 min , c ) 34 min , d ) 24 min , e ) 12 min
d
multiply(divide(6, divide(5, 4)), 5)
divide(n1,n0)|divide(n2,#0)|multiply(n1,#1)|
physics
the age of father 8 years ago was thrice the age of his son . 5 years hence , father ' s age will be twice that of his son . the ratio of their present ages is :
let the ages of father and son 8 years ago be 3 x and x years respectively . then , ( 3 x + 8 ) + 5 = 2 [ ( x + 8 ) + 5 ] 3 x + 13 = 2 x + 26 x = 13 . required ratio = ( 3 x + 8 ) : ( x + 8 ) = 47 : 21 . answer : option d
a ) 47 : 11 , b ) 37 : 21 , c ) 27 : 21 , d ) 47 : 21 , e ) 47 : 31
d
divide(add(multiply(subtract(multiply(const_2, add(8, 5)), add(8, 5)), const_3), 8), add(subtract(multiply(const_2, add(8, 5)), add(8, 5)), 8))
add(n0,n1)|multiply(#0,const_2)|subtract(#1,#0)|add(n0,#2)|multiply(#2,const_3)|add(n0,#4)|divide(#5,#3)
general
if the average ( arithmetic mean ) of ( 2 a + 16 ) and ( 3 a - 8 ) is 69 , what is the value of a ?
( ( 2 a + 16 ) + ( 3 a - 8 ) ) / 2 = ( 5 a + 8 ) / 2 = 69 a = 26 the answer is a .
a ) 26 , b ) 30 , c ) 28 , d ) 36 , e ) 42
a
divide(subtract(multiply(69, 2), subtract(16, 8)), add(2, 3))
add(n0,n2)|multiply(n0,n4)|subtract(n1,n3)|subtract(#1,#2)|divide(#3,#0)
general
what is the remainder when 43 ^ 89 is divided by 5 ?
"the units digit of the exponents of 3 cycle in a group of 4 : { 3 , 9 , 7 , 1 } 89 has the form 4 k + 1 so the units digit of 43 ^ 89 is 3 . the remainder when dividing by 5 is 3 . the answer is d ."
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
d
subtract(divide(5, const_2), multiply(43, 43))
divide(n2,const_2)|multiply(n0,n0)|subtract(#0,#1)|
general
the value of 99 ^ ( 91 / 99 ) x 99 is :
( 100 â € “ 8 / 99 ) x 99 = 9900 â € “ 8 = 9892 . answer : c
a ) 9989 , b ) 9896 , c ) 9892 , d ) 9809 , e ) 9810
c
multiply(power(99, divide(91, 99)), 99)
divide(n1,n0)|power(n0,#0)|multiply(n0,#1)
general
for any integer k greater than 1 , the symbol k * denotes the product of all the fractions of the form 1 / t , where t is an integer between 1 and k , inclusive . what is the value of 3 * / 5 * ?
"when dealing with ' symbolism ' questions , it often helps to ' play with ' the symbol for a few moments before you attempt to answer the question that ' s asked . by understanding how the symbol ' works ' , you should be able to do the latter calculations faster . here , we ' re told that k * is the product of all th...
a ) 5 , b ) 5 / 4 , c ) 4 / 5 , d ) 1 / 4 , e ) 1 / 5
b
divide(divide(divide(1, const_3), const_3), add(1, const_4))
add(n0,const_4)|divide(n2,const_3)|divide(#1,const_3)|divide(#2,#0)|
general