Datasets:
ericsun153
/
mathqa_shuffle_question_test

Dataset card Data Studio Files
xet
Community
Problem
stringlengths
11
628
Rationale
stringlengths
1
2.74k
options
stringlengths
37
137
correct
stringclasses
5 values
annotated_formula
stringlengths
6
848
linear_formula
stringlengths
7
357
category
stringclasses
6 values
bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
work done by the leak in 1 hour = 1 / 4 - 1 / 8 = 1 / 8 the leak will empty the tank in 8 hours answer is c
a ) 10 hours , b ) 12 hours , c ) 8 hours , d ) 5 hours , e ) 15 hours
c
divide(8, const_1)
divide(n1,const_1)
physics
if the angles of an n sided polygon are in a . p and a > = 20 and d > = 20 then wat is the maximum possible value of n ?
"i think it should be d . i can buy 8 250 - pack for rs 22.95 * 8 = $ 183.60 now , i can buy 6 20 - pack for 3.05 * 5 = $ 18.30 now , i am left with only $ 1.15 . i can not but anything with this . hence total hotdogs = 250 * 8 + 20 * 5 = 2120"
a ) 1,108 , b ) 2,100 , c ) 2,108 , d ) 2,120 , e ) 2,256
d
multiply(divide(203, 22.95), 250)
divide(n6,n5)|multiply(n4,#0)|
general
a set consists of 12 numbers , all are even or multiple of 5 . if 4 numbers are even and 10 numbers are multiple of 5 , how many numbers is multiple of 10 ?
"both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 9 : 00 , in 5 hrs , the time will be 14 : 00 answer ( c )"
a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
c
add(divide(add(700, 50), subtract(500, divide(700, const_2))), 09)
add(n4,n6)|divide(n4,const_2)|subtract(n5,#1)|divide(#0,#2)|add(n2,#3)|
physics
simplify : 81 x 81 + 68 x 68 - 2 x 81 x 68 .
answer : option ' d ' that is , 1 girl can do one time of the work in 3 days . therefore , 7 girls can do 7 times work in the same 3 days itself .
a ) 1 1 / 5 days , b ) 2 days , c ) 2 1 / 5 days , d ) 3 days , e ) 4 days
d
multiply(divide(3, 3), 3)
divide(n0,n0)|multiply(n0,#0)
physics
each of the cucumbers in 100 pounds of cucumbers is composed of 99 % water , by weight . after some of the water evaporates , the cucumbers are now 97 % water by weight . what is the new weight of the cucumbers , in pounds ?
"principal = ( 100 x 4043.25 ) / ( 9 x 5 ) = 404325 / 45 = 8985 . answer b"
a ) 5768 , b ) 8985 , c ) 2345 , d ) 6474 , e ) 8723
b
divide(divide(multiply(4043.25, const_100), 9), 5)
multiply(n0,const_100)|divide(#0,n1)|divide(#1,n2)|
gain
if 50 % of ( x - y ) = 30 % of ( x + y ) then what percent of x is y ?
"for the 1 st no . there are 2 digits after decimal for the 2 nd no . there are 2 digits after decimal total no . of decimals = 4 req . no . of digits = ( n - 1 ) = ( 4 - 1 ) = 3 answer : d"
a ) 5 , b ) 6 , c ) 4 , d ) 3 , e ) 8
d
divide(52.416, 0.68)
divide(n3,n4)|
general
in a company of 11 employees , 5 employees earn $ 32,000 , 4 employees earn $ 45,000 , and the 2 highest - paid employees earn the same amount . if the average annual salary for the 11 employees is $ 48,000 , what is the annual salary for each of the highest - paid employees ?
let distance be x km travelling at 10 kmph reach at 2 pm travelling at 15 kmph reach at 12 noon = > time taken when travelling at 10 km - time taken when travelling at 15 km = 2 hrs x / 10 - x / 15 = 2 3 x - 2 x * 30 x = 60 time needed if travelled at 10 kmph = 60 / 10 = 6 hrs = > reach at 1 pm = > ( 6 - 1 ) = 5 hrs req speed = 60 / 5 = 12 kmph answer b
a ) 8 kmph , b ) 12 kmph , c ) 10 kmph , d ) 14 kmph , e ) 15 kmph
b
divide(add(15, 10), 2)
add(n1,n3)|divide(#0,n0)
physics
if a speaks the truth 30 % of the times , b speaks the truth 40 % of the times . what is the probability that at least one will tell the truth
"( 600 * 3 * 4 ) / 100 = 72 600 + 72 = 672 answer : a"
a ) 672 , b ) 246 , c ) 258 , d ) 856 , e ) 653
a
multiply(power(add(const_1, divide(4, const_100)), 3), 600)
divide(n3,const_100)|add(#0,const_1)|power(#1,n2)|multiply(n0,#2)|
gain
the average of 10 consecutive odd numbers is 22 . what is the sum of the first 3 numbers ?
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 600 resolutions . = 600 * 2 * 22 / 7 * 22.4 = 84403 cm = 844.03 m answer : b"
a ) 843.03 m , b ) 844.03 m , c ) 845.03 m , d ) 846.03 m , e ) 847.03 m
b
divide(multiply(multiply(multiply(divide(add(multiply(add(const_3, const_4), const_3), const_1), add(const_3, const_4)), 22.4), const_2), 600), const_100)
add(const_3,const_4)|multiply(#0,const_3)|add(#1,const_1)|divide(#2,#0)|multiply(n0,#3)|multiply(#4,const_2)|multiply(n1,#5)|divide(#6,const_100)|
physics
the average age of 22 students in a group is 12 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
"angle between hands of a clock when the minute hand is behind the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( h − m / 5 ) + m / 2 degree when the minute hand is ahead of the hour hand , the angle between the two hands at m minutes past h ' o clock = 30 ( m / 5 − h ) − m / 2 degree here h = 7 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 7 − 30 / 5 ) + 30 / 2 = 30 ( 7 − 6 ) + 15 = 30 × 1 + 15 = 45 ° answer is d ."
a ) 35 ° , b ) 65 ° , c ) 55 ° , d ) 45 ° , e ) 95 °
d
divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)
add(const_1,const_4)|divide(const_60,const_2)|multiply(const_3,const_4)|subtract(#2,const_1)|divide(#2,#3)|multiply(#0,#3)|multiply(#4,#5)|subtract(#6,#1)|multiply(#7,#3)|divide(#8,const_2)|
physics
during a sale , the price of a pair of shoes is marked down 10 % from the regular price . after the sale ends , the price goes back to the original price . what is the percent of increase to the nearest percent from the sale price back to the regular price for the shoes ?
"explanation : the difference between any divisor and the corresponding remainder is 14 , l . c . m of 26 , 36,46 - 14 = 10764 - 14 = 10750 answer : option b"
a ) 10570 , b ) 10750 , c ) 17050 , d ) 10075 , e ) 10085
b
add(46, lcm(26, 36))
lcm(n0,n1)|add(n2,#0)|
general
a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 50 + 25 + 10 ) / 100 = 85 / 100 = 0.85 . answer is b
a ) 0.9 , b ) 0.85 , c ) 0.6 , d ) 0.8 , e ) 0.5
b
divide(subtract(100, add(7, 8)), 100)
add(n4,n5)|subtract(n0,#0)|divide(#1,n0)
other
the wages earned by robin is 20 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
length after removing pole is 12 / 3 = 4 then before removing pole is 2 ( ' coz | 2 | 2 | is | 4 | ) i . e . gap between two poles is 2 m 1 km = 1000 m then split 1000 m by 2 m = > we have 500 sections or gaps then no . of poles is 500 + 1 st pole = 501 poles therefore n = 501 . answer : b
a ) 500 , b ) 501 , c ) 502 , d ) 503 , e ) 504
b
subtract(add(add(add(add(multiply(multiply(12, 3), const_12), const_10), multiply(const_10, const_4)), const_10), const_10), 1)
multiply(n1,n2)|multiply(const_10,const_4)|multiply(#0,const_12)|add(#2,const_10)|add(#3,#1)|add(#4,const_10)|add(#5,const_10)|subtract(#6,n0)
physics
how long does a train 120 m long traveling at 60 kmph takes to cross a bridge of 170 m in length ?
10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 55 = 2.75 grams of red pigment
a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 2.75 , e ) 4.5
d
multiply(divide(55, multiply(const_100, const_2)), 10)
multiply(const_100,const_2)|divide(n1,#0)|multiply(n5,#1)
gain
if p / q = 3 / 7 , then 2 p + q = ?
"solution angle traced by hour hand in 13 / 3 hrs = ( 360 / 12 x 13 / 3 ) ° = 130 ° angle traced by min . hand in 20 min = ( 360 / 60 x 20 ) ° = 120 ° required angle = ( 130 - 120 ) ° = 10 ° . answer c"
a ) 0 ° , b ) 5 ° , c ) 10 ° , d ) 20 ° , e ) none
c
divide(multiply(subtract(multiply(divide(multiply(const_3, const_4), subtract(multiply(const_3, const_4), const_1)), multiply(add(const_4, const_1), subtract(multiply(const_3, const_4), const_1))), divide(const_60, const_2)), subtract(multiply(const_3, const_4), const_1)), const_2)
add(const_1,const_4)|divide(const_60,const_2)|multiply(const_3,const_4)|subtract(#2,const_1)|divide(#2,#3)|multiply(#0,#3)|multiply(#4,#5)|subtract(#6,#1)|multiply(#7,#3)|divide(#8,const_2)|
physics
a box contain the number of balls which is as much times greater than 15 as much times lesser than 240 . the no . of ball is ?
"p : q = 48000 : 24000 = 2 : 1 . answer : c"
a ) 2 : 6 , b ) 2 : 3 , c ) 2 : 1 , d ) 17 : 9 , e ) 17 : 4
c
divide(add(multiply(add(add(2, const_3), const_3), multiply(add(2, const_3), 2)), add(2, const_3)), add(multiply(const_3, multiply(add(2, const_3), 2)), add(2, const_3)))
add(n2,const_3)|add(#0,const_3)|multiply(n2,#0)|multiply(#1,#2)|multiply(#2,const_3)|add(#0,#3)|add(#0,#4)|divide(#5,#6)|
gain
a bakery has 6 employees . it pays annual salaries of $ 19000 to each of 2 employees , $ 21000 to 1 employee , and $ 22000 to each of the remaining 3 employees . which number is closest to the average ( arithmetic mean ) annual salary of these employees ?
"income of 6 months = ( 6 × 95 ) – debt = 570 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 840 average monthly income = 840 ÷ 10 = 84 answer e"
a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 84
e
divide(add(add(multiply(95, 6), multiply(60, 4)), 30), add(6, 4))
add(n0,n2)|multiply(n0,n1)|multiply(n2,n3)|add(#1,#2)|add(n4,#3)|divide(#4,#0)|
general
the units digit of ( 10 ) ^ ( 87 ) + ( 93 ) ^ ( 46 ) is :
"on dividing 6709 by 9 , we get remainder = 4 therefore , required number to be subtracted = 4 answer : c"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
c
subtract(6709, multiply(add(multiply(add(const_4, const_1), const_10), add(const_4, const_2)), 9))
add(const_2,const_4)|add(const_1,const_4)|multiply(#1,const_10)|add(#0,#2)|multiply(n1,#3)|subtract(n0,#4)|
general
a light flashes every 5 seconds , how many times will it flash in ? of an hour ?
"first 12 min = 90 * 12 / 60 = 18 km 2 nd 12 min = 110 * 12 / 60 = 22 km 3 rd 12 min = 130 * 12 / 60 = 26 km total time 12.3 = 36 min e"
a ) 52 , b ) 48 , c ) 44 , d ) 40 , e ) 36
e
add(add(add(12, 12), 12), 12)
add(n1,n1)|add(n1,#0)|add(n1,#1)|
physics
each machine of type a has 3 steel parts and 3 chrome parts . each machine of type b has 6 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 60 steel parts and 44 chrome parts , how many machines are in the group
"let the number be x . then 60 % of 3 / 5 of x = 18 60 / 100 * 3 / 5 * x = 18 x = ( 18 * 25 / 9 ) = 50 required number = 50 . correct option : d"
a ) 80 , b ) 100 , c ) 75 , d ) 50 , e ) none of these
d
divide(18, multiply(divide(60, const_100), divide(3, 5)))
divide(n0,const_100)|divide(n1,n2)|multiply(#0,#1)|divide(n3,#2)|
gain
a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 75 , the runs scored by b are ?
"let x be the number of liters of ethanol added to the gas tank . 0.05 ( 18 ) + x = 0.1 ( 18 + x ) 0.9 x = 1.8 - 0.9 x = 1 liter the answer is a ."
a ) 1 , b ) 1.5 , c ) 1.8 , d ) 2.4 , e ) 3
a
divide(multiply(18, 5), subtract(const_100, 10))
multiply(n0,n1)|subtract(const_100,n3)|divide(#0,#1)|
general
the decimal 0.1 is how many times greater than the decimal ( 0.01 ) ^ 3 ?
explanation : if arun doubles his speed , he needs 3 hour less . double speed means half time . hence , half of the time required by arun to cover 30 km = 3 hour i . e . , time required by arun to cover 30 km = 6 hour arun ' s speed = 30 / 6 = 5 kmph answer is b
a ) 8 kmph , b ) 5 kmph , c ) 4 kmph , d ) 7 kmph , e ) 9 kmph
b
divide(30, multiply(add(1, const_2), const_2))
add(n2,const_2)|multiply(#0,const_2)|divide(n0,#1)
physics
a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 27 , the how old is b ?
reduce in consumption = r / ( 100 + r ) * 100 % = 8 / 108 * 100 = 7.41 % answer is b
a ) 7.5 % , b ) 7.41 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %
b
multiply(divide(divide(8, const_100), add(divide(8, const_100), const_1)), const_100)
divide(n0,const_100)|add(#0,const_1)|divide(#0,#1)|multiply(#2,const_100)
general
in a can , there is a mixture of milk and water in the ratio 3 : 2 . if the can is filled with an additional 6 liters of milk , the can would be full and the ratio of milk and water would become 2 : 1 . find the capacity of the can ?
"a 2 = 104976 = > a = 324 4 a = 1296 1296 * 12 = 15552 answer : e"
a ) 15840 , b ) 3388 , c ) 2667 , d ) 8766 , e ) 15552
e
multiply(square_perimeter(square_edge_by_area(104976)), 12)
square_edge_by_area(n1)|square_perimeter(#0)|multiply(n0,#1)|
physics
a student committee on academic integrity has 56 ways to select a president and vice president from a group of candidates . the same person can not be both president and vice president . how many candidates are there ?
"explanation : let the numbers be 5 x , 4 x and 3 x , then , ( 5 x + 4 x + 3 x ) / 3 = 360 = > 12 x = 360 * 3 = > x = 90 largest number 5 x = 5 * 90 = 450 answer : b"
a ) 30 , b ) 450 , c ) 27 , d ) 21 , e ) 22
b
add(multiply(multiply(5, 3), const_100), multiply(4, 3))
multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)|
general
there has been successive increases of 20 % and then 10 % in the price of gas from the previous month . by what percentage should a driver reduce gas consumption so that the expenditure does not change ?
explanation : let c ' s investment = rs . x b ' s investment = rs . ( x - 3000 ) a ' s investment = rs . ( x - 3000 + 6000 ) = rs . ( x + 3000 ) now , ( a + b + c ) ' s investment = rs . 72000 = > x + ( x - 3000 ) + ( x + 3000 ) = 72000 = > 3 x = 72000 = > x = 24000 hence , a ' s investment = rs . 27000 b ' s investment = rs . 21000 c ' s investment = rs . 24000 ratio of the capitals of a , b and c = 27000 : 21000 : 24000 = 9 : 7 : 8 a ' s share = rs . [ ( 9 / 24 ) × 8640 ] = rs . 3240 answer : option a
a ) rs . 3240 , b ) rs . 2520 , c ) rs . 2880 , d ) rs . 3360 , e ) none of these
a
multiply(8640, divide(add(divide(subtract(72000, add(6000, 3000)), const_3), 6000), 72000))
add(n1,n2)|subtract(n0,#0)|divide(#1,const_3)|add(n1,#2)|divide(#3,n0)|multiply(n3,#4)
general
the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 9 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
"this is how i used to calculate which i think works pretty well : if you let the average of the 20 other numbers equal a , can you write this equation for sum of the list ( s ) n + 20 a = s the question tells us that n = 4 a plug this back into the first equation and you get that the sum is 24 a 4 a + 20 a = 24 a therefore fraction e of n to the total would be 4 a / 24 a or 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 man cycling along the road noticed that every 15 minutes a bus overtakes him and every 5 minutes he meets an oncoming bus . if all buses and the cyclist move at a constant speed , what is the time interval between consecutive buses ?
"let 4300331 - x = 2535618 then x = 4300331 - 2535618 = 1764713 answer is c"
a ) 1865113 , b ) 1775123 , c ) 1764713 , d ) 1675123 , e ) none of them
c
multiply(4300331, power(add(const_4, const_1), const_4))
add(const_1,const_4)|power(#0,const_4)|multiply(n0,#1)|
general
the cross - section of a water channel is a trapezium in shape . if the channel is 14 meters wide at the top and 8 meters wide at the bottom and the area of cross - section is 990 square meters , what is the depth of the channel ( in meters ) ?
"e euro 2000 let the shares of a , b , c and d be euro 5 x , euro 2 x , euro 4 x and euro 3 x respectively . then , 4 x - 3 x = 1000 x = 1000 . b ' s share = euro 2 x = euro ( 2 x 1000 ) = euro 2000 ."
a ) euro 1000 , b ) euro 3000 , c ) euro 5000 , d ) euro 4000 , e ) euro 2000
e
multiply(multiply(subtract(4, 3), 1000), 3)
subtract(n2,n3)|multiply(n4,#0)|multiply(n3,#1)|
general
the average salary per head of the entire staff of an office including the officers and clerks is rs . 90 . the average salary of officers is rs . 500 and that of the clerks is rs . 84 . if the number of officers is 2 , find the number of officers in the office ?
"4 / 3 : 4 / 5 = 20 : 12 = 5 : 3 answer : d"
a ) 10 : 6 , b ) 10 : 3 , c ) 15 : 3 , d ) 5 : 3 , e ) 30 : 3
d
divide(4, 5)
divide(n2,n3)|
other
the effective annual rate of interest corresponding to a nominal rate of 14 % per annum payable half - yearly is ?
c . i . = [ 3000 * ( 1 + 15 / 100 ) 2 - 3000 ] = ( 3000 * 23 / 20 * 23 / 20 - 3000 ) = rs . 967.5 . sum = ( 483.75 * 100 ) / ( 5 * 6 ) = rs . 1612.5 answer : c
a ) 1525.2 , b ) 1256.3 , c ) 1612.5 , d ) 1548.5 , e ) 1254.5
c
divide(divide(subtract(multiply(3000, power(add(const_1, divide(15, const_100)), 2)), 3000), const_2), multiply(5, divide(6, const_100)))
divide(n4,const_100)|divide(n1,const_100)|add(#0,const_1)|multiply(n0,#1)|power(#2,n3)|multiply(n2,#4)|subtract(#5,n2)|divide(#6,const_2)|divide(#7,#3)
gain
miller street begins at baker street and runs directly east for 4.5 kilometers until it ends when it meets turner street . miller street is intersected every 250 meters by a perpendicular street , and each of those streets other than baker street and turner street is given a number beginning at 1 st street ( one block east of baker street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of turner street . what is the highest - numbered street that intersects miller street ?
"if b is 1 , 3 , 5 , or 15 , then gcd of a and b is 1 , 3 , 5 , and 15 respectively . so , by poe the answer must be c . still : if b is a multiple of 18 , then a is 15 smaller than a multiple of 18 , so not a multiple of 18 , so both of them can not be divisive by 18 . answer : c ."
a ) 1 , b ) 3 , c ) 18 , d ) 15 , e ) 5
c
add(divide(15, 20), const_2)
divide(n1,n0)|add(#0,const_2)|
general
two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 249 marks in the second test and failed by 66 marks in that test . find the pass mark in the first test ?
"0.1 m = 0.60 e = > e / m = 1 / 6 * 100 = 16 % so answer is e . m - # of motorists e - # of motorists exceeding speed"
a ) 10.5 % , b ) 12.5 % , c ) 15 % , d ) 22 % , e ) 16 %
e
divide(const_100, multiply(multiply(divide(10, const_100), divide(40, const_100)), const_100))
divide(n0,const_100)|divide(n1,const_100)|multiply(#0,#1)|multiply(#2,const_100)|divide(const_100,#3)|
gain
50 % of the population of a village is 23040 . the total population of the village is ?
"r = 4 ï € r 2 = 16 r = 5 ï € r 2 = 25 25 ï € â € “ 9 ï € 100 - - - - ? = > 36 % . answer : d"
a ) 42 % , b ) 39 % , c ) 38 % , d ) 36 % , e ) 26 %
d
subtract(power(5, const_2), power(4, const_2))
power(n1,const_2)|power(n0,const_2)|subtract(#0,#1)|
geometry
a certain class of students is being divided into teams . the class can either be divided into 16 teams with an equal number of players on each team or 24 teams with an equal number of players on each team . what is the lowest possible number of students in the class ?
"s . i = ( p * r * t ) / 100 80 = 800 r / 100 r = 80 / 8 = 10 % answer a"
a ) 10 , b ) 12.5 , c ) 25 , d ) 12 , e ) 14.5
a
multiply(divide(80, multiply(400, 2)), const_100)
multiply(n0,n2)|divide(n1,#0)|multiply(#1,const_100)|
gain
10 women can complete a work in 7 days and 10 children take 14 days to complete the work . how many days will 8 women and 12 children take to complete the work ?
"sol . ( x × 4 ) = ( 0.20 × 2 ) ⇒ x = 0.4 / 4 = 0.1 . answer c"
a ) 0.2 , b ) 0.3 , c ) 0.1 , d ) 0.5 , e ) none
c
divide(multiply(0.20, 2), 4)
multiply(n0,n2)|divide(#0,n1)|
general
the triplicate ratio of 1 : 9 is ?
"explanation : 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 option b"
a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
b
divide(225, subtract(26, const_1))
subtract(n1,const_1)|divide(n0,#0)|
physics
how many positive integers less than 250 are multiple of 4 but not multiples of 6 ?
let cost price = x profit = y selling price = x + y 50 y = 20 ( x + y ) 30 y = 20 x percentage profit = y / x ∗ 100 = 20 / 30 ∗ 100 = 66.667 answer = a
a ) 66.67 % , b ) 33.33 % , c ) 40 % , d ) 25 % , e ) 20 %
a
multiply(subtract(divide(50, subtract(50, 20)), const_1), const_100)
subtract(n0,n1)|divide(n0,#0)|subtract(#1,const_1)|multiply(#2,const_100)
gain
paul sells encyclopedias door - to - door . he earns $ 150 on every paycheck , regardless of how many sets he sells . in addition , he earns commission as follows : commission sales 10 % $ 0.00 - $ 10 , 000.00 5 % $ 10 , 000.01 - - - > he does not earn double commission . that is , if his sales are $ 12,000 , he earns 10 % on the first $ 10,000 and 5 % on the remaining $ 2,000 . his largest paycheck of the year was $ 1,320 . what were his sales for that pay period ?
"the total number of ways to choose 2 apples is 10 c 2 = 45 the number of ways that include the spoiled apple is 9 c 1 = 9 p ( the spoiled apple is included ) = 9 / 45 = 1 / 5 the answer is e ."
a ) 2 / 9 , b ) 3 / 8 , c ) 2 / 7 , d ) 1 / 6 , e ) 1 / 5
e
divide(choose(subtract(10, 1), 1), choose(10, 2))
choose(n0,n2)|subtract(n0,n1)|choose(#1,n1)|divide(#2,#0)|
probability
220 metres long yard , 21 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
"last term = first term + ( total no . of terms - 1 ) consecutive difference s is a set of 85 consecutive multiples of 5 . if the smallest number in s is 90 , then the greatest number in s is first term = 90 ; total terms = 85 ; difference = 5 90 + ( 84 ) 5 = 510 ans e"
a ) 158 , b ) 597 , c ) 599 , d ) 402 , e ) 510
e
add(90, multiply(subtract(85, const_1), 5))
subtract(n0,const_1)|multiply(n1,#0)|add(n2,#1)|
general
three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 1800 . their h . c . f is ?
"a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 6 meters from either end . the probability of this is 12 / 14 = 6 / 7 . the answer is d ."
a ) 5 / 14 , b ) 3 / 14 , c ) 8 / 21 , d ) 6 / 7 , e ) 2 / 5
d
multiply(const_2, divide(const_2, 14))
divide(const_2,n0)|multiply(#0,const_2)|
geometry
for any integer p , * p is equal to the product of all the integers between 1 and p , inclusive . how many prime numbers are there between * 9 + 3 and * 9 + 9 , inclusive ?
"let the side for growing cabbages this year be x ft . thus the area is x ^ 2 . let the side for growing cabbages last year be y ft . thus , the area was y ^ 2 . the area would have increased by 191 sq ft as each cabbage takes 1 sq ft space . x ^ 2 - y ^ 2 = 191 ( x + y ) ( x - y ) = 191 191 is a prime number and thus it will be ( 96 + 95 ) * ( 96 - 95 ) . thus x = 96 and y = 95 x ^ 2 = 96 ^ 2 = 9216 the answer is c ."
a ) 7,251 , b ) 8406 , c ) 9216 , d ) 10,348 , e ) can not be determined
c
power(add(divide(191, const_2), add(const_0_25, const_0_25)), const_2)
add(const_0_25,const_0_25)|divide(n1,const_2)|add(#0,#1)|power(#2,const_2)|
geometry
3 people candidates contested an election and they received 1136 , 7636 and 11628 votes respectively . what is the percentage of the total votes did the winning candidate get ?
"( 3 * 8 + 2 * 4 ) : ( 4 * 8 + 5 * 4 ) 8 : 13 8 / 21 * 630 = 240 answer : a"
a ) 240 , b ) 288 , c ) 277 , d ) 877 , e ) 361
a
multiply(divide(630, add(add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))), add(multiply(4000, 8), multiply(add(4000, 1000), subtract(const_12, 8))))), add(multiply(3000, 8), multiply(subtract(3000, 1000), subtract(const_12, 8))))
add(n1,n3)|multiply(n0,n2)|multiply(n1,n2)|subtract(n0,n3)|subtract(const_12,n2)|multiply(#3,#4)|multiply(#0,#4)|add(#1,#5)|add(#2,#6)|add(#7,#8)|divide(n5,#9)|multiply(#7,#10)|
gain
| x + 3 | – | 4 - x | = | 7 + x | how many solutions will this equation have ?
"compounded annually means that the interest is applied once per year . one can have 10 % annual interest compounded monthly - in this case 10 % / 12 would be applied each month , or 10 % annual interest compounded daily etc . with respect to the problem at hand , at the end of two years , tim would have 1,000 ( 1.10 ) ^ 2 = 1,000 ( 1.21 ) = 1,210 and lana would have 2,000 ( 1.05 ) ^ 2 = 2,000 ( 1.1025 ) = 2,205 thus , tim earned 210 dollars , while lana earned 205 dollars the difference is $ 5 and the answer is a ."
a ) $ 5 , b ) $ 15 , c ) $ 50 , d ) $ 100 , e ) $ 105
a
subtract(subtract(multiply(1,000, power(add(const_1, divide(10, const_100)), 2)), 1,000), subtract(multiply(power(add(const_1, divide(5, const_100)), 2), 2,000), 2,000))
divide(n1,const_100)|divide(n3,const_100)|add(#0,const_1)|add(#1,const_1)|power(#2,n4)|power(#3,n4)|multiply(n0,#4)|multiply(n2,#5)|subtract(#6,n0)|subtract(#7,n2)|subtract(#8,#9)|
gain
a ratio between two numbers is 4 : 5 and their l . c . m . is 200 . the first number is
at 12 : 24 - minute hand will be at 24 * 6 = 144 degrees from position of 12 . - hour hand will move by 2 * 6 = 12 degree during the same time so the difference between the two hands will be 144 - 12 = 132 degrees . answer : e
a ) 115 , b ) 120 , c ) 124 , d ) 130 , e ) 132
e
subtract(multiply(24, multiply(const_3, const_2)), 12)
multiply(const_2,const_3)|multiply(n1,#0)|subtract(#1,n0)
physics
a trader bought a car at 30 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?
"3 x ^ 2 - 1.8 x + 0.7 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 3 * 0.6 * ( 0.6 ) + 0.7 = 0 + 0.7 = 0.7 answer : d"
a ) − 0.3 , b ) 0 , c ) 0.3 , d ) 0.7 , e ) 2.46
d
subtract(multiply(divide(divide(subtract(power(3, 2), power(1.8, 0.7)), const_1000), const_1000), 3), divide(divide(subtract(power(3, 2), power(1.8, 0.7)), const_1000), const_1000))
power(n0,n1)|power(n2,n3)|subtract(#0,#1)|divide(#2,const_1000)|divide(#3,const_1000)|multiply(n0,#4)|subtract(#5,#4)|
general
if x ^ 2 + y ^ 2 = 20 and xy = 3 , then ( x − y ) ^ 2 =
( 7000 + 28 ) / 100 * 100 = 7028 answer : a
a ) 7028 , b ) 4028 , c ) 3128 , d ) 3256 , e ) 5264
a
multiply(add(divide(28, 100), 70), const_100)
divide(n1,n2)|add(n0,#0)|multiply(#1,const_100)
general
an article is bought for rs . 675 and sold for rs . 1100 , find the gain percent ?
let the length of the train be l metres and speeds of the train arun and sriram be r , a and s respectively , then - - - - - - - - - - ( i ) and - - - - - - - - - ( ii ) from eq . ( i ) and ( ii ) 3 ( r - a ) = 2 ( r + k ) r = 3 a + 2 k in 30 minutes ( i . e 1800 seconds ) , the train covers 1800 r ( distance ) but the arun also covers 1800 a ( distance ) in the same time . therefore distance between arun and sriram , when the train has just crossed sriram = 1800 ( r - a ) - 24 ( a + k ) time required = = ( 3600 - 24 ) = 3576 s e
a ) 2534 , b ) 3545 , c ) 3521 , d ) 4564 , e ) 3576
e
subtract(divide(multiply(subtract(divide(add(36, 24), subtract(36, 24)), const_1), multiply(multiply(const_10, const_3), const_60)), const_2), 24)
add(n1,n2)|multiply(const_10,const_3)|subtract(n1,n2)|divide(#0,#2)|multiply(#1,const_60)|subtract(#3,const_1)|multiply(#4,#5)|divide(#6,const_2)|subtract(#7,n2)
physics
5.40 can be expressed in terms of percentage as
"assume : jose does 1 job in x days , so jose does 1 / x job in a day jane does 1 job in y days , so jane does 1 / y job in a day together , they does ( x + y ) / xy job in a day . this is equals to 1 / 20 . so ( x + y ) / xy = 1 / 10 10 ( x + y ) = xy next , we ' re told 1 job takes 25 days to complete if jose and jane each does half the work . so since jose does 1 job in x days , he wil need x / 2 days to do half the job . jane similarly will need y / 2 days to do the other half . x / 2 + y / 2 = 25 x + y = 50 so xy = 500 the answer choices are : 25 days 30 days 60 days 65 days 36 days from the answer choices , so i ' ll go for 25 days for jose and 20 days for jane . answer : a"
a ) 25 days , b ) 30 days , c ) 60 days , d ) 65 days , e ) 36 days
a
multiply(const_3, 10)
multiply(n0,const_3)|
physics
jack and jill are marathon runners . jack can finish a marathon ( 42 km ) in 3.5 hours and jill can run a marathon in 4.2 hours . what is the ratio of their average running speed ? ( jack : jill )
"explanation : required difference = ( 5 ( 1 / 3 ) of rs . 5000 ) - ( 3 ( 1 / 2 ) of rs . 5000 ) = ( 16 / 3 – 7 / 2 ) % of rs . 5000 = ( 11 / 6 ) x ( 1 / 100 ) x 5000 = rs . 91.66 answer d"
a ) rs . 156.66 , b ) rs . 111.23 , c ) rs . 120.66 , d ) rs . 91.66 , e ) none of these
d
subtract(multiply(add(divide(add(5, divide(1, 5)), const_100), 1), divide(5000, add(divide(add(divide(1, 2), 1), const_100), 1))), 5000)
divide(n1,n0)|divide(n1,n5)|add(n0,#0)|add(n1,#1)|divide(#2,const_100)|divide(#3,const_100)|add(n1,#4)|add(n1,#5)|divide(n6,#7)|multiply(#6,#8)|subtract(#9,n6)|
general
sum of two numbers prime to each other is 20 and their l . c . m . is 99 . what are the numbers ?
"option b 20 + 20 t = 50 t t = 0.6"
a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.5 , e ) 2
b
divide(20, subtract(50, 20))
subtract(n1,n0)|divide(n2,#0)|
physics
a rectangle with width 8 and diagonal 30 . find the area ?
"number of diagonals in any polygon can be found using this formula : n ( n - 3 ) / 2 here n = 5 no . of diagonals = 5 ( 5 - 3 ) / 2 = 5 ans a"
a ) 5 , b ) 8 , c ) 9 , d ) 10 , e ) 12
a
multiply(subtract(multiply(const_2, const_4), const_3), divide(multiply(const_2, const_4), const_2))
multiply(const_2,const_4)|divide(#0,const_2)|subtract(#0,const_3)|multiply(#1,#2)|
geometry
the diameters of two spheres are in the ratio 1 : 2 what is the ratio of their surface area ?
"let the length and the width be 4 x and 3 x respectively . area = ( 4 x ) ( 3 x ) = 5808 12 x ^ 2 = 5808 x ^ 2 = 484 x = 22 the ratio of the width and the area is 3 x : 12 x ^ 2 = 1 : 4 x = 1 : 88 the answer is d ."
a ) 1 : 76 , b ) 1 : 80 , c ) 1 : 84 , d ) 1 : 88 , e ) 1 : 92
d
divide(divide(sqrt(multiply(3, 5808)), const_2), 5808)
multiply(n2,n1)|sqrt(#0)|divide(#1,const_2)|divide(#2,n2)|
geometry
if 7 a - 3 b = 10 b + 50 = - 12 b - 2 a , what is the value of 9 a + 9 b ?
"explanation : ( 100 + g ) / ( 100 + x ) = true measure / faulty measure x = 0 true measure = 1000 faulty measure = 990 100 + g / 100 + 0 = 1000 / 990 100 + g = 100 / 99 * 100 g = 1.01 answer : c"
a ) 1.05 , b ) 1.06 , c ) 1.01 , d ) 1.08 , e ) 1.09
c
multiply(divide(subtract(multiply(add(add(const_4, const_1), add(const_4, const_1)), const_100), 990), 990), const_100)
add(const_1,const_4)|add(#0,#0)|multiply(#1,const_100)|subtract(#2,n0)|divide(#3,n0)|multiply(#4,const_100)|
gain
mary can do a piece of work in 12 days . rosy is 50 % more efficient than mary . the number of days taken by rosy to do the same piece of work is ?
the total number of ways to choose 2 apples is 9 c 2 = 36 the number of ways that include the spoiled apple is 8 c 1 = 8 p ( the spoiled apple is included ) = 8 / 36 = 2 / 9 the answer is d .
a ) 2 / 3 , b ) 2 / 5 , c ) 2 / 7 , d ) 2 / 9 , e ) 2 / 11
d
divide(choose(subtract(9, 1), 1), choose(9, 2))
choose(n0,n2)|subtract(n0,n1)|choose(#1,n1)|divide(#2,#0)
probability
an article with cost price of 245 is sold at 34 % profit . what is the selling price ?
"think of 100 people total : from the first fact , 26 of these are women with fair hair . from the second fact , these 20 women make up 40 % of the total fair haired population . we can then make a ratio of 60 : 40 fair haired men to fair haired women . this means that ( 60 / 40 ) * 26 equals the number of fair haired men , which is 39 men with fair hair . add this 39 to the 26 women and get 65 fair haired men and women out of 100 total men and women . 65 % e"
a ) 25 , b ) 30 , c ) 50 , d ) 55 , e ) 65
e
multiply(divide(26, 40), const_100)
divide(n0,n1)|multiply(#0,const_100)|
gain
a dealer offers a cash discount of 16 % and still makes a profit of 25 % when he further allows 60 articles to be sold at the cost price of 50 articles to a particular sticky bargainer . how much percent above the cost price were his articles listed ?
"ratio of rates of working of a and b = 2 : 1 ratio of times taken = 1 : 2 a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 24 a + b 1 day work = 1 / 12 + 1 / 24 = 3 / 24 = 1 / 8 a and b can finish the work in 8 days answer is c"
a ) 2 days , b ) 3 days , c ) 8 days , d ) 5 days , e ) 6 days
c
inverse(add(inverse(24), multiply(const_2, inverse(24))))
inverse(n0)|multiply(#0,const_2)|add(#0,#1)|inverse(#2)|
physics
there are 6 people in the elevator . their average weight is 170 lbs . another person enters the elevator , and increases the average weight to 151 lbs . what is the weight of the 7 th person .
"2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n + 2 ^ 2 n = 4 ^ 20 = > 4 x 2 ^ 2 n = 4 ^ 20 = 2 ^ 40 = > 2 ^ 2 x 2 ^ 2 n = 2 ^ 40 = > 2 ^ ( 2 n + 2 ) = 2 ^ 40 = > 2 n + 2 = 40 = > n = 19 so . answer will be c ."
a ) 3 , b ) 6 , c ) 19 , d ) 23 , e ) 24
c
divide(subtract(multiply(20, 2), 2), 2)
multiply(n0,n9)|subtract(#0,n0)|divide(#1,n0)|
general
a fruit seller had some oranges . he sells 10 % oranges and still has 360 oranges . how many oranges he had originally ?
"diver = ( 8 * 3 ) + 3 = 27 6 * quotient = 27 quotient = 4.5 dividend = ( divisor * quotient ) + remainder dividend = ( 27 * 4.5 ) + 8 = 129.5 b"
a ) 110.6 , b ) 129.5 , c ) 130.5 , d ) 86 , e ) 88
b
add(multiply(add(multiply(8, const_3), 3), divide(add(multiply(8, const_3), 3), 6)), 8)
multiply(n0,const_3)|add(n2,#0)|divide(#1,n1)|multiply(#1,#2)|add(n0,#3)|
general
a boat having a length 3 m and breadth 3 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
"let ' s see pick 6 / 100 first then we can only pick 1 other pair from the 800 so total will be 6 / 80 * 100 simplify and you get 3 / 4000 answer is d"
a ) 3 / 40000 , b ) 1 / 3600 , c ) 9 / 2000 , d ) 3 / 4000 , e ) 1 / 15
d
divide(1, const_3)
divide(n3,const_3)|
probability
. 002 / ? = . 01
"let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 20 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 24 has unit digit 6 . . . . . . . . . . hold b ) 2.5 feet . . . . . . . . . 25 * 25 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 26 has unit digit 6 . . . . . . . . . . . elimate ( area is more than stipulated ) d ) 4 feet . . . . . . . . . . . . 28 * 28 has unit digit 4 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 30 has unit digit 0 . . . . . . . . . . . eliminate answer : a"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
a
divide(subtract(sqrt(add(power(subtract(20, const_1), const_2), subtract(576, rectangle_area(20, 20)))), subtract(20, const_1)), const_2)
rectangle_area(n0,n1)|subtract(n1,const_1)|power(#1,const_2)|subtract(n2,#0)|add(#2,#3)|sqrt(#4)|subtract(#5,#1)|divide(#6,const_2)|
geometry
p has $ 21 more than what q and r together would have had if both b and c had 1 / 5 of what p has . how much does p have ?
the percent of the budget for transportation is 100 - ( 61 + 10 + 6 + 5 + 3 ) = 15 % 100 % of the circle is 360 degrees . then ( 15 % / 100 % ) * 360 = 54 degrees the answer is c .
['a ) 18 °', 'b ) 36 °', 'c ) 54 °', 'd ) 72 °', 'e ) 90 °']
c
divide(multiply(const_360, subtract(const_100, add(add(add(add(61, 10), 6), 5), 3))), 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
how many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph ?
let a be the event ‘ the number on the card drawn is even ’ and b be the event ‘ the number on the card drawn is greater than 3 ’ . we have to find p ( a | b ) . now , the sample space of the experiment is s = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 } then a = { 2 , 4 , 6 , 8 , 10 } , b = { 4 , 5 , 6 , 7 , 8 , 9 , 10 } and a n b = { 4 , 6 , 8 , 10 } also p ( a ) = 5 / 2 , p ( b ) = 7 / 10 and p ( a n b ) = 4 / 10 then p ( a | b ) = p ( a n b ) / p ( b ) = ( 4 / 10 ) / ( 7 / 10 ) = 4 / 7 b )
a ) 3 / 7 , b ) 4 / 7 , c ) 5 / 7 , d ) 7 / 11 , e ) 9 / 11
b
multiply(divide(const_4, 10), divide(10, subtract(10, 3)))
divide(const_4,n0)|subtract(n0,n3)|divide(n0,#1)|multiply(#0,#2)
general
the l . c . m of 22 , 54 , 108 , 135 and 198 is
"a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean w = 74 . answer : a ."
a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
a
divide(add(multiply(58, 3), multiply(98, 2)), add(2, 3))
add(n1,n3)|multiply(n0,n3)|multiply(n1,n2)|add(#1,#2)|divide(#3,#0)|
general
if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 85 , what is the value of c â ˆ ’ a ?
"let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 450 / 3 = 150 sq m l b = 150 i . e . , l * l / 3 = 150 l 2 = 450 = > l = 21.21 answer : c"
a ) 65 , b ) 44 , c ) 21.21 , d ) 16 , e ) 14
c
multiply(sqrt(divide(divide(450, 5), const_3)), const_3)
divide(n1,n2)|divide(#0,const_3)|sqrt(#1)|multiply(#2,const_3)|
gain
the membership of a committee consists of 3 english teachers , 4 mathematics teachers , and 2 social studies teachers . if 2 committee members are to be selected at random to write the committee ’ s report , what is the probability that the two members selected will both be social teachers ?
"for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 9 = 144 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 144 pi / 200 pi = 0.72 a"
a ) 72 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
a
multiply(multiply(power(divide(8, 10), const_2), divide(9, 8)), const_100)
divide(n0,n2)|divide(n1,n3)|power(#1,const_2)|multiply(#0,#2)|multiply(#3,const_100)|
physics
the length of a rectangular floor is more than its breadth by 200 % . if rs . 324 is required to paint the floor at the rate of rs . 3 per sq m , then what would be the length of the floor ?
"w = 2 desks t = 2.5 hrs rate of 2 carpenters = 2 × r rate = work done / time 2 xr = 2 / 2.5 r = 1 / 2.5 = 2 / 5 ( this is the rate of each carpenter ) work done by 4 carpenters in 1 hrs = 4 × rate of each carpenter x time = 4 × 2 / 5 × 1 = 1.6 desks a is the correct answer ."
a ) 1.6 . , b ) 3.6 . , c ) 4.2 . , d ) 5.5 . , e ) 6.4
a
multiply(multiply(divide(divide(2, divide(1, 2)), 2), 4), 1)
divide(n2,n0)|divide(n0,#0)|divide(#1,n0)|multiply(n1,#2)|multiply(n2,#3)|
physics
in what ratio must rice of rs . 25 per kg be mixed with rice of rs . 12 per kg so that cost of mixture is rs . 20 per kg ?
"21 trees have 20 gaps between them , required distance ( 220 / 20 ) = 11 d"
a ) 10 , b ) 12 , c ) 14 , d ) 11 , e ) 17
d
divide(220, add(subtract(21, 2), const_1))
subtract(n1,n2)|add(#0,const_1)|divide(n0,#1)|
physics
the average age of a family of 6 members is 26 years . if the age of the youngest member is 10 years , what was the average age of the family at the birth of the youngest member ?
"number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 10 = 50 km imo , correct answer is ` ` d . ' '"
a ) 20 km , b ) 30 km , c ) 40 km , d ) 50 km , e ) 60 km
d
multiply(60, divide(multiply(5, 10), 60))
multiply(n1,n2)|divide(#0,n0)|multiply(n0,#1)|
physics
after decreasing 24 % in the price of an article costs rs . 1140 . find the actual cost of an article ?
let x be the distance from his house to the school . x / 10 = x / 12 + 2 6 x = 5 x + 120 x = 120 km the answer is e .
a ) 100 , b ) 105 , c ) 110 , d ) 115 , e ) 120
e
multiply(multiply(10, 12), divide(subtract(12, 10), add(1, 1)))
add(n1,n1)|multiply(n0,n2)|subtract(n2,n0)|divide(#2,#0)|multiply(#3,#1)
physics
the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years q in which the population would be doubled assuming there is no emigration or immigration is
"ans 25 reverse of 52 answer : b"
a ) 49 , b ) 25 , c ) 36 , d ) 64 , e ) 56
b
multiply(52, divide(43, 34))
divide(n0,n1)|multiply(n2,#0)|
general
the marked price of a book is 20 % more than the cost price . after the book is sold , the vendor realizes that he had wrongly raised the cost price by a margin of 25 % . if the marked price of the book is rs . 30 , what is the original cost price of the book ?
"speed of the first bullet train = 120 / 10 m / sec = 12 m / sec . speed of the second bullet train = 120 / 30 m / sec = 4 m / sec . relative speed = ( 12 + 4 ) = 16 m / sec . required time = ( 120 + 120 ) / 16 sec = 15 sec . d"
a ) 13 sec . , b ) 14 sec . , c ) 12 sec . , d ) 15 sec . , e ) 19 sec .
d
divide(add(120, 120), add(speed(120, 10), speed(120, 30)))
add(n2,n2)|speed(n2,n0)|speed(n2,n1)|add(#1,#2)|divide(#0,#3)|
physics
a man is 24 years older than his son . in three years , his age will be twice the age of his son . the present age of the son is
( 1 / 2 + 1 / 7 ) t = 2 t = 28 / 9 answer : a
a ) 28 / 9 , b ) 4 / 3 , c ) 15 / 8 , d ) 9 / 4 , e ) 15 / 4
a
multiply(divide(const_1, add(divide(const_1, 2), divide(const_1, 7))), const_2)
divide(const_1,n0)|divide(const_1,n1)|add(#0,#1)|divide(const_1,#2)|multiply(#3,const_2)
physics
there are 3 red shoes & 7 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
"16 students are interested , 8 are not interested prob = 1 - 8 c 2 / 24 c 2 = 1 - ( 8 * 7 / ( 24 * 23 ) ) = 1 - 7 / 69 = 62 / 69 answer : d"
a ) 1 / 14 , b ) 4 / 49 , c ) 2 / 7 , d ) 62 / 69 , e ) 13 / 14
d
divide(subtract(choose(24, const_2), choose(subtract(24, multiply(24, divide(4, 6))), const_2)), choose(24, const_2))
choose(n2,const_2)|divide(n0,n1)|multiply(n2,#1)|subtract(n2,#2)|choose(#3,const_2)|subtract(#0,#4)|divide(#5,#0)|
gain
two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 25 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
"let the two positive numbers be 5 x and 8 x respectively . 8 x - 5 x = 15 3 x = 15 = > x = 5 = > smaller number = 5 x = 25 . answer : a"
a ) 25 , b ) 66 , c ) 88 , d ) 89 , e ) 53
a
divide(multiply(15, 5), const_4)
multiply(n0,n2)|divide(#0,const_4)|
other
two kinds of vodka are mixed in the ratio 2 : 6 and 6 : 3 and they are sold fetching the profit 10 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
"800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 5 , - 5 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 4 × 4 ) = 25 / 2 ; so z = 25 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 25 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 25 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 25 / 2 . clearly s = √ 25 / 2 = 5 / √ 2 , oranswer choice ( b ) ."
a ) 16 , b ) 5 / √ 2 , c ) 8 , d ) 2 √ 2 , e ) ( √ 2 ) / 3
b
sqrt(divide(multiply(5, 5), const_2))
multiply(n0,n0)|divide(#0,const_2)|sqrt(#1)|
general
two numbers are respectively 50 % and 20 % more than a third number . the percentage that is first of the second is ?
let no . of bicycles be x & no . of wagons be y so , 2 x + 4 y = 190 by solving , we get no . of bicycles = 39 ( wheels = > 2 * 39 = 78 ) no . of wagons = 28 ( wheels = > 4 * 28 = 112 ) answer : e
a ) 35 , b ) 36 , c ) 37 , d ) 38 , e ) 39
e
multiply(divide(190, add(multiply(4, const_2), const_2)), const_2)
multiply(n0,const_2)|add(#0,const_2)|divide(n1,#1)|multiply(#2,const_2)
physics
if jake loses 5 pounds , he will weigh thrice as much as his sister . together they now weigh 285 pounds . what is jake ' s present weight , in pounds ?
"total expenditure = 40 + 25 + 15 + 5 = 85 % saving = ( 100 - 85 ) = 15 % 15 / 100 × salary = 1500 , salary = 10000 rs . answer : d"
a ) 4000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
d
divide(multiply(1500, const_100), 5)
multiply(n4,const_100)|divide(#0,n3)|
gain
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets euro 1000 more than d , what is b ' s share ?
"the percent of tagged fish in the second catch is 2 / 90 * 100 = 2.22 % . we are told that 2.22 % approximates the percent of tagged fish in the pond . since there are 90 tagged fish , then we have 0.022 x = 90 - - > x = 4,091 . answer : e ."
a ) 400 , b ) 625 , c ) 1250 , d ) 2500 , e ) 4091
e
divide(90.00001, divide(2, 90))
divide(n2,n1)|divide(n0,#0)|
gain
two integers are in the ratio of 1 to 3 . if 10 is added to the smaller number , the ratio becomes 2 to 1 . find the larger integer .
"good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 5 of the garden is green , so , since all the flowers must be either green or yellow , we know that 4 / 5 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 4 / 5 * 1 / 2 = 2 / 5 , or c ."
a ) 1 / 7 , b ) 1 / 8 , c ) 2 / 5 , d ) 3 / 4 , e ) 7 / 8
c
multiply(subtract(1, divide(1, 5)), divide(1, 2))
divide(n2,n3)|divide(n0,n1)|subtract(n2,#1)|multiply(#0,#2)|
probability
one day , connie plays a game with a fair 6 - sided die . connie rolls the die until she rolls a 6 , at which point the game ends . if she rolls a 6 on her first turn , connie wins 6 dollars . for each subsequent turn , connie wins 1 6 of the amount she would have won the previous turn . what is connie ' s expected earnings from the game ?
"100 * ( 20 / 100 ) = 20 - - - 2 ? - - - 1 = > rs . 10 100 - - - 80 ? - - - 10 = > rs . 12.5 answer : c"
a ) 12.6 , b ) 12.1 , c ) 12.5 , d ) 12.4 , e ) 12.7
c
multiply(divide(divide(multiply(divide(20, const_100), 100), 2), multiply(divide(20, const_100), 100)), const_100)
divide(n0,const_100)|multiply(n2,#0)|divide(#1,n1)|divide(#2,#1)|multiply(#3,const_100)|
gain
if x is equal to the sum of the integers from 40 to 50 , inclusive , and y is the number of even integers from 40 to 50 , inclusive , what is the value of x + y ?
"t = 110 / 36 * 18 / 5 = 11 sec answer : d"
a ) 6 sec , b ) 7 sec , c ) 8 sec , d ) 11 sec , e ) 2 sec
d
divide(110, multiply(36, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
convert 40 miles into yards ?
"a = 7 x , b = 7 z therefore ( 7 x . 10 + 7 z ) - ( 10 x + z ) = ( 7 - 1 ) ( 10 x + z ) = 6 . ( 10 x + z ) number should be divisible by 6 d"
a ) 30 , b ) 36 , c ) 42 , d ) 63 , e ) 66
d
add(add(subtract(add(multiply(7, 7), multiply(7, 10)), add(multiply(7, 10), 7)), 10), const_3)
multiply(n1,n1)|multiply(n1,n4)|add(#0,#1)|add(n1,#1)|subtract(#2,#3)|add(n4,#4)|add(#5,const_3)|
general
anne bought doughnuts for a class breakfast party . she bought 12 chocolate doughnuts , 6 coconut doughnuts , and 8 jam - filled doughnuts . how many doughnuts did anne buy in all ?
"number of students in group a = 45 students who forget homework in group a = 20 % of 45 = 9 students number of students in group b = 55 students who forget homework in group b = 40 % of 55 = 22 students total number of students = 45 + 55 = 100 students who forgot homework = 9 + 22 = 31 students percentage of students who forget homework = 31 / 100 * 100 = 31 % answer : d"
a ) 23 % , b ) 25 % , c ) 29 % , d ) 31 % , e ) 36 %
d
multiply(divide(add(divide(multiply(45, 20), const_100), divide(multiply(55, 40), const_100)), add(45, 55)), const_100)
add(n0,n1)|multiply(n0,n2)|multiply(n1,n3)|divide(#1,const_100)|divide(#2,const_100)|add(#3,#4)|divide(#5,#0)|multiply(#6,const_100)|
gain
eric throws 2 dice , and his score is the sum of the values shown . sandra throws one dice and her score is the square of the value shown . what is the probabilty that sandras score will be strictly higher than erics score ? ?
"production during these 5 days = total production in a month - production in first 25 days . = 30 x 43 - 25 x 50 = 40 ∴ average for last 5 days = 40 / 5 = 8 c"
a ) 20 , b ) 36 , c ) 8 , d ) 50 , e ) 59
c
divide(subtract(multiply(add(25, 5), 43), multiply(25, 50)), 5)
add(n1,n2)|multiply(n0,n1)|multiply(n3,#0)|subtract(#2,#1)|divide(#3,n2)|
general
a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 10 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
solution : 10 v 2 area of square = 1 / 2 * ( length of diagonal ) 2 area of square 1 = * ( 5 v 2 ) 2 = 25 area of square 2 = 4 * 25 = 100 length of diagonal of square 2 = v 2 * area = v 2 * 100 = v 200 = 10 v 2 cm answer is c
['a ) 20 v 2', 'b ) 10', 'c ) 10 v 2', 'd ) 20', 'e ) 25']
c
multiply(const_10, sqrt(2))
sqrt(n2)|multiply(#0,const_10)
geometry
two cyclist start on a circular track from a given point but in opposite direction with speeds of 7 m / s and 8 m / s . if the circumference of the circle is 360 meters , after what time will they meet at the starting point ?
"let t be the tier price , p be total price = 12000 per the given conditions : 0.12 t + 0.08 ( p - t ) = 1440 - - - - > t = 12000 . d is the correct answer ."
a ) $ 1600 , b ) $ 6000 , c ) $ 6050 , d ) $ 1200 , e ) $ 8000
d
divide(subtract(1440, multiply(multiply(multiply(const_3, multiply(const_2, const_3)), const_1000), divide(8, const_100))), subtract(divide(12, const_100), divide(8, const_100)))
divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_3)|multiply(#2,const_3)|subtract(#1,#0)|multiply(#3,const_1000)|multiply(#0,#5)|subtract(n3,#6)|divide(#7,#4)|
general
a straight line in the xy - plane has a slope of 2 and a y - intercept of 2 . on this line , what is the x - coordinate of the point whose y - coordinate is 550 ?
"am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 73 x = 71 answer : a"
a ) 71 , b ) 75 , c ) 85 , d ) 83 , e ) 82
a
subtract(multiply(4, const_2), multiply(2, const_2))
multiply(n1,const_2)|multiply(n0,const_2)|subtract(#0,#1)|
general
a computer store offers employees a 30 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 900 dollars and marked up the price 30 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 30 % off retail price ) as opposed to the final retail price .
"1904 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1700 . answer : a"
a ) 1700 , b ) 2777 , c ) 2889 , d ) 27670 , e ) 2771
a
divide(1904, add(divide(multiply(divide(add(multiply(2, 5), 2), 5), 5), const_100), const_1))
multiply(n1,n3)|add(n1,#0)|divide(#1,n3)|multiply(n0,#2)|divide(#3,const_100)|add(#4,const_1)|divide(n4,#5)|
general
john and andrew can finish the work 9 days if they work together . they worked together for 6 days and then andrew left . john finished the remaining work in another 6 days . in how many days john alone can finish the work ?
"a 11 ( x + y ) â € “ ( y + z ) = 11 x â € “ z = 11"
a ) 11 , b ) 15 , c ) 12 , d ) 17 , e ) 19
a
divide(11, const_1)
divide(n0,const_1)|
general
car z travels 48 miles per gallon of gasoline when driven at a constant rate of 45 miles per hour , but travels 20 percent fewer miles per gallon of gasoline when driven at a constant rate of 60 miles per hour . how many miles does car z travel on 10 gallons of gasoline when driven at a constant rate of 60 miles per hour ?
"( place value of 5 ) - ( face value of 5 ) = ( 50000 - 5 ) = 49995 answer : option d"
a ) 973 , b ) 6973 , c ) 5994 , d ) 49995 , e ) none of these
d
subtract(multiply(const_10, 5), 5)
multiply(n0,const_10)|subtract(#0,n0)|
general
if a # b = ab – b + b ^ 2 , then 3 # 4 =
"xyt / ( x + y ) x = 5 , y = 10 , t = 3 5 * 10 * 3 / 5 + 10 = 150 / 50 = 10 answer : c"
a ) 15 , b ) 18 , c ) 10 , d ) 12 , e ) 14
c
divide(multiply(multiply(5, 10), 3), multiply(5, 10))
multiply(n0,n1)|multiply(n2,#0)|divide(#1,#0)|
physics
if p / q = 3 / 7 , then 2 p + q = ?
"solution correct sum = ( 36 x 50 + 47 - 23 ) = 1824 . â ˆ ´ correct mean = 1824 / 50 = 36.48 . answer d"
a ) 35.24 , b ) 36.16 , c ) 36.22 , d ) 36.48 , e ) none
d
divide(add(multiply(36, 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
the ratio of the area of a square to that of the square drawn on its diagonal is
"let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 324 / 3 = 108 sq m l b = 108 i . e . , l * l / 3 = 108 l 2 = 324 = > l = 18 . answer : c"
a ) 27 m , b ) 24 m , c ) 18 m , d ) 21 m , e ) none of these
c
multiply(sqrt(divide(divide(324, 3), const_3)), const_3)
divide(n1,n2)|divide(#0,const_3)|sqrt(#1)|multiply(#2,const_3)|
gain
the speed of a boat in still water in 22 km / hr and the rate of current is 5 km / hr . the distance travelled downstream in 24 minutes is :
"90 % 104 % - - - - - - - - 14 % - - - - 182 100 % - - - - ? = > rs : 1300 answer : d"
a ) s : 1000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1300 , e ) s : 1027
d
divide(multiply(182, const_100), subtract(add(const_100, 4), subtract(const_100, 10)))
add(const_100,n2)|multiply(n1,const_100)|subtract(const_100,n0)|subtract(#0,#2)|divide(#1,#3)|
gain
reeya obtained 40 , 60 , 70 , 80 and 80 out of 100 in different subjects , what will be the average
"the incomes of a and b be 3 p and 4 p . expenditures = income - savings ( 3 p - 100 ) and ( 4 p - 100 ) the ratio of their expenditure = 1 : 4 ( 3 p - 100 ) : ( 4 p - 100 ) = 1 : 4 8 p = 300 = > p = 37.5 their incomes = 112.5 , 150 answer : d"
a ) 112.5 , 158.5 , b ) 180.5 , 150 , c ) 100 , 200 , d ) 112.5 , 150 , e ) 122.5 , 150
d
multiply(3, divide(100, 4))
divide(n2,n4)|multiply(n0,#0)|
other
if 5 ^ 5 × 5 ^ x = ( 125 ) ^ 4 , then what is the value of x ?
"there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 10 . plugging it in , we get 35 diagonals ! answer ( b ) ."
a ) 875 , b ) 35 , c ) 1425 , d ) 2025 , e ) 2500
b
divide(multiply(subtract(10, const_3), 10), const_2)
subtract(n0,const_3)|multiply(n0,#0)|divide(#1,const_2)|
geometry
what is the max number of rectangular boxes , each measuring 5 inches by 2 inches by 7 inches , that can be packed into a rectangular packing box measuring 15 inches by 20 inches by 35 inches , if all boxes are aligned in the same direction ?
"2 3 / 4 - 1 2 / 5 = 11 / 4 - 7 / 5 = ( 55 - 28 ) / 20 = 27 / 20 2 / 3 - 1 / 3 = ( 6 - 3 ) / 3 = 3 / 3 = 1 so 27 / 20 / 1 = 27 - 20 answer - d"
a ) 17 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 27 / 20 , e ) 51 / 44
d
subtract(divide(add(multiply(const_10, 2), 2), 4), divide(add(const_10, 1), 5))
add(n3,const_10)|multiply(const_10,n0)|add(n0,#1)|divide(#0,n5)|divide(#2,n2)|subtract(#4,#3)|
general
steve traveled the first 2 hours of his journey at 35 mph and the remaining 3 hours of his journey at 80 mph . what is his average speed for the entire journey ?
time of meeting = distance / relative speed = 36 / 8 + 4 = 36 / 12 = 3 hrs after 5 am = 8 am answer is a
a ) 8 am , b ) 6 am , c ) 7 am , d ) 10 am , e ) 8 pm
a
add(5, divide(36, add(4, 8)))
add(n1,n2)|divide(n3,#0)|add(n0,#1)
physics
in 1979 approximately 1 / 3 of the 32.3 million airline passengers traveling to or from the united states used kennedy airport . if the number of such passengers that used miami airport was 1 / 2 the number that used kennedy airport and 4 times the number that used logan airport , approximately how many millions of these passengers used logan airport that year ?
n = 4 k + 1 = 7 j + 3 let ' s start at 1 = 4 ( 0 ) + 1 and keep adding 4 until we find a number in the form 7 j + 3 . 1 , 5 , 9 , 13 , 17 = 7 ( 2 ) + 3 the next such number is 17 + 4 * 7 = 45 . 17 + 45 = 62 the answer is c .
a ) 54 , b ) 58 , c ) 62 , d ) 66 , e ) 70
c
add(add(multiply(7, const_2), 3), add(multiply(7, multiply(const_2, const_3)), 3))
multiply(n2,const_2)|multiply(const_2,const_3)|add(n3,#0)|multiply(n2,#1)|add(n3,#3)|add(#2,#4)
general