Problem
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628
| Rationale
stringlengths 1
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| options
stringlengths 37
137
| correct
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stringlengths 6
848
| linear_formula
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| category
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|---|---|---|---|---|---|---|
if two integers x , y ( x > y ) are selected from - 10 to 1 ( inclusive ) , how many possible cases are there ?
|
"out of 100 pounds 99 % or 99 pounds is water and 1 pound is non - water . after somewaterevaporates the cucumbers become 94 % water and 6 % of non - water , so now 1 pound of non - water composes 6 % of cucucmbers , which means that the new weight of cucumbers is 1 / 0.06 = 16 pounds . answer : b ."
|
a ) 2 , b ) 16 , c ) 92 , d ) 96 , e ) 98
|
b
|
multiply(divide(subtract(100, 99), subtract(100, 94)), 100)
|
subtract(n0,n1)|subtract(n0,n2)|divide(#0,#1)|multiply(#2,n0)|
|
gain
|
the average of first six multiples of 3 is
|
"the average of 5 numbers is 6.8 the sum of 5 numbers will be 6.8 x 5 = 34 the average of 5 number after one of the number is multiplied by 4 is 9.2 the sum of the numbers will now be 9.2 x 5 = 46 so the sum has increased by 46 - 34 = 12 let the number multiplied by 4 be n then , 4 n = n + 12 or 3 n = 12 or n = 4 answer : - d"
|
a ) 1.5 , b ) 3.0 , c ) 3.9 , d ) 4.0 , e ) 6.0
|
d
|
subtract(multiply(9.2, 5), multiply(6.8, 5))
|
multiply(n0,n3)|multiply(n0,n1)|subtract(#0,#1)|
|
general
|
a train consists of 12 boggies , each boggy 15 metres long . the train crosses a telegraph post in 18 seconds . due to some problem , two boggies were detached . the train now crosses a telegraph post in
|
"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"
|
a ) 14 , b ) 12 , c ) 13 , d ) 15 , e ) 16
|
d
|
divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)
|
multiply(n0,const_2)|multiply(#0,const_4)|add(#1,const_1)|sqrt(#2)|add(#3,const_1)|divide(#4,const_2)|
|
general
|
( 4300331 ) - ? = 2535618
|
"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 = 10 , m = 30 and minute hand is behind the hour hand . hence the angle = 30 ( h − m / 5 ) + m / 2 = 30 ( 10 − 30 / 5 ) + 30 / 2 = 30 ( 10 − 6 ) + 15 = 30 × 4 + 15 = 135 ° answer is d ."
|
a ) 35 ° , b ) 65 ° , c ) 45 ° , d ) 135 ° , 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
|
at a summer camp with 2100 participants , 1 / 2 of the campers are aged 8 to 12 . next year , the number of campers aged 8 to 12 will increase by 1 / 3 . after this change , what percentage of the total 2100 campers will the 8 - to 12 - year - olds represent ?
|
"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 + 5 x = 20.5 minutes answer : a"
|
a ) 20.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
|
a
|
subtract(subtract(divide(const_60, const_2), 5), 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
|
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 ?
|
"explanation : let ’ s begin by looking for a pattern as we increase the exponent . 13 ^ 1 = 13 ( units digit is 3 ) 13 ^ 2 = 169 ( units digit is 9 ) 13 ^ 3 = 2197 ( units digit is 7 ) notice that a nice pattern emerges . we get : 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - 3 - 9 - 7 - 1 - … whenever n is a multiple of 4 , the units digit of 13 ^ n is 1 the units digit of 13 ^ 35 is 7 answer is b"
|
a ) 5 , b ) 7 , c ) 6 , d ) 8 , e ) 9
|
b
|
multiply(floor(divide(power(const_10, 13), 35)), 35)
|
power(const_10,n0)|divide(#0,n1)|floor(#1)|multiply(n1,#2)|
|
general
|
a train running at the speed of 110 km / hr crosses a pole in 9 sec . what is the length of the train ?
|
"the number of trailing zeros in the decimal representation of n ! , the factorial of a non - negative integer n , can be determined with this formula : n 5 + n 52 + n 53 + . . . + n 5 k , where k must be chosen such that 5 k ≤ n x = 1 * 2 * 3 . . . . * 25 = 25 ! no . of trailing zeros in 25 ! = 25 / 5 + 25 / 5 ^ 2 = 6 100 ^ k = 10 ^ 2 k → k = 6 / 2 = 3 c"
|
a ) 5 , b ) 4 , c ) 3 , d ) 6 , e ) 7
|
c
|
add(divide(25, const_10), 1)
|
divide(n1,const_10)|add(#0,n0)|
|
general
|
one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 150 cm when it touches the floor on third time . what is the value of the original height ?
|
let length = 2 x meters and breadth = 3 x meter . now , area = ( 1 / 6 ) x 1000 m 2 = 5000 / 3 m 2 so , 2 x * 3 x = 5000 / 3 < = > x 2 = 2500 / 9 < = > x = 50 / 3 therefore length = 2 x = ( 100 / 3 ) m = 33 ( 1 / 3 ) m and breadth = 3 x = 3 ( 50 / 3 ) m = 50 m . answer is a
|
['a ) 50', 'b ) 30', 'c ) 20', 'd ) 40', 'e ) 10']
|
a
|
divide(multiply(divide(multiply(const_10, const_1000), 6), 3), const_100)
|
multiply(const_10,const_1000)|divide(#0,n3)|multiply(n1,#1)|divide(#2,const_100)
|
geometry
|
if x < y < z and y - x > 7 , where x is an even integer and y and z are odd integers , what is the least possible value of z - x ?
|
"that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 10 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 10 × 8 = 12 days b )"
|
a ) 10 days , b ) 12 days , c ) 13 days , d ) 11 days , e ) 9 days
|
b
|
divide(multiply(multiply(12, 10), 8), multiply(8, 10))
|
multiply(n0,n2)|multiply(n3,n4)|multiply(n1,#0)|divide(#2,#1)|
|
physics
|
what is the smallest positive perfect square that is divisible by 4 , 9 , and 18 ?
|
"the number of nurses at the hospital is ( 7 / 10 ) * 240 = 168 . the answer is a ."
|
a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
|
a
|
multiply(divide(240, add(3, 7)), 7)
|
add(n1,n2)|divide(n0,#0)|multiply(n2,#1)|
|
other
|
what percent is 400 gm of 1 kg ?
|
"explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1125 820 x + 1125 * 441 x = 605.03 so , value of each installment = rs . 605.03 answer : option d"
|
a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 605.03 , e ) 646.33
|
d
|
divide(multiply(power(add(divide(5, const_100), const_1), 2), 1125), 2)
|
divide(n2,const_100)|add(#0,const_1)|power(#1,n1)|multiply(n0,#2)|divide(#3,n1)|
|
gain
|
in a games hour 4 different types of players came to the ground ? cricket 11 , hokey 15 , football 21 , softball 15 . how many players are present in the ground ?
|
"abel in the 2 days that he worked completed 1 / 4 of the job = 3 / 4 remains then if ben had to leave 3 days before the completion , this means that carla had to work alone for these 3 days in which she completed 1 / 5 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 3 / 20 3 / 20 ( t ) = 3 / 20 - - - > t = 1 therefore , these 1 day worked plus the 3 days that carla had to work by herself add to 4 days answer : a"
|
a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 10
|
a
|
multiply(add(2, 3), 3)
|
add(n3,n4)|multiply(n4,#0)|
|
physics
|
if x is 20 percent greater than 55 , then x =
|
"x = √ 2 and y also = √ 2 applying the function ( √ 2 + √ 2 ) ^ 2 - ( √ 2 - √ 2 ) ^ 2 = ( 2 √ 2 ) ^ 2 - 0 = 4 x 2 = 8 . note : alternative approach is the entire function is represented as x ^ 2 - y ^ 2 = ( x + y ) ( x - y ) which can be simplified as ( x + y + x - y ) ( x + y - ( x - y ) ) = ( 2 x ) ( 2 y ) = 4 xy . substituting x = √ 2 and y = √ 2 you get the answer 8 . answer b"
|
a ) 0 , b ) 8 , c ) 10 , d ) 15 , e ) 20
|
b
|
power(add(sqrt(2), sqrt(2)), 2)
|
sqrt(n2)|add(#0,#0)|power(#1,n0)|
|
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 ?
|
i believe the answer is c . please see below for explanation . if jamshid can paint a dence in 50 percent less time then taimour we can infer the following rate j = 2 t if working together they can do the job in 8 hours we can infer 1 = 2 t + t * 4 = > 1 / 12 working alone taimour can do the job in 1 = 1 / 12 * hours = > 12 answer c
|
a ) 6 hours , b ) 8 hours , c ) 12 hours , d ) 24 hours , e ) 32 hours
|
c
|
multiply(4, const_3)
|
multiply(n1,const_3)
|
physics
|
find the area , diameter = 11 m .
|
"total number of students studying both are 100 + 300 - 200 = 200 ( subtracting the 200 since they were included in the both the other numbers already ) . so 40 % of total is 200 , so 100 % is 500 answer is b"
|
a ) 550 , b ) 500 , c ) 600 , d ) 650 , e ) 700
|
b
|
add(100, 300)
|
add(n0,n1)|
|
general
|
in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :
|
"one possible case is : rainy - rainy - rainy - not rainy - not rainy - not rainy . the probability of this case is ( 1 / 2 ) ^ 6 = 1 / 64 the number of possible cases is 6 c 3 = 20 . p ( exactly 3 rainy days ) = 20 * 1 / 64 = 5 / 16 the answer is b ."
|
a ) 3 / 16 , b ) 5 / 16 , c ) 7 / 32 , d ) 11 / 32 , e ) 17 / 64
|
b
|
multiply(4, power(divide(const_1, const_2), 4))
|
divide(const_1,const_2)|power(#0,n2)|multiply(n2,#1)|
|
general
|
26 % of employees are women with fair hair . 40 % of fair - haired employees are women . what percent of employees have fair hair ?
|
"answer let √ n / 20 = 4 then √ n = 20 x 4 = 80 ∴ n = 80 x 80 = 6400 . correct option : b"
|
a ) 76 , b ) 6400 , c ) 304 , d ) 1296 , e ) none
|
b
|
power(multiply(4, 20), const_2)
|
multiply(n0,n1)|power(#0,const_2)|
|
general
|
in one hour , a boat goes 8 km along the stream and 2 km against the stream . the sped of the boat in still water ( in km / hr ) is :
|
"the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 45 / 3 = 15 kmph answer : d"
|
a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
|
d
|
subtract(45, divide(multiply(45, const_2), const_3))
|
multiply(n0,const_2)|divide(#0,const_3)|subtract(n0,#1)|
|
physics
|
after decreasing 25 % in the price of an article costs rs . 1500 . find the actual cost of an article ?
|
"the problem with your solution is that we do n ' t choose 1 shoe from 28 but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 27 ( as after taking one at random there are 27 shoes left and only one is the pair of the first one ) = 1 / 27 answer : d"
|
a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 27 , e ) 1 / 9
|
d
|
divide(const_1, subtract(28, const_1))
|
subtract(n1,const_1)|divide(const_1,#0)|
|
general
|
in the first 10 overs of a cricket game , the run rate was only 5.2 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
|
a = 1 , b = 5 , c = 4 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 4 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 16 ) ) / 2 = ( - 5 â ± 3 ) / 2 x 1 = ( - 5 + 3 ) / 2 = - 2 / 2 = - 1 x 2 = ( - 5 - 1 ) / 2 = - 6 / 2 = - 3 b
|
a ) 1 , b ) - 3 , c ) 3 , d ) 2 , e ) 0
|
b
|
divide(subtract(5, sqrt(subtract(power(5, const_2), multiply(const_4, 4)))), const_2)
|
multiply(n2,const_4)|power(n1,const_2)|subtract(#1,#0)|sqrt(#2)|subtract(n1,#3)|divide(#4,const_2)
|
general
|
rhonda picked 2 pen from the table , if there were 7 pens on the table and 5 belongs to jill , what is the probability that the 2 pen she picked does not belong to jill ? .
|
"10 % of 1000 gives 100 . so 100 attends chess and 10 % of 100 gives 10 . so 10 enrolled for swimming answer : b"
|
a ) 1 , b ) 10 , c ) 100 , d ) 50 , e ) 20
|
b
|
divide(multiply(divide(multiply(10, 1000), const_100), 10), const_100)
|
multiply(n0,n1)|divide(#0,const_100)|multiply(n2,#1)|divide(#2,const_100)|
|
gain
|
in a company of 170 employees , 110 are females . a total of 80 employees have advanced degrees and the rest have a college degree only . if 25 employees are males with college degree only , how many employees are females with advanced degrees ?
|
anyway , in this question , there is no discount but the mark up is given as 40 % of the selling price . so it is not 20 % of $ 150 but instead , 20 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 20 % of s = s s = 150 / 0.8 profit = 150 / 0.8 - 150 = which is calculated on cost price in % terms . so 37.5 / 150 * 100 = 25 % is profit . e
|
a ) 45 % , b ) 40 % , c ) 35 % , d ) 30 % , e ) 25 %
|
e
|
divide(multiply(subtract(divide(150, subtract(const_1, divide(20, const_100))), 150), const_100), 150)
|
divide(n1,const_100)|subtract(const_1,#0)|divide(n0,#1)|subtract(#2,n0)|multiply(#3,const_100)|divide(#4,n0)
|
gain
|
in plutarch enterprises , 70 % of the employees are marketers , 10 % are engineers , and the rest are managers . marketers make an average salary of $ 50000 a year , and engineers make an average of $ 80000 . what is the average salary for managers if the average for all employees is also $ 80000 ?
|
time of meeting = distance / relative speed = 15 / 3 + 2 = 15 / 5 = 3 hrs after 4 pm = 7 pm answer is c
|
a ) 8 pm , b ) 6 pm , c ) 7 pm , d ) 10 pm , e ) 5 pm
|
c
|
add(4, divide(15, add(2, 3)))
|
add(n1,n2)|divide(n3,#0)|add(n0,#1)
|
physics
|
at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 11.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
|
"number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 3 and 4 are adjacent - consider 3 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 3 and 2 can be arranged as 32 or 23 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : b"
|
a ) 48 , b ) 72 , c ) 76 , d ) 78 , e ) 90
|
b
|
subtract(multiply(multiply(multiply(5, 24), 3), const_2), multiply(multiply(multiply(24, 3), const_2), const_2))
|
multiply(n1,n4)|multiply(n3,n4)|multiply(n3,#0)|multiply(#1,const_2)|multiply(#2,const_2)|multiply(#3,const_2)|subtract(#4,#5)|
|
general
|
a hollow iron pipe is 21 cm long and its external diameter is 8 cm . if the thickness of the pipe is 1 cm and iron weighs 8 g / cm ^ 3 , then the weight of the pipe is :
|
"in a parallelogram opposite angles are equal and the angles at each side are supplementary to each other ( supplementary angles are two angles that add up to 180 ° ) . given : x + ( x + 20 ) = 180 - - > x = 80 . answer : b ."
|
a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
|
b
|
divide(subtract(divide(const_3600, const_10), multiply(20, const_2)), const_4)
|
divide(const_3600,const_10)|multiply(n0,const_2)|subtract(#0,#1)|divide(#2,const_4)|
|
geometry
|
at 6 ′ o a clock ticks 6 times . the time between first and last ticks is 20 seconds . how long does it tick at 12 ′ o clock
|
explanation : sum of the present ages of a , b and c = ( 27 × 3 + 3 × 3 ) years = 90 years . sum of the present ages of b and c = ( 20 × 2 + 5 × 2 ) years = 50 years . a ' s present age = 90 – 50 = 40 years . answer : c
|
a ) 22 , b ) 88 , c ) 40 , d ) 87 , e ) 17
|
c
|
subtract(add(multiply(27, 3), multiply(3, 3)), add(multiply(20, const_2), multiply(5, const_2)))
|
multiply(n0,n1)|multiply(n0,n0)|multiply(n3,const_2)|multiply(n2,const_2)|add(#0,#1)|add(#2,#3)|subtract(#4,#5)
|
general
|
the weight of a hollow sphere is directly dependent on its surface area . the surface area of a sphere is 4 π · r ^ 2 , where r is the radius of the sphere . if a hollow sphere of radius 0.15 cm made of a certain metal weighs 8 grams , a hollow sphere of radius 0.3 cm made of the same metal would weigh how many grams t ?
|
ratio of times taken by a and b = 1 : 3 . the time difference is ( 3 - 1 ) 2 days while b take 3 days and a takes 1 day . if difference of time is 2 days , b takes 3 days . if difference of time is 60 days , b takes ( 3 / 2 * 60 ) = 90 days so , a takes 30 days to do the work . a ' s 1 day ' s work = 1 / 30 b ' s 1 day ' s work = 1 / 90 ( a + b ) ' s 1 day ' s work = ( 1 / 30 + 1 / 90 ) = 4 / 90 = 2 / 45 a and b together can do the work in 45 / 2 = 22 1 / 2 days answer = b
|
a ) 20 days , b ) 22 1 / 2 days , c ) 24 days , d ) 25 days , e ) 30 days
|
b
|
multiply(add(const_4, const_1), divide(const_1, add(divide(const_1, divide(60, const_2)), divide(const_1, add(divide(60, const_2), 60)))))
|
add(const_1,const_4)|divide(n0,const_2)|add(n0,#1)|divide(const_1,#1)|divide(const_1,#2)|add(#3,#4)|divide(const_1,#5)|multiply(#0,#6)
|
physics
|
if both 5 ^ 2 and 3 ^ 3 are factors of n x ( 2 ^ 5 ) x ( 6 ) x ( 7 ^ 3 ) , what is the smallest possible positive value of n ?
|
"74330 largest 30347 smallest - - - - - - - - - - - - - 43983 answer : c"
|
a ) 70983 , b ) 43893 , c ) 43983 , d ) 43883 , e ) 43823
|
c
|
subtract(add(add(add(multiply(multiply(3, const_100), const_10), multiply(0, const_100)), multiply(4, const_10)), 7), add(add(add(const_1000, multiply(4, const_100)), multiply(0, const_10)), 3))
|
multiply(n0,const_100)|multiply(n3,const_100)|multiply(n1,const_10)|multiply(n1,const_100)|multiply(n3,const_10)|add(#3,const_1000)|multiply(#0,const_10)|add(#6,#1)|add(#5,#4)|add(#7,#2)|add(n0,#8)|add(n2,#9)|subtract(#11,#10)|
|
general
|
what is the number of integers from 1 to 1000 ( inclusive ) that are divisible by neither 20 nor by 35 ?
|
"2 ( l + 120 ) = 600 = > l = 180 m answer : b"
|
a ) 286 m , b ) 180 m , c ) 200 m , d ) 166 m , e ) 187 m
|
b
|
subtract(divide(600, const_2), 120)
|
divide(n0,const_2)|subtract(#0,n1)|
|
physics
|
in a forest 140 deer were caught , tagged with electronic markers , then released . a week later , 50 deer were captured in the same forest . of these 50 deer , it was found that 5 had been tagged with the electronic markers . if the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest , and if no deer had either left or entered the forest over the preceding week , what is the approximate number of deer in the forest ?
|
"along one edge , the number of small cubes that can be cut = 100 / 20 = 5 along each edge 20 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 5 * 5 * 5 = 125 answer : e"
|
a ) 2878 , b ) 2778 , c ) 1000 , d ) 120 , e ) 125
|
e
|
divide(power(power(20, const_2), const_3), power(20, const_3))
|
power(n0,const_2)|power(n0,const_3)|power(#0,const_3)|divide(#2,#1)|
|
physics
|
how many liters of water must be evaporated from 50 liters of a 6 - percent sugar solution to get a 10 - percent solution ?
|
explanation : in such a case the middle number ( c ) is the average ∴ c = 20 and d = 22 and e = 24 required percentage = 22 / 24 x 100 = 91.7 answer : option b
|
a ) 90.1 , b ) 91.7 , c ) 97.1 , d ) 101.1 , e ) 107.1
|
b
|
multiply(divide(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), add(add(add(add(subtract(20, divide(add(add(add(const_2, multiply(const_2, const_2)), multiply(const_2, const_3)), multiply(const_2, const_4)), 5)), const_2), const_2), const_2), const_2)), const_100)
|
multiply(const_2,const_2)|multiply(const_2,const_3)|multiply(const_2,const_4)|add(#0,const_2)|add(#3,#1)|add(#4,#2)|divide(#5,n0)|subtract(n1,#6)|add(#7,const_2)|add(#8,const_2)|add(#9,const_2)|add(#10,const_2)|divide(#10,#11)|multiply(#12,const_100)
|
general
|
an item is being sold for $ 10 each . however , if a customer will “ buy at least 3 ” they have a promo discount of 30 % . also , if a customer will “ buy at least 10 ” items they will deduct an additional 8 % to their “ buy at least 3 ” promo price . if sam buys 10 pcs of that item how much should he pay ?
|
"2 ( 3 x + x ) = 72 l = 27 b = 9 lb = 27 * 9 = 243 answer : c"
|
a ) 432 , b ) 212 , c ) 243 , d ) 992 , e ) 212
|
c
|
multiply(multiply(divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))), const_3), divide(72, add(multiply(const_3, const_2), multiply(const_1, const_2))))
|
multiply(const_2,const_3)|multiply(const_1,const_2)|add(#0,#1)|divide(n0,#2)|multiply(#3,const_3)|multiply(#3,#4)|
|
geometry
|
in a graduate physics course , 70 percent of the students are male and 40 percent of the students are married . if two - sevenths of the male students are married , what fraction of the female students is single ?
|
"first of all you should remember that there is a difference in left and right sock . now no . of way to select any of the sock = 5 and for second = 4 so total methods = 5 * 4 = 20 answer : b"
|
a ) 19 , b ) 20 , c ) 30 , d ) 32 , e ) 25
|
b
|
add(choose(5, 2), choose(5, 2))
|
choose(n0,n1)|add(#0,#0)|
|
probability
|
3 - twentieths of the members of a social club are retirees who are also bridge players , 5 - twentieths of the members are retirees , and one - half of the members are bridge players . if 120 of the members are neither retirees nor bridge players , what is the total number of members in the social club ?
|
"m ^ 2 is divisible by 48 so m ^ 2 must be multiple of 48 . if the value of m is multiples of 12 then it will satisfy the condition . if we if m is 12 or 24 or 36 then it ans is d but if m = 48 then answer should be 16 . is the question right ? or am i missing some thing ? d"
|
a ) 3 , b ) 6 , c ) 8 , d ) 12 , e ) 16
|
d
|
multiply(const_3, divide(divide(36, const_3), const_3))
|
divide(n1,const_3)|divide(#0,const_3)|multiply(#1,const_3)|
|
general
|
find how many positive integers less than 10000 are there such thatthe sum of the digits of the no . is divisible by 3 ?
|
"let p be the original price and let x be the number of items sold originally . the original income is p * x . after the changes , the income is 0.9 p * 1.1 x = 0.99 * ( p * x ) , a decrease of 1 % . the answer is a ."
|
a ) 1 % , b ) 3 % , c ) 5 % , d ) 7 % , e ) 9 %
|
a
|
subtract(subtract(10, 10), divide(10, 10))
|
divide(n1,n0)|subtract(n1,n0)|subtract(#1,#0)|
|
gain
|
compute all real solutions to 16 x + 4 x + 1 - 96 = 0
|
the lcm of 2 and 8 is 8 . divide 2400 / 8 = 300 . xxx . so c is your answer .
|
a ) 104 , b ) 208 , c ) 300 , d ) 832 , e ) 833
|
c
|
add(divide(subtract(8, 2400), 2), const_1)
|
subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)|
|
general
|
of the 100 people in a room , 4 / 5 are women . if 3 / 5 of the people are married , what is the maximum number of women in the room who could be unmarried ?
|
"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 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
|
a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
|
d
|
divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))
|
add(const_1,const_1)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)|
|
general
|
a rectangular tiled patio is composed of 90 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 90 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
|
"speed = 128 * 5 / 18 = 36 m / sec time taken = 110 / 36 = 3.1 sec . answer : c"
|
a ) 2.5 sec , b ) 2.9 sec , c ) 3.1 sec , d ) 8.7 sec , e ) 8.5 sec
|
c
|
divide(110, multiply(128, const_0_2778))
|
multiply(n1,const_0_2778)|divide(n0,#0)|
|
physics
|
joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 36400 , how many months will it take joan to pay back her mortgage ?
|
"the number needs to be divisible by 3 ^ 2 , 3 * 7 , and 7 ^ 2 . the smallest such perfect square is 3 ^ 2 * 7 ^ 2 = 441 the answer is c ."
|
a ) 225 , b ) 324 , c ) 441 , d ) 529 , e ) 900
|
c
|
add(multiply(multiply(multiply(9, power(const_3, const_2)), 21), const_2), multiply(21, 49))
|
multiply(n1,n2)|power(const_3,const_2)|multiply(n0,#1)|multiply(n1,#2)|multiply(#3,const_2)|add(#4,#0)|
|
geometry
|
pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
|
"relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 160 + 160 = 320 m . required time = 320 * 9 / 250 = 288 / 25 = 11.52 sec . answer : e"
|
a ) 10.52 sec , b ) 18.8 sec , c ) 14.52 sec , d ) 10.8 sec , e ) 11.52 sec
|
e
|
divide(add(160, 160), multiply(add(60, 40), const_0_2778))
|
add(n0,n1)|add(n2,n3)|multiply(#1,const_0_2778)|divide(#0,#2)|
|
physics
|
in the coordinate plane , a circle centered on point ( - 3 , 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
|
44 ropes measure a feet or 12 * a inches 1 rope will measure = 12 * a / 44 = 6 * a / 22 = 3 * a / 11 b piece of rope measure = b * 3 * a / 11 = 3 ab / 11 hence , the answer is e .
|
a ) 44 / ab , b ) 11 / 3 ab , c ) 6 / 11 ab , d ) ab / 44 , e ) 3 ab / 11
|
e
|
divide(const_12, 44)
|
divide(const_12,n0)
|
general
|
what is the largest number of 4 digits which is divisible by 15 , 25 , 40 and 75 ?
|
"it is monthly compound rate = 5 / 12 % per month 70000 * ( 1 + 5 / 1200 ) ^ 4 - 70000 = 1173.98 answer : c"
|
a ) 1171.98 , b ) 1172.98 , c ) 1173.98 , d ) 1174.98 , e ) 1175.98
|
c
|
divide(multiply(multiply(multiply(const_3, const_100), const_100), multiply(5, divide(4, multiply(4, const_3)))), const_100)
|
multiply(const_100,const_3)|multiply(const_3,n1)|divide(n1,#1)|multiply(#0,const_100)|multiply(n2,#2)|multiply(#3,#4)|divide(#5,const_100)|
|
gain
|
harkamal purchased 8 kg of grapes at the rate of 70 per kg and 9 kg of mangoes at the rate of 75 per kg . how much amount did he pay to the shopkeeper ?
|
"solution relative speed = ( 48 - 40 ) kmph = 8 kmph = ( 8 x 5 / 18 ) m / sec = ( 40 / 18 ) m / sec time taken = ( 350 x 18 / 40 ) sec = 157.5 sec . answer c"
|
a ) 72 sec , b ) 132 sec , c ) 157.5 sec , d ) 252 sec , e ) none
|
c
|
multiply(const_3600, divide(divide(add(200, 150), const_1000), subtract(48, 40)))
|
add(n0,n1)|subtract(n3,n2)|divide(#0,const_1000)|divide(#2,#1)|multiply(#3,const_3600)|
|
physics
|
a train is 410 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
|
"lets say the indicated weight is x for $ 10 but the trader actually get 1.1 x for $ 10 now he tells to the customer that its 1.1 ( 1.1 x ) = 1.21 x and charges the price accordingly i . e . 1.21 x * 10 / x = 12.1 so profit % = ( 12.1 - 10 ) / 10 = 0.21 = 21 % answer : b"
|
a ) 20 % , b ) 21 % , c ) 21.33 % , d ) 22.109 % , e ) 23 %
|
b
|
subtract(multiply(divide(add(const_100, 10), const_100), add(const_100, 10)), const_100)
|
add(n0,const_100)|add(n1,const_100)|divide(#1,const_100)|multiply(#0,#2)|subtract(#3,const_100)|
|
gain
|
the digital sum of a number is the sum of its digits . for how many of the positive integers 24 - 140 inclusive is the digital sum a multiple of 7 ?
|
"2 * 22 / 7 * 14 * x = 2288 = > x = 26 answer : a"
|
a ) 26 , b ) 28 , c ) 17 , d ) 12 , e ) 88
|
a
|
divide(2288, multiply(multiply(const_2, divide(add(add(multiply(const_3, const_100), multiply(const_1, const_10)), const_4), const_100)), 14))
|
multiply(const_100,const_3)|multiply(const_1,const_10)|add(#0,#1)|add(#2,const_4)|divide(#3,const_100)|multiply(#4,const_2)|multiply(n0,#5)|divide(n1,#6)|
|
physics
|
jerry travels 8 miles at an average speed of 40 miles per hour , stops for 14 minutes , and then travels another 20 miles at an average speed of 60 miles per hour . what is jerry ’ s average speed , in miles per hour , for this trip ?
|
"explanation : 18800 / 470 / 20 = ( 18800 / 470 ) / 20 = 40 / 20 = 2 answer : b"
|
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
|
b
|
divide(18800, 470)
|
divide(n0,n1)|
|
general
|
a line that passes through ( – 3 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
|
given there are 50 students in the seaside summer camp , 90 % of 50 = 45 boys and remaining 5 girls . now here 90 % are boys and 10 % are girls . now question is asking about how many boys do we need to add , to make the girls percentage to 5 or 5 % . . if we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it . now boys are 95 % and girls are 5 % . ( out of 100 students = 95 boys + 5 girls ) . imo option a is correct .
|
a ) 50 . , b ) 45 . , c ) 40 . , d ) 30 . , e ) 25 .
|
a
|
subtract(divide(multiply(subtract(50, divide(multiply(90, 50), const_100)), const_100), 5), 50)
|
multiply(n0,n1)|divide(#0,const_100)|subtract(n0,#1)|multiply(#2,const_100)|divide(#3,n2)|subtract(#4,n0)
|
general
|
x can do a piece of work in 4 hours ; y and z together can do it in 3 hours , while x and z together can do it in 2 hours . how long will y alone take to do it ?
|
let their prices be 3 x , 5 x and 7 x . then , 2 x + 6 x + 8 x = ( 15000 * 3 ) or x = 2812.5 . cost of cheapest item = 2 x = rs . 5625 . answer : c
|
a ) 2379 , b ) 2889 , c ) 5625 , d ) 9000 , e ) 28311
|
c
|
divide(multiply(3, 15000), 8)
|
multiply(n0,n1)|divide(#0,n4)
|
general
|
for any integer n greater than 1 , n * denotes the product of all the integers from 1 to n , inclusive . how many prime numbers t are there between 6 * + 2 and 6 * + 6 , inclusive ?
|
"at 2 : 00 pm , the truck and the car are 340 km apart . the truck and the car complete a distance of 80 km each hour . the time it takes to meet is 340 / 80 = 4.25 hours . they will meet at 6 : 15 pm . the answer is d ."
|
a ) 5 : 30 , b ) 5 : 45 , c ) 6 : 00 , d ) 6 : 15 , e ) 6 : 30
|
d
|
divide(subtract(divide(378, 38), 1), add(1, divide(42, 38)))
|
divide(n4,n2)|divide(n3,n2)|add(n0,#1)|subtract(#0,n0)|divide(#3,#2)|
|
physics
|
bag a contains red , white and blue marbles such that the red to white marble ratio is 1 : 3 and the white to blue marble ratio is 2 : 3 . bag b contains red and white marbles in the ratio of 1 : 4 . together , the two bags contain 42 white marbles . how many red marbles could be in bag a ?
|
"5 x 3 = 15 . sum of decimal places = 4 0.05 x 0.03 = 0.0015 answer : option c"
|
a ) 0.00015 , b ) 0.015 , c ) 0.0015 , d ) 0.15 , e ) 1.5
|
c
|
multiply(divide(0.05, 0.03), const_100)
|
divide(n0,n1)|multiply(#0,const_100)|
|
general
|
mr . das decided to walk down the escalator of a mall . he found that if he walks down 26 steps , he requires 30 seconds to reach the bottom . however , if he steps down 34 stair she would only require 18 seconds to get to the bottom . if the time is measured from the moment the top step begins to descend to the time he steps off the last step at the bottom , find out the height of the stair way insteps ?
|
"explanation : let the number be 1 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 1 = a / 30 = > a = 30 answer : a"
|
a ) 30 , b ) 81 , c ) 60 , d ) 27 , e ) 11
|
a
|
divide(const_3.0, divide(divide(const_1, multiply(const_3, add(const_2, 1))), const_2))
|
add(const_2,const_3)|multiply(#0,const_3)|divide(const_1,#1)|divide(#2,const_2)|divide(n0,#3)|
|
general
|
john makes $ 40 a week from his job . he earns a raise and now makes $ 70 a week . what is the % increase ?
|
in the following venn diagram , f and e represent people who read french and english respectively . now , [ f + ( { f ∩ e } ) + e ] = 15 - 3 ( or ) f + e + ( f ∩ e ) = 12 . . . . . . ( 1 ) also , f + ( f ∩ e ) = 7 ; e + ( f ∩ e ) = 8 . by adding , f + e + 2 ( f ∩ e ) = 15 - - - - - - - - - - ( 2 ) by subtracting ( 1 ) from ( 2 ) , we get ( f ∩ e ) = 3 . ∴ 3 of them read both french and english . answer : b
|
a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 5
|
b
|
subtract(add(8, 7), subtract(15, 3))
|
add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)
|
other
|
two friends c and d leave point c and point d simultaneously and travel towards point d and point c on the same route at their respective constant speeds . they meet along the route and immediately proceed to their respective destinations in 32 minutes and 50 minutes respectively . how long will d take to cover the entire journey between point d and point c ?
|
"let the actual distance traveled be x km . then , x / 10 = ( x + 20 ) / 14 4 x - 200 = > x = 50 km . answer : a"
|
a ) 50 km , b ) 16 km , c ) 18 km , d ) 29 km , e ) 19 km
|
a
|
multiply(10, divide(20, subtract(14, 10)))
|
subtract(n0,n1)|divide(n2,#0)|multiply(n1,#1)|
|
general
|
when a certain number x is divided by 54 , the remainder is 22 . what is the remainder when x is divided by 18 ?
|
"sum of 1 st n odd no . s = 1 + 3 + 5 + 7 + . . . = n ^ 2 so , sum of 1 st 36 odd numbers = 36 ^ 2 = 1296 answer : c"
|
a ) 1294 , b ) 1295 , c ) 1296 , d ) 1297 , e ) 1298
|
c
|
multiply(multiply(36, const_2), divide(36, const_2))
|
divide(n0,const_2)|multiply(n0,const_2)|multiply(#0,#1)|
|
general
|
for all even integers n , h ( n ) is defined to be the sum of the even integers between 4 and n , inclusive . what is the value of h ( 18 ) / h ( 10 ) ?
|
"though 2 * ( 15 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 14 , so he ' ll play 28 matches . similarly , second guy has to play with the rest of 13 as his 2 games with the first guy are already played . so he plays 26 matches . this continues like this and the total matches are 28 + 26 + 24 . . . + 2 28 + 26 + . . . + 2 = 2 ( 14 + 13 + . . . + 1 ) = 2 ( ( 14 * 15 ) / 2 ) = 14 * 15 = 210 . answer : c"
|
a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 225
|
c
|
multiply(15, subtract(15, const_1))
|
subtract(n0,const_1)|multiply(n0,#0)|
|
general
|
if an integer n is to be chosen at random from the integers 1 to 96 , inclusive , what is the probability that n ( n + 1 ) ( n + 2 ) will be divisible by 8 ?
|
"explanation : let width = x then , height = 6 x and length = 48 x 48 x ã — 6 x ã — x = 36000 x = 5 answer : b"
|
a ) 4 m , b ) 5 m , c ) 6 m , d ) 7 m , e ) 8 m
|
b
|
power(divide(36000, multiply(multiply(6, 8), 6)), divide(const_1, const_3))
|
divide(const_1,const_3)|multiply(n0,n1)|multiply(n0,#1)|divide(n2,#2)|power(#3,#0)|
|
physics
|
there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?
|
answer let one - third of 600 is n % of 120 . ∵ 600 / 3 = ( n x 120 ) / 100 ∴ n = ( 200 x 100 ) / 120 = 166.6 correct option : e
|
a ) 313.2 , b ) 30.1 , c ) 12.24 , d ) none of these , e ) 166.6
|
e
|
multiply(const_100, divide(divide(600, const_3), 120))
|
divide(n0,const_3)|divide(#0,n1)|multiply(#1,const_100)
|
gain
|
in a certain game , a large container is filled with red , yellow , green , and blue beads worth , respectively , 7 , 5 , 3 , and 2 points each . a number of beads are then removed from the container . if the product of the point values of the removed beads is 30 , 870000 , how many red beads were removed ?
|
"a 58 - sided convex polygon has 58 vertices . if we examine a single vertex , we can see that we can connect it with 55 other vertices to create a diagonal . note that we ca n ' t connect the vertex to itself and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 58 vertices can be connected with 55 vertices to create a diagonal then the total number of diagonals would be ( 58 ) ( 55 ) = 3190 however , we must recognize that we have counted every diagonal twice . to account for counting each diagonal twice , we must divide 3190 by 2 to get 1595 . the answer is c ."
|
a ) 870 , b ) 1125 , c ) 1595 , d ) 2560 , e ) 3190
|
c
|
divide(factorial(58), multiply(factorial(subtract(58, const_2)), factorial(const_2)))
|
factorial(n0)|factorial(const_2)|subtract(n0,const_2)|factorial(#2)|multiply(#3,#1)|divide(#0,#4)|
|
general
|
a rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered . if the area of the field is 10 sq . feet , how many feet of fencing will be required ?
|
let weight of side of beef before processing = x ( 65 / 100 ) * x = 545 = > x = ( 545 * 100 ) / 65 = 838 answer d
|
a ) 191 , b ) 355 , c ) 737 , d ) 838 , e ) 1,560
|
d
|
divide(multiply(545, const_100), subtract(const_100, 35))
|
multiply(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)
|
gain
|
rob also compared the empire state building and the petronas towers . what is the height difference between the two if the empire state building is 435 m tall and the petronas towers is 458 m tall ?
|
4.5 km / 250 m = 18 . however , the street at the 4.5 - km mark is not 18 th street ; it is turner street . therefore , the highest numbered street is 17 th street . the answer is c .
|
a ) 15 th , b ) 16 th , c ) 17 th , d ) 18 th , e ) 19 th
|
c
|
subtract(divide(4.5, divide(250, const_1000)), 1)
|
divide(n1,const_1000)|divide(n0,#0)|subtract(#1,n2)
|
physics
|
a boat running upstream takes 8 hours 48 minutes to cover a certain distance , while it takes 4 hours to cover the same distance running downstream . what is the ratio between the speed of the boat and speed of the water current respectively ?
|
solution : first , model the pressure ( p ) in terms of depth ( d ) with a linear equation . we will find the equation p = md + b use ( 0 , 15 ) and ( 33 , 30 ) to find m m = 30 - 15 / 33 - 0 m = 15 / 33 = 0.45 p = 0.45 d + b use ( 0 , 15 ) to find b 15 = 0.45 × 0 + b 15 = b p = 0.45 d + 15 25000 = 0.45 d + 15 25000 - 15 = 0.45 d + 15 - 15 24985 = 0.45 d d = 24985 / 0.45 = 55522 feet answer a
|
['a ) 55522 feet', 'b ) 45522 feet', 'c ) 35522 feet', 'd ) 25522 feet', 'e ) none']
|
a
|
divide(divide(subtract(25000, 15), divide(subtract(30, 15), multiply(33, multiply(const_4, const_3)))), multiply(const_4, const_3))
|
multiply(const_3,const_4)|subtract(n3,n0)|subtract(n2,n0)|multiply(n1,#0)|divide(#2,#3)|divide(#1,#4)|divide(#5,#0)
|
geometry
|
107 x 107 + 93 x 93 = ?
|
total number of students = 34 let a be the number of students have a brothers . let b be the number of students have a sisters . aub = number of students have either brothers or sisters = 34 - 9 = 25 n ( aub ) = n ( a ) + n ( b ) - n ( anb ) 25 = 16 + 15 - n ( anb ) n ( anb ) = 31 - 25 n ( anb ) = 6 the number of students having both brother and sisters = 6 answer : c
|
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
|
c
|
subtract(add(16, 15), subtract(34, 9))
|
add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)
|
other
|
what number has a 3 : 4 ratio to the number 400 ?
|
"area of a parallelogram = base * height = 26 * 12 = 312 cm 2 answer : e"
|
a ) 281 , b ) 284 , c ) 288 , d ) 255 , e ) 312
|
e
|
multiply(26, 12)
|
multiply(n0,n1)|
|
geometry
|
the length of a rectangular plot is thrice its breadth . if the area of the rectangular plot is 1323 sq m , then what is the breadth of the rectangular plot ?
|
"f ( x ) = x ^ 2 + bx + c . if f ( 3 ) = 0 and f ( - 3 ) = 0 , then b + c = f ( 3 ) = 0 = 9 + 3 b + c - - - taking 9 to the other side - > 3 b + c = - 9 f ( - 3 ) = 0 = 9 - 3 b + c - - - taking - 3 b + c to the other side - > 3 b - c = 9 when we add these 2 equations , we get 6 b = 0 - - - > b = 0 and while substituting b = 0 we get c = - 9 . b + c = - 9 - - - answer e"
|
a ) 18 , b ) 15 , c ) - 15 , d ) - 21 , e ) - 9
|
e
|
negate(divide(subtract(power(3, 2), 3), add(3, 3)))
|
add(n3,n1)|power(n3,n0)|subtract(#1,n1)|divide(#2,#0)|negate(#3)|
|
general
|
if 5 < x < 9 and y = x + 3 , what is the greatest possible integer value of x + y ?
|
a and b did the work for some days . after that , b completed the remaining work in 46 days . in 46 days , word done by b = 1 80 x 46 = 23 45 remaining work = 1 – 23 / 45 = 17 / 45 remaining work is done by both a and b together = 17 / 45 x 90 x 80 / 90 + 80 = 16 days c
|
a ) 12 days , b ) 18 days , c ) 16 days , d ) 19 days , e ) 21 days
|
c
|
subtract(divide(subtract(const_1, multiply(divide(const_1, 80), 46)), add(divide(const_1, 80), divide(const_1, 90))), const_2)
|
divide(const_1,n1)|divide(const_1,n0)|add(#0,#1)|multiply(n2,#0)|subtract(const_1,#3)|divide(#4,#2)|subtract(#5,const_2)
|
physics
|
16.02 ã — 0.1 = ?
|
"here , x = 40 and y = 47 therefore second number = [ [ ( 100 - y ) / ( 100 - x ) ] x 100 ] % of first number = [ [ ( 100 - 47 ) / ( 100 - 40 ) ] x 100 ] % of first number i . e , 88.3 % of the first . answer : b"
|
a ) 95 % , b ) 88 % , c ) 85 % , d ) 90 % , e ) none of these
|
b
|
multiply(subtract(add(40, const_1), 40), const_10)
|
add(n0,const_1)|subtract(#0,n0)|multiply(#1,const_10)|
|
general
|
x , a , z , and b are single digit positive integers . x = 1 / 7 a . z = 1 / 7 b . ( 10 a + b ) – ( 10 x + z ) could not equal
|
"75 % - - - 10 125 % - - - ? 75 / 125 * 10 = 6 answer : a"
|
a ) 6 , b ) 9 , c ) 10 , d ) 89 , e ) 81
|
a
|
multiply(divide(const_1, multiply(add(const_100, 25), divide(const_1, subtract(const_100, 25)))), 10)
|
add(n2,const_100)|subtract(const_100,n1)|divide(const_1,#1)|multiply(#0,#2)|divide(const_1,#3)|multiply(n0,#4)|
|
gain
|
what is the least value of x . so that 22 x 57 is divisible by 3 .
|
"explanation : 1 / 0.05 = ( 1 * 100 ) / 5 = 100 / 5 = 20 option d"
|
a ) 25.5 , b ) 2.5 , c ) 25 , d ) 20 , e ) none of these
|
d
|
divide(1, 0.05)
|
divide(n0,n1)|
|
general
|
a train 310 meters long is running with a speed of 60 kmph . in what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going ?
|
"amit ’ s one day ’ s work = 1 / 15 amit ’ s 3 day ’ s work = 1 / 15 * 3 = 1 / 5 work left = 1 - 1 / 5 = 4 / 5 ananthu ’ s one day ’ s work = 1 / 60 ananthu can do work in = 4 / 5 * 60 = 48 days so total days = 48 + 3 = 51 days answer : e"
|
a ) 38 days , b ) 40 days , c ) 43 days , d ) 45 days , e ) 51 days
|
e
|
add(divide(subtract(const_1, multiply(inverse(15), 3)), inverse(60)), 3)
|
inverse(n0)|inverse(n1)|multiply(#0,n2)|subtract(const_1,#2)|divide(#3,#1)|add(#4,n2)|
|
physics
|
on a sum of money , the simple interest for 2 years is rs . 324 , while the compound interest is rs . 340 , the rate of interest being the same in both the cases . the rate of interest is
|
"2 d / 70 = 6 ( because time = 4 + 2.5 - 0.5 hrs ) = > d = 210 answer - d"
|
a ) 90 , b ) 120 , c ) 150 , d ) 210 , e ) 300
|
d
|
divide(multiply(70, subtract(add(4, 2.5), const_1)), const_2)
|
add(n0,n1)|subtract(#0,const_1)|multiply(n3,#1)|divide(#2,const_2)|
|
physics
|
a circle in the coordinate plane passes through points ( - 3 , - 2 ) and ( 1 , - 4 ) . what is the smallest possible area of that circle ?
|
"b 8 1 / 7 â € “ 1 / 56 = 1 / 8 = > 8"
|
a ) 11 , b ) 8 , c ) 21 , d ) 20 , e ) 25
|
b
|
add(inverse(subtract(divide(const_1, 7), divide(const_1, 56))), divide(const_2, add(const_2, const_3)))
|
add(const_2,const_3)|divide(const_1,n0)|divide(const_1,n1)|divide(const_2,#0)|subtract(#1,#2)|inverse(#4)|add(#3,#5)|
|
physics
|
the sum of the first 50 positive even integers is 2550 . what is the sum q of even integers from 102 to 200 inclusive ?
|
explanation : let t be the time after kajol starts , when she meets ajay , then \ inline t = \ frac { 300 } { ( x + y ) } this should be less than 2.5 or ( x + y ) > 120 since y = \ inline \ frac { 3 x } { 2 } \ inline \ rightarrow y > 72 this ( y > 72 ) is greater than 67.5 km / h and hence shahrukh will always overtake ajay before he meets kajol . answer : d
|
a ) 32 , b ) 21 , c ) 27 , d ) none of these , e ) 18
|
d
|
divide(subtract(multiply(multiply(20, const_3), const_10), multiply(20, const_3)), add(const_3, add(const_4, const_1)))
|
add(const_1,const_4)|multiply(n2,const_3)|add(#0,const_3)|multiply(#1,const_10)|subtract(#3,#1)|divide(#4,#2)
|
physics
|
the mean of 50 observations was 36 . it was found later that an observation 47 was wrongly taken as 23 . the corrected new mean is
|
"each 20 kilometers , 1 gallon is needed . we need to know how many 20 kilometers are there in 180 kilometers ? 180 / 20 = 9 * 1 gallon = 9 gallons correct answer b"
|
a ) 8.5 gallons , b ) 9 gallons , c ) 6.5 gallons , d ) 5.5 gallons , e ) 6 gallons
|
b
|
divide(180, 20)
|
divide(n1,n0)|
|
physics
|
a train running at the speed of 50 km / hr crosses a post in 4 seconds . what is the length of the train ?
|
"explanation : we have : l = 20 ft and lb = 680 sq . ft . so , b = 34 ft . length of fencing = ( l + 2 b ) = ( 20 + 68 ) ft = 88 ft . answer : d"
|
a ) 34 , b ) 40 , c ) 68 , d ) 88 , e ) 98
|
d
|
add(multiply(divide(680, 20), const_2), 20)
|
divide(n1,n0)|multiply(#0,const_2)|add(n0,#1)|
|
geometry
|
an amount at compound interest sums to rs . 17640 / - in 2 years and to rs . 19404 / - in 3 years at the same rate of interest . find the rate percentage ?
|
"explanation : lot the total number of workers be v then , 8 ooov = ( 18000 * 9 ) + 6000 ( v - 9 ) < = > 2000 v = 108000 < = > v = 54 answer : b ) 54"
|
a ) 22 , b ) 54 , c ) 88 , d ) 37 , e ) 29
|
b
|
add(9, divide(multiply(9, subtract(18000, 8000)), subtract(8000, 6000)))
|
subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)|
|
general
|
the ratio of spinsters to cats is 2 to 7 . if there are 40 more cats than spinsters , how many spinsters are there ?
|
"explanation : n 2 = 702 = 4900 answer : option a"
|
a ) 4900 , b ) 4970 , c ) 4990 , d ) 4980 , e ) 4960
|
a
|
add(divide(divide(70, divide(divide(divide(divide(divide(70, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(70, divide(divide(divide(divide(divide(70, const_2), const_2), const_2), const_2), const_2)), const_2))))
|
divide(n0,const_2)|divide(#0,const_2)|divide(#1,const_2)|divide(#2,const_2)|divide(#3,const_2)|divide(n0,#4)|divide(#5,const_2)|sqrt(#6)|add(#7,const_1)|add(#8,#6)|
|
general
|
if x and y are integers such that x ^ 2 = 2 y and xy = 32 , then x – y = ?
|
"let c . p . be $ 100 . then , s . p . = $ 125 let marked price be $ x . then , 95 / 100 x = 125 x = 12500 / 95 = $ 131.6 now , s . p . = $ 131.6 , c . p . = $ 100 profit % = 31.6 % . a"
|
a ) 131.6 , b ) 120 , c ) 130 , d ) 110 , e ) 150
|
a
|
multiply(const_100, divide(add(const_100, 25), subtract(const_100, 5)))
|
add(n1,const_100)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)|
|
gain
|
an aeroplane covers a certain distance at a speed of 300 kmph in 6 hours . to cover the same distance in 1 2 / 3 hours , it must travel at a speed 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 ( - 4 , - 4 ) 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 ) = 8 ; so z = 8 . the next step requires us to find the length of a side of a cube that has a face area equal to 8 . 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 8 . 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 = 8 . clearly s = √ 8 = 2 √ 2 , oranswer choice ( d ) ."
|
a ) q = 16 , b ) q = 8 √ 2 , c ) q = 8 , d ) q = 2 √ 2 , e ) ( √ 2 ) / 3
|
d
|
sqrt(divide(multiply(4, 4), const_2))
|
multiply(n0,n0)|divide(#0,const_2)|sqrt(#1)|
|
general
|
a man has $ 480 in the denominations of one - dollar , 5 - dollar notes and 10 - dollar . the number of dollars of each denomination is equal . what is the total number of dollar that he has ?
|
"p = 10 ( 100 / 10 ) 2 = > p = 1000 answer : d"
|
a ) 1500 , b ) 1992 , c ) 9921 , d ) 1000 , e ) 2789
|
d
|
multiply(multiply(divide(10, multiply(10, 2)), const_100), multiply(10, 2))
|
multiply(n0,n1)|divide(n2,#0)|multiply(#1,const_100)|multiply(#2,#0)|
|
general
|
the current in a river is 5 mph . a boat can travel 20 mph in still water . how far up the river can the boat travel if the round trip is to take 10 hours ?
|
"approximate . 1 / . 03 = 100 / 3 = 33 1 / . 37 = 100 / 37 = 3 denominator becomes 33 + 3 = 36 5 / 36 = . 1388 answer ( b )"
|
a ) 0.004 , b ) 0.1388 , c ) 2.775 , d ) 3.6036 , e ) 36.036
|
b
|
inverse(add(divide(5, 0.03), divide(5, 0.37)))
|
divide(n0,n2)|divide(n0,n4)|add(#0,#1)|inverse(#2)|
|
general
|
what is 15 percent of rs . 34 ?
|
"let us calculate both the length and width of the room in centimeters . length = 7 meters and 68 centimeters = 768 cm width = 4 meters and 32 centimeters = 432 cm as we want the least number of square tiles required , it means the length of each square tile should be as large as possible . further , the length of each square tile should be a factor of both the length and width of the room . hence , the length of each square tile will be equal to the hcf of the length and width of the room = hcf of 768 and 432 = 48 thus , the number of square tiles required = ( 768 x 432 ) / ( 48 x 48 ) = 16 x 9 = 144 answer : b"
|
a ) 107 , b ) 144 , c ) 175 , d ) 165 , e ) 130
|
b
|
divide(multiply(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), multiply(gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32)), gcd(add(multiply(7, const_100), 68), add(multiply(4, const_100), 32))))
|
multiply(n0,const_100)|multiply(n2,const_100)|add(n1,#0)|add(n3,#1)|gcd(#2,#3)|multiply(#2,#3)|multiply(#4,#4)|divide(#5,#6)|
|
general
|
of 30 applicants for a job , 16 had at least 4 years ' experience , 21 had degrees , and 5 had less than 4 years ' experience and did not have a degree . how many of the applicants had at least 4 years ' experience and a degree ?
|
"exp : we have , m 1 d 1 = m 2 d 2 600 * 25 = 300 * d 2 d 2 = 600 * 25 / 300 = 50 days . answer : d"
|
a ) 35 days , b ) 40 days , c ) 45 days , d ) 50 days , e ) 55 days
|
d
|
divide(multiply(600, 25), 300)
|
multiply(n0,n1)|divide(#0,n2)|
|
physics
|
a contractor undertakes to built a walls in 50 days . he employs 30 peoples for the same . however after 25 days he finds that only 40 % of the work is complete . how many more man need to be employed to complete the work in time ?
|
answer : d ) 55 km
|
a ) 65 , b ) 38 , c ) 20 , d ) 55 , e ) 21
|
d
|
subtract(subtract(140, 35), add(25, 25))
|
add(n1,n1)|subtract(n0,n4)|subtract(#1,#0)|
|
physics
|
if x and y are both odd prime numbers and x < y , how many distinct positive integer e factors does 2 xy have ?
|
explanation : 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ ( 1 ÷ 1 ) } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 ÷ 1 } ] = 1 ÷ [ 1 + 1 ÷ { 1 + 1 } ] = 1 ÷ [ 1 + 1 ÷ 2 ] = 1 ÷ [ 1 + ( 1 / 2 ) ] = 1 ÷ 3 / 2 = 1 × 3 / 2 = 1 × 2 / 3 = 2 / 3 answer : option c
|
a ) 5 / 3 , b ) 4 / 3 , c ) 2 / 3 , d ) 1 / 3 , e ) 1 / 5
|
c
|
divide(1, add(1, divide(1, add(1, divide(1, 1)))))
|
divide(n0,n0)|add(n0,#0)|divide(n0,#1)|add(n0,#2)|divide(n0,#3)
|
general
|
in a fuel station the service costs $ 1.50 per car , every liter of fuel costs 0.35 $ . assuming that you own 3 limos and 2 fleet vans and all fuel tanks are empty . how much will it cost to fuel all cars together if a limo tank is 32 liters and an fleet van tank is 75 % bigger ?
|
given : 15 < x ( x + 1 ) < 170 . now , it ' s better to test the answer choices here rather than to solve : if x = 4 then x ( x + 1 ) = 20 > 15 - - > so , the least value is 4 . test for the largest value : if x = 12 then x ( x + 1 ) = 12 * 13 = 156 > 150 answer : c .
|
a ) 3 and 15 , b ) 3 and 20 , c ) 4 and 12 , d ) 4 and 14 , e ) 5 and 14
|
c
|
add(multiply(add(floor(sqrt(15)), const_1), const_100), subtract(floor(sqrt(150)), const_1))
|
sqrt(n0)|sqrt(n1)|floor(#0)|floor(#1)|add(#2,const_1)|subtract(#3,const_1)|multiply(#4,const_100)|add(#6,#5)
|
general
|
the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 20 percent , and on day 3 , it is discounted an additional 40 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
|
"let n be the total number of books sold . hence n = 75 + 50 + 64 + 78 + 135 = 402 let m be the books not sold m = 1000 - n = 1000 - 402 = 598 percentage books not sold / total number of books = 598 / 1000 = 59.8 = 59.8 % correct answer a"
|
a ) 59.8 % , b ) 23.8 % , c ) 66.5 % , d ) 34.9 % , e ) 43.5 %
|
a
|
multiply(divide(subtract(1000, add(add(add(75, 50), add(64, 78)), 135)), 1000), const_100)
|
add(n1,n2)|add(n3,n4)|add(#0,#1)|add(n5,#2)|subtract(n0,#3)|divide(#4,n0)|multiply(#5,const_100)|
|
gain
|
a pet store regularly sells pet food at a discount of 10 percent to 30 percent from the manufacturer ’ s suggested retail price . if during a sale , the store discounts an additional 20 percent from the discount price , what would be the lowest possible price of a container of pet food that had a manufacturer ’ s suggested retail price o f $ 25.00 ?
|
"slope = ( y 2 - y 1 ) / ( x 2 - x 1 ) = > k = ( k + 4 ) / ( 2 + 1 ) = > 3 k = k + 4 = > k = 2 ans d it is !"
|
a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
|
d
|
divide(4, 2)
|
divide(n1,n2)|
|
general
|
if a boat is rowed downstream for 24 km in 4 hours and upstream for 48 km in 24 hours , what is the speed of the boat and the river ?
|
"c 3200 let the amount with r be $ r r = 2 / 3 ( total amount with p and q ) r = 2 / 3 ( 8000 - r ) = > 3 r = 16000 - 2 r = > 5 r = 16000 = > r = 3200 ."
|
a ) 2400 , b ) 2403 , c ) 3200 , d ) 2539 , e ) 1930
|
c
|
divide(multiply(8000, multiply(const_2, const_2)), add(add(multiply(divide(multiply(const_2, const_2), const_3), const_3), multiply(const_1, const_3)), multiply(const_1, const_3)))
|
multiply(const_2,const_2)|multiply(const_1,const_3)|divide(#0,const_3)|multiply(n0,#0)|multiply(#2,const_3)|add(#4,#1)|add(#5,#1)|divide(#3,#6)|
|
general
|
what is the sum of all 3 digit integers formed using the digits 34 and 5 ( repetition is allowed )
|
"less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a"
|
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
|
a
|
min(min(divide(15, add(2, divide(1, 2))), floor(divide(16, add(divide(3, 4), 2)))), divide(8, add(divide(1, 3), 1)))
|
divide(n1,n4)|divide(n1,n0)|divide(n4,n5)|add(n1,#0)|add(n0,#1)|add(n0,#2)|divide(n11,#3)|divide(n9,#4)|divide(n10,#5)|floor(#8)|min(#7,#9)|min(#6,#10)|
|
general
|
convert 1.8 hectares in ares
|
"let ' s see , the way i did it was 16 / 25 are clerical out of 3600 so 2304 are clerical 2304 reduced by 1 / 4 is 2304 * 1 / 4 so it reduced 576 people , so there is 1728 clerical people left but since 576 people left , it also reduced from the total of 3600 so there are 3024 people total since 1728 clerical left / 3024 people total you get ( a ) 57 %"
|
a ) 57 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
|
a
|
multiply(divide(multiply(divide(16, 25), subtract(1, divide(1, 4))), add(multiply(divide(16, 25), subtract(1, divide(1, 4))), subtract(1, divide(16, 25)))), const_100)
|
divide(n1,n2)|divide(n3,n4)|subtract(n3,#1)|subtract(n3,#0)|multiply(#0,#2)|add(#4,#3)|divide(#4,#5)|multiply(#6,const_100)|
|
general
|
a corporation that had $ 2 billion in profits for the year paid out $ 100 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
|
"solution let the numbers be x and x ( x + 1365 ) . then , x + 1365 = 6 x + 15 ‹ = › 5 x = 1350 . ‹ = › x = 270 . answer d"
|
a ) 240 , b ) 250 , c ) 260 , d ) 270 , e ) none
|
d
|
divide(subtract(1365, 15), subtract(6, const_1))
|
subtract(n0,n2)|subtract(n1,const_1)|divide(#0,#1)|
|
general
|
in 60 litres mixture milk and water are in the ratio 3 : 1 . after adding how many liters of water its ratio will become 3 : 2
|
"present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 33 2 x - 7 = 33 2 x = 33 + 7 x = 40 / 2 x = 20 z = x + 7 = 20 + 7 = 27 answer : c"
|
a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
|
c
|
add(divide(add(33, 7), const_2), 7)
|
add(n0,n1)|divide(#0,const_2)|add(n0,#1)|
|
general
|
if w / x = 1 / 3 and w / y = 4 / 15 , then ( x + y ) / y =
|
"correct answer : ( c ) determine the range of xy by multiplying the two extremes of each individual range together . the smallest value of xy must be greater than 100 * 9 . the largest value must be less than 199 * 100 . this means that 900 < xy < 19,900 . ( c ) is outside of this range , so it is not a possible product of xy ."
|
a ) 19,104 , b ) 19,303 , c ) 19 , 956.732 , d ) 19,502 , e ) 19,809
|
c
|
add(100, const_1)
|
add(n3,const_1)|
|
general
|
set q consists of integers { 3 , - 8 , y , 19 , - 6 } and set b consists of integers { k , - 3 , 0 , 16 , - 5 , 9 } . number l represents the median of set q , number m represents mode of set b and number z = l ^ m . if y is an integer greater than 21 , for what value of k will z be a divisor of 26 ?
|
"y = 0.5 * 0.5 * x = x / 4 y % * x = 9 ( y / 100 ) * x = 9 ( x / 400 ) * x = 9 x ^ 2 = 9 * 400 x = 60 the answer is b ."
|
a ) 20 , b ) 60 , c ) 100 , d ) 120 , e ) 150
|
b
|
multiply(multiply(divide(50, 9), divide(50, 9)), const_1000)
|
divide(n0,n2)|divide(n1,n2)|multiply(#0,#1)|multiply(#2,const_1000)|
|
general
|
machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 60 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 6 minutes ?
|
60 kmph = 50 / 3 m / sec 50 / 3 * 18 = 300 m answer : b
|
a ) 120 m , b ) 300 m , c ) 190 m , d ) 150 m , e ) 160 m
|
b
|
multiply(divide(multiply(60, const_1000), const_3600), 18)
|
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)
|
physics
|
a can finish a work in 24 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
|
"100 = x + x - 20 + 23 - 23 x = 60 , so , product a = 60 % , product b = 40 % , both = 23 % , neither = 23 % 23 % of the total no . of people should be an integer . so , a , bc are out . 60 % of d and 40 % of d are both integers . so , d satisfies all conditions . so , answer is d ."
|
a ) 46 , b ) 80 , c ) w . 90 , d ) w . 100 , e ) 200
|
d
|
add(subtract(divide(add(add(subtract(const_100, 23), 23), 20), const_2), 20), divide(add(add(subtract(const_100, 23), 23), 20), const_2))
|
subtract(const_100,n1)|add(n1,#0)|add(n0,#1)|divide(#2,const_2)|subtract(#3,n0)|add(#3,#4)|
|
other
|
in a school with 620 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
|
"a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . t * 23 + 39 = 25 * ( t + 1 ) t = 7 ans . ( a )"
|
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
|
a
|
subtract(divide(subtract(39, 15), add(2, 1)), 1)
|
add(n1,n3)|subtract(n0,n2)|divide(#1,#0)|subtract(#2,n3)|
|
general
|
a number when divided by 243 gives a remainder 26 , what remainder will be obtained by dividing the same number 14 ?
|
total earning for the week = rs ( 4 × 18 + 4 × 22 - 20 ) = rs 140 average earning = rs 140 / 7 = rs 20 . answer : c
|
a ) rs 18.95 , b ) rs 16 , c ) rs 20 , d ) rs 25.71 , e ) none of these
|
c
|
divide(subtract(add(multiply(4, 18), multiply(4, 22)), 20), add(const_4, const_3))
|
add(const_3,const_4)|multiply(n0,n1)|multiply(n0,n3)|add(#1,#2)|subtract(#3,n4)|divide(#4,#0)
|
general
|
a computer store offers employees a 10 % discount off the retail price . if the store purchased a computer from the manufacturer for $ 800 dollars and marked up the price 10 % to the final retail price , how much would an employee save if he purchased the computer at the employee discount ( 10 % off retail price ) as opposed to the final retail price .
|
ratio of times taken by mary and rosy = 150 : 100 = 3 : 2 suppose rosy takes x days to do the work . 3 : 2 : : 12 : x = > x = 8 days . hence , rosy takes 8 days to complete the work . answer : b
|
a ) 7 , b ) 8 , c ) 9 , d ) 11 , e ) 10
|
b
|
divide(12, add(const_1, divide(50, const_100)))
|
divide(n1,const_100)|add(#0,const_1)|divide(n0,#1)
|
physics
|
a man can row 11 kmph in still water . when the river is running at 1.2 kmph , it takes him 1 hour to row to a place and back . what is the total distance traveled by the man ?
|
"largest 4 - digit number = 999 88 ) 999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 999 - 55 ) = 9944 . a )"
|
a ) a ) 9944 , b ) b ) 9954 , c ) c ) 9967 , d ) d ) 9969 , e ) e ) 9970
|
a
|
square_area(const_pi)
|
square_area(const_pi)|
|
general
|
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