Datasets:
ericsun153
/
mathqa_question_token_drop_test

Dataset card Data Studio Files
xet
Community
Problem
stringlengths
3
32
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
if do3?
"explanation : explanation : clearly , from 1 to 100 , there are ten numbers with 3 as the unit ' s digit - 3 , 13 , 23 , 33 , 43 , 53 , 63 , 73 , 83 , 93 ; and ten numbers with 3 as the ten ' s digit - 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 . so , required number = 10 + 10 = 20 . answer : c"
a ) 11 , b ) 18 , c ) 20 , d ) 21 , e ) 22
c
divide(subtract(100, 1), 3)
subtract(n1,n0)|divide(#0,n2)|
general
the. is :
"clearly , the numbers are ( 23 x 10 ) and ( 23 x 11 ) . larger number = ( 23 x 11 ) = 253 . answer : option b"
a ) 276 , b ) 253 , c ) 322 , d ) 345 , e ) 395
b
multiply(23, 11)
multiply(n0,n2)|
other
at rs years?
"explanation : 250 = ( 1750 x 5 xr ) / 100 250 = ( 175 xr ) / 2 500 = ( 175 xr ) r = 500 / 175 r = 2 6 / 7 % answer : option c"
a ) 4 % , b ) 3 6 / 7 % , c ) 2 6 / 7 % , d ) 5 % , e ) 6 %
c
multiply(divide(divide(subtract(2000, 1750), 1750), 5), const_100)
subtract(n1,n0)|divide(#0,n0)|divide(#1,n2)|multiply(#2,const_100)|
gain
tim lan lan?
tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice c meet the 2 : 1 ( tim : elan = 40 : 20 ) ratio of maintaining total distance traveled 60 miles so correct answer c
a ) 30 miles . , b ) 35 miles . , c ) 40 miles . , d ) 60 miles . , e ) 65 miles .
c
multiply(divide(10, add(5, 10)), 60)
add(n1,n2)|divide(n1,#0)|multiply(n0,#1)
physics
if y?
"y = 1.9 x x = y / 1.9 = 10 y / 19 x is 9 / 19 less which is 47.4 % less than y . the answer is d ."
a ) 35.7 % , b ) 39.8 % , c ) 43.2 % , d ) 47.4 % , e ) 51.2 %
d
multiply(divide(90, add(90, const_100)), const_100)
add(n0,const_100)|divide(n0,#0)|multiply(#1,const_100)|
general
what in seconds?
"speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 40 seconds , the train can travel 25 / 2 * 40 = 500 meters 500 = length of train + length of bridge length of bridge = 500 - 166 = 334 meters the answer is d ."
a ) 310 , b ) 318 , c ) 326 , d ) 334 , e ) 342
d
subtract(multiply(multiply(45, const_0_2778), 40), 166)
multiply(n1,const_0_2778)|multiply(n2,#0)|subtract(#1,n0)|
physics
the. person?
"solution total weight increased = ( 10 x 4.2 ) kg = 42 kg . weight of new person = ( 65 + 42 ) kg = 107 kg . answer a"
a ) 107 kg , b ) 80 kg , c ) 120 kg , d ) 90 kg , e ) 100
a
add(65, multiply(10, 4.2))
multiply(n0,n1)|add(n2,#0)|
general
if y?
"x + y = x + x + 3 = 2 x + 3 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 8.5 then x + y = 8.5 + 11.5 = 20 . the answer is b ."
a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
b
add(add(3, const_10), const_10)
add(n2,const_10)|add(#0,const_10)|
general
a divided class?
"let total no of students in the class be n so , we are told that n is divisible by both 8 24 so , lets find the least common multiple of 8 24 , ie 24 so our answer is ( d ) 24"
a ) 6 , b ) 36 , c ) 48 , d ) 24 , e ) 72
d
lcm(8, 24)
lcm(n0,n1)|
general
a patio layout?
"r * c = 90 and ( 11 + 4 ) ( c - 2 ) = 90 - - > r = 11 and c = 8 . answer : d ."
a ) 5 , b ) 6 , c ) 10 , d ) 11 , e ) 28
d
divide(90, divide(add(negate(4), sqrt(add(power(4, 2), multiply(4, multiply(90, 2))))), 2))
multiply(n0,n1)|negate(n2)|power(n2,n1)|multiply(n2,#0)|add(#3,#2)|sqrt(#4)|add(#1,#5)|divide(#6,n1)|divide(n0,#7)|
geometry
what )?
"- > the ones place of ( ~ 3 ) ^ n repeats after 4 times like 3  9  7  1  3 . the ones place of ( ~ 4 ) ^ n repeats after 2 times like 4  6  4 . then , 3 ^ 5 = 3 ^ 4 * 1 + 1  3 ^ 1 . , 4 ^ 13 = 4 ^ 2 * 6 + 1 = 4 ^ 1 = ~ 4 which is ( 3 ^ 5 ) ( 4 ^ 13 )  ( 3 ^ 1 ) ( ~ 4 ) = ( ~ 3 ) ( ~ 4 ) = ~ 2 . therefore , the answer is a ."
a ) 2 , b ) 4 , c ) 6 , d ) 7 , e ) 8
a
add(add(const_4, const_3), const_2)
add(const_3,const_4)|add(#0,const_2)|
general
the even three?
"middle no = 63 / 3 = 21 ans e"
a ) 14 , b ) 23 , c ) 25 , d ) 29 , e ) 21
e
add(add(power(add(add(divide(subtract(subtract(63, const_10), const_2), const_4), const_2), const_2), const_2), power(add(add(add(divide(subtract(subtract(63, const_10), const_2), const_4), const_2), const_2), const_2), const_2)), add(power(divide(subtract(subtract(63, const_10), const_2), const_4), const_2), power(add(divide(subtract(subtract(63, const_10), const_2), const_4), const_2), const_2)))
subtract(n0,const_10)|subtract(#0,const_2)|divide(#1,const_4)|add(#2,const_2)|power(#2,const_2)|add(#3,const_2)|power(#3,const_2)|add(#5,const_2)|add(#4,#6)|power(#5,const_2)|power(#7,const_2)|add(#9,#10)|add(#11,#8)|
physics
a how colour?
"each face of the cube has 8 x 8 = 64 cubelets . on each face , only the interior cubelets are painted one colour . on each side , 6 x 6 = 36 cubelets are painted one colour . since the cube has six sides , the number of cubes with one colour is 6 * 36 = 216 the answer is a ."
a ) 216 , b ) 264 , c ) 296 , d ) 312 , e ) 324
a
divide(subtract(512, multiply(multiply(const_4, const_2), const_3)), const_2)
multiply(const_2,const_4)|multiply(#0,const_3)|subtract(n0,#1)|divide(#2,const_2)|
geometry
of150 year?
"150 employees 70 are full - time 100 have worked at company x for at least a year 20 employees at company x who aren ’ t full - time and haven ’ t worked at company x for at least a year . how many full - time employees of company x have worked at the company for at least a year ? 150 - 70 = 80 employees not full time 80 - 20 = 60 employees not full time who worked over a year 100 employees have worked at company x for at least a year - 60 employees not full time who worked over a year = 40 full - time employees of company x have worked at the company for at least a year ans b"
a ) 20 , b ) 40 , c ) 50 , d ) 80 , e ) 100
b
subtract(subtract(150, 70), 20)
subtract(n0,n1)|subtract(#0,n3)|
general
p is income?
"make r = 10 p = 0.6 r = 6 q = 0.8 p = 4.8 s = 0.6 p = 3.6 for that we get p = 12 and q 8.8 so 12 / 8.8 = 3 / 2.2 ans : d"
a ) 11 / 12 , b ) 13 / 17 , c ) 13 / 19 , d ) 15 / 11 , e ) 11 / 19
d
divide(add(multiply(40, const_100), multiply(40, subtract(const_100, 20))), add(multiply(40, const_100), multiply(add(40, 20), 40)))
add(n0,n1)|multiply(n4,const_100)|multiply(n0,const_100)|subtract(const_100,n1)|multiply(n4,#3)|multiply(n4,#0)|add(#1,#4)|add(#2,#5)|divide(#6,#7)|
general
if - x =
"we ' re given the equation 6 - 12 / x = 7 - 7 / x . we ' re asked for the value of x . the common - denominator of these 4 numbers is x , so we need to multiply both sides of the equation by x , giving us . . . 6 x - 12 x / x = 7 x - 7 x / x we can then eliminate that denominator , which gives us . . . . 6 x - 12 = 7 x - 7 - 5 = x a"
a ) - 5 , b ) 19 , c ) - 7 / 5 , d ) 1 , e ) 5 / 6
a
divide(add(7, 12), subtract(6, 7))
add(n3,n1)|subtract(n0,n2)|divide(#0,#1)|
general
the angle perimeter?
"perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 14 ) + 2 ( 14 ) = 33 + 28 = 61 cm answer : b"
a ) 91.5 cm , b ) 61 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
b
multiply(multiply(const_2, divide(multiply(subtract(14, const_3), const_2), add(const_4, const_3))), 14)
add(const_3,const_4)|subtract(n0,const_3)|multiply(#1,const_2)|divide(#2,#0)|multiply(#3,const_2)|multiply(n0,#4)|
physics
| - have?
"| x | = x when x > = 0 ( x is either positive or 0 ) | x | = - x when x < 0 ( note here that you can put the equal to sign here as well x < = 0 because if x = 0 , | 0 | = 0 = - 0 ( all are the same ) so the ' = ' sign can be put with x > 0 or with x < 0 . we usually put it with ' x > 0 ' for consistency . a"
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
a
divide(multiply(add(4, 3), const_2), 8)
add(n0,n1)|multiply(#0,const_2)|divide(#1,n2)|
general
in how ground?
"total number of players = 11 + 15 + 21 + 15 = 62 answer is c"
a ) 70 , b ) 52 , c ) 62 , d ) 49 , e ) 50
c
add(add(11, 15), add(21, 15))
add(n1,n2)|add(n3,n4)|add(#0,#1)|
physics
how to length?
"d = 120 + 170 = 290 m s = 60 * 5 / 18 = 50 / 3 t = 290 * 3 / 50 = 17.4 sec answer : d"
a ) sec , b ) sec , c ) sec , d ) sec , e ) sec
d
divide(add(120, 170), multiply(60, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
physics
what is )?
"6 / 7 / 21 / 3 = 6 / 49 . . . imo option d ."
a ) 3 : 7 , b ) 1 : 3 , c ) 3 : 21 , d ) 6 : 49 , e ) 3 : 49
d
divide(6, const_60)
divide(n0,const_60)|
general
a totalae?
"let price of a sundae = s price of ice cream bar = . 6 $ 125 * . 6 + 125 * s = 275 = > 125 * s = 200 = > s = 1.6 answer e"
a ) $ 0.60 , b ) $ 0.80 , c ) $ 1.00 , d ) $ 1.20 , e ) $ 1.60
e
divide(subtract(275.00, multiply(125, 0.60)), 125)
multiply(n0,n3)|subtract(n2,#0)|divide(#1,n1)|
general
aman inning.
"let the average after 6 th inning = x then , average after 5 th inning = x - 2 5 ( x - 2 ) + 50 = 6 x x = 10 - 50 = 40 answer is a"
a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 80
a
add(subtract(50, multiply(6, 2)), 2)
multiply(n1,n2)|subtract(n0,#0)|add(n2,#1)|
general
49 ^?
"49 ã — 49 ã — 49 = 7 ? or , 7 ( 2 ) ã — 7 ( 2 ) ã — 7 ( 2 ) = 7 ? or 7 ( 6 ) = 7 ? or , ? = 6 answer d"
a ) 4 , b ) 7 , c ) 8 , d ) 6 , e ) none of these
d
add(subtract(power(49, const_2), 49), subtract(power(49, const_2), 49))
power(n0,const_2)|power(n2,const_2)|subtract(#0,n0)|subtract(#1,n2)|add(#2,#3)|
general
a is circle?
"the distance between the two points is sqrt ( 20 ) . radius = sqrt ( 20 ) / 2 area = pi * ( sqrt ( 20 ) / 2 ) ^ 2 d . 5 π"
a ) 13 π , b ) 26 π , c ) 262 √ π , d ) 5 π , e ) 64 π
d
square_area(divide(sqrt(add(multiply(add(3, 1), add(3, 1)), multiply(add(2, 4), add(2, 4)))), 2))
add(n0,n2)|add(n1,n3)|multiply(#0,#0)|multiply(#1,#1)|add(#2,#3)|sqrt(#4)|divide(#5,n1)|square_area(#6)|
geometry
the hence hence?
"a + b = 90 , a = 2 b 2 b + b = 90 = > b = 30 then a = 60 . 5 years , their ages will be 65 and 35 . sum of their ages = 65 + 35 = 100 . answer : e"
a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 100
e
add(add(multiply(divide(90, 5), const_2), 5), add(divide(90, 5), 5))
divide(n0,n1)|add(#0,n1)|multiply(#0,const_2)|add(#2,n1)|add(#3,#1)|
general
the between meet?
"suppose they meet x hrs after 8 a . m . then , ( distance moved by first in x hrs ) + [ distance moved by second in ( x - 1 ) hrs ] = 330 60 x + 75 ( x - 1 ) = 330 = > x = 3 so , they meet at ( 8 + 3 ) i . e . , 11 a . m . answer : c"
a ) 12 , b ) 10 , c ) 11 , d ) 09 , e ) 03
c
add(divide(add(330, 75), add(60, 75)), 8)
add(n0,n4)|add(n2,n4)|divide(#0,#1)|add(n1,#2)|
physics
a clubs.
"basically , this question is asking you to figure out how many students are being double - counted . a - club has 180 members ( 1 / 2 of 360 ) b - club has 225 members ( 5 / 8 of 360 ) c - club has 270 members ( 3 / 4 of 360 ) we can create an equation to solve this : 180 + 225 + 270 = n + x + 2 y where n is the number of students , x is the number of students in two clubs , and y is the number of students in three clubs . the question provides y for us ( 135 ) . 180 + 225 + 270 = 360 + x + 270 x = 405 - 360 = 45 a"
a ) 45 , b ) 40 , c ) 35 , d ) 50 , e ) 55
a
subtract(subtract(add(add(divide(multiply(360, 1), 2), divide(multiply(360, 5), 8)), divide(multiply(360, 3), 4)), multiply(divide(multiply(360, 3), 8), 2)), 360)
multiply(n0,n1)|multiply(n0,n3)|multiply(n0,n5)|divide(#0,n2)|divide(#1,n4)|divide(#2,n6)|divide(#2,n4)|add(#3,#4)|multiply(n2,#6)|add(#7,#5)|subtract(#9,#8)|subtract(#10,n0)|
general
the a is?
"let c . p . of the article be rs . x . then , required ratio = 108 % of x / 106 % of x = 108 / 106 = 54 / 53 = 54 : 53 answer : d"
a ) 52 : 56 , b ) 52 : 53 , c ) 52 : 50 , d ) 54 : 53 , e ) 52 : 51
d
divide(add(const_100, 8), add(const_100, 6))
add(n0,const_100)|add(n1,const_100)|divide(#0,#1)|
gain
reen loan interest?
"let rate = r % and time = r years . then , 1200 x r x r / 100 = 588 12 r 2 = 588 r 2 = 49 r = 7 . answer : b"
a ) 3.6 , b ) 7 , c ) 18 , d ) can not be determined , e ) none of these
b
sqrt(divide(multiply(588, const_100), 1200))
multiply(n1,const_100)|divide(#0,n0)|sqrt(#1)|
gain
what22?
"substitute y by 2 in x + 5 y = 24 x + 5 ( 2 ) = 24 x + 10 = 24 if we substitute x by 14 in x + 10 = 24 , we have 14 + 10 = 24 . hence x = 14 correct answer e"
a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 14
e
subtract(24, multiply(5, 2))
multiply(n0,n2)|subtract(n1,#0)|
general
the wages robin?
"let wage of erica = 10 wage of robin = 1.2 * 10 = 12 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 12 ) / 12 * 100 % = 4 / 12 * 100 % = 33 % answer b"
a ) 18.75 % , b ) 33 % , c ) 30 % , d ) 50 % , e ) 100 %
b
multiply(divide(subtract(add(const_100, 60), add(const_100, 20)), add(const_100, 20)), const_100)
add(n1,const_100)|add(n0,const_100)|subtract(#0,#1)|divide(#2,#1)|multiply(#3,const_100)|
general
there first number?
let the two numbers be x and y . ( 1 / 10 ) * x + y = ( 6 / 5 ) * y ( 1 / 10 ) * x = ( 1 / 5 ) * y x / y = 2 / 1 = 2 / 1 the answer is e .
a ) 3 : 2 , b ) 4 : 3 , c ) 8 : 7 , d ) 5 : 8 , e ) 2 : 1
e
divide(divide(const_1, divide(10, const_2)), divide(const_1, 10))
divide(n0,const_2)|divide(const_1,n0)|divide(const_1,#0)|divide(#2,#1)
general
each total total?
2 * 6 = 12 . answer is b .
a ) 16 , b ) 12 , c ) 18 , d ) 22 , e ) 08
b
multiply(2, 6)
multiply(n0,n2)|
general
a, dozen?
"40 * ( 40 / 100 ) = 16 - - - 60 ? - - - 12 = > rs . 3.2 answer : c"
a ) 1.2 , b ) 2.2 , c ) 3.2 , d ) 4.2 , e ) 5
c
multiply(const_12, divide(multiply(40, divide(40, const_100)), 60))
divide(n0,const_100)|multiply(n0,#0)|divide(#1,n1)|multiply(#2,const_12)|
gain
in empty -?
"service cost of 3 van and 2 truck = 2.05 * ( 3 + 2 ) = 10.5 fuel in 3 van = 3 * 70 = 210 litre fuel in 2 trucks = 2 * 70 ( 1 + 120 / 100 ) = 308 total fuel ( van + truck ) = 518 litre total fuel cost = 518 * 0.6 = 310.8 total cost = fuel + service = 310.8 + 10.25 = 321.05 answer is b"
a ) 312.6 $ , b ) 321.05 $ , c ) 343.7 $ , d ) 398.85 $ , e ) 412.12 $
b
add(multiply(multiply(add(70, divide(multiply(70, 120), const_100)), 2), 0.6), multiply(multiply(70, 3), 0.6))
multiply(n4,n5)|multiply(n2,n4)|divide(#0,const_100)|multiply(n1,#1)|add(n4,#2)|multiply(n3,#4)|multiply(n1,#5)|add(#6,#3)|
general
a he transaction?
"in such a case there is always a loss loss % = ( 16 / 10 ) ^ 2 = 64 / 25 = 2.56 % answer is b"
a ) 2 % , b ) 2.56 % , c ) 3.12 % , d ) 4.65 % , e ) 5.12 %
b
multiply(divide(subtract(add(multiply(divide(const_100, add(const_100, 16)), 675958), multiply(divide(const_100, subtract(const_100, 16)), 675958)), add(675958, 675958)), add(multiply(divide(const_100, add(const_100, 16)), 675958), multiply(divide(const_100, subtract(const_100, 16)), 675958))), const_100)
add(n1,const_100)|add(n0,n0)|subtract(const_100,n1)|divide(const_100,#0)|divide(const_100,#2)|multiply(n0,#3)|multiply(n0,#4)|add(#5,#6)|subtract(#7,#1)|divide(#8,#7)|multiply(#9,const_100)|
gain
in and service?
"( 10 / 100 ) workers = 16 = > number of workers = 160 ( 60 / 100 ) * workers = x + 16 = > x = 96 answer a"
a ) 96 , b ) 64 , c ) 50 , d ) 144 , e ) 160
a
divide(subtract(divide(multiply(divide(16, divide(10, const_100)), 90), const_100), multiply(divide(16, divide(10, const_100)), divide(const_1, const_2))), multiply(const_2, const_4))
divide(n3,const_100)|divide(const_1,const_2)|multiply(const_2,const_4)|divide(n2,#0)|multiply(n4,#3)|multiply(#3,#1)|divide(#4,const_100)|subtract(#6,#5)|divide(#7,#2)|
gain
a other m?
"area = ( l + b – d ) d ( 120 + 60 – 10 ) 10 = > 1700 m 2 1700 * 3 = rs . 5100 answer : a"
a ) s . 5100 , b ) s . 3900 , c ) s . 3228 , d ) s . 3922 , e ) s . 3928
a
multiply(multiply(subtract(add(120, 60), 10), 10), 3)
add(n0,n1)|subtract(#0,n2)|multiply(n2,#1)|multiply(n3,#2)|
geometry
the even inclusive?
"2 + 4 + 6 + 8 + . . . + 100 = 2550 502 + 504 + . . . + 600 = 50 ( 500 ) + ( 2 + 4 + . . . + 100 ) = 25,000 + 2550 = 27,550 the answer is b ."
a ) 23,550 , b ) 27,550 , c ) 31,550 , d ) 35,550 , e ) 39,550
b
multiply(divide(add(600, 502), const_2), add(divide(subtract(600, 502), const_2), const_1))
add(n2,n3)|subtract(n3,n2)|divide(#1,const_2)|divide(#0,const_2)|add(#2,const_1)|multiply(#4,#3)|
general
if n =?
"8 ! = 40320 e . 2 ^ 10 = 512 ( 40320 / 512 ) - this is not a factor of 8 ! d . 2 ^ 8 = 256 ( 40320 / 256 ) - this is not a factor of 8 ! c . 2 ^ 6 = 64 ( 720 / 64 ) - this is a factor of 8 ! c is answer"
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
c
subtract(divide(8, const_2), const_1)
divide(n1,const_2)|subtract(#0,const_1)|
other
when x x?
"the equation that can be formed is : 3 x - 18 = 70 - x or , 4 x = 88 or , x = 22 . e answer ."
a ) - 4 , b ) - 2 , c ) 11 , d ) 13 , e ) 22
e
divide(add(70, 18), add(3, const_1))
add(n1,n2)|add(const_1,n0)|divide(#0,#1)|
general
what,66?
"by the definition of an average , we get : x + 2 x + 63 = 3 x + 63 x + 2 x + 63 = 3 x + 63 = 3 ( x + 2 ) 3 = x + 2 . = 3 ( x + 2 ) 3 = x + 2 . hence , the answer is x + 2 x + 2 or option c"
a ) x + 2 , b ) x + 2 x , c ) x + 2 x + 2 , d ) 2 x + 2 , e ) x + 2 x - 2
c
multiply(divide(divide(multiply(2, add(2, const_1)), const_2), 2), 2)
add(n0,const_1)|multiply(n0,#0)|divide(#1,const_2)|divide(#2,n0)|multiply(n1,#3)|
general
10 need work?
work done by 10 men in 1 day = 1 / 7 work done by 1 man in 1 day = ( 1 / 7 ) / 10 = 1 / 70 work done by 10 women in 1 day = 1 / 14 work done by 1 woman in 1 day = 1 / 140 work done by 5 men and 10 women in 1 day = 5 × ( 1 / 70 ) + 10 × ( 1 / 140 ) = 5 / 70 + 10 / 140 = 1 / 7 = 5 men and 10 women can complete the work in 7 days answer : option c
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 10
c
inverse(add(multiply(10, inverse(multiply(14, 10))), multiply(5, divide(inverse(7), 10))))
inverse(n1)|multiply(n0,n3)|divide(#0,n0)|inverse(#1)|multiply(n0,#3)|multiply(n4,#2)|add(#4,#5)|inverse(#6)
physics
v0 cupboard?
"explanation : cost price = 1500 / ( 0.10 + 0.10 ) = 1500 / 0.20 = rs . 7500 answer b"
a ) 7450 , b ) 7500 , c ) 7400 , d ) 7500 , e ) none of these
b
divide(1500, divide(subtract(add(const_100, 10), subtract(const_100, 10)), const_100))
add(n0,const_100)|subtract(const_100,n0)|subtract(#0,#1)|divide(#2,const_100)|divide(n1,#3)|
gain
there percentage change?
"let p be the original price per unit of gas . let x be the original gas consumption . let y be the reduced gas consumption . y * 1.1 * 1.2 * p = x * p y = x / ( 1.1 * 1.2 ) which is about 0.76 x which is a decrease of about 24 % . the answer is c ."
a ) 16 % , b ) 20 % , c ) 24 % , d ) 28 % , e ) 32 %
c
multiply(subtract(const_1, divide(const_100, add(add(const_100, 20), divide(multiply(add(const_100, 20), 10), const_100)))), const_100)
add(n0,const_100)|multiply(n1,#0)|divide(#1,const_100)|add(#0,#2)|divide(const_100,#3)|subtract(const_1,#4)|multiply(#5,const_100)|
general
the is area?
"100 * 100 = 10000 135 * 80 = 10800 answer : a"
a ) 10800 , b ) 1299 , c ) 1000 , d ) 10000 , e ) 2887
a
multiply(add(35, const_100), subtract(const_100, 20))
add(n0,const_100)|subtract(const_100,n1)|multiply(#0,#1)|
geometry
express mph?
"25 * 18 / 5 = 90 kmph answer : c"
a ) 23 , b ) 88 , c ) 90 , d ) 27 , e ) 21
c
multiply(divide(25, const_1000), const_3600)
divide(n0,const_1000)|multiply(#0,const_3600)|
physics
a same work?
"b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 24 therefore 1 work is done by a in ( 24 x 1 ) = 8 days . e"
a ) 6 , b ) 5 , c ) 5.5 , d ) 7 , e ) 8
e
divide(multiply(multiply(divide(const_1, 15), 10), 24), const_2)
divide(const_1,n1)|multiply(n2,#0)|multiply(n0,#1)|divide(#2,const_2)|
physics
a upgraded?
"let x be the number of upgraded sensors on the satellite . the number of non - upgraded sensors per unit is x / 6 . the number of non - upgraded sensors on the whole satellite is 30 ( x / 6 ) = 5 x . the fraction of sensors which have been upgraded is x / ( x + 5 x ) = x / 6 x = 1 / 6 the answer is c ."
a ) 5 / 6 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 24
c
divide(30, add(30, multiply(30, multiply(divide(1, 6), 30))))
divide(n1,n2)|multiply(n0,#0)|multiply(n0,#1)|add(n0,#2)|divide(n0,#3)|
general
a of class?
"let total no of students in the class be n so , we are told that n is divisible by both 16 24 so , lets find the least common multiple of 16 24 , ie 48 so our answer is ( c ) 48"
a ) 6 , b ) 36 , c ) 48 , d ) 60 , e ) 72
c
lcm(16, 24)
lcm(n0,n1)|
general
if for article is
"explanation : let c . p . be rs . x . then , 5 % of x = 350 - 320 = 30 x / 20 = 30 = > x = 600 answer : e"
a ) 289 , b ) 231 , c ) 200 , d ) 288 , e ) 600
e
divide(subtract(350, 320), divide(5, const_100))
divide(n0,const_100)|subtract(n1,n2)|divide(#1,#0)|
gain
a5 is :
"area of the hall = 3600 * 1500 area of each stone = ( 50 * 50 ) therefore , number of stones = ( 3600 * 1500 / 50 * 50 ) = 2160 answer : d"
a ) 180 , b ) 1800 , c ) 18 , d ) 2160 , e ) 1.8
d
divide(multiply(36, 15), divide(multiply(5, 5), const_100))
multiply(n0,n1)|multiply(n2,n3)|divide(#1,const_100)|divide(#0,#2)|
physics
on is p?
"distance between - 2 and 3 = 5 since number p is twice as many units from - 2 as - 2 is from 3 , therefore p can be - 12 since , p is less than - 2 , the value of p = - 12 answer a"
a ) – 12 , b ) – 10 , c ) – 6 , d ) 10 , e ) 14
a
subtract(negate(2), multiply(2, subtract(2, negate(2))))
negate(n2)|subtract(n0,#0)|multiply(#1,n0)|subtract(#0,#2)|
general
before that drawn?
"pete covered 2.5 * 60 = 150 miles which correspond to 6 inches on the map - - > scale in inches per mile is 6 / 150 = 1 / 25 . answer : a ."
a ) 1 / 25 , b ) 1 / 30 , c ) 1 / 10 , d ) 2 , e ) 30
a
divide(const_1, multiply(divide(2.5, 6), 60))
divide(n1,n0)|multiply(#0,n2)|divide(const_1,#1)|
physics
a. lent?
"p - 480 = ( p * 5 * 8 ) / 100 p = 800 the answer is b ."
a ) 700 , b ) 800 , c ) 900 , d ) 1000 , e ) 1100
b
divide(480, subtract(const_1, divide(multiply(5, 8), const_100)))
multiply(n0,n1)|divide(#0,const_100)|subtract(const_1,#1)|divide(n2,#2)|
gain
all ations?
detailed solution if a number written in base 6 ends with a zero , it should be a multiple of 6 . in other words , the question wants us to find all numbers from 1 to 200 that are not multiples of 6 or 7 . there are 33 multiples of 6 less than 201 . there are 28 multiples of 7 less than 201 . there are 4 multiples of 6 & 7 ( or multiple of 42 ) from 1 to 200 . so , total multiples of 6 or 7 less than 201 = 33 + 28 - 4 = 57 . number of numbers with non - zero units digit = 200 - 57 = 143 . correct answer : a
['a ) 143', 'b ) 200', 'c ) 157', 'd ) 122', 'e ) 132']
a
subtract(200, subtract(add(divide(200, 6), divide(200, 7)), divide(200, multiply(6, 7))))
divide(n1,n2)|divide(n1,n3)|multiply(n2,n3)|add(#0,#1)|divide(n1,#2)|subtract(#3,#4)|subtract(n1,#5)
other
two moving train?
"relative speed = ( 72 - 36 ) * 5 / 18 = 2 * 5 = 10 mps . distance covered in 25 sec = 25 * 10 = 250 m . the length of the faster train = 250 m . answer : b"
a ) 270 , b ) 250 , c ) 187 , d ) 257 , e ) 271
b
multiply(divide(subtract(72, 36), const_3_6), 25)
subtract(n0,n1)|divide(#0,const_3_6)|multiply(n2,#1)|
physics
an probability red?
option ( b ) is correct p ( both are red ) , 6 c 2 / 13 c 2 = 5 / 26 answer b
a ) 6 / 13 , b ) 5 / 26 , c ) 6 / 26 , d ) 9 / 26 , e ) 10 / 27
b
divide(divide(multiply(6, 5), const_2), divide(multiply(add(add(6, 5), 2), subtract(add(add(6, 5), 2), const_1)), const_2))
add(n0,n1)|multiply(n0,n1)|add(n2,#0)|divide(#1,const_2)|subtract(#2,const_1)|multiply(#2,#4)|divide(#5,const_2)|divide(#3,#6)
other
if of j?
"imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 30 % of 350 , comes out to be 105 . . . . 200 % of 10 is 20 . . . . ( 105 * 100 ) / 20 = 525 . . . . ans : c"
a ) 0.35 , b ) 3.5 , c ) 525 , d ) 350 , e ) 3500
c
multiply(divide(multiply(divide(multiply(multiply(125, 150), 175), multiply(multiply(25, 50), 75)), 30), 200), const_100)
multiply(n0,n2)|multiply(n1,n3)|multiply(n4,#0)|multiply(n5,#1)|divide(#2,#3)|multiply(n6,#4)|divide(#5,n7)|multiply(#6,const_100)|
gain
solve 15
"2 x + 1 = - 15 x = - 8 a"
a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
a
divide(negate(add(15, 1)), 2)
add(n1,n2)|negate(#0)|divide(#1,n0)|
general
a, period?
"total weekly income over 5 weeks = $ 556 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2220 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2220 = $ 1280 from this , we subtract base salary for 2 weeks i . e $ 350 * 2 = $ 700 therefore , commission = $ 1280 - $ 700 = $ 580 for 2 weeks avg weekly commission = $ 290 answer b"
a ) $ 150 , b ) $ 290 , c ) $ 365 , d ) $ 715 , e ) $ 730
b
subtract(divide(subtract(multiply(500, 7), add(add(add(556, 413), add(436, 420)), 395)), const_2), 350)
add(n2,n3)|add(n4,n5)|multiply(n7,n8)|add(#0,#1)|add(n6,#3)|subtract(#2,#4)|divide(#5,const_2)|subtract(#6,n0)|
general
a downstream current?
"speed of boat in still water ( b ) = 4.8 km / hr . speed of boat with stream ( down stream ) , d = b + u speed of boat against stream ( up stream ) , u = b – u it is given upstream time is twice to that of down stream . ⇒ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) ⇒ u = b / 3 = 1.6 km / hr . answer : e"
a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.6
e
divide(subtract(multiply(4.8, const_2), 4.8), const_3)
multiply(n0,const_2)|subtract(#0,n0)|divide(#1,const_3)|
general
125 of4?
"milk = 3 / 5 * 125 = 75 liters water = 50 liters 75 : ( 50 + p ) = 3 : 4 150 + 3 p = 400 = > p = 50 50 liters of water are to be added for the ratio become 3 : 4 . answer : d"
a ) 12 liters , b ) 32 liters , c ) 41 liters , d ) 50 liters , e ) 34 liters
d
multiply(divide(125, add(3, 2)), 2)
add(n1,n2)|divide(n0,#0)|multiply(n2,#1)|
general
a were is :
let there be x pupils in the class . total increase in marks = ( x * 1 / 2 ) = x / 2 . x / 2 = ( 35 - 23 ) = > x / 2 = 12 = > x = 24 . answer : e
a ) 30 , b ) 80 , c ) 20 , d ) 25 , e ) 24
e
multiply(subtract(35, 23), const_2)
subtract(n0,n1)|multiply(#0,const_2)
general
there are end?
"total number of apples in the basket initially = 1000 each child picks up = 1 + 2 + 3 + 4 + 5 + 6 = 6 * 7 / 2 = 21 total number of apples picked up by 10 children = 21 * 10 = 210 number of apples left in the end = 1000 - 210 = 790 answer is d"
a ) 90 , b ) 91 , c ) 210 , d ) 790 , e ) 910
d
subtract(1000, multiply(add(add(multiply(add(1, 6), divide(10, const_2)), divide(10, const_2)), 1), 10))
add(n0,n1)|divide(n3,const_2)|multiply(#0,#1)|add(#1,#2)|add(#3,n1)|multiply(#4,n3)|subtract(n4,#5)|
general
in random prize?
"total draws = prizes + blanks = 100 + 300 = 400 probability of getting a prize = 100 / 400 = 1 / 4 correct option is e"
a ) 1 / 2 , b ) 5 / 400 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 4
e
divide(300, add(100, 300))
add(n0,n1)|divide(n1,#0)|
probability
the cm resolutions?
"in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 400 * 2 * 22 / 7 * 22.4 = 56320 cm = 563.2 m answer : e"
a ) 708 m , b ) 704 m , c ) 774 m , d ) 714 m , e ) 563.2 m
e
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), 400), 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
q of age?
explanation : given r – q = q – t and r + t = 50 which gives q = 25 as the difference between r & q and q & t is same so answer is 25 years answer : c
a ) 23 , b ) 28 , c ) 25 , d ) 19 , e ) 11
c
divide(50, const_2)
divide(n0,const_2)
general
if21 y?
"24 x + 21 y = 3 ( 8 x + 7 y ) which will be a minimum positive number when 8 x + 7 y = 1 . 8 ( 1 ) + 7 ( - 1 ) = 1 then 3 ( 8 x + 7 y ) can have a minimum positive value of 3 . the answer is a ."
a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
a
subtract(24, 21)
subtract(n0,n1)|
general
the he3?
"average = total runs / no . of innings = 32 so , total = average x no . of innings = 32 * 20 = 640 now increase in avg = 4 runs . so , new avg = 32 + 3 = 35 runs total runs = new avg x new no . of innings = 35 * 21 = 735 runs made in the 11 th inning = 735 - 640 = 95 answer : a"
a ) 95 , b ) 106 , c ) 122 , d ) 116 , e ) 122
a
subtract(multiply(add(20, const_1), add(3, 32)), multiply(20, 32))
add(n0,const_1)|add(n1,n2)|multiply(n0,n1)|multiply(#0,#1)|subtract(#3,#2)|
general
a. percent?
"500 - - - 150 100 - - - ? = > 30 % answer : b"
a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
b
multiply(divide(subtract(650, 500), 500), const_100)
subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
jo many mortgage?
"joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 36400 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 364 so we have 1 , 3 , 9 , 27 . . . . . 36400 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 364 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 364 x - 2 = 1 - 3 ^ n - 728 = 1 - 3 ^ n - 729 = - 3 ^ n 729 = 3 ^ n ( negatives cancel out ) 729 can also be re written as 3 ^ 6 therefore ; 3 ^ 6 = 3 ^ n thus n = 6 ( a )"
a ) 6 , b ) 8 , c ) 10 , d ) 11 , e ) 13
a
divide(log(add(divide(multiply(36400, const_2), 100), const_1)), log(const_3))
log(const_3)|multiply(n1,const_2)|divide(#1,n0)|add(#2,const_1)|log(#3)|divide(#4,#0)|
general
the average6 is
"solution average = 6 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 90 / 5 . = 18 answer b"
a ) 3 , b ) 18 , c ) 9 , d ) 12 , e ) 15
b
add(6, const_1)
add(n0,const_1)|
general
a liters?
"16 liters is 40 % of the capacity c . 16 = 0.4 c c = 16 / 0.4 = 40 liters . the answer is b ."
a ) 32 , b ) 40 , c ) 48 , d ) 54 , e ) 60
b
divide(16, subtract(divide(3, 4), divide(35, const_100)))
divide(n2,n3)|divide(n0,const_100)|subtract(#0,#1)|divide(n1,#2)|
general
in many correct?
let x be the correct answer and y be the wrong answer so the total number of questions is ( x + y ) = 150 = > 4 x - 2 y = 480 = > 6 x = 780 hence x = 130 answer : b
a ) 120 , b ) 130 , c ) 110 , d ) 150 , e ) 180
b
divide(add(480, multiply(150, 2)), add(4, 2))
add(n0,n1)|multiply(n1,n3)|add(n2,#1)|divide(#2,#0)
general
a remainder divisor?
"easy solution : n = dq 1 + 251 2 n = 2 dq 1 + 502 - ( 1 ) 2 n = dq 2 + 112 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 390 d * some integer = 390 checking all options only ( c ) syncs with it . answer c"
a ) 370 , b ) 365 , c ) 390 , d ) 456 , e ) 460
c
subtract(multiply(251, const_2), 112)
multiply(n0,const_2)|subtract(#0,n1)|
general
excluding hr hour?
"in 1 hr , the bus covers 120 km without stoppages and 40 km with stoppages . stoppage time = time take to travel ( 120 - 40 ) km i . e 80 km at 120 km / hr . stoppage time = 80 / 120 hrs = 40 min answer : e"
a ) 15 min , b ) 18 min , c ) 16 min , d ) 20 min , e ) 40 min
e
subtract(multiply(const_1, const_60), multiply(divide(40, 120), const_60))
divide(n1,n0)|multiply(const_1,const_60)|multiply(#0,const_60)|subtract(#1,#2)|
general
the is :
"first part will be zero always 2 nd part with power of three therefore , the second term has a units digit of 9 . of course 0 + 9 = 9 , a"
a ) 9 , b ) 4 , c ) 6 , d ) 8 , e ) 0
a
add(reminder(multiply(reminder(46, const_4), 93), const_10), reminder(10, const_10))
reminder(n3,const_4)|reminder(n0,const_10)|multiply(n2,#0)|reminder(#2,const_10)|add(#3,#1)|
general
consider3 her was
"explanation : principal = rs . ( 100 × 9900 / 12 × 3 ) = > rs . 27500 . answer : b"
a ) rs . 2000 , b ) rs . 27500 , c ) rs . 15000 , d ) rs . 20000 , e ) none of these
b
divide(9900, divide(multiply(3, 12), const_100))
multiply(n0,n1)|divide(#0,const_100)|divide(n2,#1)|
gain
if selling percent?
"let s . p . = $ 100 c . p . = $ 96 profit = $ 4 profit % = 4 / 96 * 100 = 25 / 6 = 4.17 % answer is a"
a ) 4.17 % , b ) 5 % , c ) 6.12 % , d ) 3.25 % , e ) 5.75 %
a
multiply(divide(subtract(const_100, 96), 96), const_100)
subtract(const_100,n0)|divide(#0,n0)|multiply(#1,const_100)|
gain
how 358?
"5 * 14 = 70 5 * 71 = 355 total no of multiples = ( 71 - 14 ) + 1 = 57 + 1 = 58 answer is e ."
a ) 54 , b ) 55 , c ) 56 , d ) 57 , e ) 58
e
add(divide(subtract(358, 70), 5), const_1)
subtract(n2,n1)|divide(#0,n0)|add(#1,const_1)|
general
a b is?
"6 * 36 : 5 * 36 : 3 * 12 6 : 5 : 1 1 / 12 * 4206 = 350.50 answer : d"
a ) 276 , b ) 289 , c ) 400 , d ) 350.5 , e ) 300
d
multiply(divide(6000, add(6000, add(multiply(5000, 3), multiply(3000, 3)))), 6000)
multiply(n1,n3)|multiply(n2,n3)|add(#0,#1)|add(n0,#2)|divide(n0,#3)|multiply(n0,#4)|
gain
a percent?
5000 - - - 750 100 - - - ? = > 15 % answer : d
a ) 1 % , b ) 5 % , c ) 10 % , d ) 15 % , e ) 20 %
d
multiply(divide(subtract(5750, 5000), 5000), const_100)
subtract(n2,n0)|divide(#0,n0)|multiply(#1,const_100)
gain
ren in alone?
renu â € ™ s one day â € ™ s work = 1 / 6 suma â € ™ s one day â € ™ s work = 1 / 5 - 1 / 6 = 1 / 30 suma can do it alone in 30 days . answer : e
a ) 10 , b ) 12 , c ) 14 , d ) 15 , e ) 30
e
inverse(subtract(divide(const_1, 5), divide(const_1, 6)))
divide(const_1,n1)|divide(const_1,n0)|subtract(#0,#1)|inverse(#2)
physics
if units?
"here , we ' re told that 5 machines can produce 20 units in 10 hours . . . . that means that each machine works for 10 hours apiece . since there are 5 machines ( and we ' re meant to assume that each machine does the same amount of work ) , then the 5 machines equally created the 20 units . 20 units / 5 machines = 4 units are made by each machine every 10 hours now that we know how long it takes each machine to make 4 units , we can break this down further if we choose to . . . 10 hours / 4 units = 2.5 hours per unit when 1 machine is working . the prompt asks us how long would it take 20 machines to produce 160 units . if 20 machines each work for 2.5 hours , then we ' ll have 20 units . since 160 units is ' 8 times ' 20 , we need ' 8 times ' more time . ( 2.5 hours ) ( 8 times ) = 20 hours final answer : [ reveal ] spoiler : c"
a ) 50 hours , b ) 40 hours , c ) 20 hours , d ) 12 hours , e ) 8 hours
c
divide(160, multiply(divide(divide(20, 10), 5), 20))
divide(n1,n2)|divide(#0,n0)|multiply(n1,#1)|divide(n4,#2)|
physics
a hour minutes?
"explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 200 - 50 ) m = 150 m . answer : d"
a ) 100 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
d
subtract(200, multiply(divide(3, const_60), const_1000))
divide(n3,const_60)|multiply(#0,const_1000)|subtract(n0,#1)|
physics
the is s?
"sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4 * 2 ) + ( 3.85 * 2 ) ] = 8 required average = ( 8 / 2 ) = 4 e"
a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 5.6 , e ) 4
e
divide(subtract(multiply(6, 3.95), add(multiply(2, 4), multiply(2, 3.85))), 2)
multiply(n0,n1)|multiply(n2,n3)|multiply(n2,n5)|add(#1,#2)|subtract(#0,#3)|divide(#4,n2)|
general
the500 is :
solution increase in 10 year = ( 80000 - 50000 ) = 30000 . increase % = ( 30000 / 50000 x 100 ) % = 60 % â ˆ ´ required average = ( 60 / 10 ) % = 6 % answer c
a ) 4.37 % , b ) 5 % , c ) 6 % , d ) 8.75 % , e ) none of these
c
divide(multiply(divide(subtract(80000, 50000), 50000), const_100), const_10)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|divide(#2,const_10)
general
calculate in upstream.
"speed in still water = ( 13 + 5 ) 1 / 2 kmph = 9 kmph . answer : b"
a ) 3 kmph , b ) 9 kmph , c ) 4 kmph , d ) 8 kmph , e ) 6 kmph
b
divide(add(13, 10), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
in throw2?
"s = { 1,2 , 3,4 , 5,6 } e = { 3,4 , 5,6 } probability = 4 / 6 = 2 / 3 answer is e"
a ) 1 / 2 , b ) 2 / 5 , c ) 1 / 3 , d ) 2 / 7 , e ) 2 / 3
e
divide(const_2, add(2, const_2))
add(n0,const_2)|divide(const_2,#0)|
probability
what from queen?
ncr = n ! / ( n - r ) ! r ! total number of possible hands = 52 c 6 52 c 6 = ( 52 ! ) / ( ( 52 - 6 ) ! × 6 ! ) 52 c 6 = 61075560 . number of hands with 2 queen and 4 non - queen cards = 4 c 2 × 48 c 4 4 c 2 = ( 4 ! ) / ( 2 ! × 2 ! ) = 6 . 48 c 4 = ( 48 ! ) / ( 44 ! × 4 ! ) = 3 × 47 × 46 × 45 = 291870 ( other 2 cards must be chosen from the rest 48 cards ) p ( 2 queen ) = ( 4 c 2 × 48 c 4 ) / 52 c 6 = 29187 / 1017926 c
a ) 1 / 23445 , b ) 113 / 22434 , c ) 29187 by 1017926 , d ) 1017926 / 29187 , e ) none of these
c
divide(multiply(choose(const_4, 2), choose(subtract(52, const_4), subtract(6, 2))), choose(52, 6))
choose(const_4,n2)|choose(n1,n0)|subtract(n1,const_4)|subtract(n0,n2)|choose(#2,#3)|multiply(#0,#4)|divide(#5,#1)
probability
car into have?
"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 130 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 130 - > y = 120 / 15 . = 8 d"
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
d
divide(subtract(130, multiply(5, 2)), add(10, 5))
add(n1,n2)|multiply(n1,n3)|subtract(n0,#1)|divide(#2,#0)|
general
if2 y?
explanation : x = y < = > 1 / q = ( 2 / q ) - 6 < = > 1 / q = 6 < = > q = 1 / 6 . answer : b
a ) 1 / 3 , b ) 1 / 6 , c ) 6 , d ) 3 , e ) 2
b
divide(subtract(2, 1), 6)
subtract(n1,n0)|divide(#0,n2)
general
a, price?
"explanation : 90 % 104 % - - - - - - - - 14 % - - - - 140 100 % - - - - ? = > rs . 1000 a )"
a ) rs . 1000 , b ) rs . 1100 , c ) rs . 1200 , d ) rs . 1250 , e ) rs . 1500
a
divide(multiply(140, 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
ar many days.
they together completed 4 / 10 work in 4 days . balance 6 / 10 work will be completed by arun alone in 50 * 6 / 10 = 30 days . answer : d
a ) 16 days . , b ) 17 days . , c ) 18 days . , d ) 30 days . , e ) 20 days .
d
subtract(50, multiply(divide(50, 10), 4))
divide(n2,n0)|multiply(n1,#0)|subtract(n2,#1)
physics
a the telescope?
"original visual range = 70 km new visual range = 150 km percent increase in the visual range by using the telescope = ( 150 - 70 ) / 70 * 100 % = 8 / 7 * 100 % = 114.28 % answer e"
a ) 30 % , b ) 33 1 / 2 % , c ) 40 % , d ) 60 % , e ) 114.28 %
e
multiply(divide(subtract(150, 70), 70), const_100)
subtract(n1,n0)|divide(#0,n0)|multiply(#1,const_100)|
general
c and l?
"gear l - - 10 rotations per 60 seconds - - 1 rotation per 6 seconds . gear r - - 40 rotations per 60 seconds - - 4 rotations per 6 seconds . first 6 seconds - - gear l makes 1 rotation . - - gear r makes 4 rotations - - net difference - - 3 rotations hence every 6 seconds the difference between the number of rotations of r and l gear is 3 units . required net difference should be 9 rotations = > 3 ( 6 seconds later ) = = > 18 seconds . answer : d ) ."
a ) a ) 6 , b ) b ) 8 , c ) c ) 10 , d ) d ) 18 , e ) e ) 15
d
divide(divide(9, subtract(divide(40, const_60), divide(10, const_60))), const_3)
divide(n1,const_60)|divide(n0,const_60)|subtract(#0,#1)|divide(n2,#2)|divide(#3,const_3)|
physics
find months.
"p = rs . 68000 , r = 50 / 3 % p . a and t = 9 / 12 years = 3 / 4 years . s . i . = ( p * r * t ) / 100 = rs . ( 68,000 * ( 50 / 3 ) * ( 3 / 4 ) * ( 1 / 100 ) ) = rs . 8500 answer is a ."
a ) rs . 8500 , b ) rs . 8000 , c ) rs . 7500 , d ) rs . 7000 , e ) rs . 6500
a
multiply(multiply(multiply(add(multiply(multiply(multiply(2, 3), const_100), const_100), multiply(multiply(multiply(3, 3), const_100), multiply(add(3, 2), 2))), divide(add(multiply(16, 3), 2), 3)), divide(multiply(3, 3), multiply(2, multiply(2, 3)))), divide(const_1, const_100))
add(n2,n3)|divide(const_1,const_100)|multiply(n3,n3)|multiply(n2,n3)|multiply(n1,n3)|add(n2,#4)|multiply(n2,#3)|multiply(#3,const_100)|multiply(#2,const_100)|multiply(#0,n2)|divide(#2,#6)|divide(#5,n3)|multiply(#7,const_100)|multiply(#8,#9)|add(#12,#13)|multiply(#14,#11)|multiply(#10,#15)|multiply(#1,#16)|
gain
three cm formed is
sol . volume of the new cube = ( 63 + 83 + 103 ) cm 3 = 1728 cm 3 . let the edge of the new cube be a cm . ∴ a 3 = 1728 ⇒ a = 12 . answer b
['a ) 10 cm', 'b ) 12 cm', 'c ) 16 cm', 'd ) 18 cm', 'e ) none']
b
cube_edge_by_volume(add(volume_cube(10), add(volume_cube(6), volume_cube(8))))
volume_cube(n0)|volume_cube(n1)|volume_cube(n2)|add(#0,#1)|add(#3,#2)|cube_edge_by_volume(#4)
physics