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ericsun153
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mathqa_question_token_drop_test

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a the train.
"speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time ( 45 ) * 9 = 405 meter answer : d"
a ) 150 meter , b ) 286 meter , c ) 186 meter , d ) 405 meter , e ) 265 meter
d
multiply(divide(multiply(162, const_1000), const_3600), 9)
multiply(n0,const_1000)|divide(#0,const_3600)|multiply(n1,#1)|
physics
a total are?
"let the maximum marks be x then , 30 % of x = 150 + 30 30 x / 100 = 180 30 x = 180 * 100 = 18000 x = 600 answer is b"
a ) 750 , b ) 600 , c ) 650 , d ) 550 , e ) 500
b
divide(add(150, 30), divide(30, const_100))
add(n1,n2)|divide(n0,const_100)|divide(#0,#1)|
general
a rate is?
"1 / x - 1 / 6 = - 1 / 8 x = 24 hrs 24 * 60 * 5 = 7200 . answer : c"
a ) 5729 , b ) 5760 , c ) 7200 , d ) 2870 , e ) 2799
c
divide(multiply(5, multiply(8, const_60)), subtract(divide(multiply(8, const_60), multiply(6, const_60)), const_1))
multiply(n2,const_60)|multiply(n0,const_60)|divide(#0,#1)|multiply(n1,#0)|subtract(#2,const_1)|divide(#3,#4)|
physics
we. buy?
"let b be the number of blue hats and let g be the number of green hats . b + g = 85 . b = 85 - g . 6 b + 7 g = 560 . 6 ( 85 - g ) + 7 g = 560 . 510 - 6 g + 7 g = 560 . g = 560 - 510 = 50 . the answer is b ."
a ) a ) 36 , b ) b ) 50 , c ) c ) 40 , d ) d ) 42 , e ) e ) 44
b
subtract(560, multiply(85, 6))
multiply(n0,n1)|subtract(n3,#0)|
general
among level employees?
"i ' m going in on this one . so let ' s say that we have the following so we know that l 1 = 72 and that c and l 1 = 0.10 x , we should set up a double set matrix btw but anyways , i ' m just explaining the point with this problem . now we are told that 0.1 x = 20 , therefore the grand total is 200 . now we know that l 2 is 200 - 72 = 128 . we also learn that c and no c are equally represented thus 100 each . therefore no c and no l 2 will be 100 - 52 = 48 . thus b is the correct answer choice"
a ) 46 , b ) 48 , c ) 56 , d ) 32 , e ) 58
b
divide(subtract(divide(20, divide(10, const_100)), 72), 2)
divide(n3,const_100)|divide(n6,#0)|subtract(#1,n4)|divide(#2,n1)|
general
the149 interest?
"1498 - 1400 = 98 is the rate of interest on $ 1400 for one year . the rate of interest = ( 100 * 98 ) / ( 1400 ) = 7 % the answer is c ."
a ) 3 % , b ) 5 % , c ) 7 % , d ) 9 % , e ) 11 %
c
divide(multiply(subtract(1498, 1400), const_100), 1400)
subtract(n1,n0)|multiply(#0,const_100)|divide(#1,n0)|
gain
a man man?
"m = 9 s = 3.1 ds = 12.1 us = 5.9 x / 12.1 + x / 5.9 = 1 x = 3.97 d = 3.97 * 2 = 7.94 answer : e"
a ) 2.21 , b ) 2.48 , c ) 9.24 , d ) 7.29 , e ) 7.94
e
multiply(divide(multiply(add(9, 3.1), subtract(9, 3.1)), add(add(9, 3.1), subtract(9, 3.1))), const_2)
add(n0,n1)|subtract(n0,n1)|add(#0,#1)|multiply(#0,#1)|divide(#3,#2)|multiply(#4,const_2)|
physics
a at ratio :
"n case of stock 1 , if he invest rs . 105 , he will get a dividend of rs . 12 ( assume face value = 100 ) in case of stock 2 , if he invest rs . 88 , he will get a dividend of rs . 8 ( assume face value = 100 ) ie , if he invest rs . ( 88 * 12 ) / 8 , he will get a dividend of rs . 12 required ratio = 105 : ( 88 × 12 ) / 8 = 105 : ( 11 × 12 ) = 35 : ( 11 × 4 ) = 35 : 44 answer : option d"
a ) 31 : 44 , b ) 31 : 27 , c ) 16 : 15 , d ) 35 : 44 , e ) 35 : 27
d
divide(multiply(105, const_2), multiply(88, const_3))
multiply(n1,const_2)|multiply(n3,const_3)|divide(#0,#1)|
other
a buses buses?
"let ' s say the distance between the buses is d . we want to determine interval = \ frac { d } { b } , where b is the speed of bus . let the speed of cyclist be c . every 15 minutes a bus overtakes cyclist : \ frac { d } { b - c } = 15 , d = 15 b - 15 c ; every 5 minutes cyclist meets an oncoming bus : \ frac { d } { b + c } = 4 , d = 4 b + 4 c ; d = 15 b - 15 c = 5 b + 5 c , - - > b = 2 c , - - > d = 15 b - 15 b / 2 = 15 b / 2 . interval = \ frac { d } { b } = \ frac { 15 / 2 b } { b } = 15 / 2 answer : e ( 15 / 2 minutes ) ."
a ) 5 minutes , b ) 6 minutes , c ) 8 minutes , d ) 9 minutes , e ) 15 / 2 minutes
e
divide(subtract(15, divide(15, divide(add(5, 15), subtract(15, 5)))), const_1)
add(n0,n1)|subtract(n0,n1)|divide(#0,#1)|divide(n0,#2)|subtract(n0,#3)|divide(#4,const_1)|
physics
r geometry passed?
explanation : number of questions attempted correctly = ( 70 % of 10 + 40 % of 30 + 60 % of 35 ) = 7 + 12 + 21 = 40 . questions to be answered correctly for 60 % = 60 % of total quotations = 60 % of 75 = 45 . he would have to answer 45 - 40 = 5 answer : a
a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
a
subtract(divide(multiply(75, 60), const_100), add(add(divide(multiply(10, 70), const_100), divide(multiply(30, 40), const_100)), divide(multiply(35, 60), const_100)))
multiply(n0,n6)|multiply(n1,n4)|multiply(n2,n5)|multiply(n3,n6)|divide(#0,const_100)|divide(#1,const_100)|divide(#2,const_100)|divide(#3,const_100)|add(#5,#6)|add(#8,#7)|subtract(#4,#9)
general
a value0?
"sqrt ( 7 x / 3 ) to be perfect square x has to 7 / 3 ans : b"
a ) 25 / 9 , b ) 7 / 3 , c ) 5 / 3 , d ) 3 / 5 , e ) 9 / 25
b
divide(7, 3)
divide(n0,n1)|
general
how240240?
"240 = 2 ^ 4 * 3 * 5 = ( 4 ) * 2 ^ 2 * 3 * 5 besides ( 4 ) , the exponents of 2 , 3 , and 5 are 2 , 1 , and 1 . there are ( 2 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 12 ways to make multiples of 4 . we must subtract 1 because one of these multiples is 240 . the answer is d ."
a ) 6 , b ) 8 , c ) 9 , d ) 11 , e ) 12
d
divide(divide(divide(240, 4), const_2), const_3)
divide(n0,n1)|divide(#0,const_2)|divide(#1,const_3)|
general
one she game?
connie has a 1 6 chance of winning 6 dollars her first turn . she has a 5 / 6 1 / 6 chance of winning 1 dollar her second turn . next , she has a 25 36 1 / 6 chance of winning 1 / 6 dollars her third turn . generalizing , connie ' s expected earnings form a geometric series with initial term 1 / 6 * 6 = 1 and common ratio 5 / 6 * 1 / 6 = 5 / 36 . hence , connie ' s expected earnings are 1 / 1 - 5 / 36 = 36 / 31 correct answer d
a ) 32 / 31 , b ) 33 / 31 , c ) 34 / 31 , d ) 36 / 31 , e ) 0 / 31
d
divide(const_1, subtract(const_1, divide(divide(subtract(6, 1), 6), 6)))
subtract(n0,n4)|divide(#0,n0)|divide(#1,n0)|subtract(const_1,#2)|divide(const_1,#3)
general
in units sale?
"0.06 * 0.05 = 0.003 = 0.3 % the answer is b ."
a ) 0.125 % , b ) 0.3 % , c ) 0.8 % , d ) 1.25 % , e ) 2.0 %
b
multiply(6, divide(5, const_100))
divide(n1,const_100)|multiply(n0,#0)|
gain
in andoes.
"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 26 = > 2 x = 26 = > x = 13 c"
a ) 11 , b ) 12 , c ) 13 , d ) 16 , e ) 18
c
divide(26, const_2)
divide(n0,const_2)|
general
a by time?
at 3 / 4 th of speed he is late by ' 2 hrs ' x - 3 / 4 ( x ) = 2 x = 8 so 8 - 2 = 6 hrs ( since 2 hrs late ) answer : c
a ) 5 hours , b ) 3 hours , c ) 6 hours , d ) 12 hours , e ) 15 hours
c
divide(multiply(multiply(multiply(divide(3, 4), 2), divide(3, 4)), 2), subtract(multiply(divide(3, 4), 2), multiply(multiply(divide(3, 4), 2), divide(3, 4))))
divide(n0,n1)|multiply(n2,#0)|multiply(#0,#1)|multiply(n2,#2)|subtract(#1,#2)|divide(#3,#4)
physics
given one answer.
because a + b = 1 , 2 a + 2 b = 2 ( a + b ) = 2 × 1 = 2 . correct answer d
a ) 3 , b ) 5 , c ) 4 , d ) 2 , e ) 1
d
subtract(add(add(2, 1), 2), add(2, 1))
add(n0,n1)|add(n1,#0)|subtract(#1,#0)
general
a sum?
"let the sums be p . now , 45 % of p = 4016.25 or , p = 8925 answer a"
a ) 8925 , b ) 8032.5 , c ) 4462.5 , d ) 8900 , e ) none of these
a
divide(multiply(const_100, 4016.25), multiply(9, 5))
multiply(n0,const_100)|multiply(n1,n2)|divide(#0,#1)|
gain
what number number?
"there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 555 ) = 2220 the answer is b ."
a ) 2210 , b ) 2220 , c ) 2230 , d ) 2240 , e ) 2250
b
multiply(add(add(multiply(add(add(5, 3), 2), const_100), multiply(add(add(const_4.0, 3), 2), const_10)), add(add(5, 3), 2)), 3)
add(n2,n3)|add(n1,#0)|multiply(#1,const_100)|multiply(#1,const_10)|add(#2,#3)|add(#4,#1)|multiply(#5,const_2)|
general
a ) ) ]
"let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 25 % are male i . e 25 / 100 * 20 = 5 geese ( males ) and now we know out of the total 20 geese , 5 are male , then 15 have to be female . now the ratio part , male geese ratios = 5 / 30 = 1 / 6 . - a female geese ratios = 15 / 70 = 3 / 14 - b cross multiply equations a and b and you get = 9 / 7 . ans e"
a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 9 / 7
e
divide(divide(divide(25, const_100), divide(30, const_100)), divide(divide(multiply(multiply(const_2, const_4), const_10), const_100), divide(30, const_100)))
divide(n1,const_100)|divide(n0,const_100)|multiply(const_2,const_4)|divide(#0,#1)|multiply(#2,const_10)|divide(#4,const_100)|divide(#5,#1)|divide(#3,#6)|
general
the. is?
"other number = ( 11 * 7700 ) / 275 = 308 . answer : c"
a ) 288 , b ) 277 , c ) 308 , d ) 988 , e ) 112
c
multiply(11, 275)
multiply(n0,n2)|
physics
a straight ae?
"ac = 11 and ab = 5 , so bc = 6 . bc = 2 cd so cd = 3 . the length of ae is ab + bc + cd + de = 5 + 6 + 3 + 7 = 21 the answer is b ."
a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
b
add(add(11, divide(subtract(11, 5), 2)), 7)
subtract(n4,n0)|divide(#0,n1)|add(n4,#1)|add(n2,#2)|
physics
in the garden?
"between the 12 mango trees , there are 11 gaps and each gap has 2 meter length also , 4 meter is left from all sides of the boundary of the garden . hence , length of the garden = ( 11 ã — 2 ) + 4 + 4 = 30 meter answer is e ."
a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
e
add(add(multiply(subtract(12, const_1), 2), divide(10, 2)), divide(10, 2))
divide(n0,n2)|subtract(n1,const_1)|multiply(n2,#1)|add(#0,#2)|add(#3,#0)|
physics
each the even?
"out of the 17 integers : 9 are odd and 8 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 9 odd numbers first 2 . 10 th number will be the first even number so we need to withdraw at least 10 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 10 . ( d )"
a ) 19 , b ) 12 , c ) 11 , d ) 10 , e ) 3
d
add(divide(17, const_2), 1)
divide(n1,const_2)|add(n0,#0)|
general
the runs matches?
sum of last 4 matches = ( ( 10 × 45 ) – ( 6 × 48 ) = 162 average = 162 / 4 = 40.5 answer : d
a ) 43.25 , b ) 43 , c ) 38 , d ) 40.5 , e ) 36
d
divide(subtract(multiply(45, 10), multiply(6, 48)), 4)
multiply(n0,n1)|multiply(n2,n3)|subtract(#0,#1)|divide(#2,n4)
general
a an % is
"explanation : let the cost price = rs 100 then , marked price = rs 140 required gain = 8 % , so selling price = rs 108 discount = 140 - 108 = 32 discount % = ( 32 / 140 ) * 100 = 22.85 % option b"
a ) 23.85 % , b ) 22.85 % , c ) 21.85 % , d ) 20.85 % , e ) none of these
b
subtract(const_100, multiply(divide(add(8, const_100), add(40, const_100)), const_100))
add(n1,const_100)|add(n0,const_100)|divide(#0,#1)|multiply(#2,const_100)|subtract(const_100,#3)|
gain
how length?
"b 16.8 sec d = 60 + 80 = 140 m s = 60 * 5 / 18 = 50 / 3 t = 140 * 3 / 50 = 8.4 sec answer is b"
a ) 5.8 sec , b ) 8.4 sec , c ) 12.4 sec , d ) 6.8 sec , e ) 1.8 sec
b
divide(add(60, 80), multiply(60, const_0_2778))
add(n0,n2)|multiply(n1,const_0_2778)|divide(#0,#1)|
physics
a the transportation?
"the percent of the budget for transportation is 100 - ( 55 + 9 + 5 + 4 + 2 ) = 25 % 100 % of the circle is 360 degrees . then ( 25 % / 100 % ) * 360 = 90 degrees the answer is e ."
a ) 18 ° , b ) 36 ° , c ) 54 ° , d ) 72 ° , e ) 90 °
e
divide(multiply(const_360, subtract(const_100, add(add(add(add(55, 9), 5), 4), 2))), const_100)
add(n0,n1)|add(n2,#0)|add(n3,#1)|add(n4,#2)|subtract(const_100,#3)|multiply(#4,const_360)|divide(#5,const_100)|
geometry
how are inclusive?
"96 / 7 = 13 . xx we are not concerned about the exact value of 96 / 7 as we just need the integers . since the values are small , we can write down the integers . the different integers between 5 and 96 / 7 would be 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12,13 total number of integers = 9 option b"
a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 15
b
add(subtract(divide(96, 7), 5), const_1)
divide(n1,n2)|subtract(#0,n0)|add(#1,const_1)|
general
s : 144
"( 256 ) ^ 2 - ( 144 ) ^ 2 = ( 256 + 144 ) ( 256 - 144 ) = 400 x 112 = 44800 answer is b"
a ) 761200 , b ) 44800 , c ) 761800 , d ) 761500 , e ) none of them
b
add(multiply(256, 256), multiply(144, 144))
multiply(n0,n1)|multiply(n2,n3)|add(#0,#1)|
general
the in feet?
"perimeter of square = p side of square = p / 4 area of square = ( p ^ 2 ) / 16 = a given that a = 2 p + 20 ( p ^ 2 ) / 16 = 2 p + 20 p ^ 2 = 32 p + 320 p ^ 2 - 32 p - 320 = 0 p ^ 2 - 40 p + 8 p - 320 = 0 p ( p - 40 ) + 8 ( p + 40 ) = 0 ( p - 40 ) ( p + 8 ) = 0 p = 40 or - 8 discarding negative value , p = 40 answer is c"
a ) 28 , b ) 36 , c ) 40 , d ) 56 , e ) 64
c
subtract(subtract(add(const_10, multiply(20, 2)), const_0_25), const_0_25)
multiply(n0,n1)|add(#0,const_10)|subtract(#1,const_0_25)|subtract(#2,const_0_25)|
geometry
which the4?
first we need to figure out what numbers are exactly divisible by 7 , 12,10 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,10 ) = 42 * 10 = 420 the numbers which will leave remainder 4 will be { 420 + 4 , 420 x 2 + 4 , , . . . } the largest such number less than or equal to 1856 is 420 * 4 + 4 or 1684 to obtain this you need to subtract 172 . b
a ) 168 , b ) 172 , c ) 182 , d ) 140 , e ) 160
b
subtract(1856, add(4, multiply(gcd(1856, lcm(lcm(7, 12), 10)), lcm(lcm(7, 12), 10))))
lcm(n1,n2)|lcm(n3,#0)|gcd(n0,#1)|multiply(#2,#1)|add(n4,#3)|subtract(n0,#4)
general
find the5?
"average = ( 5 + 10 + 15 ) / 3 = 10 answer is a"
a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 21
a
divide(add(add(add(3, const_1), add(add(3, const_1), const_2)), add(subtract(5, 3), subtract(5, const_2))), 3)
add(n0,const_1)|subtract(n1,n0)|subtract(n1,const_2)|add(#0,const_2)|add(#1,#2)|add(#0,#3)|add(#5,#4)|divide(#6,n0)|
general
the is :
"explanation : increase in 10 years = ( 242500 - 134800 ) = 107700 increase % = ( 107700 / 134800 x 100 ) % = 79 % . required average = ( 79 / 10 ) % = 7.9 % . answer : option b"
a ) 4.37 % , b ) 7.9 % , c ) 6.8 % , d ) 8.75 % , e ) none
b
add(multiply(divide(subtract(divide(subtract(subtract(subtract(multiply(multiply(const_10, const_1000), const_10), const_1000), const_1000), multiply(add(2, const_3), const_100)), multiply(add(multiply(add(const_3, const_4), const_10), add(2, const_3)), const_1000)), 1), const_10), const_100), const_4)
add(n2,const_3)|add(const_3,const_4)|multiply(const_10,const_1000)|multiply(#2,const_10)|multiply(#0,const_100)|multiply(#1,const_10)|add(#0,#5)|subtract(#3,const_1000)|multiply(#6,const_1000)|subtract(#7,const_1000)|subtract(#9,#4)|divide(#10,#8)|subtract(#11,n0)|divide(#12,const_10)|multiply(#13,const_100)|add(#14,const_4)|
general
how,5 m
"to solve this type of question , simply divide the volume of wall with the volume of brick to get the numbers of required bricks so lets solve this number of bricks = volume of wall / volume of 1 brick = 800 ∗ 600 ∗ 22.5 / 25 ∗ 11.25 ∗ 6 = 6400 answer : a"
a ) 6400 , b ) 3777 , c ) 2679 , d ) 2667 , e ) 1997
a
divide(multiply(multiply(multiply(8, const_100), multiply(6, const_100)), 22.5), multiply(multiply(25, 11.25), 6))
multiply(n3,const_100)|multiply(n4,const_100)|multiply(n0,n1)|multiply(#0,#1)|multiply(n2,#2)|multiply(n5,#3)|divide(#5,#4)|
physics
a win?
"65 % of 160 = x 0.65 * 160 = x 104 = x answer : c"
a ) 84 , b ) 94 , c ) 104 , d ) 114 , e ) 124
c
divide(multiply(65, 160), const_100)
multiply(n0,n1)|divide(#0,const_100)|
gain
a divided15?
"explanation : 80 + 25 = 105 / 15 = 7 ( remainder ) d"
a ) 3 , b ) 4 , c ) 6 , d ) 7 , e ) 9
d
subtract(subtract(subtract(80, 25), const_4), const_2)
subtract(n0,n1)|subtract(#0,const_4)|subtract(#1,const_2)|
general
a the cloth?
"sp of 1 m of cloth = 9000 / 80 = rs . 112.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 112.5 - rs . 23.5 = rs . 89 . answer : b"
a ) 22 , b ) 89 , c ) 90 , d ) 78 , e ) 80
b
subtract(divide(9000, 80), 23.5)
divide(n1,n0)|subtract(#0,n2)|
physics
a of farm?
chicken - ch cows - c sheep - s ch + c = 6 s c > ch and c > s each cow has 4 legs and 1 head each chicken has 2 legs and 1 head so 5 c + 3 ch = 100 ( sum of legs and head ) there are 2 possible solutions to this equation c = 11 and ch = 9 or c = 14 and ch = 10 since from first equation where ch + c = 6 s the sum of ch and c should be divisbile by 6 . 20 is not so the only possible solution is c = 14 and ch = 10 . so s = 4 answer : d
a ) 5 , b ) 8 , c ) 10 , d ) 4 , e ) 17
d
subtract(6, const_2)
subtract(n0,const_2)
general
in registered a?
"say there are total of 100 registered voters in that city . thus 60 are democrats and 40 are republicans . 60 * 0.75 = 45 democrats are expected to vote for candidate a ; 40 * 0.25 = 10 republicans are expected to vote for candidate a . thus total of 45 + 10 = 55 registered voters are expected to vote for candidate a , which is 55 % of the total number of registered voters . answer : d ."
a ) 50 % , b ) 53 % , c ) 54 % , d ) 55 % , e ) 57 %
d
add(multiply(60, divide(75, const_100)), multiply(subtract(const_100, 60), divide(25, const_100)))
divide(n1,const_100)|divide(n2,const_100)|subtract(const_100,n0)|multiply(n0,#0)|multiply(#1,#2)|add(#3,#4)|
gain
a can rock?
"let x be the distance to big rock . time = x / 3 + x / 7 = 1 x = 21 / 10 = 2.1 km the answer is c ."
a ) 1.5 , b ) 1.8 , c ) 2.1 , d ) 2.4 , e ) 2.7
c
multiply(divide(subtract(5, 2), add(add(5, 2), subtract(5, 2))), add(5, 2))
add(n0,n1)|subtract(n0,n1)|add(#0,#1)|divide(#1,#2)|multiply(#0,#3)|
physics
a * m?
"24 * 2 * 0.75 = 20 / 100 * 10 / 100 * 7.5 / 100 * x 24 = 1 / 100 * x = > x = 24000 answer : c"
a ) 29798 , b ) 27908 , c ) 24000 , d ) 25000 , e ) 27991
c
divide(divide(divide(multiply(multiply(multiply(24, const_100), multiply(2, const_100)), multiply(0.75, const_100)), 20), 10), 7.5)
multiply(n3,const_100)|multiply(n4,const_100)|multiply(n5,const_100)|multiply(#0,#1)|multiply(#3,#2)|divide(#4,n0)|divide(#5,n1)|divide(#6,n2)|
physics
th there club?
"30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 65 + 26 = 91 members have not passed the test , thus 0.7 * total = 91 - - > total = 130 . answer : d ."
a ) 60 , b ) 80 , c ) 100 , d ) 130 , e ) 140
d
divide(add(26, 65), divide(subtract(const_100, 65), const_100))
add(n0,n1)|subtract(const_100,n1)|divide(#1,const_100)|divide(#0,#2)|
gain
if = z?
"12 x = 16 y = 28 z 3 x = 4 y = 7 z 3 ( 4 * 7 ) = 4 ( 3 * 7 ) = 7 ( 3 * 4 ) addition = 28 + 21 + 12 = 61 answer would be multiple of 61 which is 122 answer : c"
a ) 52 , b ) 58 , c ) 122 , d ) 84 , e ) 168
c
divide(multiply(multiply(16, 28), 12), const_4)
multiply(n1,n2)|multiply(n0,#0)|divide(#1,const_4)|
general
a commission sell?
"first 100 machines = 3 % commission = 0.03 * 100 * 10000 = 30000 commission from sale of next machines = 34000 - 30000 = 4000 so 10 more machines . . total = 110 machines imo b . ."
a ) 90 , b ) 110 , c ) 105 , d ) 115 , e ) 120
b
add(100, divide(subtract(multiply(multiply(multiply(add(4, 3), multiply(3, const_2)), 100), multiply(add(4, const_1), const_2)), multiply(multiply(multiply(100, 100), divide(3, 100)), 100)), multiply(multiply(100, 100), divide(4, 100))))
add(n0,n2)|add(const_1,n2)|divide(n0,n1)|divide(n2,n1)|multiply(const_2,n0)|multiply(n1,n1)|multiply(#0,#4)|multiply(#1,const_2)|multiply(#2,#5)|multiply(#3,#5)|multiply(#6,n1)|multiply(n1,#8)|multiply(#10,#7)|subtract(#12,#11)|divide(#13,#9)|add(n1,#14)|
gain
in theoes.
"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 28 = > 2 x = 28 = > x = 14 c"
a ) 11 , b ) 12 , c ) 14 , d ) 16 , e ) 18
c
divide(28, const_2)
divide(n0,const_2)|
general
a rs percent is
"explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 26 ) = rs . 208 . profit = 208 - 150 = 58 so , profit % = ( 58 / 150 ) * 100 = 39 % option b"
a ) 12 % , b ) 39 % , c ) 14 % , d ) 15 % , e ) 16 %
b
divide(multiply(subtract(multiply(26, add(5, 3)), add(multiply(5, 18), multiply(3, 20))), const_100), add(multiply(5, 18), multiply(3, 20)))
add(n2,n3)|multiply(n0,n2)|multiply(n1,n3)|add(#1,#2)|multiply(n4,#0)|subtract(#4,#3)|multiply(#5,const_100)|divide(#6,#3)|
gain
abel in last?
abel in the 2 days that he worked completed 1 / 5 of the job = 4 / 5 remains then if ben had to leave 4 days before the completion , this means that carla had to work alone for these 4 days in which she completed 1 / 4 of the job . now together , ben and carla completed the job in ( 1 / 12 + 1 / 15 ) ( t ) = 11 / 20 3 / 20 ( t ) = 11 / 20 - - - > t = 3 2 / 3 therefore , these 3 2 / 3 days worked plus the 4 days that carla had to work by herself add to 7 2 / 3 days answer : c
a ) 6 , b ) 7 , c ) 7 2 / 3 , d ) 9 , e ) 10
c
multiply(add(2, 4), 4)
add(n3,n4)|multiply(n4,#0)
physics
j used used?
"total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 4 ) * 270 = 67 gallons total paint used = 157 gallons . option b"
a ) 18 , b ) 157 , c ) 175 , d ) 216 , e ) 250
b
add(multiply(divide(360, 4), 1), divide(subtract(360, multiply(divide(360, 4), 1)), 4))
divide(n0,n2)|multiply(n1,#0)|subtract(n0,#1)|divide(#2,n4)|add(#3,#1)|
physics
042, ___
"0 = 1 * 1 - 1 2 = 2 * 2 - 2 6 = 3 * 3 - 3 12 = 4 * 4 - 4 20 = 5 * 5 - 5 30 = 6 * 6 - 6 42 = 7 * 7 - 7 similarly 8 * 8 - 8 = 56 answer : e"
a ) 55 , b ) 85 , c ) 59 , d ) 63 , e ) 56
e
subtract(negate(20), multiply(subtract(6, 12), divide(subtract(6, 12), subtract(0,2, 6))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
the orderph?
"distance covered in 1 min = ( 66 * 1000 ) / 60 = 1100 m circumference of the wheel = ( 2 * ( 22 / 7 ) * . 70 ) = 4.4 m no of revolution per min = 1100 / 4.4 = 250 answer : e"
a ) 210 , b ) 220 , c ) 230 , d ) 240 , e ) 250
e
divide(divide(multiply(66, const_1000), const_60), multiply(multiply(divide(add(66, const_2), add(const_4, const_3)), const_2), divide(divide(140, const_100), const_2)))
add(n1,const_2)|add(const_3,const_4)|divide(n0,const_100)|multiply(n1,const_1000)|divide(#3,const_60)|divide(#2,const_2)|divide(#0,#1)|multiply(#6,const_2)|multiply(#5,#7)|divide(#4,#8)|
physics
a of be :
"explanation : let the number of hens be x and the number of cows be y . then , x + y = 50 . . . . ( i ) and 2 x + 4 y = 160 x + 2 y = 80 . . . . ( ii ) solving ( i ) and ( ii ) we get : x = 20 , y = 30 the required answer = 20 . answer : d"
a ) 22 , b ) 23 , c ) 24 , d ) 20 , e ) 28
d
divide(subtract(multiply(50, const_4), 160), const_2)
multiply(n0,const_4)|subtract(#0,n1)|divide(#1,const_2)|
general
if of women?
"we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w % = 10 / 5 = 200 % answer is c"
a ) 100 % , b ) 120 % , c ) 200 % , d ) 150 % , e ) 180 %
c
multiply(divide(const_100, 50), const_100)
divide(const_100,n0)|multiply(#0,const_100)|
gain
how11?
"650 = 10 * 65 1300 = 20 * 65 the even multiples are 65 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
b
add(divide(subtract(1301, 649), multiply(65, const_2)), const_1)
multiply(n0,const_2)|subtract(n2,n1)|divide(#1,#0)|add(#2,const_1)|
general
two trains - seconds
"explanation : relative speed = 70 + 90 = 160 km / hr ( since both trains are moving in opposite directions ) total distance = 1.1 + . 9 = 2 km time = 2 / 160 hr = 1 / 80 hr = 3600 / 80 seconds = = 45 seconds answer : option b"
a ) 56 , b ) 45 , c ) 47 , d ) 26 , e ) 25
b
multiply(divide(add(1.10, 0.9), add(70, 90)), const_3600)
add(n2,n3)|add(n0,n1)|divide(#0,#1)|multiply(#2,const_3600)|
physics
in.8?
"0,08 r = x / 100 * 0.1 r answer a"
a ) 80 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
a
multiply(divide(multiply(subtract(const_1, divide(20, const_100)), divide(10, const_100)), divide(10, const_100)), const_100)
divide(n4,const_100)|divide(n3,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(#0,#3)|divide(#4,#2)|multiply(#5,const_100)|
gain
a then, are
"one may notice that greatest possible values differ in each answer choice in contrast to the least values , which repeat . to find out the greatest value you should count the total classes ( 26 * 2 = 52 ) , then subtract the total # of teachers since we know from the question that each teacher taught at least one class ( 52 - 32 = 20 ) . thus we get a number of the available extra - classes for teachers , and all that we need is just to count how many teachers could take 2 more classes , which is 20 / 2 = 10 . so the greatest possible value of the # of teachers who had 3 classes is 10 . only answer c has this option ."
a ) 0 and 13 , b ) 0 and 14 , c ) 1 and 10 , d ) 1 and 9 , e ) 2 and 8
c
divide(subtract(multiply(26, 2), 32), 2)
multiply(n0,n1)|subtract(#0,n2)|divide(#1,n0)|
general
if2 x?
"( 2 to the power x ) - ( 2 to the power ( x - 2 ) ) = 3 ( 2 to the power 5 ) 2 ^ x - 2 ^ ( x - 2 ) = 3 . 2 ^ 5 hence x = 7 . answer is a"
a ) 7 , b ) 11 , c ) 13 , d ) 15 , e ) 17
a
add(5, 2)
add(n0,n5)|
general
convert8 ares
"1.8 hectares in ares 1 hectare = 100 ares therefore , 1.8 hectares = 1.8 × 100 ares = 180 ares . answer - c"
a ) 130 ares . , b ) 160 ares . , c ) 180 ares . , d ) 230 ares . , e ) 250 ares .
c
divide(multiply(multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)), 1.8), multiply(multiply(add(const_3, const_2), const_2), multiply(add(const_3, const_2), const_2)))
add(const_2,const_3)|multiply(#0,const_2)|multiply(#1,#1)|multiply(n0,#2)|divide(#3,#2)|
physics
in students '?
explanation : number of students appeared from school ' p ' = 100 , say number of students qualified from school ' p ' = 70 and number of students appeared from school ' q ' = 130 number of students qualified from school ' q ' = 50 % more than those qualified from school ' p ' . = 70 + 35 = 105 % of students qualified to the number of students appeared from school b = 105 / 130 * 100 = 80.76 % answer : b
a ) 80.78 % , b ) 80.76 % , c ) 80.72 % , d ) 80.79 % , e ) 80.74 %
b
multiply(divide(multiply(divide(add(50, const_100), const_100), divide(70, const_100)), divide(add(30, const_100), const_100)), const_100)
add(n2,const_100)|add(n1,const_100)|divide(n0,const_100)|divide(#0,const_100)|divide(#1,const_100)|multiply(#3,#2)|divide(#5,#4)|multiply(#6,const_100)
general
there the person?
let x be the height of the first person . then the heights are x , x + 2 , x + 4 , and x + 10 . 4 x + 16 = 4 ( 75 ) = 300 x = 71 and the fourth person has a height of 71 + 10 = 81 inches the answer is e .
a ) 73 , b ) 75 , c ) 77 , d ) 79 , e ) 81
e
add(divide(subtract(multiply(75, 4), add(6, add(4, 6))), 4), add(4, 6))
add(n0,n2)|multiply(n0,n3)|add(n2,#0)|subtract(#1,#2)|divide(#3,n0)|add(#0,#4)
general
if. n?
sum of interior angles of a polygon = ( n - 2 ) × 180 ° where n = number of sides there will be n angles which are in a . p . therefore , since we need to find maximum value of n , put minimum value for a and d . i . e . , take a = 20 and d = 20 then sum of the angles = n / 2 [ 2 × 20 + ( n − 1 ) 20 ] therefore , 10 n ( n + 1 ) = ( n − 2 ) 180 n = 14.52 since number of sides must be a positive integer , maximum value of n = 14 answer : b
a ) 12 , b ) 14 , c ) 21 , d ) 25 , e ) cant determine
b
divide(add(sqrt(subtract(power(subtract(20, const_3), const_2), multiply(const_4, multiply(divide(add(multiply(const_10, multiply(const_4, const_2)), const_100), const_10), const_2)))), subtract(20, const_3)), const_2)
multiply(const_2,const_4)|subtract(n0,const_3)|multiply(#0,const_10)|power(#1,const_2)|add(#2,const_100)|divide(#4,const_10)|multiply(#5,const_2)|multiply(#6,const_4)|subtract(#3,#7)|sqrt(#8)|add(#9,#1)|divide(#10,const_2)
general
the of be?
"sum of the 9 numbers = 207 if each number is increased by 4 , the total increase = 4 * 9 = 36 the new sum = 207 + 36 = 243 the new average = 243 / 9 = 27 . answer : c"
a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
c
multiply(23, 4)
multiply(n1,n2)|
general
a a percent?
"shopkeeper sells 800 g instead of 1000 g . so , his gain = 1000 - 800 = 200 g . thus , % gain = 200 * 100 ) / 800 = 25 % . answer : option b"
a ) 10 % , b ) 25 % , c ) 11.11 % , d ) 12 % , e ) none of these
b
multiply(divide(add(multiply(const_2, const_100), divide(const_100, const_2)), 800), const_100)
divide(const_100,const_2)|multiply(const_100,const_2)|add(#0,#1)|divide(#2,n0)|multiply(#3,const_100)|
gain
company thenesday.
"say the number of people having birthdays on wednesday is x and the number of people having birthdays on each of the other 6 days is y . then x + 6 y = 54 . now , plug options for x . only b and e give an integer value for y . but only for b x > y as needed . answer : b ."
a ) 6 , b ) 10 , c ) 8 , d ) 9 , e ) 12
b
add(const_4, add(floor(divide(58, add(const_4, const_3))), const_1))
add(const_3,const_4)|divide(n0,#0)|floor(#1)|add(#2,const_1)|add(#3,const_4)|
general
if wheel82?
"four wheeler = 20 * 4 = 80 ( max ) 2 wheel = 1 so no of 4 wheeler = 20 answer : d"
a ) 11 , b ) 12 , c ) 13 , d ) 20 , e ) 25
d
divide(subtract(82, 2), 4)
subtract(n3,n0)|divide(#0,n1)|
general
if250 is?
"50 % of x = x / 2 ; 25 % of 2500 = 25 / 100 * 2500 = 625 given that , x / 2 = 625 - 25 = > x / 2 = 600 = > x = 1200 . answer : c"
a ) 1880 , b ) 2160 , c ) 1200 , d ) 8400 , e ) 1210
c
divide(subtract(multiply(2500, divide(25, const_100)), 25), divide(50, const_100))
divide(n2,const_100)|divide(n0,const_100)|multiply(n3,#0)|subtract(#2,n1)|divide(#3,#1)|
general
a for time?
"30 men complete 0.4 work in 25 days . applying the work rule , m 1 × d 1 × w 2 = m 2 × d 2 × w 1 we have , 30 × 25 × 0.6 = m 2 × 25 × 0.4 or m 2 = 30 × 25 × 0.6 / 25 × 0.4 = 45 men answerc"
a ) 25 , b ) 30 , c ) 45 , d ) 20 , e ) none of these
c
divide(multiply(30, divide(subtract(const_100, 40), const_100)), divide(const_4, const_10))
divide(const_4,const_10)|subtract(const_100,n3)|divide(#1,const_100)|multiply(n1,#2)|divide(#3,#0)|
physics
in35 is :
"pass percentage = 100 - ( 30 + 35 - 35 ) = 100 - 30 = 70 answer : d"
a ) 10 % , b ) 20 % , c ) 30 % , d ) 70 % , e ) 50 %
d
subtract(const_100, subtract(add(30, 35), 35))
add(n0,n1)|subtract(#0,n2)|subtract(const_100,#1)|
general
in the profit?
let the cp = 100 profit = ( 320 / 100 ) × 100 = 320 sp = cp + profit = 100 + 320 = 420 if the cost increases by 25 % , new cp = ( 125 / 100 ) × 100 = 125 selling price is constant , hence new sp = 420 profit = sp – cp = 420 – 125 = 295 required percentage = ( 295 / 420 ) × 100 = 2950 / 42 = 1475 / 21 ≈ 70 answer : e
a ) 180 % , b ) 120 % , c ) 90 % , d ) 80 % , e ) 70 %
e
multiply(divide(subtract(add(320, const_100), add(25, const_100)), add(320, const_100)), const_100)
add(n0,const_100)|add(n1,const_100)|subtract(#0,#1)|divide(#2,#0)|multiply(#3,const_100)
gain
a in is :
total expenditure = 40 + 25 + 15 + 10 = 90 % saving = ( 100 - 90 ) = 10 % 10 / 100 × salary = 1200 , salary = 12000 rs . answer : a
a ) 12000 , b ) 6000 , c ) 8000 , d ) 10000 , e ) none of these
a
divide(multiply(1200, const_100), 10)
multiply(n4,const_100)|divide(#0,n3)
gain
the of is?
"explanation : lot the total number of workers be v then , 8 ooov = ( 12000 * 7 ) + 6000 ( v - 7 ) < = > 2000 v = 42000 < = > v = 21 . answer : b"
a ) 76 , b ) 21 , c ) 26 , d ) 28 , e ) 11
b
add(7, divide(multiply(7, subtract(12000, 8000)), subtract(8000, 6000)))
subtract(n2,n0)|subtract(n0,n3)|multiply(n1,#0)|divide(#2,#1)|add(n1,#3)|
general
a by chose?
"let xx be the number he chose , then 2 â ‹ … x â ˆ ’ 138 = 108 x = 123 answer : a"
a ) 123 , b ) 267 , c ) 277 , d ) 267 , e ) 120
a
divide(add(108, 138), 2)
add(n1,n2)|divide(#0,n0)|
general
two much the first
"let the third number is x . then first number = ( 100 - 30 ) % of x = 70 % of x = 7 x / 10 second number is ( 63 x / 100 ) difference = 7 x / 10 - 63 x / 100 = 7 x / 10 so required percentage is , difference is what percent of first number ( 7 x / 100 * 10 / 7 x * 100 ) % = 10 % answer : b"
a ) 8 % , b ) 10 % , c ) 9 % , d ) 11 % , e ) 12 %
b
subtract(multiply(divide(subtract(37, 30), subtract(const_100, 30)), const_100), const_10)
subtract(n1,n0)|subtract(const_100,n0)|divide(#0,#1)|multiply(#2,const_100)|subtract(#3,const_10)|
gain
express ph?
"30 * 18 / 5 = 108 kmph answer : b"
a ) 122 , b ) 108 , c ) 110 , d ) 150 , e ) 100
b
multiply(divide(30, const_1000), const_3600)
divide(n0,const_1000)|multiply(#0,const_3600)|
physics
in twiceoes.
"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 8 = > 2 x = 8 = > x = 4 b"
a ) 5 , b ) 4 , c ) 6 , d ) 3 , e ) 2
b
divide(8, const_2)
divide(n0,const_2)|
general
a after fabric?
"for first 2000 meters he does not get any discount . the price is 2 * 2000 = $ 4000 for next 1500 meters , he gets a 5 % discount . the price is 1.9 * 1500 = $ 2850 for the next 1500 meters , he gets a 7 % discount . the price is 1.86 * 1500 = $ 2790 the total price is $ 4000 + $ 2850 + $ 2790 = $ 9640 the answer is e ."
a ) $ 8280 , b ) $ 8520 , c ) $ 8710 , d ) $ 8930 , e ) $ 9640
e
multiply(multiply(2, const_3), const_100)
multiply(n4,const_3)|multiply(#0,const_100)|
gain
if log is :
"log 8 x + log 8 ( 1 / 6 ) = 1 / 3 = > ( log x / log 8 ) + ( log 1 / 6 / log 8 ) = log ( 81 / 3 ) = log 2 = > log x = log 2 – log 1 / 6 = log ( 2 * 6 / 1 ) = log 12 answer : a"
a ) 12 , b ) 16 , c ) 18 , d ) 24 , e ) 26
a
multiply(power(8, divide(1, 3)), 6)
divide(n2,n5)|power(n0,#0)|multiply(n3,#1)|
general
if squares numbers is
"sol . let the numbers be x and y . then , ( x + y ) = 12 and x 2 + y 2 = 124 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 12 ) 2 - 124 = 144 - 124 = 20 xy = 10 . answer a"
a ) 10 , b ) 44 , c ) 80 , d ) 88 , e ) 90
a
divide(subtract(power(12, const_2), 124), const_2)
power(n0,const_2)|subtract(#0,n1)|divide(#1,const_2)|
general
the the article?
"c . p . = rs . 5 x and s . p . = rs . 8 x . then , gain = rs . 3 x required ratio = 3 x : 5 x = 3 : 5 d"
a ) 23 , b ) 1 : 2 , c ) 2 : 5 , d ) 3 : 5 , e ) 25
d
divide(subtract(8, 5), 5)
subtract(n0,n1)|divide(#0,n1)|
other
tim even math?
"b 90 sum = ( n x n ) + n hence , 9 x 9 = 81 + 9 = 90"
a ) 80 , b ) 90 , c ) 30 , d ) 70 , e ) 60
b
multiply(add(9, const_1), 9)
add(n0,const_1)|multiply(n0,#0)|
physics
in ) y =
"line k passes through the origin and has slope 1 / 7 means that its equation is y = 1 / 7 * x . thus : ( x , 1 ) = ( 7 , 1 ) and ( 7 , y ) = ( 7,1 ) - - > x - y = 7 - 1 = 6 . answer : a"
a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 3
a
multiply(multiply(7, 7), divide(1, 7))
divide(n0,n3)|multiply(n1,n3)|multiply(#0,#1)|
general
find and cm.
"length = 15 cm , breadth = 13 cm perimeter of rectangle = 2 ( length + breadth ) = 2 ( 15 + 13 ) cm = 2 × 28 cm = 56 cm we know that the area of rectangle = length × breadth = ( 15 × 13 ) cm 22 = 195 cm 2 answer : d"
a ) 71 cm 2 , b ) 121 cm 2 , c ) 141 cm 2 , d ) 195 cm 2 , e ) 221 cm 2
d
square_area(15)
square_area(n0)|
geometry
out neither cricket?
"n ( a ) = 325 , n ( b ) = 175 , n ( aub ) = 400 - 50 = 350 . required number = n ( anb ) = n ( a ) + n ( b ) - n ( aub ) = 325 + 175 - 350 = 150 . answer is b"
a ) 120 , b ) 150 , c ) 100 , d ) 180 , e ) 220
b
subtract(add(175, 325), subtract(400, 50))
add(n1,n2)|subtract(n0,n3)|subtract(#0,#1)|
other
find of12.
"sum of first 20 multiples of 12 are = ( 12 × 1 ) + ( 12 × 2 ) + ( 12 × 3 ) + . . . . . . + ( 12 × 19 ) + ( 12 × 20 ) . = 12 ( 1 + 2 + 3 + . . . . . + 20 ) use the formula : n ( n + 1 ) 2 ⇒ 12 × ( 20 × 21 ) 2 = 2520 . answer : a"
a ) 2520 , b ) 3878 , c ) 2778 , d ) 27 , e ) 911
a
add(divide(divide(20, divide(divide(divide(divide(divide(20, const_2), const_2), const_2), const_2), const_2)), const_2), add(const_1, sqrt(divide(divide(20, divide(divide(divide(divide(divide(20, 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
50 menakes.
total no . of handshakes = 49 + 48 + 47 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 1225 or , if there are n persons then no . of shakehands = nc 2 = 50 c 2 = 1225 answer : c
a ) 190 , b ) 200 , c ) 1225 , d ) 220 , e ) 230
c
multiply(subtract(50, const_1), divide(50, const_2))
divide(n0,const_2)|subtract(n0,const_1)|multiply(#0,#1)
general
if by minutes?
"since the population increases at the rate of 1 person every 15 seconds , it increases by 4 people every 60 seconds , that is , by 4 people every minute . thus , in 10 minutes the population increases by 10 x 4 = 40 people . answer . a ."
a ) 40 , b ) 100 , c ) 150 , d ) 240 , e ) 300
a
multiply(divide(const_60, 15), 10)
divide(const_60,n0)|multiply(n1,#0)|
physics
real, price?
"let the retail price be = x selling price of z = 0.75 x selling price of x = 0.95 * 0.75 x = 0.71 x selling price of y = ( ( 0.75 x + 0.71 x ) / 2 ) * 0.70 = 0.73 x * 0.75 = 0.55 x 0.55 x = k * 0.71 x k = 0.55 / 0.71 = 55 / 71 answer : b"
a ) 21 / 34 , b ) 55 / 71 , c ) 25 / 34 , d ) 26 / 34 , e ) 27 / 34
b
multiply(divide(divide(multiply(divide(add(subtract(const_100, 25), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_2), subtract(const_100, 30)), const_100), multiply(subtract(const_100, 25), divide(subtract(const_100, 5), const_100))), const_10)
subtract(const_100,n1)|subtract(const_100,n0)|subtract(const_100,n2)|divide(#0,const_100)|multiply(#3,#1)|add(#4,#1)|divide(#5,const_2)|multiply(#6,#2)|divide(#7,const_100)|divide(#8,#4)|multiply(#9,const_10)|
general
if p events.
"p ( a n b ) = p ( a ) . p ( b ) p ( a n b ) = 3 / 5 . 2 / 5 p ( a n b ) = 6 / 25 . a"
a ) 6 / 25 , b ) 3 / 25 , c ) 8 / 25 , d ) 2 / 13 , e ) 3 / 17
a
multiply(divide(3, 5), divide(2, 5))
divide(n0,n1)|divide(n2,n3)|multiply(#0,#1)|
general
if last flips?
"on the first three flips , you must get heads . whats the probability of getting heads ? its 1 / 2 so for the first three flips , your probability is ( 1 / 2 ) ^ 3 = 1 / 8 now for the last two , you want to get tails only . whats the prob of getting tails ? well , its the same as prob of getting a heads , namely , 1 / 2 for the last two flips , your probability is ( 1 / 2 ) ^ 2 = 1 / 4 so your overall probability for the event in question is 1 / 8 * 1 / 4 = 1 / 32 answer : e"
a ) 3 / 5 , b ) 1 / 2 , c ) 1 / 5 , d ) 1 / 8 , e ) 1 / 32
e
power(divide(1, 2), 5)
divide(n0,n1)|power(#0,n2)|
probability
if y x?
"x < y < z to find the least possible value for z - x ; we need to find the values for z and x that can be closest to each other . if x is some even number , then what could be minimum possible odd z . if x is some even number y - x > 5 ; y > x + 5 ; minimum value for y = x + 5 + 2 = x + 7 [ note : x + 5 is as even + odd = odd and nearest odd greater than x + 5 is x + 5 + 2 ] minimum value for z = y + 2 = x + 7 + 2 = x + 9 [ note : z = y + 2 because both z and y are odd . difference between two odd numbers is 2 ] q = z - x = x + 9 - x = 9 ans : d"
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
d
add(add(5, const_2), const_2)
add(n0,const_2)|add(#0,const_2)|
general
a be originally?
originally let there be x men . less men , more days ( indirect ) : . ( x - 10 ) : x : : 100 : 110 or x - 10 / x = 100 / 110 or 11 x - 110 = 10 x or x = 110 so , originally there were 110 men . answer : d
a ) 75 , b ) 82 , c ) 100 , d ) 110 , e ) 120
d
divide(multiply(divide(add(100, 10), 10), 10), subtract(divide(add(100, 10), 10), 10))
add(n0,n1)|divide(#0,n1)|multiply(n1,#1)|subtract(#1,n1)|divide(#2,#3)
physics
how takeph?
d = 150 + 200 = 350 s = 54 * 5 / 18 = 15 mps t = 350 / 15 = 23.3 sec c ) 23.3 sec
a ) 17 sec , b ) 21 sec , c ) 23.3 sec , d ) 27.5 sec , e ) 29 sec
c
divide(add(200, 150), multiply(54, const_0_2778))
add(n0,n1)|multiply(n2,const_0_2778)|divide(#0,#1)
physics
an the square?
"percentage error in calculated area = ( 6 + 6 + ( 6 ã — 6 ) / 100 ) % = 12.36 % answer : e"
a ) 14.05 % , b ) 14.02 % , c ) 14 % , d ) 13 % , e ) 12.36 %
e
divide(multiply(subtract(square_area(add(const_100, 6)), square_area(const_100)), const_100), square_area(const_100))
add(n0,const_100)|square_area(const_100)|square_area(#0)|subtract(#2,#1)|multiply(#3,const_100)|divide(#4,#1)|
gain
l way b?
distance is same s 1 t 1 = s 2 t 2 40 t = 50 ( t - 1 ) t = 5 distance = speed * time 40 * 5 = 200 answer : b
a ) 150 , b ) 200 , c ) 450 , d ) 500 , e ) 600
b
multiply(divide(50, subtract(50, 40)), 40)
subtract(n1,n0)|divide(n1,#0)|multiply(n0,#1)
physics
unc ( chocolate?
"first , you must find the total weight of the mixture given that 80 % of it will be dough . 80 % * total = 36 = > ( 8 / 10 ) total = 36 = > total = 360 / 8 = > total = 45 oz , from there , you must find 10 % of the total 40 oz of the mixture . 20 % * total = > ( 2 / 10 ) ( 45 ) = 9 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 10 - 9 = 1 oz chocolate left over . answer : e"
a ) 2 , b ) 4 , c ) 6 , d ) 3 , e ) 1
e
multiply(divide(20, const_100), 20)
divide(n2,const_100)|multiply(n2,#0)|
gain
the a x?
"a / b = 4 / 5 m / x = ( 2 / 5 ) * 5 / ( 7 / 4 ) * 4 = 2 / 7 the answer is e ."
a ) 2 / 5 , b ) 3 / 4 , c ) 4 / 5 , d ) 5 / 4 , e ) 2 / 7
e
multiply(divide(subtract(const_100, 60), add(const_100, 75)), divide(5, 4))
add(n2,const_100)|divide(n1,n0)|subtract(const_100,n3)|divide(#2,#0)|multiply(#3,#1)|
general
in average apartments?
ratio of 2 bedroom apartment : 1 bedroom apartment = 700 : 2100 - - - - - > 1 : 3 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 4 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 4 ) * 100 - - - > 25 % answer : a
a ) 25 % , b ) 15 % , c ) 20 % , d ) 40 % , e ) 45 %
a
divide(multiply(700, const_100), add(add(multiply(const_2, const_1000), const_100), 700))
multiply(n0,const_100)|multiply(const_1000,const_2)|add(#1,const_100)|add(n0,#2)|divide(#0,#3)
general
the gallon possible?
"actual miles / gallon is = 480 / 4 = 12 miles / gallon . current engine miles / gallon is 8 miles / gallon . additional 4 miles / gallon is required to match the actual mileage . answer : b"
a ) 2 , b ) 4 , c ) 12 , d ) 40 , e ) 160
b
subtract(divide(480, 40), 8)
divide(n1,n0)|subtract(#0,n2)|
physics
the age years?
"age of the teacher = ( 23 * 13 - 22 * 12 ) = 35 years . answer : c"
a ) 31 , b ) 36 , c ) 35 , d ) 53 , e ) 57
c
add(22, const_1)
add(n0,const_1)|
general