Problem
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Rationale
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annotated_formula
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approximately how many cubic feet of water are needed to fill a circular swimming pool that is 80 feet across and 10 feet deep ?
"answer should be b . v = \ pir ^ 2 h = \ pi * 40 ^ 2 * 10 = approximately 50000"
a ) 10000 , b ) 50000 , c ) 80000 , d ) 85000 , e ) 90000
b
volume_cylinder(divide(80, const_2), 10)
divide(n0,const_2)|volume_cylinder(#0,n1)|
geometry
if shares of two persons in profits are rs . 300 and rs . 500 then ratio of their capitals is
"total profit = 1000 ratio = 300 / 500 = 3 : 5 answer : b"
a ) 3 : 4 , b ) 3 : 5 , c ) 4 : 3 , d ) 1 : 3 , e ) 1 : 5
b
divide(300, 500)
divide(n0,n1)|
other
there are 2 available positions and 50 candidates , one half of whom are democrats and another half are republicans . if it was decided that the positions would be filled at random , then what is the probability r that the both positions will be taken by members of just one party ?
"r probability of one party having both spots : ( 1 / 2 ) * ( 24 / 49 ) = 12 / 49 ( 1 / 2 ) or ( 25 / 50 ) because it does not matter which party or which person gets the first spot . ( 24 / 49 ) because after one person from a particular party is chosen , there are 24 members of the same party left out of 49 total can...
a ) 1 / 25 , b ) 12 / 49 , c ) 1 / 4 , d ) 24 / 49 , e ) 1 / 2
d
multiply(multiply(divide(subtract(divide(50, 2), const_1), subtract(50, const_1)), divide(divide(50, 2), 50)), 2)
divide(n1,n0)|subtract(n1,const_1)|divide(#0,n1)|subtract(#0,const_1)|divide(#3,#1)|multiply(#4,#2)|multiply(n0,#5)|
other
a train 270 m long , running with a speed of 108 km / hr will pass a tree in
"sol . speed = ( 108 x 5 / 18 ) m / sec . = 30 m / sec . time taken = ( 270 x 1 / 30 ) sec = 9 sec answer b"
a ) 12 sec , b ) 9 sec , c ) 16 sec , d ) 20 sec , e ) none
b
multiply(divide(270, multiply(108, const_1000)), const_3600)
multiply(n1,const_1000)|divide(n0,#0)|multiply(#1,const_3600)|
physics
a container holding 12 ounces of a solution that is 1 part alcohol to 2 parts water is added to a container holding 12 ounces of a solution that is 1 part alcohol to 3 parts water . what is the ratio of alcohol to water in the resulting solution ?
"container 1 has 12 ounces in the ratio 1 : 2 or , x + 2 x = 12 gives x ( alcohol ) = 4 and remaining water = 8 container 2 has 12 ounces in the ratio 1 : 3 or , x + 3 x = 12 gives x ( alcohol ) = 3 and remaining water = 9 mixing both we have alcohol = 4 + 3 and water = 8 + 9 ratio thus alcohol / water = 7 / 17 answer ...
a ) 2 : 5 , b ) 3 : 7 , c ) 3 : 5 , d ) 4 : 7 , e ) 7 : 17
e
divide(add(multiply(12, divide(1, add(1, 2))), multiply(12, divide(1, add(1, 3)))), subtract(add(12, 12), add(multiply(12, divide(1, add(1, 2))), multiply(12, divide(1, add(1, 3))))))
add(n1,n2)|add(n1,n5)|add(n0,n3)|divide(n1,#0)|divide(n1,#1)|multiply(n0,#3)|multiply(n3,#4)|add(#5,#6)|subtract(#2,#7)|divide(#7,#8)|
other
a and b invests rs . 3000 and rs . 4500 respectively in a business . if a doubles his capital after 6 months . in what ratio should a and b divide that year ' s profit ?
"( 3 * 6 + 6 * 6 ) : ( 4.5 * 12 ) 54 : 54 = > 1 : 1 answer : e"
a ) 6 : 8 , b ) 9 : 8 , c ) 7 : 9 , d ) 9 : 5 , e ) 1 : 1
e
divide(add(multiply(3000, 6), multiply(multiply(3000, const_2), 6)), multiply(4500, add(6, 6)))
add(n2,n2)|multiply(n0,n2)|multiply(n0,const_2)|multiply(n2,#2)|multiply(n1,#0)|add(#1,#3)|divide(#5,#4)|
gain
a train of length l is traveling at a constant velocity and passes a pole in t seconds . if the same train travelling at the same velocity passes a platform in 2 t seconds , then what is the length of the platform ?
"the train passes a pole in t seconds , so velocity v = l / t ( l + p ) / v = 2 t ( l + p ) / ( l / t ) = 2 t p = l the answer is b ."
a ) 0.5 l , b ) l , c ) 1.5 l , d ) 2 l , e ) 3
b
subtract(2, const_1)
subtract(n0,const_1)|
physics
on a test average ( arithmetic mean ) test score for 4 students is 85 . what must be 5 th student ' s score that average score for 5 students to be 86 ?
( 4 * 85 + x ) / 5 = 86 x = ( 5 * 86 ) - ( 4 * 85 ) x = 430 - 340 total score required 430 - 340 = 90 correct answer is c
a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
c
subtract(multiply(86, 5), multiply(4, 85))
multiply(n2,n4)|multiply(n0,n1)|subtract(#0,#1)
general
a 200 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds . what is the lenght of other train .
"relative speeds = ( 120 + 80 ) km / hr = 200 km / hr = ( 200 * 5 / 18 ) m / s = ( 500 / 9 ) m / s let length of train be xm x + 200 / 9 = 500 / 9 x = 300 ans is 300 m answer : b"
a ) 210 m , b ) 300 m , c ) 230 m , d ) 240 m , e ) 250 m
b
subtract(multiply(9, multiply(add(120, 80), const_0_2778)), 200)
add(n1,n2)|multiply(#0,const_0_2778)|multiply(n3,#1)|subtract(#2,n0)|
physics
sharmila works 10 hours per day on monday , wednesday and friday , and 8 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 460 per week . how much does she earn in dollars per hour ?
so , she works 30 hours in 3 days so , she works 16 hours in 2 days so in a week she works 46 hours ( 30 + 16 ) and earns $ 460 so , hourly wage is 460 / 46 = > 10 hence answer will be ( d ) 10
a ) 8 , b ) 9 , c ) 9.5 , d ) 10 , e ) 11
d
divide(460, add(multiply(10, const_3), multiply(8, const_2)))
multiply(n0,const_3)|multiply(n1,const_2)|add(#0,#1)|divide(n2,#2)
physics
( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + 0.086 + ( 0.1 ) ( power 2 ) is :
given expression = ( 0.86 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.86 ) ( power 2 ) + ( 0.86 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.86 - 0.1 ) = 0.76 answer is e
a ) 0.86 , b ) 0.68 , c ) 0.96 , d ) 0.69 , e ) 0.76
e
divide(subtract(power(0.86, 3), power(0.1, 3)), add(add(power(0.86, 2), 0.086), power(0.1, 2)))
power(n0,n1)|power(n2,n1)|power(n0,n5)|power(n2,n5)|add(n6,#2)|subtract(#0,#1)|add(#4,#3)|divide(#5,#6)
general
find the ratio in which wheat of inferior quality ( rs . 14 / kg ) be mixed with wheat of superior quality ( rs . 28 / kg ) so that the shopkeeper gains rs . 2 by selling the resulting mixture at rs . 20 / kg .
explanation : let the resulting mixture be 1 kg , and x kg be the amount of wheat of inferior quality . therefore , ( 1 - x ) kg is the amount of wheat of superior quality . as the shopkeeper gains rs . 2 , the cost of the mixture is rs . 18 14 * x + 28 * ( 1 - x ) = 18 14 x - 28 x + 28 = 18 14 x = 10 x = 5 / 7 ( 1 – x...
a ) 5 : 2 , b ) 5 : 9 , c ) 5 : 3 , d ) 5 : 1 , e ) 5 : 8
a
divide(divide(divide(20, 2), const_2), 2)
divide(n3,n2)|divide(#0,const_2)|divide(#1,n2)
general
george baked a total of 75 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
"3 / 5 of the 75 pizzas cooked on saturday = 45 pizzas 3 / 5 of the remaining pizzas on sunday = 18 pizzas we ' re left with ( 75 - 45 - 18 ) = 12 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 5 4 2 1 0 = ...
a ) 5 , b ) 4 , c ) 2 , d ) 6 , e ) 7
c
divide(subtract(subtract(subtract(75, multiply(75, divide(3, 7))), multiply(subtract(75, multiply(75, divide(3, 7))), divide(3, 7))), 3), subtract(subtract(subtract(75, multiply(75, divide(3, 7))), multiply(subtract(75, multiply(75, divide(3, 7))), divide(3, 7))), 3))
divide(n2,n1)|multiply(n0,#0)|subtract(n0,#1)|multiply(#0,#2)|subtract(#2,#3)|subtract(#4,n2)|divide(#5,#5)|
general
- - - - - - - - - - - - - - - - yes - - - - - - - - - no - - - - unsure subject m - - - - 500 - - - - - - - - 200 - - - - - 100 subject r - - - - 400 - - - - - - - - 100 - - - - - 300 a total of 800 students were asked whether they found two subjects , m and r , interesting . each answer was either yes or no or unsure ...
"since 150 students answered yes only for subject m , then the remaining 350 students who answered yes for subject m , also answered yes for subject r . so , 350 students answered yes for both subjects . if 350 students answered yes for both subjects , then 400 - 350 = 50 students answered yes only for subject r . so ,...
a ) 100 , b ) 250 , c ) 300 , d ) 400 , e ) 500
b
subtract(800, add(add(150, subtract(500, 150)), subtract(400, subtract(500, 150))))
subtract(n0,n7)|add(n7,#0)|subtract(n3,#0)|add(#1,#2)|subtract(n6,#3)|
general
a bag contains 6 red , 2 yellow and 4 green balls . 3 balls are drawn randomly . what is the probability that the balls drawn contain balls of different colours ?
"total number of balls = 6 + 2 + 4 = 12 n ( s ) = 12 c 3 = 12 * 11 * 10 / 3 * 2 = 220 n ( e ) = 6 c 1 * 2 c 1 * 4 c 1 = 48 probability = 48 / 220 = 12 / 55 answer is a"
a ) 12 / 55 , b ) 3 / 5 , c ) 3 / 11 , d ) 1 / 4 , e ) 7 / 16
a
divide(multiply(choose(4, const_2), choose(add(6, 2), const_1)), choose(add(add(6, 2), 4), 6))
add(n0,n1)|choose(n2,const_2)|add(n2,#0)|choose(#0,const_1)|choose(#2,n0)|multiply(#1,#3)|divide(#5,#4)|
probability
in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 50 % of all the employees are men . what % of all the employee went to the picnic ?
"total men in company 50 % means total women in company 50 % ( assume total people in company 100 % ) no of men employees attended picnic = 50 x ( 20 / 100 ) = 10 no of women employees attend picnic = 50 x ( 40 / 100 ) = 20 total percentage of employees attend the picnic = 10 + 20 = 30 % answer : a"
a ) 30 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
a
multiply(add(multiply(divide(50, const_100), divide(20, const_100)), multiply(divide(subtract(const_100, 50), const_100), divide(40, const_100))), const_100)
divide(n2,const_100)|divide(n0,const_100)|divide(n1,const_100)|subtract(const_100,n2)|divide(#3,const_100)|multiply(#0,#1)|multiply(#4,#2)|add(#5,#6)|multiply(#7,const_100)|
gain
a trader sells 80 meters of cloth for rs . 10000 at the profit of rs . 7 per metre of cloth . what is the cost price of one metre of cloth ?
"sp of 1 m of cloth = 8925 / 85 = rs . 125 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 125 - rs . 7 = rs . 118 answer : a"
a ) 118 , b ) 88 , c ) 90 , d ) 42 , e ) 22
a
subtract(divide(10000, 80), 7)
divide(n1,n0)|subtract(#0,n2)|
physics
the present ratio of students to teachers at a certain school is 35 to 1 . if the student enrollment were to increase by 50 students and the number of teachers were to increase by 5 , the ratio of students to teachers would then be 25 to 1 . what is the present number of teachers ?
"we are given that the ratio of students to teacher is 35 to 1 . we can rewrite this using variable multipliers . students : teachers = 35 x : x we are next given that student enrollment increases by 50 and the number of teachers increases by 5 . with this change the new ratio becomes 25 to 1 . we can put all this into...
a ) 5 , b ) 8 , c ) 10 , d ) 12 , e ) 15
b
divide(add(35, 25), 25)
add(n0,n4)|divide(#0,n4)|
other
if x and y are the two digits of the number 653 xy . such that this number is divisible by 80 , then x + y is equal to
since 653 xy is divisible by 5 as well as 2 . so y = 0 now 653 x 0 must be divisible by 8 so 3 x 0 must be 8 this happens when x = 2 hence , x + y = 2 + 0 = 2 answer b 2
a ) 3 , b ) 2 , c ) 4 , d ) 1 , e ) 0
b
divide(reminder(multiply(653, const_100), 80), const_10)
multiply(n0,const_100)|reminder(#0,n1)|divide(#1,const_10)
general
22 + 23 + 24 + . . . 61 + 62 + 63 = ?
"sum = 22 + 23 + 24 + . . . 61 + 62 + 63 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 63 positive integers = 63 * 64 / 2 sum of first 21 positive integers = 21 * 22 / 2 sum = 22 + 23 + 24 + . . . 61 + 62 + 63 = 63 * 64 / 2 - 21 * 22 / 2 = 1376 answer : e"
a ) 1361 , b ) 1362 , c ) 1363 , d ) 1364 , e ) 1785
e
divide(multiply(61, add(61, 22)), 23)
add(n0,n3)|multiply(n3,#0)|divide(#1,n1)|
general
matt and peter can do together a piece of work in 24 days . after they have worked together for 12 days matt stops and peter completes the remaining work in 10 days . in how many days peter complete the work separately .
"together they complete the job in 24 days means they complete 12 / 24 of the job after 12 days . peter completes the remaining ( 12 / 24 ) of the job in 10 days which means that the whole job ( 1 ) can be completed in x days . x = 12 / ( 12 / 24 ) = 24 a"
a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 28
a
divide(10, subtract(const_1, multiply(12, divide(const_1, 24))))
divide(const_1,n0)|multiply(n1,#0)|subtract(const_1,#1)|divide(n2,#2)|
physics
a train which has 600 m long , is running 60 kmph . in what time will it cross a person moving at 6 kmph in same direction ?
"time taken to cross a moving person = length of train / relative speed time taken = 600 / ( ( 60 - 6 ) ( 5 / 18 ) = 600 / 54 * ( 5 / 18 ) = 600 / 15 = 40 sec answer : d"
a ) 42 sec , b ) 44 sec , c ) 46 sec , d ) 40 sec , e ) 50 sec
d
divide(600, subtract(divide(60, const_3_6), divide(divide(6, const_2), const_3_6)))
divide(n1,const_3_6)|divide(n2,const_2)|divide(#1,const_3_6)|subtract(#0,#2)|divide(n0,#3)|
physics
when tossed , a certain coin has equal probability of landing on either side . if the coin is tossed 3 times , what is the probability that it will land on the same side each time ?
"winning scenario is if we ' ll have either three tails ( ttt ) or three heads ( hhh ) : 1 / 2 * 1 / 2 * 1 / 2 + 1 / 2 * 1 / 2 * 1 / 2 = 1 / 4 . answer : b ."
a ) 1 / 8 , b ) 1 / 4 , c ) 1 / 3 , d ) 3 / 8 , e ) 1 / 2
b
divide(const_1, power(const_2, 3))
power(const_2,n0)|divide(const_1,#0)|
probability
machine p can print one lakh books in 8 hours . machine q can print the same number of books in 10 hours while machine r can print the same in 12 hours . all the machines started printing at 9 a . m . machine p is stopped at 11 a . m . and the remaining two machines complete work . approximately at what time will the p...
explanation : work done by p in 1 hour = 1 / 8 work done by q in 1 hour = 1 / 10 work done by r in 1 hour = 1 / 12 work done by p , q and r in 1 hour = 1 / 8 + 1 / 10 + 1 / 12 = 37 / 120 work done by q and r in 1 hour = 1 / 10 + 1 / 12 = 22 / 120 = 11 / 60 from 9 am to 11 am , all the machines were operating . ie , the...
a ) 3 pm , b ) 2 pm , c ) 1 : 00 pm , d ) 11 am , e ) 12 am
c
floor(add(11, divide(subtract(const_1, multiply(subtract(11, 9), add(divide(const_1, 12), add(divide(const_1, 8), divide(const_1, 10))))), add(divide(const_1, 10), divide(const_1, 12)))))
divide(const_1,n0)|divide(const_1,n1)|divide(const_1,n2)|subtract(n4,n3)|add(#0,#1)|add(#1,#2)|add(#4,#2)|multiply(#6,#3)|subtract(const_1,#7)|divide(#8,#5)|add(n4,#9)|floor(#10)
physics
three numbers are in the ratio 4 : 5 : 6 and their average is 30 . the largest number is :
"explanation : let the numbers be 4 x , 5 x and 6 x . therefore , ( 4 x + 5 x + 6 x ) / 3 = 30 15 x = 90 x = 6 largest number = 6 x = 36 . answer : c"
a ) 33 , b ) 77 , c ) 36 , d ) 18 , e ) 16
c
add(multiply(multiply(4, 6), const_100), multiply(5, 6))
multiply(n0,n2)|multiply(n1,n2)|multiply(#0,const_100)|add(#2,#1)|
general
by selling a book for 270 , 20 % profit was earned . what is the cost price of the book ?
"sp = 120 % of cp ; : . cp = 270 Γ— 100 / 120 = 225 option ' b '"
a ) 215 , b ) 225 , c ) 230 , d ) 235 , e ) 240
b
original_price_before_gain(20, 270)
original_price_before_gain(n1,n0)|
gain
the scoring system in a certain football competition goes as follows : 3 points for victory , 1 point for a draw , and 0 points for defeat . each team plays 20 matches . if a team scored 10 points after 5 games , what is the least number of the remaining matches it has to win to reach the 45 - point mark by the end of ...
"to get 45 points as end of season we need another 35 points or more from remaining 15 matches : option a = 6 * 3 + 9 * 1 = 27 option b = 7 * 3 + 8 * 1 = 29 option c = 8 * 3 + 7 * 1 = 31 option d = 9 * 3 + 6 * 1 = 33 option e = 10 * 3 + 5 * 1 = 35 hence option e - 10"
a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
e
add(floor(divide(subtract(subtract(45, 10), subtract(20, 5)), const_2)), 1)
subtract(n6,n4)|subtract(n3,n5)|subtract(#0,#1)|divide(#2,const_2)|floor(#3)|add(#4,n1)|
general
the price of lunch for 15 people was $ 208.00 , including a 15 percent gratuity for service . what was the average price per person , excluding the gratuity ?
"take the initial price before the gratuity is 100 the gratuity is calculated on the final price , so as we assumed the final bill before adding gratuity is 100 so gratuity is 15 % of 100 is 15 so the total price of meals is 115 so the given amount i . e 208 is for 115 then we have to calculate for 100 for 115 208 for ...
a ) $ 11.73 , b ) $ 12.60 , c ) $ 13.80 , d ) $ 14.00 , e ) $ 15.87
b
multiply(multiply(divide(208.00, add(const_100, 15)), const_100), divide(const_1, 15))
add(n0,const_100)|divide(const_1,n0)|divide(n1,#0)|multiply(#2,const_100)|multiply(#1,#3)|
general
if the area of a circle decreases by 36 % , then the radius of a circle decreases by
"if area of a circle decreased by x % then the radius of a circle decreases by ( 100 βˆ’ 10 √ 100 βˆ’ x ) % = ( 100 βˆ’ 10 √ 100 βˆ’ 36 ) % = ( 100 βˆ’ 10 √ 64 ) % = 100 - 80 = 20 % answer a"
a ) 20 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
a
multiply(subtract(const_1, sqrt(divide(subtract(const_100, 36), const_100))), const_100)
subtract(const_100,n0)|divide(#0,const_100)|sqrt(#1)|subtract(const_1,#2)|multiply(#3,const_100)|
geometry
if n is a positive integer and n ^ 2 is divisible by 450 , then what is the largest positive integer that must divide n ?
"450 = 2 * 3 ^ 2 * 5 ^ 2 if 450 divides n ^ 2 , then n must be divisible by 2 * 3 * 5 = 30 the answer is c ."
a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
c
multiply(sqrt(divide(450, 2)), 2)
divide(n1,n0)|sqrt(#0)|multiply(n0,#1)|
general
if the given two numbers are respectively 7 % and 14 % of a third number , then what percentage is the first of the second ?
"here , l = 7 and m = 14 therefore , first number = l / m x 100 % of second number = 7 / 14 x 100 % of second number = 50 % of second number answer : d"
a ) 20 % , b ) 25 % , c ) 18 % , d ) 50 % , e ) none of these
d
multiply(divide(divide(7, const_100), divide(14, const_100)), const_100)
divide(n0,const_100)|divide(n1,const_100)|divide(#0,#1)|multiply(#2,const_100)|
gain
the average of first 9 prime numbers is ?
"sum of 10 prime no . = 100 average = 100 / 9 = 11.11 answer : b"
a ) 10.11 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11
b
add(9, const_1)
add(n0,const_1)|
general
a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 120 kg . what is the maximum weight of the crates on a single trip ?
"max no . of crates = 6 . max weight = 120 kg max . weight carried = 6 * 120 = 720 kg = e"
a ) 1250 , b ) 625 , c ) 600 , d ) 7500 , e ) 720
e
multiply(6, 120)
multiply(n2,n3)|
general
the ratio of the ages of mini and minakshi is 4 : 3 . the sum of their ages is 21 years . the ratio of their ages after 8 years will be
"let mini ’ s age = 4 x and minakshi ’ s age = 3 x then 4 x + 3 x = 21 x = 3 mini ’ s age = 12 years and minakshi ’ s age = 9 years ratio of their ages after 8 years = ( 12 + 8 ) : ( 9 + 8 ) = 20 : 17 answer : b"
a ) 2 : 3 , b ) 20 : 17 , c ) 5 : 4 , d ) 3 : 5 , e ) 6 : 11
b
divide(add(multiply(4, divide(21, add(4, 3))), 8), add(multiply(3, divide(21, add(4, 3))), 8))
add(n0,n1)|divide(n2,#0)|multiply(n0,#1)|multiply(n1,#1)|add(n3,#2)|add(n3,#3)|divide(#4,#5)|
general
a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 1.7 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
"72 km / hr = 1.2 km / min the total distance is 1.8 km . 1.8 / 1.2 = 1.5 minutes the answer is c ."
a ) 0.9 , b ) 1.2 , c ) 1.5 , d ) 1.8 , e ) 2.1
c
multiply(divide(add(1.7, divide(100, const_1000)), 72), const_60)
divide(n0,const_1000)|add(n2,#0)|divide(#1,n1)|multiply(#2,const_60)|
physics
the difference between a number and its two - fifth is 510 . what is 5 % of that number ?
"let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 5 % of 850 = 425 . answer : a"
a ) 425 , b ) 300 , c ) 255 , d ) 300 , e ) 400
a
divide(multiply(510, add(const_4, const_1)), add(const_1, const_2))
add(const_1,const_4)|add(const_1,const_2)|multiply(n0,#0)|divide(#2,#1)|
general
the contents of two vessels containing copper and tin in the ratio 1 : 2 and 2 : 5 are mixed in the ratio 1 : 4 . the resulting mixture will have copper and tin in the ratio ?
"the ratio of copper and tin the new vessel = ( 1 / 3 * 1 / 5 + 2 / 7 * 4 / 5 ) : ( 2 / 3 * 1 / 5 + 5 / 7 * 4 / 5 ) = 31 / 105 : 74 / 105 = 31 : 74 answer is c"
a ) 15 : 32 , b ) 21 : 28 , c ) 31 : 74 , d ) 33 : 37 , e ) 41 : 92
c
divide(add(multiply(1, 2), multiply(2, 2)), add(multiply(2, 2), multiply(5, 2)))
multiply(n0,n1)|multiply(n2,n2)|multiply(n1,n1)|multiply(n2,n3)|add(#0,#1)|add(#2,#3)|divide(#4,#5)|
other
a can do a piece of work in 4 days . b can do it in 8 days . with the assistance of c they completed the work in 2 days . find in how many days can c alone do it ?
"c = 1 / 2 - 1 / 4 - 1 / 8 = 1 / 8 = > 8 days answer : b"
a ) 22 days , b ) 8 days , c ) 67 days , d ) 1 days , e ) 18 days
b
divide(multiply(4, 8), divide(subtract(multiply(4, 8), multiply(add(divide(multiply(4, 8), 4), divide(multiply(4, 8), 8)), 2)), 2))
multiply(n0,n1)|divide(#0,n0)|divide(#0,n1)|add(#1,#2)|multiply(n2,#3)|subtract(#0,#4)|divide(#5,n2)|divide(#0,#6)|
physics
a cargo ships engines failed 100 miles away from the port . due to the changing wind direction , it is moving 12 miles towards the port and 6 miles away from the port . if the wind pattern remains same , how many miles it will travel before reaching the port ?
ships overall distance covered per cycle is + 6 miles take 100 - 6 take 94 / 6 to lowest divisible number - 90 / 6 this means that it will take 15 ` ` overall ' ' actions to reach the 90 th mile . - 15 * 18 miles added later set cycle start at 90 . travel 10 miles and reach the anchor point - add 10 to total 15 * 18 + ...
a ) a - 179 , b ) b - 240 , c ) c - 280 , d ) d - 100 , e ) e - 155
c
subtract(add(100, 12), 6)
add(n0,n1)|subtract(#0,n2)
physics
if x and y are sets of integers , x # y denotes the set of integers that belong to set x or set y , but not both . if x consists of 8 integers , y consists of 18 integers , and 6 of the integers are in both x and y , then x # y consists of how many integers ?
"the number of integers that belong to set x only is 8 - 6 = 2 ; the number of integers that belong to set y only is 18 - 6 = 12 ; the number of integers that belong to set x or set y , but not both is 2 + 12 = 14 . answer : b ."
a ) 6 , b ) 14 , c ) 22 , d ) 30 , e ) 174
b
add(subtract(18, 6), subtract(8, 6))
subtract(n1,n2)|subtract(n0,n2)|add(#0,#1)|
other
a circular logo is enlarged to fit the lid of a jar . the new diameter is 50 per cent larger than the original . by what percentage has the area of the logo increased ?
"let old diameter be 4 , so radius is 2 old area = 4 Ο€ new diameter is 6 , so radius is 3 new area = 9 Ο€ increase in area is 5 Ο€ % increase in area = 5 / 4 * 100 so , % increase is 125 % answer will be ( d )"
a ) 50 , b ) 80 , c ) 100 , d ) 125 , e ) 250
d
multiply(divide(subtract(power(add(divide(multiply(50, const_2), const_1000), const_3), const_2), const_4), const_4), const_100)
multiply(n0,const_2)|divide(#0,const_1000)|add(#1,const_3)|power(#2,const_2)|subtract(#3,const_4)|divide(#4,const_4)|multiply(#5,const_100)|
geometry
a train with a length of 100 meters , is traveling at a speed of 72 km / hr . the train enters a tunnel 3.5 km long . how many minutes does it take the train to pass through the tunnel from the moment the front enters to the moment the rear emerges ?
"72 km / hr = 1.2 km / min the total distance is 3.6 km . 3.6 / 1.2 = 3 minutes the answer is a ."
a ) 3 , b ) 4.2 , c ) 3.4 , d ) 5.5 , e ) 5.7
a
multiply(divide(add(3.5, divide(100, const_1000)), 72), const_60)
divide(n0,const_1000)|add(n2,#0)|divide(#1,n1)|multiply(#2,const_60)|
physics
if 0.5 % of a = 80 paise , then the value of a is ?
"answer ∡ 0.5 / 100 of a = 80 / 100 ∴ a = rs . ( 80 / 0.5 ) = rs . 160 correct option : b"
a ) rs . 170 , b ) rs . 160 , c ) rs . 1.70 , d ) rs . 4.25 , e ) none
b
divide(80, 0.5)
divide(n1,n0)|
gain
it takes 2 team of farm workers 12 days to completely prepare a piece of land for planting . if both team of workers were to work separately , one of them can complete the work 10 days earlier than the other , how many days will it take each of them to separately complete the work ?
work = ( a ) ( b ) / ( a + b ) where a and b are the individual times of each entity . here , we ' re told that ( working together ) the two team of workers would complete a job in 12 days . this means that ( individually ) each of team would take more than 12 days to do the job . answers d , a and b are illogical , si...
a ) 12 and 22 , b ) 11 and 21 , c ) 15 and 25 , d ) 9 and 19 , e ) 20 and 30
e
add(subtract(subtract(add(multiply(add(multiply(10, 12), multiply(10, 2)), 10), multiply(multiply(10, 12), 10)), add(multiply(add(const_3, const_4), const_10), const_100)), multiply(add(multiply(10, 12), multiply(10, 2)), 10)), multiply(10, const_100))
add(const_3,const_4)|multiply(n2,const_100)|multiply(n1,n2)|multiply(n0,n2)|add(#2,#3)|multiply(n2,#2)|multiply(#0,const_10)|add(#6,const_100)|multiply(n2,#4)|add(#8,#5)|subtract(#9,#7)|subtract(#10,#8)|add(#1,#11)
physics
find compound interest on $ 8000 at 15 % per annum for 2 years 4 months , compounded annually .
time = 2 years 4 months = 2 ( 4 / 12 ) years = 2 ( 1 / 3 ) years . amount = $ [ 8000 x ( 1 + Β­ ( 15 / 100 ) ) 2 x ( 1 + ( ( 1 / 3 ) * 15 ) / 100 ) ] = $ [ 8000 * ( 23 / 20 ) * ( 23 / 20 ) * ( 21 / 20 ) ] = $ 11109 . . : . c . i . = rs . ( 11109 - 8000 ) = $ 3109 . answer a .
a ) 3109 , b ) 3209 , c ) 3108 , d ) 3107 , e ) 3100
a
add(add(multiply(8000, divide(15, const_100)), multiply(add(8000, multiply(8000, divide(15, const_100))), divide(15, const_100))), multiply(add(add(8000, multiply(8000, divide(15, const_100))), multiply(add(8000, multiply(8000, divide(15, const_100))), divide(15, const_100))), divide(divide(15, const_100), const_3)))
divide(n1,const_100)|divide(#0,const_3)|multiply(n0,#0)|add(n0,#2)|multiply(#3,#0)|add(#2,#4)|add(#3,#4)|multiply(#6,#1)|add(#5,#7)
gain
the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what is the weight of the new person ?
"explanation : total increase in weight = 8 Γ£ β€” 2.5 = 20 if x is the weight of the new person , total increase in weight = x Γ’ Λ† ’ 45 = > 20 = x - 45 = > x = 20 + 45 = 65 answer : option b"
a ) 75 kg , b ) 65 kg , c ) 85 kg , d ) 80 kg , e ) 60 kg
b
add(multiply(8, 2.5), 45)
multiply(n0,n1)|add(n2,#0)|
general
in what time will a train 100 m long cross an electric pole , it its speed be 54 km / hr ?
"speed = 54 * 5 / 18 = 15 m / sec time taken = 100 / 15 = 6.67 sec . answer : c"
a ) 2.5 , b ) 2.9 , c ) 6.67 , d ) 2.8 , e ) 2.1
c
divide(100, multiply(54, const_0_2778))
multiply(n1,const_0_2778)|divide(n0,#0)|
physics
find the area of a triangle whose sides are 41 cm , 28 cm , 15 cm . also , find the length of the altitude corresponding to the largest side of the triangle .
semi - perimeter of the triangle = ( a + b + c ) / 2 = ( 41 + 28 + 15 ) / 2 = 84 / 2 = 42 cm therefore , area of the triangle = √ ( s ( s - a ) ( s - b ) ( s - c ) ) = √ ( 42 ( 42 - 41 ) ( 42 - 28 ) ( 42 - 15 ) ) cm Β² = √ ( 42 Γ— 1 Γ— 27 Γ— 14 ) cm Β² = √ ( 3 Γ— 3 Γ— 3 Γ— 3 Γ— 2 Γ— 2 Γ— 7 Γ— 7 ) cm Β² = 3 Γ— 3 Γ— 2 Γ— 7 cm Β² = 126 cm...
['a ) 4.1 cm', 'b ) 5.1 cm', 'c ) 6.1 cm', 'd ) 7.1 cm', 'e ) 8.1 cm']
c
divide(multiply(triangle_area_three_edges(41, 28, 15), const_2), 41)
triangle_area_three_edges(n0,n1,n2)|multiply(#0,const_2)|divide(#1,n0)
geometry
alex takes a loan of $ 8,000 to buy a used truck at the rate of 6 % simple interest . calculate the annual interest to be paid for the loan amount .
"from the details given in the problem principle = p = $ 8,000 and r = 6 % or 0.06 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 8,000 x 1 x 0.06 = 480.00 annual interest to be paid = $ 480 answer : a"
a ) 480 , b ) 520 , c ) 460 , d ) 400 , e ) 520
a
divide(multiply(multiply(multiply(6, const_100), sqrt(const_100)), 6), const_100)
multiply(n1,const_100)|sqrt(const_100)|multiply(#0,#1)|multiply(n1,#2)|divide(#3,const_100)|
gain
if john covers a certain distance in 1 hr . 24 min . by covering two third of the distance at 4 kmph and the rest at 5 kmph , then find the total distance
explanation : let the total distance be y km . then , ( 2 / 3 ) y / 4 + ( 1 / 3 ) y / 5 = 7 / 5 y / 6 + y / 15 = 7 / 5 7 y = 42 y = 6 km answer b
a ) 4 km , b ) 6 km , c ) 6.8 km , d ) 7.2 km , e ) none of these
b
add(multiply(4, multiply(divide(const_2, const_3), add(1, divide(24, const_60)))), multiply(multiply(subtract(const_1, divide(const_2, const_3)), add(1, divide(24, const_60))), 5))
divide(n1,const_60)|divide(const_2,const_3)|add(n0,#0)|subtract(const_1,#1)|multiply(#2,#1)|multiply(#2,#3)|multiply(n2,#4)|multiply(n3,#5)|add(#6,#7)
physics
in how many ways 4 boys and 3 girls can be seated in a row so that they are alternative ?
"4 boys can be seated in 4 ! three girls can be seated in 3 ! required number = 4 ! 3 ! = 144 answer is b"
a ) 120 , b ) 144 , c ) 160 , d ) 210 , e ) 180
b
multiply(factorial(4), factorial(3))
factorial(n0)|factorial(n1)|multiply(#0,#1)|
probability
if ( 10 ^ 4 * 3.456789 ) ^ 10 is written as a single term , how many digits would be to the right of the decimal place ?
"3.456789 ^ 10 has 6 * 10 = 60 decimal places . 10 ^ 40 moves the decimal place to the right 40 places . ( 10 ^ 4 * 3.456789 ) ^ 10 has 60 - 40 = 20 digits after the decimal point . the answer is c ."
a ) 12 , b ) 16 , c ) 20 , d ) 32 , e ) 48
c
multiply(10, const_2)
multiply(n3,const_2)|
general
if each edge of cube increased by 30 % , the percentage increase in
"100 Γ— ( 130 ) / 100 Γ— ( 130 ) / 100 = 169 = > 69 % answer is a ."
a ) 69 , b ) 72 , c ) 64 , d ) 61 , e ) 75
a
multiply(const_100, divide(subtract(power(add(const_100, 30), const_3), power(const_100, const_3)), power(const_100, const_3)))
add(n0,const_100)|power(const_100,const_3)|power(#0,const_3)|subtract(#2,#1)|divide(#3,#1)|multiply(#4,const_100)|
gain
a certain drink of type a is prepared by mixing 4 parts milk with 3 parts fruit juice . another drink of type b is prepared by mixing 4 parts of fruit juice and 3 parts of milk . how many liters of fruit juice must be added to 63 liters of drink a to convert it to drink b ?
"in 63 liters of drink a , there are 36 liters of milk and 27 liters of juice . with 36 liters of milk , we need a total of 48 liters of juice to make drink b . we need to add 21 liters of juice . the answer is c ."
a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
c
subtract(divide(multiply(multiply(divide(4, add(4, 3)), 63), 4), 3), multiply(divide(3, add(4, 3)), 63))
add(n0,n1)|divide(n0,#0)|divide(n1,#0)|multiply(n4,#1)|multiply(n4,#2)|multiply(n0,#3)|divide(#5,n1)|subtract(#6,#4)|
general
what is the remainder when 15487 ^ ( 62177037 ) is divided by 5 ?
"we need to find the units digit of the number . the units digit of powers of seven repeats 7 , 9 , 3 , and 1 cyclically . since 62177037 has the form 4 a + 1 , the units digit is 7 . then the remainder when dividing by 5 is 2 . the answer is c ."
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
c
reminder(multiply(62177037, 15487), 5)
multiply(n0,n1)|reminder(#0,n2)|
general
james went on a diet 12 months ago when he weighed 222 pounds . if he now weighs 198 pounds and continues to lose at the same average monthly rate , in approximately how many months will he weigh 190 pounds ?
222 - 198 = 24 pounds lost in 12 months 24 / 12 = 2 , so joe is losing weight at a rate of 2 pounds per month . . . . in approximately how many months will he weigh 190 pounds ? a simple approach is to just list the weights . now : 198 lbs in 1 month : 196 lbs in 2 months : 194 lbs in 3 months : 192 lbs in 4 months : 1...
a ) 3 , b ) 3.5 , c ) 4 , d ) 4.5 , e ) 5
c
divide(12, divide(subtract(222, 198), subtract(198, 190)))
subtract(n1,n2)|subtract(n2,n3)|divide(#0,#1)|divide(n0,#2)
general
the dimensions of a rectangular solid are 4 inches , 5 inches , and 9 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is n...
answer : b .
a ) 2 : 5 , b ) 5 : 9 , c ) 5 : 16 , d ) 25 : 7 , e ) 32 : 25
b
divide(const_10, add(add(multiply(9, const_2), const_2), const_1))
multiply(n2,const_2)|add(#0,const_2)|add(#1,const_1)|divide(const_10,#2)|
geometry
there are cats got together and decided to kill the mice of 999951 . each cat kills equal number of mice and each cat kills more number of mice than cats there were . then what are the number of cats ?
"999951 can be written as 1000000 Γ’ € β€œ 49 = 10002 Γ’ € β€œ 72 ie of the form a 2 - b 2 = ( a + b ) ( a - b ) = ( 1000 + 7 ) * ( 1000 - 7 ) = ( 1007 ) * ( 993 ) given that number of cats is less than number if mice . so number of cats is 993 and number of mice were 1007 answer b"
a ) 941,1009 , b ) 993,1007 , c ) 991,1009 , d ) 791,1009 , e ) 931,1009
b
divide(999951, add(multiply(const_100, const_10), add(const_3, const_2)))
add(const_2,const_3)|multiply(const_10,const_100)|add(#0,#1)|divide(n0,#2)|
general
a taxi company costs $ 2.75 for the first quarter - mile and 12.5 cents for each additional quarter mile . what is the maximum distance you can travel with $ 6.50 ?
use reverse calculation - total cost = fixed cost ( for 1 / 4 miles ) + variable cost ( distance travelled ) or , 6.50 = 2.75 + 0.125 * d or , 3.75 = d / 8 or , d = 30 quarter miles so , total distance = ( 30 + 1 ) quarter miles so , distance = 31 / 4 = > 73 / 4 miles hence answer will be ( d )
a ) 4 miles , b ) 5 3 / 4 miles , c ) 6 1 / 2 miles , d ) 7 3 / 4 miles , e ) 8 1 / 4 miles
d
add(multiply(divide(multiply(subtract(6.5, 2.75), const_100), 12.5), const_0_25), const_0_25)
subtract(n2,n0)|multiply(#0,const_100)|divide(#1,n1)|multiply(#2,const_0_25)|add(#3,const_0_25)
general
claire has a total of 96 pets consisting of gerbils and hamsters only . one - quarter of the gerbils are male , and one - third of the hamsters are male . if there are 25 males altogether , how many gerbils does claire have ?
"g + h = 96 . . . 1 ; g / 4 + h / 3 = 25 . . . . 2 or 3 g + 4 h = 25 * 12 = 300 g = 96 - h or 3 ( 96 - h ) + 4 h = 300 h = 300 - 288 = 12 then g = 96 - 12 = 84 a"
a ) 84 , b ) 50 , c ) 54 , d ) 57 , e ) 60
a
add(subtract(96, 25), const_1)
subtract(n0,n1)|add(#0,const_1)|
general
find 94 Γ— Γ— 97
"here both numbers are less than 100 . so they are deficient of - 6 and - 3 compared with 100 . so answer : c"
a ) 93 / 198 , b ) 93 / 12 , c ) 93 / 18 , d ) 93 / 10 , e ) 93 / 11
c
divide(94, 97)
divide(n0,n1)|
general
a 1200 m long train crosses a tree in 120 sec , how much time will i take to pass a platform 800 m long ?
"l = s * t s = 1200 / 120 s = 10 m / sec . total length ( d ) = 2000 m t = d / s t = 2000 / 10 t = 200 sec answer : b"
a ) 266 sec , b ) 200 sec , c ) 776 sec , d ) 166 sec , e ) 997 sec
b
divide(add(1200, 800), divide(1200, 120))
add(n0,n2)|divide(n0,n1)|divide(#0,#1)|
physics
at what rate percent of simple interest will a sum of money double itself in 11 years ?
"let sum = x . then , s . i . = x . rate = ( 100 * s . i . ) / ( p * t ) = ( 100 * x ) / ( x * 11 ) = 100 / 11 = 9.09 % answer : a"
a ) 9.09 % , b ) 4.54 % , c ) 8 . 2 % , d ) 4.94 % , e ) 5.54 %
a
divide(const_100, 11)
divide(const_100,n0)|
gain
if m and n are positive integers and m ^ 2 + n ^ 2 = 137 , what is the value of m ^ 3 + n ^ 3 ?
you need to integers which squared are equal 40 . which could it be ? let ' s start with the first integer : 1 ^ 2 = 1 2 ^ 2 = 4 3 ^ 2 = 9 4 ^ 2 = 16 5 ^ 2 = 25 6 ^ 2 = 36 7 ^ 2 = 49 8 ^ 2 = 64 9 ^ 2 = 81 10 ^ 2 = 100 11 ^ 2 = 121 stop . the integers ca n ' t be greater than 6 or we will score above 137 . the second in...
a ) 72 , b ) 224 , c ) 320 , d ) 512 , e ) 1,395
e
gcd(137, const_4)
gcd(n2,const_4)
general
if the product of the integers from 1 to n is divisible by 630 , what is the least possible value of n ?
"630 = 2 x 3 x 3 x 5 x 7 n must include at least up to the number 7 . the answer is a ."
a ) 7 , b ) 14 , c ) 21 , d ) 28 , e ) 35
a
multiply(divide(divide(divide(630, const_3), add(const_3, const_4)), add(const_3, const_4)), const_3)
add(const_3,const_4)|divide(n1,const_3)|divide(#1,#0)|divide(#2,#0)|multiply(#3,const_3)|
general
a monkey start climbing up a tree 22 ft tall . each hour it hops 3 ft and slips back 2 ft . how much time would it take the monkey to reach the top .
"if monkey hops 3 ft and slips back 2 ft in a hour , it means the monkey hops ( 3 ft - 2 ft ) = 1 ft / hr . similarly in 19 hrs it wil be 19 ft . bt since the height of the tree is 22 ft , so if the monkey hops up the tree in the next hr i . e 20 th hr then it reaches at the top of the tree . hence it takes 20 hrs for ...
a ) 15 hrs , b ) 18 hrs , c ) 20 hrs , d ) 17 hrs , e ) 16 hrs
c
subtract(divide(22, subtract(3, 2)), 2)
subtract(n1,n2)|divide(n0,#0)|subtract(#1,n2)|
physics
the first doughnut is priced at $ 1 and then if you purchase additional doughnuts as dozens then the price is $ 6 / dozen . what is the total number of doughnuts purchased if you paid $ 26 ?
"$ 26 = 4 * $ 6 + $ 2 the number of doughnuts is 4 * 12 + 2 = 50 the answer is a ."
a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58
a
multiply(divide(26, 6), const_12)
divide(n2,n1)|multiply(#0,const_12)|
general
when you draw 2 dices together , find the probability of getting a total of 6 ?
s = { ( 1,1 ) , ( 1,2 ) , ( 1,3 ) , ( 1,4 ) , ( 1,5 ) , ( 1,6 ) , ( 4,1 ) , ( 4,2 ) , ( 4,3 ) , ( 4,4 ) , ( 4,5 ) , ( 4,6 ) , ( 2,1 ) , ( 2,2 ) , ( 2,3 ) , ( 2,4 ) , ( 2,5 ) , ( 2,6 ) , ( 5,1 ) , ( 5,2 ) , ( 5,3 ) , ( 5,4 ) , ( 5,5 ) , ( 5,6 ) , ( 3,1 ) , ( 3,2 ) , ( 3,3 ) , ( 3,4 ) , ( 3,5 ) , ( 3,6 ) , ( 6,1 ) , ( 6,...
a ) 3 / 13 , b ) 2 / 31 , c ) 5 / 36 , d ) 7 / 41 , e ) 7 / 43
c
add(divide(2, power(6, 2)), divide(const_3, power(6, 2)))
power(n1,n0)|divide(n0,#0)|divide(const_3,#0)|add(#1,#2)
probability
elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 50 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twic...
"bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 50 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 50 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) ...
a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 24 , e ) $ 28
d
subtract(multiply(50, const_2), 76)
multiply(n0,const_2)|subtract(#0,n1)|
general
a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
[ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
c
divide(600, divide(5, const_100))
divide(n0,const_100)|divide(n4,#0)
general
a man took a loan at rate of 12 % per annum simple interest . after 3 years he had to pay 9000 interest . the principal amount borrowed by him was .
explanation : s . i . = p Γ’ Λ† β€” r Γ’ Λ† β€” t / 100 = > p = s . i . Γ’ Λ† β€” 100 / r Γ’ Λ† β€” t = > p = 9000 Γ’ Λ† β€” 100 / 12 Γ’ Λ† β€” 3 = rs 25000 option b
a ) rs 14000 , b ) rs 25000 , c ) rs 16000 , d ) rs 17000 , e ) none of these
b
divide(multiply(9000, const_100), multiply(12, 3))
multiply(n2,const_100)|multiply(n0,n1)|divide(#0,#1)
gain
tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 9 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
"( 1 mph + 9 mph ) / 2 = 5 mph correct option is : d"
a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 5 mph , e ) 0.5 mph
d
divide(add(1, 9), const_2)
add(n0,n1)|divide(#0,const_2)|
physics
suppose you want to buy 3 loaves of bread that cost $ 2.25 each and a jar of peanut butter that costs $ 2 . a jar of jelly is $ 2.75 , but you don Γ’ € β„’ t need any jelly . you have $ 14 . how much money will you have left over ?
the jelly is extra information . 14.00 Γ’ € β€œ 3 x 2.25 Γ’ € β€œ 2.00 = 14.00 Γ’ € β€œ 6.75 Γ’ € β€œ 2.00 = 5.25 . you have $ 5.25 left . correct answer c
a ) $ 1.50 , b ) $ 2.50 , c ) $ 5.25 , d ) $ 4.50 , e ) $ 5.50
c
subtract(subtract(14, multiply(3, 2.25)), 2)
multiply(n0,n1)|subtract(n4,#0)|subtract(#1,n2)
general
a batsman scored 110 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
"number of runs made by running = 110 - ( 3 x 4 + 8 x 6 ) = 110 - ( 60 ) = 50 now , we need to calculate 50 is what percent of 110 . = > 50 / 110 x 100 = 45.45 % answer : e"
a ) 50 % , b ) 40 % , c ) 60 % , d ) 70 % , e ) 45.45 %
e
multiply(divide(subtract(110, add(multiply(3, 8), multiply(8, 3))), 110), const_100)
multiply(n1,n2)|multiply(n1,n2)|add(#0,#1)|subtract(n0,#2)|divide(#3,n0)|multiply(#4,const_100)|
general
a man can row 3.6 km / hr in still water . it takes him twice as long to row upstream as to row downstream . what is the rate of the current ?
"speed of boat in still water ( b ) = 3.6 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 . β‡’ downstream speed is twice to that of upstream . so b + u = 2 ( b – u ) β‡’ u = b / 3 = 1.2 km / hr ...
a ) 1.9 , b ) 1.7 , c ) 1.2 , d ) 1.5 , e ) 1.1
c
divide(subtract(multiply(3.6, const_2), 3.6), const_3)
multiply(n0,const_2)|subtract(#0,n0)|divide(#1,const_3)|
general
two cars are traveling in the same direction along the same route . the red car travels at a constant speed of 30 miles per hour , and the black car is traveling at a constant speed of 50 miles per hour . if the red car is 20 miles ahead of the black car , how many hours will it take the black car to overtake the red c...
"option c 20 + 30 t = 50 t t = 1"
a ) 0.1 , b ) 0.6 , c ) 1 , d ) 1.2 , e ) 2
c
divide(20, subtract(50, 30))
subtract(n1,n0)|divide(n2,#0)|
physics
the population of locusts in a certain swarm doubles every two hours . if 4 hours ago there were 1,000 locusts in the swarm , in approximately how many hours will the swarm population exceed 32,000 locusts ?
"- 4 hours : 1,000 - 2 hours : 2,000 now : 4,000 + 2 hours : 8,000 + 4 hours : 16,000 + 6 hours : 32,000 answer : c"
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 9
c
subtract(multiply(log(divide(power(4, 4), const_2)), const_2), 4)
power(n0,n0)|divide(#0,const_2)|log(#1)|multiply(#2,const_2)|subtract(#3,n0)|
general
find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg
"by the rule of alligation : cost of 1 kg rice of 1 st kind cost of 1 kg rice of 2 nd kind required ratio = 60 : 80 = 3 : 4 answer : b"
a ) 2 : 0 , b ) 3 : 4 , c ) 2 : 1 , d ) 2 : 2 , e ) 2 : 8
b
divide(subtract(6.30, 5.70), subtract(7.10, 6.30))
subtract(n2,n1)|subtract(n0,n2)|divide(#0,#1)|
other
in an election , candidate a got 75 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favour of candidate .
"total number of invalid votes = 15 % of 560000 = 15 / 100 Γ— 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 75 % therefore , the number of valid votes polled in favour of candidate a = 75 % of 476000 = 75 / 100 Γ— 476000 = 35700000...
a ) 357000 , b ) 357003 , c ) 277677 , d ) 699377 , e ) 267877
a
multiply(multiply(560000, subtract(const_1, divide(15, const_100))), divide(75, const_100))
divide(n0,const_100)|divide(n1,const_100)|subtract(const_1,#1)|multiply(n2,#2)|multiply(#0,#3)|
gain
there is a 40 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot...
"only the prime numbers greater than 10 and less than 40 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , and 37 . the total is 8 . the answer is d ."
a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 10
d
add(10, 2)
add(n2,n5)|
physics
the average salary of all the workers in a workshop is $ 1000 . the average salary of 5 technicians is $ 5000 and the average salary of the rest is $ 500 . the total number of workers in the shop is ?
"let the total number of workers be x 1000 x = 5000 * 5 + 500 ( x - 5 ) x = 25 answer is a"
a ) 25 , b ) 20 , c ) 15 , d ) 30 , e ) 18
a
divide(subtract(multiply(5, 5000), multiply(500, 5)), subtract(1000, 500))
multiply(n1,n2)|multiply(n1,n3)|subtract(n0,n3)|subtract(#0,#1)|divide(#3,#2)|
general
you have been given a physical balance and 7 weights of 43 , 45 , 30 , 33 , 28 , 37 and 55 kgs . keeping weights on one pan and object on the other , what is the maximum you can weigh less than 145 kgs .
55 + 43 + 45 = 143 answer : b
a ) 145 , b ) 143 , c ) 147 , d ) 141 , e ) 142
b
add(add(add(45, 30), 33), 37)
add(n2,n3)|add(n4,#0)|add(n6,#1)
general
united telephone charges a base rate of $ 11.00 for service , plus an additional charge of $ 0.25 per minute . atlantic call charges a base rate of $ 12.00 for service , plus an additional charge of $ 0.20 per minute . for what number of minutes would the bills for each telephone company be the same ?
"lets take number of minutesx . given that , 11 + 0.25 x = 12 + 0.2 x - > 0.05 x = 2 - > x = 20 minutes ans c"
a ) 2 minutes , b ) 10 minutes , c ) 20 minutes , d ) 40 minutes , e ) 60 minutes
c
divide(subtract(12.00, 11.00), subtract(0.25, 0.20))
subtract(n2,n0)|subtract(n1,n3)|divide(#0,#1)|
general
if the ratio of a to b is 8 to 3 and the ratio of b to c is 1 to 5 , what is the ratio of a to c ?
"a : b = 8 : 3 - - 1 b : c = 1 : 5 = > b : c = 3 : 15 - - 2 from 1 and 2 , we get a : c = 8 : 15 answer a"
a ) 8 / 15 , b ) 1 / 3 , c ) 2 / 5 , d ) 4 / 5 , e ) 7 / 6
a
divide(multiply(8, 1), multiply(3, 5))
multiply(n0,n2)|multiply(n1,n3)|divide(#0,#1)|
other
the least number which when divided by 5 , 67 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is :
solution l . c . m . of 5 , 6 , 7 , 8 = 840 . so , required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 . so , required number = ( 840 Γ— 2 + 3 ) = 1683 . answer b
a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
b
add(multiply(multiply(multiply(5, add(5, const_1)), add(5, const_2)), 8), 3)
add(n0,const_2)|add(n0,const_1)|multiply(n0,#1)|multiply(#0,#2)|multiply(n2,#3)|add(n3,#4)
general
the monthly incomes of a and b are in the ratio 5 : 2 . b ' s monthly income is 12 % more than c ' s monthly income . if c ' s monthly income is rs . 16000 , then find the annual income of a ?
b ' s monthly income = 16000 * 112 / 100 = rs . 17920 b ' s monthly income = 2 parts - - - - > rs . 17920 a ' s monthly income = 5 parts = 5 / 2 * 17920 = rs . 44800 a ' s annual income = rs . 44800 * 12 = rs . 537600 answer : a
a ) rs . 537600 , b ) rs . 180000 , c ) rs . 201600 , d ) rs . 504000 , e ) none of these
a
multiply(multiply(multiply(16000, add(const_1, divide(12, const_100))), divide(5, 2)), 12)
divide(n0,n1)|divide(n2,const_100)|add(#1,const_1)|multiply(n3,#2)|multiply(#0,#3)|multiply(n2,#4)
other
1 , 13 , 35 , 67 , 109 , ____
"1 , 13 , 35 , 67 , 109 , . . . . . 13 = 1 + 12 35 = 13 + 22 67 = 35 + 32 109 = 67 + 42 so 109 + 52 = 161 answer : a"
a ) 161 , b ) 154 , c ) 216 , d ) 158 , e ) none
a
subtract(negate(67), multiply(subtract(13, 35), divide(subtract(13, 35), subtract(1, 13))))
negate(n3)|subtract(n1,n2)|subtract(n0,n1)|divide(#1,#2)|multiply(#3,#1)|subtract(#0,#4)|
general
two cars start from the opposite places of a main road , 150 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run onl...
answer : a ) 65 km
a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
a
subtract(subtract(150, 35), add(25, 25))
add(n1,n1)|subtract(n0,n4)|subtract(#1,#0)|
physics
a sum of money at simple interest amounts to rs . 820 in 3 years and to rs . 854 in 4 years . the sum is :
"s . i . for 1 year = rs . ( 854 - 820 ) = rs . 34 . s . i . for 3 years = rs . ( 34 x 3 ) = rs . 102 . principal = rs . ( 820 - 102 ) = rs . 718 . answer : b"
a ) 647 , b ) 718 , c ) 654 , d ) 847 , e ) 976
b
subtract(820, divide(multiply(subtract(854, 820), 3), 4))
subtract(n2,n0)|multiply(n1,#0)|divide(#1,n3)|subtract(n0,#2)|
gain
what is the least number . which should be added to 0.0568 to make it a perfect square ?
"0.0568 + 0.0008 = 0.0576 ( 0.24 ) ^ 2 answer : e"
a ) 0.0004 , b ) 0.0009 , c ) 0.0002 , d ) 0.0003 , e ) 0.0008
e
subtract(multiply(divide(add(add(const_12, const_4), const_2), const_100), divide(add(add(const_12, const_4), const_2), const_100)), 0.0568)
add(const_12,const_4)|add(#0,const_2)|divide(#1,const_100)|multiply(#2,#2)|subtract(#3,n0)|
general
the average of first five multiples of 5 is :
"explanation : ( 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 5 x 15 / 5 = 15 answer : b"
a ) 9 , b ) 15 , c ) 17 , d ) 8 , e ) 10
b
add(5, const_1)
add(n0,const_1)|
general
a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick . the thickness of the bottom is :
"explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) Γ— ( 260 - 10 ) Γ— ( 110 - x ) ] = 8000 Γ— 1000 = > 320 Γ— 250 Γ— ( 110 - x ) = 8000 Γ— 1000 = > ( 110 - x ) = 8000 Γ— 1000 / 320 = 100 = > x = 10 cm = 1 dm . answer : b"
a ) 90 cm , b ) 1 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
b
subtract(multiply(multiply(3.3, 2.6), 1.1), divide(8000, const_1000))
divide(n0,const_1000)|multiply(n1,n2)|multiply(n3,#1)|subtract(#2,#0)|
physics
a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 380 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
"orchestra seats - a balcony seats - b a + b = 380 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 380 = 3320 - 3040 = 280 i . e . a = 70 and b = 380 - 70 = 310 more seats in balcony than orchestra = b - a = 310 - 70 = 240 answer :...
a ) 90 , b ) 110 , c ) 120 , d ) 130 , e ) 240
e
subtract(divide(subtract(multiply(12, 380), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtract(12, 8)), subtract(380, divide(subtract(multiply(12, 380), add(add(multiply(const_3, const_1000), multiply(const_3, const_100)), multiply(const_2, const_10))), subtrac...
multiply(n0,n2)|multiply(const_1000,const_3)|multiply(const_100,const_3)|multiply(const_10,const_2)|subtract(n0,n1)|add(#1,#2)|add(#5,#3)|subtract(#0,#6)|divide(#7,#4)|subtract(n2,#8)|subtract(#8,#9)|
general
in an electric circuit , two resistors with resistances x and y are connected in parallel . if r is the combined resistance of these two resistors , then the reciprocal of r is equal to the sum of the reciprocals of x and y . what is r if x is 5 ohms and y is 6 ohms ?
1 / r = 1 / x + 1 / y 1 / r = 1 / 5 + 1 / 6 = 11 / 30 r = 30 / 11 the answer is d .
a ) 7 / 30 , b ) 11 / 30 , c ) 11 / 15 , d ) 30 / 11 , e ) 15 / 11
d
divide(multiply(6, 5), add(5, 6))
add(n0,n1)|multiply(n0,n1)|divide(#1,#0)
general
in a practice paper at 2 iim . com , questions were given from 5 topics . out of the appearing students , 10 % passed in all topics while 10 % did not pass in any . of the remaining , 20 % passed in one topic only and 25 % in two topics only . if 24 % of the total students passed 4 topics only and 500 students passed i...
detailed solution let the number of appearing students be 100 . pass only in 0 topic – 10 1 – 16 ( 20 % of 80 ) 2 – 20 ( 25 % of 80 ) 3 – 20 % ( 100 – ( 16 + 20 + 24 + 20 ) ) 4 – 24 % 5 – 20 % therefore , 20 % of x = 500 = ) x = 2500 correct answer : a
a ) 2500 , b ) 2000 , c ) 1600 , d ) 4545 , e ) 6565
a
divide(500, divide(subtract(const_100, add(add(add(divide(multiply(subtract(subtract(const_100, 10), 10), add(20, 25)), const_100), 24), 10), 10)), const_100))
add(n4,n5)|subtract(const_100,n2)|subtract(#1,n2)|multiply(#0,#2)|divide(#3,const_100)|add(n6,#4)|add(n2,#5)|add(n2,#6)|subtract(const_100,#7)|divide(#8,const_100)|divide(n8,#9)
general
a person buys an article at rs . 650 . at what price should he sell the article so as to make a profit of 10 % ?
"cost price = rs . 650 profit = 10 % of 650 = rs . 65 selling price = cost price + profit = 650 + 65 = rs . 715 answer : b"
a ) 600 , b ) 715 , c ) 269 , d ) 261 , e ) 281
b
add(650, multiply(650, divide(10, const_100)))
divide(n1,const_100)|multiply(n0,#0)|add(n0,#1)|
gain
wink , inc . follows a certain procedure that requires two tasks to be finished independently in order for a job to be done . on any given day , there is a 7 / 8 probability that task 1 will be completed on time , and a 1 / 5 probability that task 2 will be completed on time . on a certain day , what is the probability...
"p ( 1 and not 2 ) = 7 / 8 * ( 1 - 1 / 5 ) = 7 / 10 . answer : d ."
a ) 1 / 20 , b ) 3 / 40 , c ) 13 / 40 , d ) 7 / 10 , e ) 13 / 22
d
multiply(divide(7, 8), subtract(1, divide(1, 7)))
divide(n0,n1)|divide(n3,n0)|subtract(n2,#1)|multiply(#0,#2)|
probability
a mixture contains milk and water in the ratio 3 : 2 . on adding 10 litters of water , the ratio of milk to water becomes 2 : 3 . total quantity of milk & water before adding water to it ?
"explanation : milk : water = 3 : 2 after adding 10 liters of water milk : water = 2 : 3 olny water patrs increase when mixture of water milk : wate = 3 : 2 = 2 * ( 3 : 2 ) = 6 : 4 after adding 10 liters of water milk : water = 2 : 3 = 3 * ( 2 : 3 ) = 6 : 9 milk parts always same short cut method : milk : water = 6 : 4...
a ) 10 , b ) 30 , c ) 50 , d ) 20 , e ) 30
d
divide(multiply(10, divide(2, 3)), subtract(divide(3, add(3, 2)), multiply(divide(2, add(3, 2)), divide(2, 3))))
add(n0,n1)|divide(n1,n0)|divide(n0,#0)|divide(n1,#0)|multiply(n2,#1)|multiply(#3,#1)|subtract(#2,#5)|divide(#4,#6)|
general
a drink vendor has 80 liters of maaza , 144 liters of pepsi and 368 liters of sprite . he wants to pack them in cans , so that each can contains the same number of liters of a drink , and does n ' t want to mix any two drinks in a can . what is the least number of cans required ?
"the number of liters in each can = hcf of 80 , 144 and 368 = 16 liters . number of cans of maaza = 80 / 16 = 5 number of cans of pepsi = 144 / 16 = 9 number of cans of sprite = 368 / 16 = 23 the total number of cans required = 5 + 9 + 23 = 37 cans . answer : b"
a ) 35 , b ) 37 , c ) 42 , d ) 30 , e ) 38
b
add(divide(368, gcd(gcd(80, 144), 368)), add(divide(80, gcd(gcd(80, 144), 368)), divide(144, gcd(gcd(80, 144), 368))))
gcd(n0,n1)|gcd(n2,#0)|divide(n0,#1)|divide(n1,#1)|divide(n2,#1)|add(#2,#3)|add(#5,#4)|
general
( 112 % of 2348 ) Γ· 4.98 = ?
"explanation : ? = ( 112 x 2348 / 100 ) Γ· 5 = 2630 / 5 = 526 = 525 answer : option c"
a ) 505 , b ) 515 , c ) 525 , d ) 538 , e ) 567
c
divide(multiply(divide(112, const_100), 2348), 4.98)
divide(n0,const_100)|multiply(n1,#0)|divide(#1,n2)|
general