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a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
b
add(divide(60, add(const_4, const_1)), const_2)
how many zeroes are there at the end of the number n , if n = 60 ! + 120 ! ?
the number of zeroes at the end of 60 ! will be less than the number of zeroes at the end of 120 ! hence it is sufficient to calculate the number of zeroes at the end of 60 ! the number of zeroes = [ 60 / 5 ] + [ 60 / 25 ] + [ 60 / 125 ] = 12 + 2 + 0 = 14 the answer is b .
a = 4 + 1 b = 60 / a c = b + 2
a ) 1 , b ) 13 , c ) 26 , d ) 24 , e ) 1014
d
multiply(add(subtract(13, const_10), const_2), add(subtract(13, const_10), const_2))
if x is a sum of all even integers on the interval 13 . . . 61 and y is their number , what is the gcd ( x , y ) ?
"x = 14 + 16 + . . . + 60 = ( largest + smallest ) / 2 * ( # of terms ) = ( 14 + 60 ) / 2 * 24 = 37 * 24 . gcd of 24 and 37 * 22 is 24 . answer : d ."
a = 13 - 10 b = a + 2 c = 13 - 10 d = c + 2 e = b * d
a ) 360 , b ) 288 , c ) 600 , d ) 888 , e ) 121
a
multiply(divide(multiply(30, add(const_3, 2)), subtract(40, 30)), 40)
a train leaves delhi at 11 a . m . at a speed of 30 kmph . another train leaves at 2 p . m . at a speed of 40 kmph on the same day and in the same direction . how far from delhi , will the two trains meet ?
"d = 30 * 3 = 90 rs = 40 – 30 = 10 t = 90 / 10 = 9 d = 40 * 9 = 360 km answer : a"
a = 3 + 2 b = 30 * a c = 40 - 30 d = b / c e = d * 40
a ) 0.125 , b ) 0.25 , c ) 0.375 , d ) 0.5 , e ) 0.666
b
multiply(power(divide(const_1, const_2), 2), 2)
if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land tails up exactly twice in 2 consecutive flips ?
"total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h tt , thus probability is = p ( tt ) = 1 / 4 = . 25 answer : b"
a = 1 / 2 b = a ** 2 c = b * 2
a ) 104 , b ) 100 , c ) 50 , d ) 89 , e ) 90
c
add(divide(subtract(19, 7600), 8), const_1)
how many multiples of 8 are less than 7600 , and also multiples of 19 ?
"lcm of 8 & 19 = 152 tried dividing 7600 by 152 got quotient 50 ' so c is answer"
a = 19 - 7600 b = a / 8 c = b + 1
a ) 21 , b ) 28 . , c ) 35 . , d ) 49 . , e ) 52 .
a
add(const_3, const_2)
in a rectangular axis system , what is the area of a parallelogram with the coordinates : ( 5,7 ) , ( 12,7 ) , ( 2,3 ) , ( 9,3 ) ?
"area of parallelogram = b * h . base = distance in x coordinates between ( 2,3 ) and ( 9,3 ) = 7 height = difference in y coordinates between ( 5,7 ) and ( 2,3 ) = 3 . area = 7 * 3 = 21 . answer : a"
a = 3 + 2
a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
e
floor(divide(265, 12))
on dividing 265 by a number , the quotient is 12 and the remainder is 1 . find the divisor .
"d = ( d - r ) / q = ( 265 - 1 ) / 12 = 264 / 12 = 22 e )"
a = 265 / 12 b = math.floor(a)
a ) 14.3 % , b ) 13.67 % , c ) 33 % , d ) 28.6 % , e ) 49.67 %
b
multiply(multiply(divide(divide(divide(2, 7), 2), add(divide(divide(2, 7), 2), subtract(const_1, divide(2, 7)))), const_100), const_3)
of the 12,210 employees of the anvil factory , 2 / 7 are journeymen . if half of the journeymen were laid off , what percentage of the total remaining employees would be journeymen ?
"the exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers ( also because otherwise the ratio would be incorrect ) . since the question is about percentages , the actual numbers will be meaningless , as only the ratio of that number versus others will be meaningful . nonetheless , for those who are curious , each 1 / 7 portion represents ( 14210 / 7 ) 2,030 employees . this in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers . if half the journeymen were laid off , that would mean 1 / 7 of the total current workforce would be removed . this statistic is what leads many students to think that since half the journeymen are left , the remaining journeymen would represent half of what they used to be , which means 1 / 7 of the total workforce . if 1 / 7 of the workforce is journeymen , and 1 / 7 is roughly 14.3 % , then answer choice a should be the right answer . in this case , though , it is merely the tempting trap answer choice . what changed between the initial statement and the final tally ? well , you let go of 1 / 7 of the workforce , so the total number of workers went down . the remaining workers are still 1 / 7 of the initial workers , but the group has changed . the new workforce is smaller than the original group , specifically 6 / 7 of it because 1 / 7 was eliminated . the remaining workers now account for 1 / 7 out of 6 / 7 of the force , which if we multiply by 7 gives us 1 out of 6 . this number as a percentage is answer choice b , 13.67 % . using the absolute numbers we calculated before , there were 4,060 journeymen employees out of 14,210 total . if 2,030 of them are laid off , then there are 2,030 journeyman employees left , but now out of a total of ( 14,210 - 2,030 ) 12,180 employees . 2,030 / 12,180 is exactly 1 / 6 , or 16.67 % . the answer will work with either percentages or absolute numbers , but the percentage calculation will be significantly faster and applicable to any similar situation . the underlying principle of percentages ( and , on a related note , ratios ) can be summed up in the brainteaser i like to ask my students : if you ’ re running a race and you overtake the 2 nd place runner just before the end , what position do you end up in ? the correct answer is 2 nd place . percentages , like ratios and other concepts of relative math , depend entirely on the context . whether 100 % more of something is better than 50 % more of something else depends on the context much more than the percentages quoted . when it comes to percentages on the gmat , the goal is to understand them enough to instinctively not fall into the traps laid out for you . b"
a = 2 / 7 b = a / 2 c = 2 / 7 d = c / 2 e = 2 / 7 f = 1 - e g = d + f h = b / g i = h * 100 j = i * 3
a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 7 , d ) 1 / 2 , e ) 3
d
divide(divide(add(11, 44), const_2), 55)
given two sets a = { 11 , 44 , 55 } and b = { 01 } , if one number is chosen from each set at random , what is the probability that the sum of both numbers is an even number
one way to look at it : the number from set a can be anything . the number selected from set b will determine whether the sum is odd or even . for example , if a 4 is selected from set a , we need a 0 from set b to get an even sum . if a 5 is selected from set a , we need a 1 from set b to get an even sum . and so on . so , p ( sum is even ) = p ( select any number from set aandselect the number from set b that makes the sum even ) = p ( select any number from set a ) xp ( select the number from set b that makes the sum even ) = 1 x 1 / 2 = 1 / 2 = d
a = 11 + 44 b = a / 2 c = b / 55
a ) 7 , b ) 8 , c ) 9 , d ) 3 , e ) 2
b
divide(divide(divide(lcm(2, 4472), 4472), const_4), const_4)
what is the least value of x , so that 2 x 4472 is divisible by 9
"explanation : the sum of the digits of the number is divisible by 9 . then the number is divisible by 9 . 2 + x + 4 + 4 + 7 + 2 = 19 + x least value of x may be ' 8 ' , so that the total 19 + 8 = 27 is divisible by 9 . answer : option b"
a = math.lcm(2, 4472) b = a / 4472 c = b / 4 d = c / 4
a ) 5000 , b ) 5750 , c ) 2878 , d ) 2990 , e ) 2771
b
divide(multiply(230, const_100), subtract(const_100, add(subtract(const_100, 20), multiply(subtract(const_100, 20), divide(20, const_100)))))
a man saves 20 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 20 % , he is only able to save rs . 230 per month . what is his monthly salary ?
"income = rs . 100 expenditure = rs . 80 savings = rs . 20 present expenditure 80 * ( 20 / 100 ) = rs . 96 present savings = 100 â € “ 96 = rs . 4 100 - - - - - - 4 ? - - - - - - - - - 230 = > 5750 answer : b"
a = 230 * 100 b = 100 - 20 c = 100 - 20 d = 20 / 100 e = c * d f = b + e g = 100 - f h = a / g
a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 1 / 9 , e ) 1 / 3
c
divide(multiply(76, subtract(76, const_1)), multiply(250, subtract(250, const_1)))
a shipment of 250 smartphones contains 76 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
"probability of chosing one defective phone from a lot of 250 which ontains 76 defective phones is = ( 76 / 250 ) probability of chosing one defective phone from a lot of 249 ( we already picked one ) which ontains 75 ( we already picked one ) defective phones is = ( 75 / 249 ) combined probability of series of events = product of the probabilities = ( 76 / 250 ) * ( 75 / 249 ) 76 / 250 is close to ( 7 / 23 ) and ( 75 / 249 ) = ( 25 / 83 ) so answer is ( 7 / 23 ) * ( 25 / 83 ) = ( 1 / 11 ) so , answer will be c"
a = 76 - 1 b = 76 * a c = 250 - 1 d = 250 * c e = b / d
a ) a . 4 , b ) b . 8 , c ) c . 10 , d ) d . 12 , e ) e . 16
d
subtract(divide(multiply(48, 80), multiply(divide(const_3, const_4), 80)), 48)
if 48 machine can finish a job in 80 days , then how many more machines would be needed to finish the job in one - fifth less time ?
"you might think of this in a management context - we can use the principle of ' person - hours ' to solve any problem where we have identical workers . so , using simpler numbers , suppose you know that 6 identical employees , working simultaneously , would finish a job in 5 hours . then that job requires 6 * 5 = 30 total hours of person - work . if instead you wanted the job done in 3 hours , you ' d assign 30 / 3 = 10 employees to do the job , because you want to get a total of 30 hours of work from the employees . we can solve this problem identically . if 48 machines ( identical ones , i assume ) work simultaneously for 80 days , they will do a total of 48 * 80 machine - days of work . so the job requires 48 * 80 days of machine work in total . we instead want the job done in 1 / 5 less time , so in 64 days . so we ' ll need 48 * 80 / 64 = 60 machines , or 12 additional machines . d"
a = 48 * 80 b = 3 / 4 c = b * 80 d = a / c e = d - 48
a ) 16000 , b ) 18000 , c ) 20000 , d ) 22000 , e ) 24000
c
divide(multiply(multiply(25, const_100), multiply(16, const_100)), multiply(20, 10))
a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is
"explanation : number of bricks = courtyard area / 1 brick area = ( 2500 × 160020 × 10 ) = 20000 answer : option c"
a = 25 * 100 b = 16 * 100 c = a * b d = 20 * 10 e = c / d
a ) 82 kmph , b ) 76 kmph , c ) 44 kmph , d ) 58 kmph , e ) 56 kmph
a
multiply(const_3_6, subtract(divide(add(112, 108), 6), multiply(const_0_2778, 50)))
a train 108 m long is moving at a speed of 50 km / hr . it crosses a train 112 m long coming from opposite direction in 6 seconds . what is the speed of the second train ?
explanation : total distance = 108 + 112 = 220 m time = 6 s relative speed = distance / time = 220 / 6 m / s = 110 / 3 m / s = ( 110 / 3 ) × ( 18 / 5 ) km / hr = 132 km / hr = > 50 + speed of second train = 132 km / hr = > speed of second train = 132 - 50 = 82 km / hr answer : option a
a = 112 + 108 b = a / 6 c = const_0_2778 * 50 d = b - c e = const_3_6 * d
a ) 54 , b ) 45 , c ) 65 , d ) 78 , e ) 64
a
add(40, 14)
john found that the average of 15 numbers is 40 . if 14 is added to each number then the mean of number is ?
( x + x 1 + . . . x 14 ) / 15 = 40 54 option a
a = 40 + 14
a ) 23.57 , b ) 23.54 , c ) 23.5 , d ) 24.55 , e ) 25.14
e
floor(divide(circumface(divide(divide(multiply(const_2, add(14, 18)), const_4), const_2)), const_2))
the perimeter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
"let the side of the square be a cm . perimeter of the rectangle = 2 ( 18 + 14 ) = 64 cm perimeter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circumference of the semicircle = 1 / 2 ( ∏ ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 25.14 cm to two decimal places answer : e"
a = 14 + 18 b = 2 * a c = b / 4 d = c / 2 e = circumface / ( f = math.floor(e, 2)
a ) 32 , b ) 180 , c ) 60 , d ) 27 , e ) 11
b
divide(const_3.0, divide(divide(const_1, multiply(const_3, add(const_2, 6))), const_2))
when 6 is added to half of one - third of one - fifth of a number , the result is one - fifteenth of the number . find the number ?
"explanation : let the number be 26 + 1 / 2 [ 1 / 3 ( a / 5 ) ] = a / 15 = > 6 = a / 30 = > a = 180 answer : b"
a = 2 + 6 b = 3 * a c = 1 / b d = c / 2 e = 3 / 0
a ) 15.5 minutes , b ) 31 minutes , c ) 35 minutes , d ) 62 minutes , e ) 93 minutes
a
divide(31, const_2)
danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 31 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
"danny ' s time is 31 minutes . the time to reach halfway is 15.5 minutes . steve ' s time is 62 minutes . the time to reach halfway is 31 minutes . the time difference is 31 - 15.5 = 15.5 minutes the answer is a ."
a = 31 / 2
a ) 0.35 , b ) 0.55 , c ) 0.65 , d ) 0.75 , e ) 0.85
a
divide(subtract(140, 90), 140)
in a group of 140 people , 90 have an age of more 30 years , and the others have an age of less than 20 years . if a person is selected at random from this group , what is the probability the person ' s age is less than 20 ?
"number of people whose age is less than 20 is given by 140 - 90 = 50 probability p that a person selected at random from the group is less than 20 is given by 50 / 140 = 0.35 correct answer a"
a = 140 - 90 b = a / 140
['a ) 10 %', 'b ) 19 %', 'c ) 20 %', 'd ) 36 %', 'e ) 30 %']
b
multiply(subtract(const_1, power(divide(subtract(const_100, 10), const_100), const_2)), const_100)
if radius of a circle is reduced by 10 % , then how much % of its area will be reduced ?
let initial radius = a then , area = π a ^ 2 . new radius = 90 % of a = 9 a / 10 . new area = π * 81 a ^ 2 / 100 = 81 / 100 π a ^ 2 reduce in area = [ π a ^ 2 - 81 / 100 π a ^ 2 ] = 19 / 100 π a ^ 2 % reduce = [ ( 19 * π a ^ 2 / 100 ) * ( 1 * 100 / π a ^ 2 ) ] % = 19 % answer b
a = 100 - 10 b = a / 100 c = b ** 2 d = 1 - c e = d * 100
a ) 933.4 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 1312
a
multiply(subtract(power(21, const_2), power(const_10, const_2)), divide(add(multiply(12, const_2), const_2), add(const_4, const_3)))
a rope of which a calf is tied is increased from 12 m to 21 m , how much additional grassy ground shall it graze ?
"π ( 212 – 122 ) = 933.4 answer : a"
a = 21 ** 2 b = 10 ** 2 c = a - b d = 12 * 2 e = d + 2 f = 4 + 3 g = e / f h = c * g
a ) 160 , b ) 200 , c ) 250 , d ) 350 , e ) none
a
subtract(multiply(12, 640), multiply(add(11, divide(9, 12)), 640))
in a school with 640 students , the average age of the boys is 12 years and that of the girls is 11 years . if the average age of the school is 11 years 9 months , then the number of girls in the school is
sol . let the number of grils be x . then , number of boys = ( 640 - x ) . then , ( 11 3 / 4 × 640 ) ⇔ 11 x + 12 ( 640 - x ) ⇔ x = 7680 - 7520 ⇔ 160 . answer a
a = 12 * 640 b = 9 / 12 c = 11 + b d = c * 640 e = a - d
a ) 30 , b ) 31 , c ) 32 , d ) 32 , e ) 37
b
subtract(multiply(4, const_2), multiply(2, const_2))
if the average ( arithmetic mean ) of x , x + 2 , and x + 4 is 33 , what is the value of x ?
"am of x , x + 2 , and x + 4 = x + ( x + 2 ) + ( x + 4 ) / 3 = 3 x + 6 / 3 = x + 2 given that x + 2 = 33 x = 31 correct option : b"
a = 4 * 2 b = 2 * 2 c = a - b
a ) 2 / 5 , b ) 1 / 6 , c ) 1 / 4 , d ) 1 / 9 , e ) 2 / 9
e
multiply(4, add(divide(const_1, 30), divide(const_1, 45)))
two persons a and b can complete a piece of work in 30 days and 45 days respectively . if they work together , what part of the work will be completed in 4 days ?
"a ' s one day ' s work = 1 / 30 b ' s one day ' s work = 1 / 45 ( a + b ) ' s one day ' s work = 1 / 30 + 1 / 45 = 1 / 18 the part of the work completed in 4 days = 4 ( 1 / 18 ) = 2 / 9 . answer e"
a = 1 / 30 b = 1 / 45 c = a + b d = 4 * c
a ) 10 , b ) 11 , c ) 18 , d ) 13 , e ) 14
c
divide(subtract(690, multiply(75, 2.00)), 30)
30 pens and 75 pencils were purchased for 690 . if the average price of a pencil was 2.00 , find the average price of a pen .
"since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 690 – 150 ) = 540 ∴ average price of a pen = 540 ⁄ 60 = 18 answer c"
a = 75 * 2 b = 690 - a c = b / 30
a ) 4 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 16 % increase , e ) none of these
d
subtract(divide(multiply(subtract(const_100, 20), add(const_100, 45)), const_100), const_100)
if the price of a tv is first decreased by 20 % and then increased by 45 % , then the net change in the price will be :
"explanation : solution : let the original price be rs . 100 . new final price = 145 % of ( 80 % of 100 ) = rs . 145 / 100 * 80 / 100 * 100 = rs . 116 . . ' . increase = 16 % answer : d"
a = 100 - 20 b = 100 + 45 c = a * b d = c / 100 e = d - 100
a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 25
d
divide(divide(300, 5), 3)
two dogsled teams raced across a 300 mile course in wyoming . team a finished the course in 3 fewer hours than team e . if team a ' s average speed was 5 mph greater than team e ' s , what was team e ' s average mph ?
this is a very specific format that has appeared in a handful of real gmat questions , and you may wish to learn to recognize it : here we have a * fixed * distance , and we are given the difference between the times and speeds of two things that have traveled that distance . this is one of the very small number of question formats where backsolving is typically easier than solving directly , since the direct approach normally produces a quadratic equation . say team e ' s speed was s . then team e ' s time is 300 / s . team a ' s speed was then s + 5 , and team a ' s time was then 300 / ( s + 5 ) . we need to find an answer choice for s so that the time of team a is 3 less than the time of team e . that is , we need an answer choice so that 300 / ( s + 5 ) = ( 300 / s ) - 3 . you can now immediately use number properties to zero in on promising answer choices : the times in these questions will always work out to be integers , and we need to divide 300 by s , and by s + 5 . so we want an answer choice s which is a factor of 300 , and for which s + 5 is also a factor of 300 . so you can rule out answers a and c immediately , since s + 5 wo n ' t be a divisor of 300 in those cases ( sometimes using number properties you get to the correct answer without doing any other work , but unfortunately that ' s not the case here ) . testing the other answer choices , if you try answer d , you find the time for team e is 15 hours , and for team a is 12 hours , and since these differ by 3 , as desired , d is correct .
a = 300 / 5 b = a / 3
a ) 28 days , b ) 60 days , c ) 20 days , d ) 30 days , e ) 40 days
a
divide(subtract(10, add(divide(10, 50), divide(10, 40))), divide(10, 50))
a and b can do a piece of work in 40 days and 50 days respectively . they work together for 10 days and b leaves . in how many days the whole work is completed ?
"explanation : ( a + b ) ’ s 10 days work = 10 [ 1 / 40 + 1 / 50 ] = 10 [ 5 + 4 / 200 ] = 9 / 20 a complete remaining work in 9 / 20 * 40 = 18 total work = 10 + 18 = 28 days answer : option a"
a = 10 / 50 b = 10 / 40 c = a + b d = 10 - c e = 10 / 50 f = d / e
a ) rs . 22000 , b ) rs . 24500 , c ) rs . 26500 , d ) rs . 28500 , e ) none of these
d
add(add(add(13000, 5000), 1000), multiply(divide(add(add(13000, 5000), 1000), const_100), 50))
sahil purchased a machine at rs 13000 , then got it repaired at rs 5000 , then gave its transportation charges rs 1000 . then he sold it with 50 % of profit . at what price he actually sold it .
explanation : question seems a bit tricky , but it is very simple . just calculate all cost price , then get 150 % of cp . c . p . = 13000 + 5000 + 1000 = 19000 150 % of 19000 = 150 / 100 * 19000 = 28500 option d
a = 13000 + 5000 b = a + 1000 c = 13000 + 5000 d = c + 1000 e = d / 100 f = e * 50 g = b + f
['a ) 28', 'b ) 36', 'c ) 40', 'd ) 56', 'e ) 84']
b
multiply(const_4, 9)
the area of a square field is a square feet and the perimeter is p feet . if 6 a = 6 ( 2 p + 9 ) , what is the perimeter of the field , in feet ? ( here a = a ^ 2 )
you can also solve this via using the given numbers in the answer choices ! of course you need to be aware of the basic properties as outlined by the other posts above ( a = x ^ 2 and p = 4 x ) starting with d you will notice that x = 14 is way too big for your area ( 14 ^ 2 ) and will not satisfy : 6 a = 6 ( 2 p + 9 ) or a = 2 p + 9 - - > eliminate d and e now pick b ( its either too big , then its a , or too small then you know its c or it is b itsself ) and picking b indeed solves the problem ! ( 36 / 4 - - > 9 ; a = 9 ^ 2 = 81 and 81 = 2 x 36 + 9 )
a = 4 * 9
a ) 13 , b ) 11 , c ) 16 , d ) 17 , e ) 18
b
add(divide(subtract(multiply(floor(divide(43, 3)), 3), multiply(add(floor(divide(10, 3)), const_1), 3)), 3), const_1)
how many numbers from 10 to 43 are exactly divisible by 3 ?
"12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 . 11 numbers . 10 / 3 = 3 and 43 / 3 = 14 = = > 14 - 3 = 11 . therefore 11 digits b )"
a = 43 / 3 b = math.floor(a) c = b * 3 d = 10 / 3 e = math.floor(d) f = e + 1 g = f * 3 h = c - g i = h / 3 j = i + 1
a ) 200 , b ) 400 , c ) 600 , d ) 800 , e ) 900
b
multiply(divide(3, subtract(divide(const_60.0, 30), const_1)), const_60)
working together , printer a and printer b would finish the task in 30 minutes . printer a alone would finish the task in 50 minutes . how many pages does the task contain if printer b prints 3 pages a minute more than printer a ?
"30 * a + 30 * b = x pages in 30 mins printer a will print = 30 / 50 * x pages = 3 / 5 * x pages thus in 30 mins printer printer b will print x - 3 / 5 * x = 2 / 5 * x pages also it is given that printer b prints 3 more pages per min that printer a . in 30 mins printer b will print 90 more pages than printer a thus 3 / 5 * x - 2 / 5 * x = 90 = > x = 400 pages answer : b"
a = const_60 / 0 b = a - 1 c = 3 / b d = c * const_60
a ) 1600 , b ) 1700 , c ) 1800 , d ) 1900 , e ) 2000
c
multiply(multiply(36, divide(3, const_60)), const_1000)
train speed 36 kph . dist travelled in 3 minutes in meters
36 kmph = 10 m / sec d = 10 * 180 = 1800 meters answer : c
a = 3 / const_60 b = 36 * a c = b * 1000
a ) 1 , b ) 25 , c ) 35 , d ) 45 , e ) 75
a
multiply(divide(subtract(multiply(divide(40, 100), 300), multiply(divide(65, 100), multiply(300, divide(60, 100)))), 300), 100)
300 first - time customers of a fashion store were surveyed for their shopping experience right after leaving the store . 60 % of the customers in the survey had purchased clothes for less than $ 100 . 40 % of the customers in the survey reported they were overall satisfied with their purchase . 65 % of the customers that had purchased clothes for less than $ 100 reported they were overall satisfied with their purchase . what percent of the customers surveyed purchased clothes for at least $ 100 and reported that they were not overall satisfied with their purchase ?
"out of 300 - 180 purchased for less than 100 $ 120 for more out of 300 - 120 responded as satisfied and 180 responded disatisfied out of 180 ( purchased less than 100 $ ) - 65 % = 117 responded as satisfied , so remaining satisfied are 120 - 117 = 3 so 3 is what percentage of 300 - 1 % so the answer should be a"
a = 40 / 100 b = a * 300 c = 65 / 100 d = 60 / 100 e = 300 * d f = c * e g = b - f h = g / 300 i = h * 100
a ) 50 , b ) 51 , c ) 52 , d ) 53 , e ) 54
d
subtract(78, subtract(subtract(148, 92), 31))
in a company of 148 employees , 92 are females . a total of 78 employees have advanced degrees and the rest have a college degree only . if 31 employees are males with college degree only , how many employees are females with advanced degrees ?
"the number of males is 148 - 92 = 56 . the number of males with advanced degrees is 56 - 31 = 25 . the number of females with advanced degrees is 78 - 25 = 53 . the answer is d ."
a = 148 - 92 b = a - 31 c = 78 - b
a ) 39 % , b ) 20 % , c ) 40 % , d ) 74 % , e ) 83 %
c
multiply(divide(subtract(1260, 900), 900), const_100)
a cycle is bought for rs . 900 and sold for rs . 1260 , find the gain percent ?
"900 - - - - 360 100 - - - - ? = > 40 % answer : c"
a = 1260 - 900 b = a / 900 c = b * 100
a ) 50 kmph , b ) 60 kmph , c ) 32 kmph , d ) 80 kmph , e ) 90 kmph
c
divide(288, multiply(divide(3, 2), 6))
a van takes 6 hours to cover a distance of 288 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
time = 6 distence = 288 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 288 / 9 = 32 kmph c
a = 3 / 2 b = a * 6 c = 288 / b
a ) 299 , b ) 277 , c ) 350 , d ) 270 , e ) 281
c
subtract(multiply(multiply(divide(72, const_3600), const_1000), 30), 250)
a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 30 sec . what is the length of the goods train ?
"speed = 72 * 5 / 18 = 20 m / sec . time = 30 sec . let the length of the train be x meters . then , ( x + 250 ) / 30 = 20 x = 350 m . answer : c"
a = 72 / 3600 b = a * 1000 c = b * 30 d = c - 250
a ) 168 ° , b ) 228 ° , c ) 156 ° , d ) 224 ° , e ) 164 °
e
multiply(divide(multiply(add(multiply(multiply(8, const_2), const_10), const_100), const_2), add(add(add(5, 6), 7), 12)), 10)
the ratio of the adjacent angles of a parallelogram is 8 : 10 . also , the ratio of the angles of quadrilateral is 5 : 6 : 7 : 12 . what is the sum of the smaller angle of the parallelogram and the second largest angle of the quadrilateral ?
"the measures of the adjacent angles of a parallelogram add up to be 180 ° given so , 8 x + 10 x = 180 ° or , 18 x = 180 ° or , x = 10 ° hence the angles of the parallelogram are 80 ° and 100 ° further it is given we know sum of all the four angles of a quadrilateral is 360 ° so , 5 y + 6 y + 7 y + 12 y = 360 ° or , 5 y + 6 y + 7 y + 12 y = 360 ° or , 30 y = 360 ° or , y = 12 ° hence the angles of the quadrilateral are 60 ° , 72 , 84 ° and 144 ° will be 80 ° + 84 ° = 164 ° answer : e"
a = 8 * 2 b = a * 10 c = b + 100 d = c * 2 e = 5 + 6 f = e + 7 g = f + 12 h = d / g i = h * 10
a ) 540 , b ) 570 , c ) 619 , d ) 649 , e ) 560
e
multiply(divide(364, divide(add(const_100, 30), const_100)), 2)
if the price of a certain computer increased 30 percent from d dollars to 364 dollars , then 2 d =
before price increase price = d after 30 % price increase price = d + ( 30 / 100 ) * d = 1.3 d = 364 ( given ) i . e . d = 364 / 1.3 = $ 280 i . e . 2 d = 2 * 280 = 560 answer : option e
a = 100 + 30 b = a / 100 c = 364 / b d = c * 2
a ) 456578972 , b ) 436567874 , c ) 653658791 , d ) 725117481 , e ) 725107482
e
multiply(subtract(9999, const_4), 72518)
find the value of 72518 x 9999 = m ?
"72518 x 9999 = 72518 x ( 10000 - 1 ) = 72518 x 10000 - 72518 x 1 = 725180000 - 72518 = 725107482 e"
a = 9999 - 4 b = a * 72518
a ) 15 : 8 , b ) 8 : 15 , c ) 2 : 5 , d ) 5 : 2 , e ) 13 : 6
a
divide(multiply(3, multiply(divide(8, subtract(multiply(divide(add(const_100, 50), const_100), 10), divide(5, 2))), divide(5, 2))), add(divide(8, subtract(multiply(divide(add(const_100, 50), const_100), 10), divide(5, 2))), 6))
ratio of two numbers x and y is 2 : 5 . if x is increased by 50 % and y is increased by 8 then the new ratio becomes 3 : 10 . what is the ratio 3 y : ( x + 6 )
"let : x = 2 n y = 5 n 3 n / ( 5 n + 5 ) = 3 / 10 30 n = 3 * ( 5 n + 5 ) n = 1 so , x = 2 ; y = 5 3 y / ( x + 6 ) = 15 / 8 answer = a"
a = 100 + 50 b = a / 100 c = b * 10 d = 5 / 2 e = c - d f = 8 / e g = 5 / 2 h = f * g i = 3 * h j = 100 + 50 k = j / 100 l = k * 10 m = 5 / 2 n = l - m o = 8 / n p = o + 6 q = i / p
a ) 24 , b ) 25 , c ) 35 , d ) 36 , e ) 37
e
multiply(divide(19, 6), const_12)
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 doughnut purchased if you paid $ 19 ?
"a is the number of dozen of doughnuts at a price of $ 6 / dozen 1 + 6 a = 19 a = 3 the total number of doughnuts purchased - - > 1 + 3 * 12 = 37 answer : e"
a = 19 / 6 b = a * 12
a ) 66.4 % , b ) 61.4 % , c ) 77.4 % , d ) 65 % , e ) 53.9 %
b
divide(add(59, 65), const_2)
factory x ' s bulbs work for over 4000 hours in 59 % of cases , whereas factory y ' s bulbs work for over 4000 hours in 65 % of cases . it is known that factory x supplies 60 % of the total bulbs available . what is the chance that a purchased bulb will work for longer than 4000 hours ?
"for x , 60 % of 59 % will work . for y , 40 % of 65 % will work . * 40 % is the rest of the bulb supply in the market . so , the probability that a purchased bulb will work is : 0.60 ( 0.59 ) = . 354 0.40 ( 0.65 ) = 0.26 the combined probability then is 35.4 + 26.00 = 61.4 % ans b"
a = 59 + 65 b = a / 2
a ) 28 m , b ) 20 m , c ) 22 m , d ) 23 m , e ) 24 m
e
multiply(4, 6)
walking 6 / 7 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
speed ratio = 1 : 6 / 7 = 7 : 6 time ratio = 6 : 4 1 - - - - - - - - 6 4 - - - - - - - - - ? = > 24 m answer : e
a = 4 * 6
a ) 50 , b ) 100 , c ) 625 , d ) 800 , e ) 1250
d
multiply(84, multiply(divide(20, 6), divide(20, 7)))
if 6 a = 7 b = 20 , then 84 ab =
"6 a * 7 b = 20 * 20 = 400 42 ab = 400 i . e . 84 ab = 800 answer : option d"
a = 20 / 6 b = 20 / 7 c = a * b d = 84 * c
a ) 109 , b ) 108 , c ) 109 , d ) 106 , e ) 101
b
multiply(divide(180, 6), const_3_6)
a 180 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
"s = 180 / 6 * 18 / 5 = 108 kmph answerb"
a = 180 / 6 b = a * const_3_6
a ) 12 days , b ) 18 days , c ) 24 days , d ) 30 days , e ) none of these
b
multiply(divide(subtract(subtract(30, 20), const_1), subtract(30, 20)), 20)
a is twice efficient as b and together they do the same work in as much time as c and d together . if c and d can complete the work in 20 and 30 daysrespectively , working alone , then in how many days a can complete the work individually :
explanation : a + b = c + d | | | | ratio of efficiency 10 x + 5 x 9 x + 6 x | ________| | _________| 15 x 15 x therefore , ratio of efficiency of a : c = 10 : 9 therefore , ratio of days taken by a : c = 9 : 10 therefore , number of days taken by a = 18 days answer : b
a = 30 - 20 b = a - 1 c = 30 - 20 d = b / c e = d * 20
a ) 9 % , b ) 10 % , c ) 23 % , d ) 21 % , e ) 22 %
c
multiply(divide(subtract(multiply(add(500, multiply(const_3, 500)), divide(19, const_100)), multiply(500, divide(7, const_100))), multiply(const_3, 500)), const_100)
a $ 500 investment and a $ 1,500 investment have a combined yearly return of 19 percent of the total of the two investments . if the $ 500 investment has a yearly return of 7 percent , what percent yearly return does the $ 1,500 investment have ?
"the equation we can form the question : return on total investment = sum of individual investments ( 500 + 1500 ) ( 19 ) = ( 500 â ˆ — 7 ) + ( 1500 x ) , where x is the return on investment of 1500 . solving the equation , we get x = 23 % ( option c ) answer : c"
a = 3 * 500 b = 500 + a c = 19 / 100 d = b * c e = 7 / 100 f = 500 * e g = d - f h = 3 * 500 i = g / h j = i * 100
a ) 34,200 , b ) 36,200 , c ) 38,200 , d ) 42,200 , e ) 38,971
e
divide(sqrt(multiply(multiply(multiply(subtract(divide(add(add(300, 300), 300), 2), 300), subtract(divide(add(add(300, 300), 300), 2), 300)), subtract(divide(add(add(300, 300), 300), 2), 300)), divide(add(add(300, 300), 300), 2))), const_1000)
it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , such that a , b , c are the lengths of sides of the triangle . if the triangle has 300 , 300 , and 300 as the side ’ s lengths , what is the triangle ’ s area ?
it is well known that a triangle ’ s area is √ ( p ( p - a ) ( p - b ) ( p - c ) ) , when p = ( a + b + c ) / 2 , - > p = ( 300 + 300 + 300 ) / 2 = 450 , area = √ ( 450 ( 450 - 300 ) ( 450 - 300 ) ( 450 - 300 ) ) = 38,971 . therefore , the answer is e .
a = 300 + 300 b = a + 300 c = b / 2 d = c - 300 e = 300 + 300 f = e + 300 g = f / 2 h = g - 300 i = d * h j = 300 + 300 k = j + 300 l = k / 2 m = l - 300 n = i * m o = 300 + 300 p = o + 300 q = p / 2 r = n * q s = math.sqrt(r) t = s / 1000
a ) 69 . , b ) 73 . , c ) 81 . , d ) 95 . , e ) 108 .
d
subtract(subtract(450, 320), subtract(250, divide(multiply(250, 86), const_100)))
in the fifth grade at parkway elementary school there are 450 students . 320 students are boys and 250 students are playing soccer . 86 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
"total students = 450 boys = 320 , girls = 130 total playing soccer = 250 86 % of 250 = 215 are boys who play soccer . girls who play soccer = 35 . total girls who do not play soccer = 130 - 35 = 95 . correct option : d"
a = 450 - 320 b = 250 * 86 c = b / 100 d = 250 - c e = a - d
a ) a ) 40 , b ) b ) 30 , c ) c ) 20 , d ) d ) 10 , e ) e ) 5
c
subtract(const_60, multiply(const_60, divide(32, 48)))
excluding stoppages , the speed of a train is 48 kmph and including stoppages it is 32 kmph . of how many minutes does the train stop per hour ?
"explanation : t = 16 / 48 * 60 = 20 answer : option c"
a = 32 / 48 b = const_60 * a c = const_60 - b
a ) 1 , b ) 6 , c ) 34 , d ) 79 , e ) 85
a
subtract(80, subtract(add(45, 40), 6))
at a kennel with 80 dogs , 45 of the dogs wear tags and 40 wear flea collars . if 6 of the dogs wear both , then how many of the dogs wear neither a collar nor tags ?
dogs wear neither a collar nor tags = 80 - ( 45 + 40 - 6 ) dogs wear neither a collar nor tags = 80 - 79 dogs wear neither a collar nor tags = 80 - 79 hence , answer will be 1 answer : a
a = 45 + 40 b = a - 6 c = 80 - b
a ) 12.5 % , b ) 40 % , c ) 180 % , d ) 125 % , e ) none
c
multiply(divide(9, 5), const_100)
the ratio 9 : 5 expressed as a percent equals
"solution 9 : 5 = 9 / 5 = ( 9 / 5 x 100 ) % . = 180 % . answer c"
a = 9 / 5 b = a * 100
a ) 910 , b ) 510 , c ) 728 , d ) 628 , e ) 810
c
multiply(divide(divide(subtract(multiply(7, add(const_10, const_1)), multiply(const_1, 7)), subtract(multiply(7, const_2), multiply(const_1, 7))), const_2), add(multiply(7, const_2), multiply(7, add(const_10, const_1))))
the sum of all two digit numbers divisible by 7 is
"required numbers are 14 , 21,28 . . . . . 98 this is an a . p . in which a = 14 , d = 7 and l = 98 . let the number of terms in it be n . then t = 98 so a + ( n - 1 ) d = 98 . 14 + ( n - 1 ) * 7 = 98 , 14 + 7 n - 7 = 98 7 + 7 n = 98 7 n = 98 - 7 n = 91 / 7 then n = 13 . required sum = n / 2 ( a + l ) = 13 / 2 ( 14 + 98 ) = 728 answer is c ."
a = 10 + 1 b = 7 * a c = 1 * 7 d = b - c e = 7 * 2 f = 1 * 7 g = e - f h = d / g i = h / 2 j = 7 * 2 k = 10 + 1 l = 7 * k m = j + l n = i * m
a ) 370 , b ) 365 , c ) 380 , d ) 367 , e ) 460
d
subtract(multiply(241, const_2), 115)
a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 115 . find the divisor ?
"easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 115 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 367 d * some integer = 367 checking all options only ( d ) syncs with it . answer d"
a = 241 * 2 b = a - 115
a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
e
floor(add(reminder(add(subtract(multiply(divide(47, const_100), 1442), multiply(divide(36, const_100), 1412)), 65), const_10), const_1))
find the value of x . ( 47 % of 1442 - 36 % of 1412 ) + 65 = x ?
e ) 5
a = 47 / 100 b = a * 1442 c = 36 / 100 d = c * 1412 e = b - d f = e + 65 g = reminder + ( h = math.floor(g, 1)
a ) 3.8 , b ) 4.2 , c ) 4.6 , d ) 5.0 , e ) 5.4
b
power(add(power(4, 2), add(1, power(2, const_3))), const_0_33)
the edges of three metal cubes are 1 cm , 2 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
"the total volume is 1 ^ 3 + 2 ^ 3 + 4 ^ 3 = 73 the edge of the new cube is the cube root of 73 which is about 4.2 cm . the answer is b ."
a = 4 ** 2 b = 2 ** 3 c = 1 + b d = a + c e = d ** const_0_33
a ) 72 , b ) 75 , c ) 78 , d ) 81 , e ) 84
c
multiply(add(add(subtract(multiply(2, const_10), 2), 1), multiply(2, const_10)), 3)
every letter in the alphabet has a number value that is equal to its place in the alphabet . thus , the letter a has a value of 1 , the letter b has a value of 2 , the letter c has a value of 3 , etc . . . the number value of a word is obtained by adding up the value of the letters in the word and then multiplying that sum by the length of the word . what is the number value of the word ` ` dog ' ' ?
"` ` dog ' ' = ( 4 + 15 + 7 ) * 3 = 78 . the answer is c ."
a = 2 * 10 b = a - 2 c = b + 1 d = 2 * 10 e = c + d f = e * 3
a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 9
e
subtract(subtract(multiply(3, 6), add(subtract(21, 6), 3)), 6)
the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 21 . what is the last numbers ?
"a + b + c = 18 b + c + d = 15 a + d = 21 a – d = 3 a + d = 21 2 d = 18 d = 9 answer : e"
a = 3 * 6 b = 21 - 6 c = b + 3 d = a - c e = d - 6
['a ) 360', 'b ) 480', 'c ) 720', 'd ) 960', 'e ) 1000']
d
divide(multiply(multiply(divide(divide(multiply(600, 10), 5), 15), 20), 3), 5)
15 ants can move 600 sugar cubes of 10 grams each to their home in 5 hours . then how many sugar cubes of 5 grams each , will 20 ants move in 3 hours ?
d 15 ants move 600 / 5 = 120 sugar cubes of 10 grams in 1 hour . 5 grams sugar cubes will take less time to move . thus if weight of the sugar cube is 5 grams , 15 ants will move 120 x 10 / 5 = 240 sugar cubes in 1 hour . more ants , more sugar cubes they can move . 20 ants will move 240 x 20 / 15 = 320 sugar cubes in 1 hour thus in 3 hours , 20 ants will move 320 x 3 = 960 sugar cubes of 5 grams .
a = 600 * 10 b = a / 5 c = b / 15 d = c * 20 e = d * 3 f = e / 5
a ) 1000 , b ) 1200 , c ) 4800 , d ) 3600 , e ) 8400
c
multiply(multiply(divide(80, multiply(10, 6)), const_100), multiply(10, 6))
find the sum the difference between the compound and s . i . on a certain sum of money for 6 years at 10 % per annum is rs . 80 of money ?
"p = 80 ( 100 / 10 ) 6 = > p = 1500 answer : c"
a = 10 * 6 b = 80 / a c = b * 100 d = 10 * 6 e = c * d
a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 3 : 2 , e ) 2 : 5
d
divide(subtract(divide(const_1, 4), divide(const_1, 5)), subtract(divide(const_1, 5), divide(const_1, multiply(const_2, const_4))))
a grocery store bought some mangoes at a rate of 5 for a dollar . they were separated into two stacks , one of which was sold at a rate of 4 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
"the cost price of a mango = 1 / 5 dollars . the selling price of a mango from the first stack = 1 / 4 dollars - - > the profit from one mango = 1 / 4 - 1 / 5 = 1 / 20 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 5 - 1 / 6 = 1 / 30 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 20 * 30 / 1 = 3 : 2 d"
a = 1 / 4 b = 1 / 5 c = a - b d = 1 / 5 e = 2 * 4 f = 1 / e g = d - f h = c / g
a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 50
e
subtract(add(add(add(add(add(const_1, power(const_2, const_2)), power(const_3, const_2)), power(const_4, const_2)), power(add(const_4, const_1), const_2)), power(6, const_2)), add(add(add(const_4, const_3), 6), add(add(add(add(const_2, const_3), add(const_4, const_1)), add(const_4, const_3)), add(add(const_2, const_3), 6))))
what is the positive difference between the sum of the squares of the first 6 positive integers and the sum of the prime numbers between the first square and fourth square ?
forget conventional ways of solving math questions . in ps , ivy approach is the easiest and quickest way to find the answer . the sum of the squares of the first 4 positive integers = 1 ^ 2 + 2 ^ 2 + 3 ^ 2 + 4 ^ 2 + 5 ^ 2 + 6 ^ 2 = 91 the sum of the prime numbers between the first square ( = 1 ) and fourth square ( = 16 ) = 2 + 3 + 5 + 7 + 11 + 13 = 41 . so the difference between 41 and 91 is 50 . so the answer is ( e ) .
a = 2 ** 2 b = 1 + a c = 3 ** 2 d = b + c e = 4 ** 2 f = d + e g = 4 + 1 h = g ** 2 i = f + h j = 6 ** 2 k = i + j l = 4 + 3 m = l + 6 n = 2 + 3 o = 4 + 1 p = n + o q = 4 + 3 r = p + q s = 2 + 3 t = s + 6 u = r + t v = m + u w = k - v
a ) 16 % , b ) 33.33 % , c ) 17 % , d ) 17.61 % , e ) 17.56 %
b
multiply(divide(subtract(80, 60), 60), const_100)
john makes $ 60 a week from his job . he earns a raise and now makes $ 80 a week . what is the % increase ?
"increase = ( 20 / 60 ) * 100 = ( 2 / 6 ) * 100 = 33.33 % . b"
a = 80 - 60 b = a / 60 c = b * 100
a ) 200 , b ) 384 , c ) 345 , d ) 244 , e ) 896
e
multiply(28, 32)
find the area of a parallelogram with base 28 cm and height 32 cm .
"area of a parallelogram = base * height = 28 * 32 = 896 cm 2 answer : option e"
a = 28 * 32
a ) 2 days , b ) 8 days , c ) 6 days , d ) 7 days , e ) 10 days
b
add(multiply(18, const_2.0), divide(18, 3))
a can complete a work in 18 days and b can do the same work in 10 days . if a after doing 3 days , leaves the work , find in how many days b will do the remaining work ?
"the required answer = ( 18 - 3 ) * 5 / 18 = 150 / 18 = 8 days answer is b"
a = 18 * 2 b = 18 / 3 c = a + b
a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0
a
sqrt(5)
what is the range of all the roots of | x ^ 2 - 5 | = x ?
"we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 5 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 5 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 5 or x = 1 i guess range is 5 - 1 = 4 a"
a = math.sqrt(5)
a ) 3.9 , b ) 5 , c ) 5.3 , d ) 1.5 , e ) 5.2
b
divide(15, const_3)
a man can swim in still water at 15 km / h , but takes twice as long to swim upstream than downstream . the speed of the stream is ?
"m = 15 s = x ds = 15 + x us = 15 - x 15 + x = ( 15 - x ) 2 15 + x = 30 - 2 x 3 x = 15 x = 5 answer : b"
a = 15 / 3
a ) 76 , b ) 86 , c ) 90 , d ) 88 , e ) 78
d
subtract(divide(add(multiply(134, const_2), const_2), const_3), const_2)
there are 134 toys coloured red and white in a box . two red toys are removed from the lot and now there are twice as many red ones as white ones . how many of red colour toys are there now ?
r + w = 134 two red toys are removed from the lot and now there are twice red ones as white ones r - 2 = 2 w sub 1 st one we get 134 - w - 2 = 2 w 132 = 3 w w = 44 r = 88 actually red will be 90 now 88 answer : d
a = 134 * 2 b = a + 2 c = b / 3 d = c - 2
a ) 22244428 , b ) 22255538 , c ) 22233328 , d ) 22266628 , e ) 22233327
c
multiply(divide(2224, 9997), const_100)
2224 × 9997 = ?
"c 22233328 2224 × 9997 = 2224 × ( 10000 - 3 ) = 2224 × 10000 - 2224 × 3 = 22240000 - 6672 = 22233328"
a = 2224 / 9997 b = a * 100
a ) 19 , b ) 27 , c ) 29 , d ) 46 , e ) 28
d
divide(add(340, multiply(multiply(const_0_2778, 36), 12)), multiply(const_0_2778, 36))
a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 340 m long platform ?
"let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 340 ) / 36 * 5 / 18 = 46 min . answer : d"
a = const_0_2778 * 36 b = a * 12 c = 340 + b d = const_0_2778 * 36 e = c / d
a ) 13500 , b ) 12000 , c ) 12500 , d ) 15000 , e ) 15500
c
divide(500, subtract(multiply(divide(10, const_100), divide(subtract(const_100, 20), const_100)), multiply(divide(20, const_100), divide(20, const_100))))
a shopkeeper sells 20 % of his stock at 20 % profit ans sells the remaining at a loss of 10 % . he incurred an overall loss of rs . 500 . find the total worth of the stock ?
"let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 6 / 5 = 6 x / 25 the sp of 80 % of the stock = 4 / 5 * x * 0.9 = 24 x / 25 total sp = 6 x / 25 + 18 x / 25 = 49 x / 50 overall loss = x - 24 x / 50 = x / 25 x / 25 = 500 = > x = 12500 answer : c"
a = 10 / 100 b = 100 - 20 c = b / 100 d = a * c e = 20 / 100 f = 20 / 100 g = e * f h = d - g i = 500 / h
a ) 10 , b ) 4 √ 2 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
a
sqrt(add(power(multiply(sqrt(25), sqrt(const_2)), const_2), power(multiply(sqrt(25), sqrt(const_2)), const_2)))
triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?
"ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10"
a = math.sqrt(25) b = math.sqrt(2) c = a * b d = c ** 2 e = math.sqrt(25) f = math.sqrt(2) g = e * f h = g ** 2 i = d + h j = math.sqrt(i)
a ) 20 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 55 %
d
multiply(divide(subtract(divide(2, 12), divide(4, 48)), divide(2, 12)), const_100)
a pharmaceutical company received $ 2 million in royalties on the first $ 12 ; million in sales of generic equivalent of one of its products and then $ 4 million in royalties on the next $ 48 million in sales . by approximately what percent did the ratio of royalties to sales decrease from the first $ 12 million in sales to the next $ 48 million in sales ?
change in ratio of royalties to sales = 2 / 12 - 4 / 48 = 1 / 12 % decrease = ( 1 / 12 ) / ( 2 / 12 ) * 100 = 50 % ( approx ) answer : d )
a = 2 / 12 b = 4 / 48 c = a - b d = 2 / 12 e = c / d f = e * 100
a ) 266.69 , b ) 266.67 , c ) 266.66 , d ) 263.66 , e ) 266.61
d
divide(multiply(const_100, 60), divide(multiply(25, 90), const_100))
an ore contains 25 % of an alloy that has 90 % iron . other than this , in remaining 75 % of the ore , there is no iron . how many kgs of the ore are needed to obtain 60 kg . of pure iron . ?
"explanation : let us take 100 x kgs of ore . now it contains 25 x kgs of alloy and it contains 90 % ( 25 x ) kgs of iron . 90 % ( 25 x ) = 60 kg ⇒ x = 60 × 10090 × 12560 × 10090 × 125 = 8383 so iron ore required = 100 × 8383 = 266.66 answer : d"
a = 100 * 60 b = 25 * 90 c = b / 100 d = a / c
a ) 0.09 , b ) 0.9 , c ) 9 , d ) 90 , e ) none of the above
a
divide(multiply(15, add(add(multiply(multiply(add(const_3, const_2), const_2), multiply(multiply(const_3, const_4), const_100)), multiply(multiply(add(const_3, const_4), add(const_3, const_2)), multiply(add(const_3, const_2), const_2))), add(const_3, const_3))), const_100)
what is 15 % of 2 / 3 of 0.4 ?
"the best way to solve these questions is to convert every term into fraction ( 15 / 100 ) * ( 2 / 3 ) * ( 4 / 10 ) = 120 / 3000 = 0.04 option a"
a = 3 + 2 b = a * 2 c = 3 * 4 d = c * 100 e = b * d f = 3 + 4 g = 3 + 2 h = f * g i = 3 + 2 j = i * 2 k = h * j l = e + k m = 3 + 3 n = l + m o = 15 * n p = o / 100
a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 35 degrees , e ) 74 degrees
d
subtract(43, subtract(multiply(48, const_4), multiply(46, const_4)))
the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 43 degrees . find the temperature on friday ?
m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 43 tu + w + th = 192 - 43 = 149 f = 184 – 149 = 35 answer : d
a = 48 * 4 b = 46 * 4 c = a - b d = 43 - c
a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 9 , d ) 1 / 6 , e ) 1 / 3
c
multiply(divide(3, power(3, const_2)), divide(3, power(3, const_2)))
what is the probability that the sum of two dice will yield a 4 , and then when both are thrown again , their sum will again yield a 4 ? assume that each die has 3 sides with faces numbered 1 to 3 .
"solution - rolling dices is an independent event . the combinations to get 4 are ( 1,3 ) , ( 3,1 ) , ( 2,2 ) , and total combinations of both dices is 9 . the probability of getting 4 in first attempt is 3 / 9 = 1 / 3 . probability of getting 4 again in second attempt = ( 1 / 3 ) * ( 1 / 3 ) = 1 / 9 . ans c"
a = 3 ** 2 b = 3 / a c = 3 ** 2 d = 3 / c e = b * d
a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
c
subtract(119, subtract(add(144, 119), 232))
in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology ?
"greatest possible number taken both should be 144 ( as it is maximum for one ) smallest possible number taken both should be given by total - neither = a + b - both both = a + b + neither - total ( neither must be 0 to minimize the both ) so 144 + 119 + 0 - 232 = 31 greatest - smallest is 144 - 31 = 113 so answer must be c . 113"
a = 144 + 119 b = a - 232 c = 119 - b
a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
b
subtract(add(add(const_2, const_3), const_4), add(const_2, const_3))
albert father was 48 years of age when she was born while her mother was 46 years old when her brother 2 years younger to her was born . what is the difference between the ages of her parents ?
mother ' s age when albert ' s brother was born = 46 years father ' s age when albert ' s brother was born = 48 + 2 = 50 years required difference = 50 - 46 = 4 years answer is b
a = 2 + 3 b = a + 4 c = 2 + 3 d = b - c
a ) 9000 , b ) 3000 , c ) 5000 , d ) 1300 , e ) 9200
e
divide(5888, subtract(const_1, divide(multiply(12, 3), const_100)))
what was the principal , if at 12 % per annum the interest after 3 years amounted to rs . 5888 less than the sum lent ?
p - 2336 = ( p * 12 * 3 ) / 100 p = 9200 answer : e
a = 12 * 3 b = a / 100 c = 1 - b d = 5888 / c
a ) 4 , b ) 3 , c ) 1 , d ) 5 , e ) 7
d
divide(82, 11)
what is the 14 th digit to the right of the decimal point in the decimal equivalent of 82 / 11 ?
"82 / 11 = 7.4545 . . . . 45 is non - repeating terminating decimal . the 14 th digit to the right of decimal point will be 5 . answer d"
a = 82 / 11
a ) 80 , b ) 81 , c ) 82 , d ) 83 , e ) 84
a
add(divide(multiply(multiply(divide(90, const_100), add(10, const_100)), 2), 3), 14)
on thursday mabel handled 90 transactions . anthony handled 10 % more transactions than mabel , cal handled 2 / 3 rds of the transactions that anthony handled , and jade handled 14 more transactions than cal . how much transactions did jade handled ?
"solution : mabel handled 90 transactions anthony handled 10 % more transactions than mabel anthony = 90 + 90 × 10 % = 90 + 90 × 0.10 = 90 + 9 = 99 cal handled 2 / 3 rds of the transactions than anthony handled cal = 2 / 3 × 99 = 66 jade handled 14 more transactions than cal . jade = 66 + 14 = 80 jade handled = 80 transactions . answer : a"
a = 90 / 100 b = 10 + 100 c = a * b d = c * 2 e = d / 3 f = e + 14
a ) 19 : 2 , b ) 18 : 3 , c ) 11 : 1 , d ) 11 : 5 , e ) 11 : 4
d
divide(add(divide(multiply(62.5, 12), const_100), divide(multiply(87.5, 4), const_100)), add(subtract(12, divide(multiply(62.5, 12), const_100)), subtract(4, divide(multiply(87.5, 4), const_100))))
two vessels p and q contain 62.5 % and 87.5 % of alcohol respectively . if 12 litres from vessel p is mixed with 4 litres from vessel q , the ratio of alcohol and water in the resulting mixture is ?
"quantity of alcohol in vessel p = 62.5 / 100 * 2 = 15 / 2 litres quantity of alcohol in vessel q = 87.5 / 100 * 4 = 7 / 2 litres quantity of alcohol in the mixture formed = 15 / 2 + 7 / 2 = 11 litres as 16 litres of mixture is formed , ratio of alcohol and water in the mixture formed = 11 : 5 answer : d"
a = 62 * 5 b = a / 100 c = 87 * 5 d = c / 100 e = b + d f = 62 * 5 g = f / 100 h = 12 - g i = 87 * 5 j = i / 100 k = 4 - j l = h + k m = e / l
a ) 99 , b ) 277 , c ) 48 , d ) 96 , e ) 22
d
subtract(divide(multiply(1.9, const_1000), divide(multiply(60, const_1000), const_3600)), divide(multiply(2.1, const_1000), divide(multiply(90, const_1000), const_3600)))
two trains are moving in opposite directions at 60 km / hr and 90 km / hr . their lengths are 1.9 km and 2.1 km respectively . the time taken by the slower train to cross the faster train in seconds is ?
"relative speed = 60 + 90 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . distance covered = 1.9 + 2.1 = 4 km = 4000 m . required time = 4000 * 3 / 125 = 96 sec . answer : d"
a = 1 * 9 b = 60 * 1000 c = b / 3600 d = a / c e = 2 * 1 f = 90 * 1000 g = f / 3600 h = e / g i = d - h
a ) $ 015 , b ) $ 0.20 , c ) $ 0.30 , d ) $ 0.40 , e ) $ 0.45
d
divide(multiply(add(const_1, const_1), 0.60), add(const_1, const_2))
on a certain day , orangeade was made by mixing a certain amount of orange juice with an equal amount of water . on the next day , orangeade was made by mixing the same amount of orange juice with twice the amount of water . on both days , all the orangeade that was made was sold . if the revenue from selling the orangeade was the same for both days and if the orangeade was sold at $ 0.60 per glass on the first day , what was the price r per glass on the second day ?
"on the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade ; on the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade ; so , the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to 3 . naturally the ratio of the # of glasses of orangeade made on the first day to the # of glasses of orangeade made on the second day is 2 to 3 . we are told thatthe revenue from selling the orangeade was the same for both daysso the revenue from 2 glasses on the first day equals to the revenue from 3 glasses on the second day . say the price of the glass of the orangeade on the second day was $ x then 2 * 0.6 = 3 * x - - > x = $ 0.4 . answer : d ."
a = 1 + 1 b = a * 0 c = 1 + 2 d = b / c
a ) 8 , b ) 6 , c ) 4 , d ) 2 , e ) 10
a
subtract(multiply(multiply(subtract(multiply(7, 4), multiply(5, 4)), 2), divide(3, 2)), multiply(subtract(multiply(7, 4), multiply(5, 4)), 2))
two numbers are in the ratio of 2 : 3 . if 4 is added in both numbers the ratio becomes 5 : 7 . find the difference between numbers .
we ' re told that two numbers are in the ratio of 2 : 3 . thus , the two numbers could be . . . 2 and 3 4 and 6 6 and 9 8 and 12 10 and 15 etc . we ' re told that adding 4 to each number changes the ratio of the numbers to 5 : 7 . we ' re asked for the difference between the original numbers . since adding 4 makes the first number a multiple of 5 , this limits the possibilities . . . . 2 + 4 = 6 not possible 4 + 4 = 8 not possible 6 + 4 = 10 this is possible . . . using this example , we would have . . . 6 and 9 , after adding 4 to each , becomes 10 and 13 . . . this is not a ratio of 5 to 7 though ( even though it ' s pretty close ) , so we have to keep looking . . . . the next value that becomes a multiple of 5 when you add 4 to it is . . . 16 . . . 16 + 4 = 20 with 16 and 24 , after adding 4 to each , we have 20 and 28 . this is a ratio of 5 to 7 , so we have our pair of original numbers . the difference between them is 8 . final answer : a
a = 7 * 4 b = 5 * 4 c = a - b d = c * 2 e = 3 / 2 f = d * e g = 7 * 4 h = 5 * 4 i = g - h j = i * 2 k = f - j
a ) s . 6000 , b ) s . 9000 , c ) s . 10800 , d ) s . 9649 , e ) s . 9980
d
divide(multiply(6600, const_100), subtract(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), divide(multiply(subtract(subtract(const_100, 20), divide(multiply(subtract(const_100, 20), 10), const_100)), 5), const_100)))
after successive discounts of 20 % , 10 % and 5 % a certain good is sold for rs . 6600 . find the actual price of the good .
"let actual price was 100 . after three successive discount this will become , 100 = = 20 % discount = > 80 = = 10 % discount = > 72 = = 5 % discount = 68.4 now compare , 68.4 = 6600 1 = 6600 / 68.4 100 = ( 6600 * 100 ) / 68.4 = rs . 9649 . answer : option d"
a = 6600 * 100 b = 100 - 20 c = 100 - 20 d = c * 10 e = d / 100 f = b - e g = 100 - 20 h = 100 - 20 i = h * 10 j = i / 100 k = g - j l = k * 5 m = l / 100 n = f - m o = a / n
a ) 60 % , b ) 65 % , c ) 67 % , d ) 70 % , e ) 75 %
c
divide(add(multiply(70, 55), multiply(95, subtract(100, 70))), 100)
in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 55 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
"70 % of the class scored 55 % and 30 % of the class scored 95 % . the difference between 55 % and 95 % is 40 % . the average will be 55 % + 0.3 ( 40 % ) = 67 % . the answer is c ."
a = 70 * 55 b = 100 - 70 c = 95 * b d = a + c e = d / 100
a ) 15.5 , b ) 12.3 , c ) 10.5 , d ) 10.12 , e ) 13.12
e
multiply(const_60, divide(subtract(64, 50), 64))
excluding stoppages , the speed of a bus is 64 kmph and including stoppages , it is 50 kmph . for how many minutes does the bus stop per hour ?
"due to stoppages , it covers 14 km less . time taken to cover 14 km = ( ( 14 / 64 ) ã — 60 ) = 13.12 min . option ( e ) is correct"
a = 64 - 50 b = a / 64 c = const_60 * b
a ) 8 hours , b ) 10 hours , c ) 12 hours , d ) 24 hours , e ) none of the above
c
divide(const_1, subtract(divide(const_1, 3), subtract(divide(const_1, 2), divide(const_1, 4))))
a can do a piece of work in 4 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
"a ' s 1 hour ' s work = 1 / 4 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 2 ( a + b + c ) ' s 1 hour ' s work = ( 1 / 4 + 1 / 3 ) = 7 / 12 b ' s 1 hour ' s work = ( 7 / 12 - 1 / 2 ) = 1 / 12 b alone will take 12 hours to do the work . answer = c"
a = 1 / 3 b = 1 / 2 c = 1 / 4 d = b - c e = a - d f = 1 / e
a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,600 , e ) 3,672
e
multiply(1.02, const_3600)
the moon revolves around the earth at a speed of approximately 1.02 kilometers per second . this approximate speed is how many kilometers per hour ?
"moon revolves around the earth at a speed of 1.02 kilometers per second . one hour equal to 60 minutes . one minute equals to 60 seconds . so one hour equals to 3600 seconds . so one hour , speed = 1.02 * 3600 = 3672 kilometers per hour . option e is correct"
a = 1 * 2
a ) 40 , b ) 92 , c ) 104 , d ) 208 , e ) 80
c
add(add(add(divide(multiply(5, 16), 4), 16), divide(multiply(7, 16), 4)), divide(multiply(10, 16), 4))
the ratio of football players , baseball players , soccer players , and basketball players in a school is 10 : 7 : 5 : 4 . how many athletes are in the school if 16 players are on the basketball team ?
the ratio is 10 football players : 7 baseball players : 5 soccer players : 4 basketball players . divide 16 by 4 to find 1 ` ` part ' ' of the ratio . 16 / 4 = 4 multiply 4 by 5 to find the number of soccer players . 4 * 5 = 20 multiply 4 by 7 to find the number of baseball players . 4 * 7 = 28 multiply 4 by 10 to find the number of football players . 4 * 10 = 40 . add them all up to find total athletes . 16 + 20 + 28 + 40 = 104 the answer is c .
a = 5 * 16 b = a / 4 c = b + 16 d = 7 * 16 e = d / 4 f = c + e g = 10 * 16 h = g / 4 i = f + h
a ) 3 , b ) 4 , c ) 9 , d ) 11 , e ) 13
d
add(floor(divide(7386038, add(const_1, const_4))), floor(divide(7386038, power(add(const_1, const_4), const_2))))
7386038 is divisible by
"explanation : the given number is 7386038 . the sum of the digits at even places is = 3 + 6 + 3 = 12 . the sum of the digits at odd places is = 7 + 8 + 0 + 8 = 23 . the difference is given by 23 - 12 = 11 answer : d"
a = 1 + 4 b = 7386038 / a c = math.floor(b) d = 1 + 4 e = d ** 2 f = 7386038 / e g = math.floor(f) h = c + g
a ) 299 , b ) 277 , c ) 800 , d ) 289 , e ) 271
c
divide(multiply(add(divide(multiply(650, 20), const_100), 190), const_100), 40)
40 % of a number is more than 20 % of 650 by 190 . find the number ?
"( 40 / 100 ) * x – ( 20 / 100 ) * 650 = 190 2 / 5 x = 320 x = 800 answer : c"
a = 650 * 20 b = a / 100 c = b + 190 d = c * 100 e = d / 40
a ) 251 , b ) 260 , c ) 263 , d ) 269 , e ) 262
e
add(multiply(subtract(10, const_1), subtract(30, const_2)), const_10)
what is the sum of the digits of integer k , if k = ( 10 ^ 30 - 36 )
there are 31 digits in 10 ^ 30 when we subtract 36 from it , there will be 30 digits left . 10 ^ 30 can be written as 9999999 . . . . ( 30 times ) + 1 so , 10 ^ 30 - 36 = 9999999 . . . . ( 30 times ) + 1 - 36 = 9999999 . . . . ( 30 times ) - 35 consider the last 2 digits , 99 - 35 = 64 the last 2 digits will be 64 . and our number would be 99999 . . . . . . 99964 with 2 less 9 s after subtraction . number of 9 s left are 28 and the last two digits are 64 the sum of the digits will be ( 28 * 9 ) + 6 + 4 = 262 answer : - e
a = 10 - 1 b = 30 - 2 c = a * b d = c + 10
a ) 2 , b ) 63 , c ) 15 , d ) 21 , e ) 35
b
add(subtract(multiply(3, 7), 7), power(7, const_2))
if a # b = ab – b + b ^ 2 , then 3 # 7 =
solution - simply substitute 3 and 7 in equation in the place of a and b respectively . 3 # 7 = 3 * 7 - 7 + 7 ^ 2 = 21 - 7 + 49 = 63 . ans b
a = 3 * 7 b = a - 7 c = 7 ** 2 d = b + c
a ) 20 , b ) 110 , c ) 120 , d ) 80 , e ) 60
d
divide(12, subtract(divide(12, 10), 4))
a train covers a distance of 12 km in 10 min . if it takes 4 sec to pass a telegraph post , then the length of the train is ?
"speed = ( 12 / 10 * 60 ) km / hr = ( 72 * 5 / 18 ) m / sec = 20 m / sec . length of the train = 20 * 4 = 80 m . answer : option d"
a = 12 / 10 b = a - 4 c = 12 / b