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a ) 5 a , b ) 10 a , c ) 15 a , d ) 18 a , e ) 25 a
a
floor(divide(75, add(2, const_1)))
during a certain two - week period , 75 percent of the movies rented from a video store were comedies , and of the remaining movies rented , there were 2 / 3 times as many dramas as action movies . if no other movies were rented during that two - week period and there were a action movies rented , then how many comedies , in terms of a , were rented during that two - week period ?
"movies : 75 % comedies . 25 % remaining genre . now in this 25 % , there are only 2 categories . action movies and drama movies . if action = x ; drama movies = 2 x / 3 . total 5 x / 3 . 5 x / 3 = 25 ; x = 15 action movies : 15 % drama movies : 10 % we can say that out of 100 z , : comedies : 75 z action : 15 z drama : 10 z now action movies were a this means : a = 15 z . z = a / 15 comedies : 75 z = 75 * ( a / 15 ) 5 a a is the answer ."
a = 2 + 1 b = 75 / a c = math.floor(b)
a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
b
divide(subtract(divide(multiply(60000, 20), const_100), 7000), divide(10, const_100))
rs 60000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 7000 find money given by 10 % ?
"let first parrt is x and second part is y then x + y = 60000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 7000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 70000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 70000 = 60000 + y so y = 10000 then x = 50000 - 10000 = 40000 first part = 40000 answer : b"
a = 60000 * 20 b = a / 100 c = b - 7000 d = 10 / 100 e = c / d
a ) 0.2 % , b ) 0.4 % , c ) 0.6 % , d ) 0.8 % , e ) 1 %
d
subtract(subtract(5, 4), divide(multiply(5, 4), const_100))
in measuring the sides of a rectangle , one side is taken 5 % in excess , and the other 4 % in deficit . find the error percent in the area calculated from these measurements .
"let x and y be the sides of the rectangle . then , correct area = xy . calculated area = ( 105 / 100 ) * x * ( 96 / 100 ) * y = ( 504 / 500 ) ( xy ) error in measurement = ( 504 / 500 ) xy - xy = ( 4 / 500 ) xy error % = [ ( 4 / 500 ) xy * ( 1 / xy ) * 100 ] % = ( 4 / 5 ) % = 0.8 % . answer d 0.8 %"
a = 5 - 4 b = 5 * 4 c = b / 100 d = a - c
a ) 0 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 1
d
divide(const_2, 3)
a box contains 100 balls , numbered from 1 to 100 . if 3 balls are selected at random and with replacement from the box . if the 3 numbers on the balls selected contain two odd and one even . what is the probability g that the first ball picked up is odd numbered ?
"answer - d selecting the balls either even or odd is having probability 50 / 100 = 1 / 2 we have already selected 3 balls with 2 odd numbers and 1 even number . so we have 3 combinations ooe , oeo , eoo . we have 3 outcomes and 2 are favourable as in 2 cases 1 st number is odd . so probability g is 2 / 3 . d"
a = 2 / 3
a ) 22 , b ) 60 , c ) 4 , d ) 8 , e ) 10
c
divide(multiply(multiply(4, 4), 2), const_2)
a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 2 rows or 4 rows or 4 rows , then no tree will be left . find the least number of trees required
"explanation : the least number of trees that are required = lcm ( 2 , 4,4 ) = 4 . answer : c"
a = 4 * 4 b = a * 2 c = b / 2
a ) $ 36 , b ) $ 44 , c ) $ 52 , d ) $ 60 , e ) $ 68
c
multiply(multiply(inverse(subtract(1, divide(1, 4))), add(divide(9, const_2), 15)), const_2)
bert left the house with n dollars . he spent 1 / 4 of this at the hardware store , then $ 9 at the dry cleaners , and then half of what was left at the grocery store . when he got home , he had $ 15 left in his pocket . what was the value of n ?
started to test answer c if he had 52 , then he spent 13 at hardware store now he was left with 39 $ he spent 9 dollars on cleaning , thus he remained with 30 $ he then spent 1 / 2 of 30 , or 15 , and was left with 15 . hence , the only option that can be right is c .
a = 1 / 4 b = 1 - a c = 1/(b) d = 9 / 2 e = d + 15 f = c * e g = f * 2
a ) $ 1 , b ) $ 2 , c ) $ 3 , d ) $ 4 , e ) $ 6
d
subtract(9, reminder(329864, 9))
a company has $ 329864 in its account . what is the least amount of money ( in whole number of dollars ) that it must add to the account if the money is paid evenly among 9 of its vendors ?
to find the least amount that must be added to the account to split the money evenly among 9 of its vendors , the total divisible by 9 simply add the individual digits of the total = 3 + 2 + 9 + 8 + 6 + 4 = 32 if you add 4 , the number is divisible by 9 ( 32 + 4 ) correct option : d
a = 9 - reminder
a ) 14 sec , b ) 10 sec , c ) 12 sec , d ) 8 sec , e ) 9 sec
d
divide(112, add(10, 4))
an escalator moves towards the top level at the rate of 10 ft . sec and its length is 112 feet . if a person walks on the moving escalator at the rate of 4 feet per second towards the top level , how much time does he take to cover the entire length .
"time taken to cover the entire length = tot . dist / resultant speed = 112 / ( 10 + 4 ) = 8 sec answer : d"
a = 10 + 4 b = 112 / a
a ) 2 / 3 , b ) 1 / 2 , c ) 5 / 3 , d ) 8 / 3 , e ) 7 / 3
d
divide(2, multiply(2, 4))
if - 2 / ( a - 6 ) = 4 / ( a + 4 ) , then a = ?
"multiply all terms of the given equation by ( a - 6 ) ( a + 4 ) , simplify and solve ( a - 6 ) ( a + 4 ) [ - 2 / ( a - 6 ) ] = ( a - 6 ) ( a + 4 ) [ 4 / ( a + 4 ) ] - 2 ( a + 4 ) = 4 ( a - 6 ) a = 8 / 3 correct answer d"
a = 2 * 4 b = 2 / a
a ) 11 , b ) 12 , c ) 14 , d ) 17 , e ) 18
d
divide(34, const_2)
in a group of ducks and cows , the total number of legs are 34 more than twice the no . of heads . find the total no . of buffaloes .
"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 34 = > 2 x = 34 = > x = 17 d"
a = 34 / 2
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
a
divide(add(multiply(factorial(7), factorial(6)), multiply(factorial(7), factorial(4))), 7)
what is the units digit of ( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 ?
"( 7 ! * 6 ! + 6 ! * 4 ! ) / 2 = 6 ! ( 7 ! + 4 ! ) / 2 = 240 ( 1680 + 24 ) / 2 = 204480 units digit of the above product will be equal to 0 answer a"
a = math.factorial(7) b = math.factorial(6) c = a * b d = math.factorial(7) e = math.factorial(4) f = d * e g = c + f h = g / 7
a ) 0 , b ) 36 , c ) 13 , d ) 20 , e ) 25
b
divide(multiply(12, 63), 21)
in a division sum , the remainder is 0 . as student mistook the divisor by 12 instead of 21 and obtained 63 as quotient . what is the correct quotient ?
"12 * 63 = 756 756 % 21 = 36 answer : b"
a = 12 * 63 b = a / 21
a ) 12 , b ) 8 , c ) 6 , d ) 10 , e ) 16
a
multiply(const_4, power(27, divide(const_1, const_3)))
a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many v cubes are painted on only 2 faces ?
"1 ) draw a simple cube 2 ) draw 9 squares on each face of the cube ( so that it looks like a rubik ' s cube ) - this is what the cube will look like when it ' s cut into 27 equal smaller cubes . 3 ) remember that the outside of the cube is the part that ' s painted . . . . the mini - cubes with 2 painted sides are all on the edge of the cube , in themiddleof the edge . there are 4 in front , 4 in back and 4 more on thestripthat runs around the left / top / right / bottom of the cube . v = 4 + 4 + 4 = 12 . answer a"
a = 1 / 3 b = 27 ** a c = 4 * b
a ) 12 , b ) 14 , c ) 15 , d ) 16 , e ) 18
e
divide(multiply(divide(multiply(15, 20), subtract(30, 20)), 30), add(20, divide(multiply(15, 20), subtract(30, 20))))
a tank can supply water to a village for 30 days . if a leak at the bottom of the tank drains out 15 liters per day , the supply lasts for 20 days only . for how many days will the supply last if the leak drains out 20 liters per day ?
"losing 15 liters per day results in a loss of 300 liters in 20 days . so , those 300 liters were for 10 days , making daily consumption of the village 30 liters per day . thus the capacity of the tank is 30 * 30 = 900 liters . losing 20 liters plus 30 liters gives 50 liters per day . at this rate the supply will last 900 / 50 = 18 days . the answer is e ."
a = 15 * 20 b = 30 - 20 c = a / b d = c * 30 e = 15 * 20 f = 30 - 20 g = e / f h = 20 + g i = d / h
a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 5,000
e
divide(const_180, const_1000)
the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 12348 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
"the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 12348 pi r = 21 so area = 4 . pi . r ^ 2 = 1764 . pi = 1764 x 3.14 = 5000 ( approx ) e"
a = const_180 / 1000
a ) 23 , b ) 25 , c ) 28 , d ) 60 , e ) 240
c
divide(multiply(add(multiply(2, const_100), 40), add(multiply(4, const_100), 20)), power(divide(add(multiply(2, const_100), 40), power(const_2, const_4)), const_2))
a room of 2 m 40 cm long and 4 m 20 cm broad is to be paved with square tiles . find the least number of square tiles required to cover the floor .
"explanation : area of the room = 240 * 420 sq cm size of largest square tile = h . c . f of 240 cm and 420 cm = 60 cm area of 1 tile = 60 * 60 sq cm no . of tiles required = ( 240 * 420 ) / ( 60 * 60 ) = 28 answer : c ) 28"
a = 2 * 100 b = a + 40 c = 4 * 100 d = c + 20 e = b * d f = 2 * 100 g = f + 40 h = 2 ** 4 i = g / h j = i ** 2 k = e / j
a ) 12 , b ) 20 , c ) 21 , d ) 23 , e ) 22
e
divide(subtract(multiply(const_2, multiply(const_2, const_12)), const_4), const_2)
how many times in a day , the hands of a clock are shows opposite directions ?
"sol . in 12 hours , the hands coincide or are in opposite direction 11 times . â ˆ ´ in 24 hours , the hands coincide or are in opposite direction 22 times a day . ( between 5 and 7 they point in opposite directions at 6 o ' clock only ) answer e"
a = 2 * 12 b = 2 * a c = b - 4 d = c / 2
a ) 4 / 0 , b ) 4 / 1 , c ) 4 / 5 , d ) 4 / 2 , e ) 4 / 3
c
divide(const_4, subtract(9, const_4))
the difference between a positive proper fraction and its reciprocal is 9 / 20 . then the fraction is :
"explanation : let the required fraction be x . then , ( 1 / x ) - x = 9 / 20 1 - x ^ ( 2 ) / x = 9 / 20 = > 20 - 20 * x ^ ( 2 ) = 9 * x . 20 * x ^ ( 2 ) + 9 * x - 20 = 0 . = > ( 4 * x + 5 ) ( 5 * x - 4 ) = 0 . = > x = 4 / 5 . answer : c ) 4 / 5"
a = 9 - 4 b = 4 / a
a ) 1500 , b ) 2000 , c ) 2500 , d ) 2800 , e ) 3000
e
multiply(multiply(subtract(5, 4), 1000), const_3.0)
a sum of money is to be distributed among a , b , c , d in the proportion of 6 : 3 : 5 : 4 . if c gets rs . 1000 more than d , what is b ' s share ?
"let the shares of a , b , c and d be rs . 5 x , rs . 3 x , rs . 5 x and rs . 4 x respectively . then , 5 x - 4 x = 1000 x = 1000 . b ' s share = rs . 3 x = rs . ( 3 x 1000 ) = rs . 3000 . answer : e"
a = 5 - 4 b = a * 1000 c = b * 3
a ) 50 , b ) 100 , c ) 70 , d ) 500 , e ) 980
c
divide(686, 9.8)
a sports equipment store sold ping pong rackets for a total of $ 686 . if the average ( arithmetic mean ) price of a pair of rackets is $ 9.8 , how many pairs were sold ?
average price for a pair of rackets = $ 9.8 total cost = $ 9.8 * x = $ 686 x = 70 pairs were sold . answer : c
a = 686 / 9
a ) 5 / 7 , b ) 1 , c ) 10 / 7 , d ) 12 / 7 , e ) 24 / 7
e
inverse(add(divide(subtract(divide(add(inverse(add(add(const_4, const_1), const_4)), multiply(inverse(add(const_4, const_1)), const_2)), const_2), inverse(add(const_4, const_1))), divide(const_3, const_2)), inverse(add(const_4, const_1))))
one woman and one man can build a wall together in four hours , but the woman would need the help of two girls in order to complete the same job in the same amount of time . if one man and one girl worked together , it would take them eight hours to build the wall . assuming that rates for men , women and girls remain constant , how many hours would it take one woman , one man , and one girl , working together , to build the wall ?
"solution : let work done by man , women and girl per hour be m , w , g respectively . then , m + w = 1 / 4 - - > ( 1 ) , w + 2 g = 1 / 4 - - > ( 2 ) and m + g = 1 / 8 - - > ( 3 ) . no . of hours it would take forone woman , one man , and one girl , working together , to build the wall , n = 1 / m + w + g from ( 1 ) and ( 2 ) , m = 2 g and from ( 3 ) g = 1 / 24 , m = 1 / 12 and w = 1 / 6 . so , n = 1 / ( 7 / 24 ) = 24 / 7 option , e"
a = 4 + 1 b = a + 4 c = 1/(b) d = 4 + 1 e = 1/(d) f = e * 2 g = c + f h = g / 2 i = 4 + 1 j = 1/(i) k = h - j l = 3 / 2 m = k / l n = 4 + 1 o = 1/(n) p = m + o q = 1/(p)
a ) 80 , b ) 25 , c ) 75 , d ) 63 , e ) 90
c
subtract(multiply(const_100, add(const_10, multiply(const_3, const_2))), 1300)
what is the least number to be subtracted from 1300 to make it a perfect square ?
"the numbers less than 1300 and are squares of certain number is 1225 . the least number that should be subtracted from 1300 to make it perfect square = 1300 - 1225 = 75 . answer : c"
a = 3 * 2 b = 10 + a c = 100 * b d = c - 1300
a ) kg , b ) 70 kg , c ) 80 kg , d ) 90 kg , e ) 93 kg
e
add(multiply(8, 3.5), 65)
the average weight of 8 person ' s increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg . what might be the weight of the new person ?
"total weight increased = ( 8 x 3.5 ) kg = 28 kg . weight of new person = ( 65 + 28 ) kg = 93 kg . e )"
a = 8 * 3 b = a + 65
a ) 5 : 24 , b ) 5 : 19 , c ) 5 : 13 , d ) 5 : 22 , e ) 5 : 18
a
divide(subtract(sqrt(6400), 30), multiply(sqrt(6400), const_2))
the area of a square is 6400 sq cm . find the ratio of the breadth and the length of a rectangle whose length is thrice the side of the square and breadth is 30 cm less than the side of the square ?
"let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 6400 a = ( 6400 ) ^ 1 / 2 = 80 l = 3 a and b = a - 30 b : l = a - 30 : 2 a = 50 : 240 = 5 : 24 answer : a"
a = math.sqrt(6400) b = a - 30 c = math.sqrt(6400) d = c * 2 e = b / d
a ) 1 / 25 , b ) 1 / 6 , c ) 3 / 5 , d ) 5 , e ) 6
c
divide(divide(15, 5), 5)
if xy > 0 , 1 / x + 1 / y = 15 , and 1 / xy = 5 , then ( x + y ) / 5 = ?
( 1 / x + 1 / y ) = 15 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 15 / 5 = = > ( x + y ) / 5 = 15 / ( 5 * 5 ) = 3 / 5 . c
a = 15 / 5 b = a / 5
a ) 220 km , b ) 224 km , c ) 230 km , d ) 200 km , e ) 234 km
d
multiply(const_2, divide(multiply(multiply(21, 26), 10), add(21, 26)))
a man complete a journey in 10 hours . he travels first half of the journey at the rate of 21 km / hr and second half at the rate of 26 km / hr . find the total journey in km .
"0.5 x / 10 + 0.5 x / 10 = 20 - - > x / 10 + x / 10 = 40 - - > 2 x = 10 x 40 - - > x = ( 10 x 40 ) / 2 = 200 km . answer : d ."
a = 21 * 26 b = a * 10 c = 21 + 26 d = b / c e = 2 * d
a ) $ 14.40 , b ) $ 14.00 , c ) $ 10.00 , d ) $ 9.60 , e ) $ 5.00
c
subtract(11.00, multiply(divide(10, const_100), 11.00))
a bookseller sells his books at a 10 % markup in price . if he sells a book for $ 11.00 , how much did he pay for it ?
"let the cost price of book = x selling price of book = 11 $ markup % = 10 ( 110 / 100 ) x = 11 = > x = 10 answer c"
a = 10 / 100 b = a * 11 c = 11 - 0
a ) 0 , b ) 2 , c ) 5 , d ) 7 , e ) 9
d
add(divide(60, const_10), 1)
there are 60 doors marked with numbers 1 to 60 . there are 60 individuals marked 1 to 60 . an operation on a door is defined as changing the status of the door from open to closed or vice versa . all the doors are closed to start with . one at a time , one randomly chosen individual goes and operates the doors . the individual however operates only those doors which are a multiple of the number he / she is carrying . for example , the individual marked with number 5 operates the doors marked with 5 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , and 60 . if every individual in the group gets one turn , then how many doors are open at the end ?
if a door is closed at the start , it requires an odd number of people to operate to be open at the end . only the perfect squares have an odd number of factors . the doors which are open at the end are : 1 , 4 , 9 , 16 , 25 , 36 , 49 for a total of 7 doors . the answer is d .
a = 60 / 10 b = a + 1
a ) 7 sec , b ) 8 sec , c ) 10 sec , d ) 12 sec , e ) 14 sec
d
multiply(divide(divide(220, const_1000), subtract(59, 7)), const_3600)
a train 220 m long is running with a speed of 59 kmph . in what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going ?
"speed of the train relative to man = ( 59 + 7 ) kmph = 66 * 5 / 18 m / sec = 55 / 3 m / sec . time taken by the train to cross the man = time taken by it to cover 220 m at ( 55 / 3 ) m / sec = ( 220 * 3 / 55 ) sec = 12 sec answer : d ."
a = 220 / 1000 b = 59 - 7 c = a / b d = c * 3600
a ) a ) 5.61 , b ) b ) 8 , c ) c ) 10 , d ) d ) 17.19 , e ) e ) 24
d
max(multiply(subtract(add(55, 9), const_1), subtract(divide(9, 20), divide(9, 55))), const_4)
due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 20 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
"old time in minutes to cross 9 miles stretch = 9 * 60 / 55 = 9 * 12 / 11 = 9.81 new time in minutes to cross 9 miles stretch = 9 * 60 / 20 = 9 * 3 / 1 = 27 time difference = 17.19 ans : d"
a = 55 + 9 b = a - 1 c = 9 / 20 d = 9 / 55 e = c - d f = b * e g = max(f)
a ) 3 , b ) 6 , c ) 5 , d ) 9 , e ) 1
c
divide(add(add(1, 2), 7), 2)
the area of a triangle will be when a = 1 m , b = 2 m , c = 7 m , a , b , c being lengths of respective sides ?
s = ( 1 + 2 + 7 ) / 2 = 5 answer : c
a = 1 + 2 b = a + 7 c = b / 2
a ) 65 kmph , b ) 70 kmph , c ) 75 kmph , d ) 80 kmph , e ) 85 kmph
b
subtract(divide(divide(125, 6), const_0_2778), 5)
a train 125 m long takes 6 sec to cross a man walking at 5 kmph in a direction opposite to that of the train . find the speed of the train ?
"let the speed of the train be x kmph speed of the train relative to man = x + 5 = ( x + 5 ) * 5 / 18 m / sec 125 / [ ( x + 5 ) * 5 / 18 ] = 6 30 ( x + 5 ) = 2250 x = 70 kmph answer is b"
a = 125 / 6 b = a / const_0_2778 c = b - 5
a ) 0 , b ) 8 , c ) 4 , d ) 6 , e ) 3
b
add(add(const_4, const_3), const_2)
what is the units digit of the expression 14 ^ 7 − 15 ^ 4 ?
i think answer on this one should be b too . since we know that 14 ^ 7 > 15 ^ 4 , as will said one should always check if the number is positive .
a = 4 + 3 b = a + 2
a ) 8 , b ) 3 , c ) 4 , d ) 5 , e ) 6
a
multiply(divide(divide(subtract(1050, 750), 750), 5), const_100)
at what rate percent on simple interest will rs . 750 amount to rs . 1050 in 5 years ?
"300 = ( 750 * 5 * r ) / 100 r = 8 % . answer : a"
a = 1050 - 750 b = a / 750 c = b / 5 d = c * 100
a ) 25 hours , b ) 30 hours , c ) 20 hours , d ) 26 hours , e ) 32 hours
c
subtract(multiply(divide(120, add(add(4, 3), 5)), 5), multiply(divide(120, add(add(4, 3), 5)), 4))
the amount of time that three people worked on a special project was in the ratio of 4 to 3 to 5 . if the project took 120 hours , how many more hours did the hardest working person work than the person who worked the least ?
"let the persons be a , b , c . hours worked : a = 4 * 120 / 12 = 40 hours b = 3 * 120 / 12 = 30 hours c = 5 * 120 / 12 = 50 hours c is the hardest worker and b worked for the least number of hours . so the difference is 50 - 30 = 20 hours . answer : c"
a = 4 + 3 b = a + 5 c = 120 / b d = c * 5 e = 4 + 3 f = e + 5 g = 120 / f h = g * 4 i = d - h
a ) 1276 , b ) 1200 , c ) 2832 , d ) 1299 , e ) 1320
e
multiply(add(add(30, divide(1200, 30)), sqrt(add(power(30, 2), power(divide(1200, 30), 2)))), 11)
a rectangular farm has to be fenced one long side , one short side and the diagonal . if the cost of fencing is rs . 11 per meter . the area of farm is 1200 m 2 and the short side is 30 m long . how much would the job cost ?
"explanation : l * 30 = 1200 è l = 40 40 + 30 + 50 = 120 120 * 11 = 1320 answer : option e"
a = 1200 / 30 b = 30 + a c = 30 ** 2 d = 1200 / 30 e = d ** 2 f = c + e g = math.sqrt(f) h = b + g i = h * 11
a ) 3 / 2 , b ) 3 / 4 , c ) 8 / 11 , d ) 1 / 2 , e ) 1 / 5
c
divide(multiply(8, 5), add(multiply(8, 5), multiply(5, 3)))
a call center has two teams . each member of team a was able to process 3 / 5 calls as compared to each member of team b . if team a has 5 / 8 as many number of call center agents as team b , what fraction of the total calls was processed by team b ?
"let team b has 8 agents , so team a has 5 agents let each agent of team b picked up 5 calls , so total calls by team b = 40 so , each agent in team a picked up 3 calls , so total calls for team a = 15 fraction for team b = 40 / ( 40 + 15 ) = 8 / 11 = answer = c"
a = 8 * 5 b = 8 * 5 c = 5 * 3 d = b + c e = a / d
a ) $ 10079.44 , b ) r = $ 10815.83 , c ) $ 12652.61 , d ) $ 14232.14 , e ) $ 20598.11
b
multiply(10000, power(add(const_1, divide(divide(3.96, const_100), const_2)), const_4))
jill invests $ 10000 in an account that pays an annual rate of 3.96 % , compounding semi - annually . approximately how much r does she have in her account after two years ?
"ps . i guess one can use simple interest to solve cause the answer choices are quite spread between you can easily arrive at something near 8 % hence b the answer"
a = 3 / 96 b = a / 2 c = 1 + b d = c ** 4 e = 10000 * d
a ) $ 5.625 , b ) $ 1.00 , c ) $ 3.40 , d ) $ 5.25 , e ) $ 6.80
d
subtract(multiply(71.4, divide(add(const_100, 25), const_100)), divide(71.4, divide(subtract(const_100, 15), const_100)))
cindy has her eye on a sundress but thinks it is too expensive . it goes on sale for 15 % less than the original price . before cindy can buy the dress , however , the store raises the new price by 25 % . if the dress cost $ 71.4 after it went on sale for 15 % off , what is the difference between the original price and the final price ?
"0.85 * { original price } = $ 71.4 - - > { original price } = $ 84 . { final price } = $ 71.4 * 1.25 = $ 89.25 . the difference = $ 89.25 - $ 84 = $ 5.25 answer : d ."
a = 100 + 25 b = a / 100 c = 71 * 4 d = 100 - 15 e = d / 100 f = 71 / 4 g = c - f
a ) 2 / 131 , b ) 9 , c ) 10 , d ) 11 , e ) 12
b
subtract(add(const_4, const_4), const_1)
if ( n + 2 ) ! / n ! = 110 , n = ?
"( n + 2 ) ! / n ! = 110 rewrite as : [ ( n + 2 ) ( n + 1 ) ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] / [ ( n ) ( n - 1 ) ( n - 2 ) . . . . ( 3 ) ( 2 ) ( 1 ) ] = 132 cancel out terms : ( n + 2 ) ( n + 1 ) = 110 from here , we might just test the answer choices . since ( 11 ) ( 10 ) = 110 , we can see that n = 9 b"
a = 4 + 4 b = a - 1
a ) 17 , b ) 18 , c ) 34 , d ) 35 , e ) 36
d
divide(35, 1)
( 1 / 5 ) ^ e * ( 1 / 4 ) ^ 18 = 1 / ( 2 ( 10 ) ^ 35 ) . what is e ?
we need to arrive at a common base . - - > ( 5 ) ^ ( - e ) * 2 ^ ( - 36 ) = 2 ^ ( - 36 ) * 5 ^ ( - 35 ) 5 ^ ( - e ) = 5 ^ ( - 35 ) - e = - 35 e = 35 = d
a = 35 / 1
a ) 197 , b ) 210 , c ) 189 , d ) 278 , e ) 268
b
divide(multiply(360, add(const_100, 19)), add(subtract(const_100, 15), add(const_100, 19)))
i bought two books ; for rs . 360 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
"x * ( 85 / 100 ) = ( 360 - x ) 119 / 100 x = 210 answer : b"
a = 100 + 19 b = 360 * a c = 100 - 15 d = 100 + 19 e = c + d f = b / e
a ) 6 only , b ) 12 only , c ) 6 and 12 both , d ) by 18 only , e ) 15 only
c
add(multiply(6, const_100), multiply(2, 6))
if n is a natural number , then ( 6 n 2 + 6 n ) is always divisible by :
"( 6 n ^ 2 + 6 n ) = 6 n ( n + 1 ) , which is always divisible by 6 and 12 both , since n ( n + 1 ) is always even . answer c ) 6 and 12 both ."
a = 6 * 100 b = 2 * 6 c = a + b
a ) 3 , b ) 2 , c ) 1 , d ) 0 , e ) 4
e
subtract(subtract(13, 3), subtract(10, 4))
| 13 - 3 | - | 4 - 10 | = ?
"| 13 - 3 | - | 4 - 10 | = | 10 | - | - 6 | = 10 - 6 = 4 correct answer e"
a = 13 - 3 b = 10 - 4 c = a - b
a ) 450 min , b ) 360 min , c ) 240 min , d ) 306 min , e ) 500 min
a
divide(90, 1)
a fill pipe can fill 1 / 6 of cistern in 90 minutes in how many minutes , it can fill 5 / 6 of the cistern ?
"1 / 6 of the cistern can fill in 90 min 5 / 6 of the cistern can fill in = 90 * 6 * 5 / 6 = 450 min answer is a"
a = 90 / 1
a ) 12.1 % , b ) 12.36 % , c ) 12.94 % , d ) 13.65 % , e ) 14.56 %
b
multiply(const_100, subtract(multiply(add(const_1, divide(6, const_100)), add(const_1, divide(6, const_100))), const_1))
increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by
1.06 * 1.06 * x = 1.1236 * x the answer is b .
a = 6 / 100 b = 1 + a c = 6 / 100 d = 1 + c e = b * d f = e - 1 g = 100 * f
a ) $ 2291.7 , b ) $ 1546.8 , c ) $ 2546.5 , d ) $ 1879.3 , e ) $ 3125.3
a
divide(add(add(add(add(add(1000, 2500), 3100), 3650), 1500), 2000), 6)
the monthly salaries of 6 employees in a company are $ 1000 , $ 2500 , $ 3100 , $ 3650 , $ 1500 , $ 2000 . what is the mean of the salaries of 6 employees .
mean of the salaries = ( $ 1000 + $ 2500 + $ 3100 + $ 3650 + $ 1500 + $ 2000 ) / 6 = 13750 / 6 = $ 2291.7 answer is a
a = 1000 + 2500 b = a + 3100 c = b + 3650 d = c + 1500 e = d + 2000 f = e / 6
a ) 1 : 3 , b ) 36 : 25 , c ) 3 : 2 , d ) 4 : 5 , e ) 20 : 45
b
divide(multiply(multiply(multiply(multiply(8, const_3), multiply(10, const_2)), const_100), 8), multiply(10000, 10))
ravi and sunil are partners in a business . ravi invests rs . 18,000 for 8 months and sunil invested rs . 10000 for 10 months then after one year ratio of their profits will be
"= ( 18000 * 8 ) : ( 10000 * 10 ) = 144000 : 100000 = 36 : 25 answer : b"
a = 8 * 3 b = 10 * 2 c = a * b d = c * 100 e = d * 8 f = 10000 * 10 g = e / f
a ) 1 , b ) 1 / 2 , c ) 2 , d ) - 1 / 2 , e ) - 1
c
divide(3, subtract(5, const_1))
if | x | = 5 x - 3 , then x = ?
"answer : a approach : substituted option a i . e x = 1 . inequality satisfied . c"
a = 5 - 1 b = 3 / a
a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 43 : 134
e
divide(subtract(sqrt(4489), 24), multiply(sqrt(4489), const_2))
the area of a square is 4489 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
"let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4489 a = 67 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 43 : 134 answer : e"
a = math.sqrt(4489) b = a - 24 c = math.sqrt(4489) d = c * 2 e = b / d
a ) 39 , b ) 33 , c ) 26 , d ) 21 , e ) 36
e
subtract(divide(12, divide(2, 3)), 12)
a certain lab experiments with white and brown mice only . in one experiment , 2 / 3 of the mice are white . if there are 12 brown mice in the experiment , how many mice in total are in the experiment ?
"let total number of mice = m number of white mice = 2 / 3 m number of brown mice = 1 / 3 m = 12 = > m = 36 answer e"
a = 2 / 3 b = 12 / a c = b - 12
['a ) 4', 'b ) 5', 'c ) 6', 'd ) 7', 'e ) 2']
e
floor(divide(surface_rectangular_prism(3, 2, 0.5), multiply(const_2, const_3)))
a rectangular cube has sides measuring 3 inches long by 2 inches wide by 0.5 inches high . if the surface area of the rectangle is the same as a cube , what do the sides / walls of the cube measure ? round to the nearest whole number .
first calculate the surface area of the rectangle by multiplying the length and width of the rectangle together , then multiply by 2 to get both sides of the rectangle . this calculates to 12 inches . find the surface area of the sides of the rectangular cube . multiply the height by the length of the rectangle . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 3 inches . then multiply the width of the rectangle by the height . multiply the answer by 2 ( for the 2 sides on the rectangular cube ) . this calculates to 2 inches . add the totals together to get the rectangular cube surface area of 17 inches . since a square cube has 6 sides , divide the surface area by 6 . this calculates to 2.833 inches as the surface area of each side of the cube . the square root of 2.833 is 1.683 . rounding to the nearest whole number that makes each side of the cube measuring 2 inches . the correct answer is ( e ) .
a = surface_rectangular_prism / ( b = 2 * 3 c = math.floor(a, b)
a ) $ 2,250 , b ) $ 2,500 , c ) $ 1,600 , d ) $ 1,250 , e ) $ 1,500
c
floor(divide(subtract(subtract(multiply(500, 7.00), multiply(5.00, 100)), multiply(subtract(500, 100), 3.50)), const_1000))
company c produces toy trucks at a cost of $ 5.00 each for the first 100 trucks and $ 3.50 for each additional truck . if 500 toy trucks were produced by company c and sold for $ 7.00 each , what was company c ’ s gross profit ?
"cost of 500 trucks : ( 100 * 5 ) + ( 400 * 3.5 ) = 500 + 1400 = $ 1900 revenue : 500 * 7 = $ 3500 profit : 3500 - 1900 = $ 1600 option c is correct"
a = 500 * 7 b = 5 * 0 c = a - b d = 500 - 100 e = d * 3 f = c - e g = f / 1000 h = math.floor(g)
a ) 79.55 $ , b ) 80.63 $ , c ) 81.63 $ , d ) 80.27 $ , e ) 83.15 $
d
divide(100, add(divide(add(7, 15), const_100), const_1))
a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 100 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 15 % tip , what is the most their food can cost ?
"let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.15 * 1.07 x = 100 x = 81.27 hence , the correct option is d"
a = 7 + 15 b = a / 100 c = b + 1 d = 100 / c
a ) 1977 , b ) 1893 , c ) 1979 , d ) 1900 , e ) 1300
e
subtract(divide(subtract(multiply(2000, 54), multiply(2000, 21)), 20), 2000)
a garrison of 2000 men has provisions for 54 days . at the end of 21 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
"2000 - - - - 54 2000 - - - - 33 x - - - - - 20 x * 20 = 2000 * 33 x = 3300 2000 - - - - - - - 1300 answer : e"
a = 2000 * 54 b = 2000 * 21 c = a - b d = c / 20 e = d - 2000
a ) 240 , b ) 260 , c ) 220 , d ) 300 , e ) 360
c
add(200, multiply(200, divide(10, const_100)))
a person buys an article at $ 200 . at what price should he sell the article so as to make a profit of 10 % ?
"c 220 cost price = $ 200 profit = 10 % of 200 = $ 20 selling price = cost price + profit = 200 + 20 = 220"
a = 10 / 100 b = 200 * a c = 200 + b
a ) 6 : 1 , b ) 1 : 6 , c ) 2 : 3 , d ) 3 : 2 , e ) 4 : 1
a
divide(multiply(subtract(20, const_1), 1), multiply(4, 1))
200 liters of a mixture contains milk and water in the ratio 4 : 1 . if 20 liters of this mixture be replaced by 20 liters of milk , the ratio of milk to water in the new mixture would be ?
"quantity of milk in 200 liters if mix = 200 * 4 / 5 = 160 liters quantity of milk in 210 liters of new mix = 160 + 20 = 180 liters quantity of water in it = 210 - 180 = 30 liters ratio of milk and water in new mix = 180 : 30 = 6 : 1 answer is a"
a = 20 - 1 b = a * 1 c = 4 * 1 d = b / c
a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m
a
multiply(multiply(66, const_0_2778), 30)
if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ?
"the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a"
a = 66 * const_0_2778 b = a * 30
a ) 96 , b ) 75 , c ) 50 , d ) 25 , e ) 12
c
divide(6, subtract(6.12, floor(6.12)))
when positive integer x is divided by positive integer y , the remainder is 6 . if x / y = 6.12 , what is the value of y ?
"guys , one more simple funda . 5 / 2 = 2.5 now . 5 x 2 = 1 is the remainder 25 / 4 = 6.25 now . 25 x 4 = 1 is the remainder 32 / 5 = 6.4 now . 4 x 5 = 2 is the remainder given x / y = 6.12 and remainder is 6 so . 12 x y = 6 hence y = 50 ans c"
a = math.floor(6, 12) b = 6 - 12 c = 6 / b
a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 20 sec , e ) 25 sec
d
multiply(divide(multiply(2, const_60), add(12, 12)), subtract(16, 12))
two identical trains aa and bb running in opposite direction at same speed tale 2 min to cross each other completely . the number of bogies of aa are increased from 12 to 16 . how much more time would they now require to cross each other ?
total initial bogies is 12 + 12 = 2412 + 12 = 24 additional bogies = 16 â ˆ ’ 12 = 4 24 bogies is 12 + 12 = 24 additional bogies = 16 - 12 = 4 24 bogies take 2 min 2 * 60 / 24 * 4 = 20 sec answer d
a = 2 * const_60 b = 12 + 12 c = a / b d = 16 - 12 e = c * d
a ) 22 , b ) 88 , c ) 90 , d ) 18 , e ) 24
d
multiply(divide(5, const_1000), const_3600)
express 5 mps in kmph ?
"5 * 18 / 5 = 18 kmph answer : d"
a = 5 / 1000 b = a * 3600
a ) rs . 23 , b ) rs . 37 , c ) rs . 45 , d ) rs . 67 , e ) rs . 77
b
subtract(64, multiply(multiply(64, power(add(const_1, divide(1, 2)), const_3)), power(divide(1, 2), const_3)))
a person starting with rs . 64 and making 6 bets , wins 3 times and loses 3 times , the wins and loses occurring in random order . the chance for a win is equal to the chance for a loss . if each wager is for 1 / 2 the money remaining at the time of the bet , then the final result is ?
as the win leads to multiplying the amount by 1.5 and loss leads to multiplying the amount by 0.5 , we will multiply initial amount by 1.5 thrice and by 0.5 thrice ( in any order ) . the overall resultant will remain same . so final amount with the person will be ( in all cases ) : = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = = 64 ( 1.5 ) ( 1.5 ) ( 1.5 ) ( 0.5 ) ( 0.5 ) ( 0.5 ) = rs 2727 hence the final result is : 64 − 27 = 3764 − 27 = 37 : a loss of rs . 37 b
a = 1 / 2 b = 1 + a c = b ** 3 d = 64 * c e = 1 / 2 f = e ** 3 g = d * f h = 64 - g
a ) 1 hr , b ) 2 hrs , c ) 3 hrs , d ) 4 hrs , e ) 5 hrs
c
divide(90, add(25, 5))
a boat can travel with a speed of 25 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 90 km downstream .
"speed downstream = ( 25 + 5 ) km / hr = 30 km / hr . time taken to travel 90 km downstream = 90 / 30 hrs = 3 hrs . answer : c"
a = 25 + 5 b = 90 / a
a ) 16.67 , b ) 30 , c ) 50 , d ) 60 , e ) 70
d
divide(subtract(multiply(divide(40, const_100), 60), multiply(divide(20, const_100), 60)), subtract(divide(40, const_100), divide(20, const_100)))
how many ounces of a 60 % salt solution must be added to 60 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
"let x = ounces of 60 % salt solution to be added . 2 * 60 + . 6 x = . 4 ( 60 + x ) x = 60 answer d"
a = 40 / 100 b = a * 60 c = 20 / 100 d = c * 60 e = b - d f = 40 / 100 g = 20 / 100 h = f - g i = e / h
a ) 322 , b ) 340 , c ) 333 , d ) 327 , e ) 500
d
add(add(multiply(400, divide(50, const_100)), multiply(divide(25, const_100), 100)), multiply(divide(85, const_100), 120))
in a college , 50 % of total 400 arts students are locals . 25 % of students from 100 science students are locals and 85 % of total 120 commerce students are locals . what is the total percentage of locals from arts , science and commerce .
locals from arts = 50 % of 400 = 200 locals from science = 25 % of 100 = 25 locals from commerce = 85 % of 120 = 102 total locals = 200 + 25 + 102 = 327 d
a = 50 / 100 b = 400 * a c = 25 / 100 d = c * 100 e = b + d f = 85 / 100 g = f * 120 h = e + g
a ) 10 , b ) 15 , c ) 16 , d ) 25 , e ) 30
c
multiply(8, divide(12, 6))
12 : 6 seconds : : ? : 8 minutes
"12 * 8 = 6 * x x = 16 answer : c"
a = 12 / 6 b = 8 * a
a ) 9 / 25 , b ) 10 / 25 , c ) 6 / 10 , d ) 2 / 3 , e ) 21 / 25
e
add(multiply(divide(3, 5), divide(3, 5)), add(multiply(divide(3, 5), divide(const_2, 5)), multiply(divide(3, 5), divide(const_2, 5))))
a canoe has two oars , left and right . each oar either works or breaks . the failure or non - failure of each oar is independent of the failure or non - failure of the other . you can still row the canoe with one oar . the probability that the left oar works is 3 / 5 . the probability that the right oar works is also 3 / 5 . what is the probability y that you can still row the canoe ?
"simply look at the question from the other side . what is the probability that you can ’ t row the canoe ? this would be 2 / 5 x 2 / 5 = 4 / 25 . using the idea that the probability of something happening is 1 – the probability that it doesn ’ t happen , you can use the following equation to reach the right answer y : 1 – 4 / 25 = 21 / 25 . answer choice e ."
a = 3 / 5 b = 3 / 5 c = a * b d = 3 / 5 e = 2 / 5 f = d * e g = 3 / 5 h = 2 / 5 i = g * h j = f + i k = c + j
a ) 63 , b ) 93 , c ) 139 , d ) 147 , e ) 188
b
add(multiply(divide(subtract(132, 15), const_3), const_2), 15)
if jake loses 15 pounds , he will weigh twice as much as his sister . together they now weigh 132 pounds . what is jake ’ s present weight , in pounds ?
"lets say j is the weight of jack and s is the wt of his sister . if he loses 15 pounds , he s twice as heavy as his sister . j - 15 = 2 * s also , together they weight 132 pounds j + s = 132 solvong the 2 equation , we get j = 93 pounds ! b"
a = 132 - 15 b = a / 3 c = b * 2 d = c + 15
a ) 4.6 days , b ) 4.78 days , c ) 5.65 days , d ) 3.77 days , e ) 5.75 days
a
inverse(add(inverse(7), inverse(14)))
a and b complete a work in 7 days . a alone can do it in 14 days . if both together can do the work in how many days ?
"1 / 7 + 1 / 14 = 3 / 14 14 / 3 = 4.6 days answer : a"
a = 1/(7) b = 1/(14) c = a + b d = 1/(c)
a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 7 , e ) 1 / 13
e
inverse(add(multiply(4, subtract(4, const_1)), const_1))
a car traveled the first quarter of a certain distance at 4 times the speed it traveled the remaining distance . what proportion of the total time traveled , was the time taken to travel the first quarter of the distance ?
these problems can be solved through algebra or sly number picking . being a big fan of solving problems with numbers , let ' s pick a total distance divisible by 4 ( say 40 ) so we can break it up into quarters , and a speed that can easily be one fourth , say 10 . each quarter is thus 10 kilometers ( or miles or feet or angstroms for all it matters ) , and the runner ' s speed is 10 km / h for the first quarter and 5 / 2 km / h for the remaining quarters . he ' ll take 1 hour to do the first quarter and then 4 hours for the second quarter , 4 hours for the third and 4 hours for the fourth . on total he will take 13 hours to complete this race , of which 1 hour was spent on the first quarter . so 1 / 13 . answer e .
a = 4 - 1 b = 4 * a c = b + 1 d = 1/(c)
a ) 140 , b ) 204 , c ) 180 , d ) 200 , e ) 250
b
divide(multiply(divide(17, multiply(multiply(divide(const_1, const_4), divide(const_1, const_3)), divide(const_2, add(const_2, const_3)))), 40), const_100)
one fourth of one third of two fifth of a number is 17 . what will be 40 % of that number
"explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 17 then x = 17 * 30 = 510 40 % of 510 = 204 answer : option b"
a = 1 / 4 b = 1 / 3 c = a * b d = 2 + 3 e = 2 / d f = c * e g = 17 / f h = g * 40 i = h / 100
a ) 0.0016 , b ) 0.04 , c ) 0.16 , d ) 0.25 , e ) 0.5
b
power(divide(1, 5), 2)
what is the decimal equivalent of ( 1 / 5 ) ^ 2 ?
"( 1 / 5 ) ² = ( 1 / 5 ) ( 1 / 5 ) = 1 / 25 approach # 1 : use long division to divide 25 into 1 to get 1 / 25 = 0.04 b"
a = 1 / 5 b = a ** 2
a ) 4 / 10 , b ) 4 / 9 , c ) 6 / 5 , d ) 9 / 2 , e ) 6 / 4
b
divide(add(multiply(10, const_0_33), multiply(5, divide(const_2, const_3))), add(10, 5))
at an international conference , “ red ” world countries and “ blue ” world countries are the only participants . the ratio of “ red ” world participants to “ blue ” world participants is 10 : 5 . if one - third of “ red ” world participants are left - handed and two - thirds of “ blue ” world participants are left - handed , then what is the fraction of the participants who are left - handed ?
red : blue = 10 : 5 let red = 10 x and blue = 5 x 1 / 3 of red are left handed = > 1 / 3 * 10 x = 10 x / 3 red left handed 2 / 3 of blue are left handed = > 2 / 3 * 5 x = 10 x / 3 blue left handed fraction of participants who are left handed = total left handed / total participants = ( red left handed + blue left handed ) / total participants = ( 10 x / 3 + 10 x / 3 ) / ( 10 x + 5 x ) = 20 / 45 = 4 / 9 answer : b
a = 10 * const_0_33 b = 2 / 3 c = 5 * b d = a + c e = 10 + 5 f = d / e
a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
b
divide(subtract(multiply(5, 900), multiply(5, 700)), subtract(750, 700))
the average salary / head of allthe workers in a workshop is rs . 750 , if the average salary / head of 5 technician is rs . 900 and the average salary / head of the rest is rs . 700 , the total no . of workers in the work - shop is ?
let the total number of workers be y . so sum of salary for all workers = sum of salary of 5 technician + sum of salary for other y - 5 workers . 5 x 900 + 700 ( y - 5 ) = 750 y ⇒ 4500 + 700 y - 3500 = 750 y ⇒ 50 y = 1000 ∴ y = 20 so total number of workers = 20 b
a = 5 * 900 b = 5 * 700 c = a - b d = 750 - 700 e = c / d
a ) 37 , b ) 26 , c ) 30 , d ) 50 , e ) 11
d
divide(add(add(18, 22), multiply(10, 6)), const_2)
the average age of 10 men increases by 6 years when two women are included in place of two men of ages 18 and 22 years . find the average age of the women ?
"explanation : 18 + 22 + 10 * 6 = 100 / 2 = 50 answer : d"
a = 18 + 22 b = 10 * 6 c = a + b d = c / 2
a ) 33888 , b ) 36000 , c ) 27778 , d ) 27772 , e ) 81122
b
subtract(43000, multiply(const_60, const_100))
a started a business with an investment of rs . 70000 and after 3 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 43000 , then the share of b is ?
ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 9 ) = 7 : 36 total profit = rs . 43000 share of b = 36 / 43 ( 43000 ) = rs . 36000 answer : b
a = const_60 * 100 b = 43000 - a
a ) 125 , b ) 150 , c ) 175 , d ) 200 , e ) 225
b
multiply(divide(5, subtract(divide(30, 10), const_1)), 30)
working together , printer a and printer b would finish the task in 10 minutes . printer a alone would finish the task in 30 minutes . how many pages does the task contain if printer b prints 5 pages a minute more than printer a ?
"10 * a + 10 * b = x pages in 10 mins printer a will print = 10 / 30 * x pages = 1 / 3 * x pages thus in 10 mins printer printer b will print x - 1 / 3 * x = 2 / 3 * x pages also it is given that printer b prints 5 more pages per min that printer a . in 10 mins printer b will print 50 more pages than printer a thus 2 / 3 * x - 1 / 3 * x = 50 = > x = 150 pages answer : b"
a = 30 / 10 b = a - 1 c = 5 / b d = c * 30
a ) 300 , b ) 1200 , c ) 1500 , d ) 1800 , e ) 2000
b
multiply(divide(1500, 5), 4)
the ratio of boys to girl in a school is 5 : 4 . if there are 1500 boys in the school , how many girls are there ?
think of the ratio as 5 parts : 4 parts . divide 1500 by 5 to find 1 ` ` part ' ' of the ratio . 1500 / 5 = 300 multiply this by 4 to get 4 ` ` parts ' ' of the ratio . 300 * 4 = 1200 there are 1200 girls in the school . the answer is b
a = 1500 / 5 b = a * 4
a ) 15 mins , b ) 20 mins , c ) 25 mins , d ) 30 mins , e ) none of these
d
divide(multiply(multiply(40, const_3), const_2), add(const_4, const_4))
a tank can be filled by two pipes a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tank from empty state if b is used for the first half time and then a and b fill it together for the other half
"explanation : let the total time be x mins . part filled in first half means in x / 2 = 1 / 40 part filled in second half means in x / 2 = 1 / 60 + 1 / 40 = 1 / 24 total = x / 2 ∗ 1 / 40 + x / 2 ∗ 1 / 24 = 1 = > x / 2 ( 1 / 40 + 1 / 24 ) = 1 = > x / 2 ∗ 1 / 15 = 1 = > x = 30 mins option d"
a = 40 * 3 b = a * 2 c = 4 + 4 d = b / c
a ) 35.2 m 2 , b ) 44 m 2 , c ) 48 m 2 , d ) 36 m 2 , e ) none of these
a
multiply(4, multiply(multiply(multiply(2, divide(22, 7)), divide(1.4, 2)), 2))
the diameter of a garden roller is 1.4 m and it is 2 m long . how much area will it cover in 4 revolutions ? ( use ï € = 22 ⠁ „ 7 )
"required area covered in 5 revolutions = 4 ã — 2 ï € rh = 4 ã — 2 ã — 22 ⠁ „ 7 ã — 0.7 ã — 2 = 35.2 m 2 answer a"
a = 22 / 7 b = 2 * a c = 1 / 4 d = b * c e = d * 2 f = 4 * e
a ) 28 , b ) 12 , c ) 24 , d ) 16 , e ) 19
c
divide(48, const_2)
in a group of ducks and cows , the total number of legs are 48 more than twice the no . of heads . find the total no . of buffaloes .
"let the number of buffaloes be x and the number of ducks be y = > 4 x + 2 y = 2 ( x + y ) + 48 = > 2 x = 48 = > x = 24 c"
a = 48 / 2
a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 2 / 3 , e ) 146 / 25
d
sqrt(divide(multiply(64, const_3), multiply(216, const_2)))
two - third of a positive number and 64 / 216 of its reciprocal are equal . the number is :
"let the number be x . then , 2 / 3 x = 64 / 216 * 1 / x x 2 = 64 / 216 * 3 / 2 = 64 / 144 = 4 / 9 x = 2 / 3 answer : d"
a = 64 * 3 b = 216 * 2 c = a / b d = math.sqrt(c)
a ) 120 , b ) 60 , c ) 30 , d ) 24 , e ) 12
b
divide(12, reminder(24.2, const_1))
when positive integer m is divided by positive integer n , the remainder is 12 . if m / n = 24.2 , what is the value of n ?
n = decimal part of 24.2 * remainder i . e . ( 12 ) hence 0.2 * n = 12 n = 60 . b
a = 12 / reminder
a ) 9 , b ) 28 , c ) 63 , d ) 84 , e ) 252
a
add(21, const_1)
if x and y are positive integers and 12 x = 21 y what is the least possible value of xy ?
"12 x = 21 y = > x / y = 7 / 4 = > 4 x = 7 y 4 ( 3 ) = 7 ( 3 ) = > x * y = 9 a"
a = 21 + 1
a ) 100 m , b ) 180 m , c ) 159 m , d ) 250 m , e ) 152 m
a
subtract(multiply(500, divide(15, divide(15, const_3))), multiply(350, divide(20, divide(15, const_3))))
a train crosses a platform of 350 m in 15 sec , same train crosses another platform of length 500 m in 20 sec . then find the length of the train ?
"length of the train be ‘ x ’ x + 350 / 15 = x + 500 / 20 4 x + 1400 = 3 x + 1500 x = 100 m answer : a"
a = 15 / 3 b = 15 / a c = 500 * b d = 15 / 3 e = 20 / d f = 350 * e g = c - f
a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 1.0 e - 06 , e ) none of these
d
multiply(divide(0.001, 0.001), const_100)
0.001 ã — 0.001 = ?
"0.001 ã — 0.001 = ? or , ? = 0.000001 answer d"
a = 0 / 1 b = a * 100
a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 7
c
divide(add(20, 4), subtract(8, const_2))
if doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product , the number is
solution let the number be x . = then , 2 x + 20 = 8 x – 4 = 6 x = 24 ‹ = › x = 4 . answer c
a = 20 + 4 b = 8 - 2 c = a / b
a ) 2.25 , b ) 3.25 , c ) 10.25 , d ) 5.25 , e ) 6.25
c
subtract(power(3.5, 2), const_2)
x + ( 1 / x ) = 3.5 find x ^ 2 + ( 1 / x ^ 2 )
squaring on both sides ( x + 1 / x ) ^ 2 = 3.5 ^ 2 x ^ 2 + 1 / x ^ 2 = 12.25 - 2 x ^ 2 + 1 / x ^ 2 = 10.25 answer : c
a = 3 ** 5 b = a - 2
a ) 6084 , b ) 3788 , c ) 2077 , d ) 8262 , e ) 1812
d
subtract(add(add(add(multiply(multiply(9, const_100), const_10), multiply(5, const_100)), multiply(2, const_10)), 1), add(add(add(const_1000, multiply(2, const_100)), multiply(5, const_10)), 9))
what is the difference between the largest number and the least number written with the digits 9 , 2 , 1 , 5 ?
"explanation : 1259 9521 - - - - - - - - - - - - 8262 answer : d"
a = 9 * 100 b = a * 10 c = 5 * 100 d = b + c e = 2 * 10 f = d + e g = f + 1 h = 2 * 100 i = 1000 + h j = 5 * 10 k = i + j l = k + 9 m = g - l
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
c
multiply(divide(2, 2), multiply(const_4, 1))
the ratio of flour to water to sugar in a recipe is 7 : 2 : 1 . the ratio in a new recipe calls for a doubling of the ratio of flour to water from the original recipe and a halving of the ratio of flour to sugar . if the new recipe calls for 2 cups of water , how much sugar is required ?
"the ratio of flour to water is 14 : 2 . the ratio of flour to sugar is 3.5 : 1 = 14 : 4 . the new ratio of flour to water to sugar is 14 : 2 : 4 if we need 2 cups of water , then we need 4 cups of sugar . the answer is c ."
a = 2 / 2 b = 4 * 1 c = a * b
a ) 270 m , b ) 245 m , c ) 235 m , d ) 220 m , e ) 240 m
b
subtract(multiply(multiply(45, const_0_2778), 30), 130)
a train , 130 meters long travels at a speed of 45 km / hr crosses a bridge in 30 seconds . the length of the bridge is
explanation : assume the length of the bridge = x meter total distance covered = 130 + x meter total time taken = 30 s speed = total distance covered / total time taken = ( 130 + x ) / 30 m / s = > 45 × ( 10 / 36 ) = ( 130 + x ) / 30 = > 45 × 10 × 30 / 36 = 130 + x = > 45 × 10 × 10 / 12 = 130 + x = > 15 × 10 × 10 / 4 = 130 + x = > 15 × 25 = 130 + x = 375 = > x = 375 - 130 = 245 answer : option b
a = 45 * const_0_2778 b = a * 30 c = b - 130
a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
c
subtract(multiply(multiply(multiply(1258, 6754), 4512), 9783), subtract(multiply(multiply(multiply(1258, 6754), 4512), 9783), add(const_4, const_4)))
the unit digit in the product 1258 * 6754 * 4512 * 9783 is ?
"unit digit in the given product = unit digit in 8 * 4 * 2 * 3 = 2 answer is c"
a = 1258 * 6754 b = a * 4512 c = b * 9783 d = 1258 * 6754 e = d * 4512 f = e * 9783 g = 4 + 4 h = f - g i = c - h
a ) 671.5 , b ) 600 , c ) 672.5 , d ) 673 , e ) 773.5
b
divide(1, divide(add(multiply(const_3600, divide(1, 900)), 2), const_3600))
a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 900 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
"many approaches are possible , one of them : let the distance be 1 kilometer . time to cover this distance at 900 kilometers per hour is 1 / 900 hours = 3,600 / 900 seconds = 4 seconds ; time to cover this distance at regular speed is 900 + 2 = 902 seconds = 902 / 3,600 hours = 1 / 600 hours ; so , we get that to cover 1 kilometer 1 / 600 hours is needed - - > regular speed 600 kilometers per hour ( rate is a reciprocal of time or rate = distance / time ) . answer : b ."
a = 1 / 900 b = 3600 * a c = b + 2 d = c / 3600 e = 1 / d
a ) 50.9 , b ) 52.9 , c ) 51.9 , d ) 53.25 , e ) none of the above
c
divide(add(add(add(multiply(70, 50), multiply(35, 60)), multiply(45, 55)), multiply(42, 45)), add(add(add(70, 35), 45), 42))
a school has 4 section of chemistry in class x having 70 , 35 , 45 and 42 students . the mean marks obtained in chemistry test are 50 , 60 , 55 and 45 respectively for the 4 sections . determine the overall average of marks per student .
"required average marks = 70 ã — 50 + 35 ã — 60 + 45 ã — 55 + 42 ã — 45 / 70 + 35 + 45 + 42 = 3500 + 2100 + 2475 + 1890 / 192 = 9965 ⠁ „ 192 = 51.90 answer c"
a = 70 * 50 b = 35 * 60 c = a + b d = 45 * 55 e = c + d f = 42 * 45 g = e + f h = 70 + 35 i = h + 45 j = i + 42 k = g / j
a ) 2 , b ) 5 , c ) 12 , d ) 8 , e ) 4
e
subtract(multiply(60, divide(40, const_100)), multiply(divide(4, 5), 25))
how much is 40 % of 60 is greater than 4 / 5 of 25 ?
"( 40 / 100 ) * 60 â € “ ( 4 / 5 ) * 25 24 - 20 = 4 answer : e"
a = 40 / 100 b = 60 * a c = 4 / 5 d = c * 25 e = b - d
a ) $ 6512.50 , b ) $ 7512.50 , c ) $ 5512.50 , d ) $ 4512.50 , e ) $ 5250.00
c
add(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), divide(multiply(add(multiply(multiply(multiply(const_3, 2), const_100), const_10), divide(multiply(multiply(multiply(multiply(const_3, 2), const_100), const_10), 5), const_100)), 5), const_100))
today joelle opened an interest - bearing savings account and deposited $ 5,000 . if the annual interest rate is 5 percent compounded interest , and she neither deposits nor withdraws money for exactly 2 years , how much money will she have in the account ?
"interest for 1 st year = 5000 * 5 / 100 = 250 interest for 2 nd year = 5250 * 5 / 100 = 262.50 total = 5000 + 250 + 262.50 = 5512.50 answer : c"
a = 3 * 2 b = a * 100 c = b * 10 d = 3 * 2 e = d * 100 f = e * 10 g = f * 5 h = g / 100 i = c + h j = 3 * 2 k = j * 100 l = k * 10 m = 3 * 2 n = m * 100 o = n * 10 p = o * 5 q = p / 100 r = l + q s = r * 5 t = s / 100 u = i + t
a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
c
divide(multiply(26, 10), const_2)
if the sides of a triangle are 30 cm , 26 cm and 10 cm , what is its area ?
"the triangle with sides 30 cm , 26 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 26 * 10 = 130 cm 2 answer : option c"
a = 26 * 10 b = a / 2
a ) $ 15,202 , b ) $ 15,325 , c ) $ 16,000 , d ) $ 16,225 , e ) $ 17,155
a
multiply(divide(const_3, const_4), const_1000)
a store owner estimates that the average price of type a products will increase by 15 % next year and that the price of type b products will increase by 18 % next year . this year , the total amount paid for type a products was $ 4600 and the total price paid for type b products was $ 8400 . according to the store owner ' s estimate , and assuming the number of products purchased next year remains the same as that of this year , how much will be spent for both products next year ?
"cost of type a products next year = 1.15 * 4600 = 5290 cost of type b products next year = 1.18 * 8400 = 9912 total 5290 + 9912 = 15202 answer : a"
a = 3 / 4 b = a * 1000
a ) 151 , b ) 331 , c ) 511 , d ) 43 , e ) 87
d
multiply(18, divide(subtract(add(multiply(10, 2), 3), 7), subtract(18, 10)))
when positive integer n is divided by positive integer p , the quotient is 18 , with a remainder of 7 . when n is divided by ( p + 2 ) , the quotient is 10 and the remainder is 3 . what is the value of n ?
"n / p = 18 7 / p = 18 p + 7 n / ( p + 2 ) = 10 1 / ( p + 2 ) = 10 p + 20 + 3 solving these two equations we get p = 2 n = 43 answer is d"
a = 10 * 2 b = a + 3 c = b - 7 d = 18 - 10 e = c / d f = 18 * e
a ) 16060 , b ) 14000 , c ) 18000 , d ) 12000 , e ) none of these
d
divide(11400, add(divide(multiply(14, subtract(subtract(9, const_3), const_2)), const_100), add(divide(multiply(6, const_2), const_100), divide(multiply(9, 3), const_100))))
ashok borrowed some money at the rate of 6 % p . a . for the first two years , at the rate of 9 % p . a . for the next 3 years and at the rate of 14 % p . a . for the period beyond 5 years . if he pays a total interest of 11400 / - at the end of 9 years , how much money did he borrow ?
we have , si = p × r × t / 100 ∴ 11400 = p × 6 × 2 / 100 + p × 9 × 3 / 100 + p × 14 × 4 / 100 or , 12 p + 27 p + 56 p = 11400 × 100 or , 95 p = 11400 × 100 ∴ p = 12000 answer d
a = 9 - 3 b = a - 2 c = 14 * b d = c / 100 e = 6 * 2 f = e / 100 g = 9 * 3 h = g / 100 i = f + h j = d + i k = 11400 / j