regisss/math_qa huggingface dataset:
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 7 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 5600 , d ) 6500 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 700 x 600 x 22.5 / 25 x 11.25 x 6 = = 5600 answer : c"
Answer: c
Problem: walking with 4 / 5 of my usual speed , i arrive at the bus stop 7 minutes later than normal . how many minutes does it take to walk to the bus stop at my usual speed ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: let t = usual time = distance / usual speed t + 7 = distance / ( 4 * usual speed / 5 ) = ( 5 * distance ) / ( 4 * usual speed ) = 5 t / 4 t = 28 the answer is e .
Answer: e
Problem: a train 360 m long is running at a speed of 36 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 50 sec , b ) 29 sec , c ) 26 sec , d ) 27 sec , e ) 34 sec
Rationale: "speed = 36 * 5 / 18 = 10 m / sec total distance covered = 360 + 140 = 500 m required time = 500 * 1 / 10 = 50 sec answer : a"
Answer: a
Problem: a primitive village follows a strange custom . they have babies only to have a boy . whenever a boy is born in a family , they stop having babies and whenever a girl is born , they have a baby again and again till a boy is born . the probability of having a boy is same as the probability of having a girl . what will be the proportion of boys to girls in the village after some time ?
Options: a ) 2.1 , b ) 1.3 , c ) 5.1 , d ) 2.3 , e ) 1.1
Rationale: e 1 : 1 ( approx ) explanation : we know that the probability of having a boy or having a girl is same and thus , half of the couples will stop after having a boy child . half of the others will have a girl and will have a baby again . out of those half of the couples , half will have a boy and will stop and half will have a girl again . this will keep on going like this . now , if there are x number of couples , there will be x boys . 1 / 2 have a boy and stop : 0 girls 1 / 4 have a girl , then a boy : x / 4 girls 1 / 8 have 2 girls , then a boy : 2 * x / 8 girls 1 / 16 have 3 girls , then a boy : 3 * x / 16 girls 1 / 32 have 4 girls , then a boy : 4 * x / 32 girls … total : x boys and 1 x 2 x 3 x 4 x – + – + – + — + … = ~ x therefore , the proportion of boys to girls will be extremely close to 1 : 1
Answer: e
Problem: a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 19.36 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 77 , d ) 87 , e ) 44
Rationale: "money collected = ( 19.36 x 100 ) paise = 1936 paise . number of members = square root of 1936 = 44 answer : option e"
Answer: e
Problem: compound x contains elements a and b at an approximate ratio , by weight , of 2 : 10 . approximately how many grams of element b are there in 324 grams of compound x ?
Options: a ) 54 , b ) 162 , c ) 250 , d ) 270 , e ) 322
Rationale: "total number of fractions = 2 + 10 = 12 element b constitutes = 10 out of 12 parts of x so in 324 gms of x have 324 * 10 / 12 = 270 gms of b and 324 - 270 = 54 gms of a . cross check : - a / b = 54 / 270 = 2 / 10 ( as given ) ans d"
Answer: d
Problem: a $ 77.95 lawn chair was sold for $ 59.95 at a special sale . by approximately what percent was the price decreased ?
Options: a ) 15 % , b ) 23 % , c ) 25 % , d ) 60 % , e ) 80 %
Rationale: "listed selling price of chair = 77.95 $ discounted selling price of chair = 59.95 $ discount = 77.95 - 59.95 = 18 $ % decrease in price of chair = ( 18 / 77.95 ) * 100 % = 23 % approx answer b"
Answer: b
Problem: 50 square stone slabs of equal size were needed to cover a floor area of 98 sq . m . find the length of each stone slab ?
Options: a ) 140 cm , b ) 767 cm , c ) 88 cm , d ) 666 cm , e ) 776 cm
Rationale: "area of each slab = 98 / 50 m 2 = 1.96 m 2 length of each slab √ 1.96 = 1.4 m = 140 cm"
Answer: a
Problem: in a division sum , the divisor is 10 times the quotient and 5 times the remainder . if the remainder is 46 , the divident is
Options: a ) 4236 , b ) 4306 , c ) 4336 , d ) 5336 , e ) none
Rationale: "solution divisor = ( 5 × 46 ) = 230 . also . 10 × q = 230 ‹ = › q = 23 . and , r = 46 . dividend = ( 230 × 23 + 46 ) = 5336 . answer d"
Answer: d
Problem: a and b complete a work in 8 days . a alone can do it in 12 days . if both together can do the work in how many days ?
Options: a ) 4.8 days , b ) 3.8 days , c ) 3.65 days , d ) 3.77 days , e ) 5.75 days
Rationale: "1 / 8 + 1 / 12 = 5 / 24 24 / 5 = 4.8 days answer : a"
Answer: a
Problem: gary ’ s gas station serves an average of 14 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary ’ s station serve over the course of a typical week ?
Options: a ) 1,104 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
Rationale: "6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 14 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 14 + 10 ) = 16 * 69 = 1104 answer : a"
Answer: a
Problem: a teacher grades students ’ tests by subtracting twice the number of incorrect responses from the number of correct responses . if student a answers each of the 100 questions on her test and receives a score of 73 , how many questions did student a answer correctly ?
Options: a ) 55 , b ) 60 , c ) 73 , d ) 82 , e ) 91
Rationale: let the number of correct responses be x then the number of incorrect responses = 100 - x according to question x - 2 ( 100 - x ) = 73 ( subtracting twice of incorrect from correct ) 3 x = 273 x = 91 answer : e
Answer: e
Problem: find the value of 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) … … … … . ( 1 + 1 / 120 ) ] is
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: 3 / 11 × [ ( 1 + 1 / 3 ) ( 1 + 1 / 4 ) . . . . . . . ( 1 + 1 / 120 ) ] 3 / 11 × [ 4 / 3 + 5 / 4 × . . . . . . . . 121 / 120 ] 3 / 11 × 4 / 3 × 5 / 4 × . . . . 121 / 120 121 / 11 = 11 . a
Answer: a
Problem: 10 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 5 / 2 , b ) 2 √ 5 , c ) 5 , d ) 4 √ 2 , e ) none of these
Rationale: "area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 10 = > x / 360 * 2 * pi * r + 2 r = 20 = > 2 a / r + 2 r = 10 or 2 a + 2 r ^ 2 = 10 r = > a = r 5 - r ^ 2 = r 5 - r ^ 2 we will now max using derivations i . e 5 - 2 r = 0 r = 5 / 2 a"
Answer: a
Problem: what is the sum of all possible 3 - digit numbers that can be constructed using the digits 2 , 3 , and 4 if each digit can be used only once in each number ?
Options: a ) 1776 , b ) 1887 , c ) 1998 , d ) 2332 , e ) 2554
Rationale: "there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 222 ) + 2 ( 333 ) + 2 ( 444 ) = 1998 the answer is c ."
Answer: c
Problem: solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 8 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 30 % , b ) 33 1 / 3 % , c ) 37 1 / 2 % , d ) 40 % , e ) 50 %
Rationale: "initial solution = > 8 kg ( x : w : : 2.4 : 5.6 ) after evaporation initial solution = > 6 kg ( x : w : : 2.4 : 3.6 ) new solution = > 2 kg ( x : w : : 0.6 : 1.4 ) mixing ( initial solution + new solution ) = > 6 kg ( 2.4 : 3.6 ) + 2 kg ( 0.6 : 1.4 ) = = 8 kg [ ( 2.4 + 0.6 ) : ( 3.6 + 1.4 ) ] = 8 kg ( x : water : : 3 kg : 5 kg ) hence % of x = 3 / 8 = 37.5 % answer : c"
Answer: c
Problem: tickets to a certain concert sell for $ 20 each . the first 10 people to show up at the ticket booth received a 40 % discount , and the next 20 received a 15 % discount . if 48 people bought tickets to the concert , what was the total revenue from ticket sales ?
Options: a ) $ 600 , b ) $ 820 , c ) $ 850 , d ) $ 980 , e ) $ 1,140
Rationale: "price of 1 ticket = 20 $ revenue generated from sales of first 10 tickets = 10 * ( 60 / 100 * 20 ) = 10 * 12 = 120 revenue generated from sales of next 20 tickets = 20 * ( 85 / 100 * 20 ) = 20 * 17 = 340 revenue generated from sales of last 18 tickets = 20 * 18 = 360 revenue generated from sales of 48 tickets = 120 + 340 + 360 = 820 $ answer b"
Answer: b
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 200 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 2888 , b ) 2669 , c ) 2500 , d ) 2762 , e ) 8227
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 200 b capital = 15000 * 1 / 6 = 2500 answer : c"
Answer: c
Problem: if paint costs $ 3.20 per quart , and a quart covers 60 square feet , how much will it cost to paint the outside of a cube 10 feet on each edge ?
Options: a ) $ 1.60 , b ) $ 32.00 , c ) $ 96.00 , d ) $ 108.00 , e ) $ 196.00
Rationale: "total surface area = 6 a ^ 2 = 6 * 10 * 10 = 600 each quart covers 20 sqr ft thus total number of quarts = 600 / 60 = 10 cost will be 10 * 3.2 = $ 32 ans : b"
Answer: b
Problem: how many even number in the range between 10 to 160 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 51 , d ) 63 , e ) 76
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 160 using ap formula , we can say 160 = 10 + ( n - 1 ) * 2 or n = 76 . for 6 , 12,18 , . . . 156 using ap formula , we can say 156 = 12 + ( n - 1 ) * 6 or n = 25 . hence , only divisible by 2 but not 3 = 76 - 25 = 51 . hence , answer c"
Answer: c
Problem: the delhi express runs @ 144 kilometers per hours and it reaches destination 20 minute ahead of schedule . if it averages 100 km / hour , it reaches 24 minute behind schedule . what is the average speed it should maintain in order to reach the destination on schedule ?
Options: a ) 250 , b ) 240 , c ) 230 , d ) 245 , e ) 235
Rationale: if the destination is d kilometer and the speed in order to reach on schedule is s km / hour , the time taken to reach on schedule is d / s hours thus we get two equations : d / 144 = d / s - 1 / 3 and d / 100 = d / s + 2 / 5 and subtracting the first equation from the second we get : 44 d / 14400 = 11 / 15 thus d = 14400 x 11 / 44 x 15 = 240 answer : b
Answer: b
Problem: at a florist shop on a certain day , all corsages sold for either $ 40 or $ 45 . if 8 of the corsages that sold for $ 30 had instead sold for $ 20 , then the store ' s revenue from corsages that day would have been reduced by 20 percent . what was the store ' s actual revenue from corsages that day ?
Options: a ) $ 200 , b ) $ 400 , c ) $ 600 , d ) $ 800 , e ) $ 1000
Rationale: "i am doing it elaborately , hope it will help you . let , no . of corsages @ $ 40 = x , no . of corsages @ $ 45 = y and revenue = r so , 40 x + 45 y = r . . . . . . . . . ( 1 ) now , given the situation , 40 ( x + 8 ) + 45 ( y - 8 ) = r - . 2 r = > 40 x + 320 + 45 y - 360 = . 8 r = > 40 x + 45 y = . 8 r + 40 . . . . . . . . . . . . ( 2 ) so , r = . 8 r + 40 = > r = 200 the answer is a ."
Answer: a
Problem: when a laptop is sold for rs . 27000 , the owner loses 10 % . at what price must that laptop be sold in order to gain 10 % ?
Options: a ) 33,000 , b ) 34,000 , c ) 35,000 , d ) 36,000 , e ) 37,000
Rationale: "90 : 27000 = 110 : x x = ( 27000 x 110 ) / 90 = 33000 . hence , s . p . = rs . 33,000 . answer : option a"
Answer: a
Problem: if the radius of a circle is increased by 50 % then the area is increased by :
Options: a ) 44 % , b ) 125 % , c ) 144 % , d ) 40 % , e ) none of the above
Rationale: "initially a = pi * r 2 now r 2 = 150 / 100 r then area = pi * ( 150 r / 100 ) 2 area = 225 r / 100 that is area increases from 100 to 225 = increase in area = 125 % answer : b"
Answer: b
Problem: a certain company reported that the revenue on sales increased 40 % from 2000 to 2003 , and increased 60 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 50 % , b ) 40 % , c ) 14 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 140 and and in 2005 160 , so from 2003 to 2005 it increased by ( 160 - 140 ) / 140 = 20 / 140 = 1 / 7 = ~ 14 % . answer : c"
Answer: c
Problem: the difference between the compound interest compounded annually and simple interest for 2 years at 20 % per annum is rs . 144 . find the principal ?
Options: a ) 3629 , b ) 3608 , c ) 3600 , d ) 3613 , e ) 6192
Rationale: "p = 144 ( 100 / 5 ) 2 = > p = 3600 answer : c"
Answer: c
Problem: if xy > 0 , 1 / x + 1 / y = 6 , and 1 / xy = 5 , then ( x + y ) / 6 = ?
Options: a ) 1 / 25 , b ) 1 / 6 , c ) 1 / 5 , d ) 5 , e ) 6
Rationale: "( 1 / x + 1 / y ) = 6 canbe solved as { ( x + y ) / xy } = 5 . substituting for 1 / xy = 5 , we get x + y = 6 / 5 = = > ( x + y ) / 6 = 6 / ( 5 * 6 ) = 1 / 5 . c"
Answer: c
Problem: a train 100 meters long completely crosses a 300 meters long bridge in 12 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 76 kmph , c ) 120 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 12 = 400 / 12 * 18 / 5 = 120 answer : c"
Answer: c
Problem: a reduction of 30 % in the price of salt enables a lady to obtain 10 kgs more for rs . 200 , find the original price per kg ?
Options: a ) 7.5 , b ) 8.99 , c ) 8.0 , d ) 9.2 , e ) 8.57
Rationale: "answer : 200 * ( 30 / 100 ) = 60 - - - 10 ? - - - 1 = > rs . 6 200 - - - 140 ? - - - 6 = > rs . 8.57 . answer : e"
Answer: e
Problem: if a is a positive integer and 10 ^ a – 74 in decimal notation has digits whose sum is 440 , what is the value of a ?
Options: a ) 40 , b ) 44 , c ) 45 , d ) 46 , e ) 50
Rationale: answer e = 50 we have ( 10 ^ a ) - 74 , where the sum of the digits is 440 . 100 - 74 = 26 , so we already have 2 + 6 = 8 from the 440 . because we have a power of 10 , we will have numbers like 100 , 1000 , 10000 and so on . this minus 74 rests 26 and a lot of 9 s . e . g : 1000 - 74 = 9926 . so dividing the 432 / 9 = 48 , that ` s the number of 9 s . and we have 2 other numbers ( 2 and 6 ) wich were 00 before the subtraction . so we have 48 + 2 as an a = 50
Answer: e
Problem: if x = 7 and y = − 2 , what is the value of ( x − 2 y ) ^ y ?
Options: a ) − 100 , b ) 0.001 , c ) 0.25 , d ) 4 , e ) 8
Rationale: quickly we can spot that answer is neither integer nor negative . eliminate a , de by inversing and squaring 0.001 answer : b
Answer: b
Problem: a distributor sells a product through an on - line store , which take a commission of 20 % of the price set by the distributor . the distributor obtains the product from a producer at the price of $ 15 per item . what is the price that the buyer observers on - line if the distributor wants to maintain a 10 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 20 , d ) 22.5 , e ) 27
Rationale: producer price = $ 15 ; the distributor wants to maintain a 20 % profit on the cost of the item , thus he must get $ 15 * 1.2 = $ 18 after the store takes a commission of 10 % of the final price - - > ( final price ) * 0.9 = $ 18 - - > ( final price ) = $ 20 . answer : c .
Answer: c
Problem: if integer k is equal to the sum of all even multiples of 5 between 300 and 610 , what is the greatest prime factor of k ?
Options: a ) 32 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 10 between 300 and 610 . using arithmetic progression to find n : 610 = 300 + ( n - 1 ) 10 310 + 10 = 10 n 320 = 10 n = > n = 32 the sum would be : 32 * mean mean = [ 610 + 300 ] / 2 = 455 32 * 455 a"
Answer: a
Problem: one ton has 2200 pounds , and one pound has 16 ounces . how many packets containing wheat weighing 16 pounds and 4 ounces each would totally fill a gunny bag of capacity 13 tons ?
Options: a ) 1760 , b ) 1700 , c ) 2350 , d ) 2500 , e ) 8000
Rationale: 16 pounds and 4 ounces = 16 * 16 + 4 = 260 ounces . 13 tons = 13 * 2200 pound = 13 * 2200 * 16 ounces . hence the answer is ( 13 * 2200 * 16 ) / 260 = 1760 . answer : a .
Answer: a
Problem: find the greatest number which leaves the same remainder when it divides 25 , 62 and 105 .
Options: a ) 1 , b ) 8 , c ) 12 , d ) 16 , e ) none of these
Rationale: "105 - 62 = 43 62 - 25 = 37 105 - 25 = 80 the h . c . f of 37 , 43 and 80 is 1 . answer : a"
Answer: a
Problem: if 16 ^ y = 2 ^ 16 , what is y ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 10 , e ) 12
Rationale: "16 ^ y = 2 ^ 4 y = 2 ^ 16 4 y = 16 y = 4 the answer is b ."
Answer: b
Problem: an automobile parts supplier charges $ 25 per package of gaskets . when a customer orders more than 10 packages of gaskets , the supplier charges 4 / 5 the price for each package in excess of 10 . during a certain week , the supplier sold 60 packages of gaskets . if 25 percent of the gaskets went to company x , 15 percent to company y , and the rest to company z , what was the total amount , in dollars , that the parts supplier received in payment for the gaskets ?
Options: a ) 1305 , b ) 1545 , c ) 1375 , d ) 1345 , e ) 1455
Rationale: "$ 25 per packet of gasket in case a customer orders less than 10 in case a customer orders > 10 price per gasket = 25 * 4 / 5 = 20 a certain week the supplier sold 60 gasket 1 . he sold 25 % of the gaskets to x = 15 gaskets = 25 * 10 + 20 * 5 = 250 + 100 = 350 2 . he sold 15 % of the gaskets to y = 9 gaskets = 25 * 9 = 225 3 . he sold remaining 60 % to z = 36 gaskets = 25 * 10 = 250 + 20 * 26 = 770 thus , total money earned 350 + 225 + 770 = 1345 answer is d"
Answer: d
Problem: two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 20 % and 20 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 23 % , e ) can not be determined
Rationale: answer : a .
Answer: a
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 5 years ?
Options: a ) 3277 , b ) 2977 , c ) 9492 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 5 answer : c"
Answer: c
Problem: what percent of 16 is 16 percent of 1 ?
Options: a ) 0.001 , b ) 1 , c ) 0.1 , d ) 100 , e ) 101 .
Rationale: "16 % of 1 = ( 16 / 100 ) * 1 = 16 / 100 to determine what percentage of 16 this is : [ 16 ] [ / 100 * 16 ] * 100 = 1 % ans : b"
Answer: b
Problem: what is the length of a bridge ( in meters ) , which a train 148 meters long and travelling at 45 km / h can cross in 30 seconds ?
Options: a ) 211 , b ) 219 , c ) 227 , d ) 235 , e ) 243
Rationale: "speed = 45 km / h = 45000 m / 3600 s = 25 / 2 m / s in 30 seconds , the train can travel 25 / 2 * 30 = 375 meters 375 = length of train + length of bridge length of bridge = 375 - 148 = 227 meters the answer is c ."
Answer: c
Problem: at a loading dock , each worker on the night crew loaded 3 / 4 as many boxes as each worker on the day crew . if the night crew has 4 / 7 as many workers as the day crew , what fraction of all the boxes loaded by the two crews did the day crew load ?
Options: a ) 7 / 10 , b ) 2 / 5 , c ) 3 / 5 , d ) 4 / 5 , e ) 5 / 8
Rationale: "method : x = no . of boxes loaded by day crew . boxes by night crew = 3 / 4 * 4 / 7 x = 3 / 7 x % loaded by day crew = x / ( x + 3 / 7 x ) = 7 / 10 answer a"
Answer: a
Problem: in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 11 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 105 % , c ) 88 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,11 = 11 / 100 x = 80 * 11 / 100 x = 8.8 8.8 / 10 = 0.88 = 88 % , answer c"
Answer: c
Problem: in the standard formulation of a flavored drink the ratio by volume of flavoring to corn syrup to water is 1 : 12 : 30 . in the ` ` sport ' ' formulation , the ratio of flavoring to corn syrup is 3 times as great as in the standard formulation , and the ratio of flavoring to water is half that of the standard formulation . if a large bottle of the ` ` sport ' ' formulation contains 3 ounces of corn syrup , how many ounces of water does it contain ?
Options: a ) 45 , b ) 50 , c ) 55 , d ) 60 , e ) 63
Rationale: f : c : w 1 : 12 : 30 sport version : f : c 3 : 12 f : w 1 : 60 or 3 : 180 so c : f : w = 12 : 3 : 180 c / w = 12 / 180 = 3 ounces / x ounces x = 3 * 180 / 12 = 45 ounces of water answer : a
Answer: a
Problem: one year before the age of pramila was 4 times than her daughter swati . after 6 years the age of pramila will be 24 year greater than the age of swati . then calculate the ratio of ages of pramila and swati ?
Options: a ) 5 : 3 , b ) 16 : 3 , c ) 11 : 3 , d ) 11 : 5 , e ) 9 : 4
Rationale: let 1 year before age of swati = x years and age of pramila = 4 x years swati present age = ( x + 1 ) and pramila present age = ( 4 x + 1 ) after 6 year age of swati = ( x + 7 ) , age of pramila = ( 4 x + 7 ) so , 4 x + 7 - ( x + 7 ) = 243 x = 24 , x = 8 . ratio = ( 4 x + 7 ) : ( x + 1 ) = 33 : 9 = 11 : 3 answer c
Answer: c
Problem: somehow or other i got talked into buying something on the installment plan . i ' m notsure i got a good deal . the payments to date , according to my checkbook , have reached rs . 96 . the second year cost rs . 2.00 more than the first year ; the third year cost rs . 3.00 more thanthe second ; and the fourth year cost me rs . 4.00 more than the third . what were mypayments the first year ?
Options: a ) 18 , b ) 20 , c ) 22 , d ) 24 , e ) 26
Rationale: let payments for the first year = x given , x + x + 2 + x + 5 + x + 9 = 96 4 x + 16 = 96 x = 20 answer : b
Answer: b
Problem: if x is a sum of all even integers on the interval 23 . . . 65 and y is their number , what is the gcd ( x , y ) ?
Options: a ) 1 , b ) 21 , c ) 26 , d ) 52 , e ) 1014
Rationale: "x = 24 + 16 + . . . + 64 = ( largest + smallest ) / 2 * ( # of terms ) = ( 24 + 64 ) / 2 * 21 = 44 * 16 . gcd of 21 and 44 * 21 is 21 . answer : b ."
Answer: b
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability w that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes w = 15 / 36 . answer : c ."
Answer: c
Problem: the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 750 resolutions ?
Options: a ) 277 m , b ) 704 m , c ) 278 m , d ) 288 m , e ) 1056 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 750 resolutions . = 750 * 2 * 22 / 7 * 22.4 = 105600 cm = 1056 m answer : e"
Answer: e
Problem: 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 450 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 370 , b ) 365 , c ) 360 , d ) 380 , e ) 350
Rationale: "c 450 * t = 1 km = > t = 1 / 450 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 450 + 2 / 3600 ) = 1 = > v = 360 km / h"
Answer: c
Problem: a sum of rs . 2795 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1720 , d ) 2795 , e ) 6386
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2795 - x ) * 3 * 5 ) / 100 24 x / 100 = 41925 / 100 - 15 x / 100 39 x = 41925 = > x = 1075 second sum = 2795 – 1075 = 1720 answer : c"
Answer: c
Problem: in one year , the population , of a village increased by 25 % and in the next year , it decreased by 25 % . if at the end of 2 nd year , the population was 18750 , what was it in the beginning ?
Options: a ) 7787 , b ) 8000 , c ) 1988 , d ) 1277 , e ) 20000
Rationale: "x * 125 / 100 * 75 / 100 = 18750 x * 0.9375 = 18750 x = 18750 / 0.9375 = > 20000 answer : e"
Answer: e
Problem: a small pool filled only with water will require an additional 300 gallons of water in order to be filled to 85 % of its capacity . if pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30 % , what is the total capacity of the pool in gallons ?
Options: a ) 1000 , b ) 1250 , c ) 1300 , d ) 1529.41 , e ) 1625
Rationale: "300 gallons of water increases capacity by 30 % that means 30 % is 300 gallons , so 100 % would be = 300 * 100 / 30 = 1000 gallons now 1000 + 300 gallons is 85 % capacity of tank . so 100 % capacity would be = 1300 * 100 / 85 = 1529.41 d is the answer"
Answer: d
Problem: if 85 % of 3 / 5 of a number is 36 , then the number is ?
Options: a ) 80 , b ) 100 , c ) 70.5 , d ) 90 , e ) none of these
Rationale: "let the number be x . then 85 % of 3 / 5 of x = 36 85 / 100 * 3 / 5 * x = 36 x = ( 36 * 100 / 51 ) = 70.5 required number = 70.5 . correct option : c"
Answer: c
Problem: a jar contains a mixture of ab in the ratio 3 : 2 . when 10 l of mixture is replaced with liquid b , ratio becomes 2 : 3 . how many liters of liquid a was present in mixture initially .
Options: a ) 18 , b ) 15 , c ) 16 , d ) 20 , e ) 25
Rationale: "10 litres of mixture that is replaced will contain 6 litres of a and 4 litres of b ( as a : b = 3 : 2 ) let the initial volume of the mixture be 3 k + 2 k = 5 k so by condition , [ 3 k - 6 ] / [ 2 k - 4 + 10 ] = 2 / 3 9 k - 18 = 4 k - 8 + 20 5 k = 12 + 18 k = 6 solve for k which is k = 6 so initial volume of liquid a = 3 k = 18 litres answer : a"
Answer: a
Problem: √ 3 percent of 3 √ 3 =
Options: a ) 5.2 , b ) 1.0 , c ) 0.1 , d ) 2.0 , e ) 5.0
Rationale: "the other solutions are great , but here ' s one more approach . first , we scan the answer choices to see that they are quite spread apart . this means we can also use someapproximation all test - takers must memorize the following approximations : √ 2 ≈ 1.4 √ 3 ≈ 1.7 so , √ 3 percent of 3 √ 3 ≈ 1.7 percent of ( 3 ) ( 1.7 ) ≈ ( 1.7 / 100 ) ( 5.1 ) ≈ 8.67 / 100 ≈ 0.08 check the answer choices to see that c is the only answer that ' s close . answer : c"
Answer: c
Problem: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 40 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 10 minutes ?
Options: a ) 20 , b ) 50 , c ) 60 , d ) 40 , e ) 30
Rationale: "machine b produces 100 part in 40 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 40 / 2 = 20 minutes . now , machine a produces 100 parts in 20 minutes which is 100 / 20 = 5 parts / minute . 5 parts x a total of 10 minutes = 50 b"
Answer: b
Problem: an order was placed for the supply of a carper whose length and breadth were in the ratio of 3 : 2 . subsequently , the dimensions of the carpet were altered such that its length and breadth were in the ratio 7 : 3 but were was no change in its parameter . find the ratio of the areas of the carpets in both the cases ?
Options: a ) 8 : 6 , b ) 8 : 7 , c ) 8 : 9 , d ) 8 : 4 , e ) 8 : 1
Rationale: let the length and breadth of the carpet in the first case be 3 x units and 2 x units respectively . let the dimensions of the carpet in the second case be 7 y , 3 y units respectively . from the data , . 2 ( 3 x + 2 x ) = 2 ( 7 y + 3 y ) = > 5 x = 10 y = > x = 2 y required ratio of the areas of the carpet in both the cases = 3 x * 2 x : 7 y : 3 y = 6 x 2 : 21 y 2 = 6 * ( 2 y ) 2 : 21 y 2 = 6 * 4 y 2 : 21 y 2 = 8 : 7 answer : b
Answer: b
Problem: of the diplomats who attended a summit conference : 20 spoke french , 32 did not speak english and 20 % of the diplomats spoke neither french nor english . if 10 % of the diplomats spoke both french and english , then how many diplomats attended the conference ?
Options: a ) 70 , b ) 96 , c ) 108 , d ) 120 , e ) 150
Rationale: 2 x 2 matrix will be the easiest way to calculate this . text in black : given statements text in red : calculated values thus d = 120 is the correct answer
Answer: d
Problem: a man spends 2 / 5 of his salary on house rent , 3 / 10 of his salary on food and 1 / 8 of his salary on conveyance . if he has $ 1400 left with him , find his expenditure on food .
Options: a ) $ 400 , b ) $ 1400 , c ) $ 3400 , d ) $ 2400 , e ) $ 4400
Rationale: "part of salary left = 1 - ( 2 / 5 + 3 / 10 + 1 / 8 ) = 7 / 40 let the monthly salary be $ x then ( 7 / 40 ) of x = 1400 x = 8000 expenditure on food = $ 2400 option d"
Answer: d
Problem: in the fifth grade at parkway elementary school there are 420 students . 312 students are boys and 250 students are playing soccer . 82 % of the students that play soccer are boys . how many girl student are in parkway that is not playing soccer ?
Options: a ) 63 . , b ) 73 . , c ) 81 , d ) 91 , e ) 108
Rationale: "total students = 420 boys = 312 , girls = 108 total playing soccer = 250 82 % of 250 = 205 are boys who play soccer . girls who play soccer = 45 . total girls who do not play soccer = 108 - 45 = 63 . correct option : a"
Answer: a
Problem: x , a , z , and b are single digit positive integers . x = 1 / 5 a . z = 1 / 5 b . ( 10 a + b ) – ( 10 x + z ) could not equal
Options: a ) 36 , b ) 33 , c ) 44 , d ) 64 , e ) 56
Rationale: a = 5 x , b = 5 z therefore ( 5 x * 10 + 5 z ) - ( 10 x + z ) = ( 5 - 1 ) ( 10 x + z ) = . ( 10 x + z ) number should be divisible by 4 b
Answer: b
Problem: how much water should be added to 10 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 27 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 10 + x ) ) ) 2 = 5 % * ( 10 + x ) - - - - - - - - > x = 30 answer : c"
Answer: c
Problem: on a game show , a contestant is given 3 keys , each of which opens exactly one of 3 identical boxes . the first box contains $ 5 , the second $ 500 , and the third $ 5000 . the contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it . what is the probability that a contestant will win more than $ 5000 ?
Options: a ) 1 / 9 , b ) 4 / 6 , c ) 3 / 6 , d ) 1 / 2 , e ) 1 / 6
Rationale: let ' s call the boxes that contain $ 5 , $ 500 , and $ 5000 , respectively , box a , box b , box c . these are opened , respectively , by key a , key b , and key c . we want to know the probability of winning more than $ 5000 . notice that if the distribution of keys is : box a = key b box b = key a box c = key c then the contestant wins exactly $ 5000 , not more than $ 5000 . the only configuration that leads to winning more than $ 1000 is : box a = key a box b = key b box c = key c i . e . , getting all three keys correct . that ' s the only way to be more than $ 5000 . so , really , the question can be rephrased : what is the probability of guessing the order of keys so that each key matches the correct box ? well , for a set of three items , the number of possible permutations is 3 ! = 3 * 2 * 1 = 6 . of those 6 possible permutations , only one of them leads to all three keys being paired with the right box . so , the answer is probability = 1 / 6 answer : e
Answer: e
Problem: sakshi can do a piece of work in 20 days . tanya is 25 % more efficient than sakshi . the number of days taken by tanya to do the same piece of work :
Options: a ) 15 , b ) 16 , c ) 18 , d ) 25 , e ) 10
Rationale: "solution ratio of times taken by sakshi and tanya = 125 : 100 = 5 : 4 . suppose tanya taken x days to do the work . 5 : 4 : : 20 : x ⇒ x = ( 20 x 4 / 5 ) ⇒ x = 16 days . hence , tanya takes 16 days is complete the work . answer b"
Answer: b
Problem: there are 18 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 987 , b ) 177 , c ) 357 , d ) 267 , e ) 380
Rationale: "the total number of stations = 20 from 20 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in ² ⁰ p ₂ ways . ² ⁰ p ₂ = 20 * 19 = 380 . answer : e"
Answer: e
Problem: the perimeter of a square is 28 cm . what is the perimeter of a circle whose radius is equal to the side of the square ? ( in cm )
Options: a ) 14
b ) 28
c ) 42
d ) 44
e ) 56
Rationale: side of the square = 28 / 4 = 7 diameter of the circle = 7 x 2 = 14 perimeter of the circle = ï € xd = ( 22 / 7 ) x 14 = 44 cm answer : d
Answer: d
Problem: a boat traveled upstream 90 miles at an average speed of ( v - 3 ) miles per hour and then traveled the same distance downstream at an average speed of ( v + 3 ) miles per hour . if the trip upstream took a half hour longer than the trip downstream , then how many hours did it take the boat to travel downstream ?
Options: a ) 2.5 , b ) 2.4 , c ) 2.3 , d ) 2.2 , e ) 2.1
Rationale: 90 / ( v - 3 ) = 90 / ( v + 3 ) + 0.5 hours = > 90 ( v + 3 ) = ( v - 3 ) [ 90 + 0.5 v + 1.5 ] 90 v + 270 = ( v - 3 ) ( 183 / 2 + v / 2 ) 180 v + 540 = ( v - 3 ) ( 183 + v ) = 183 v - 549 + v ^ 2 - 3 v v ^ 2 - 1089 = 0 = > v = 33 miles / hr = > time downstream = 90 / 36 = 30 / 12 = 5 / 2 = 2.5 hrs answer a 2.5
Answer: a
Problem: in a certain country 1 / 3 of 4 = 6 . assuming the same proportion , what would be the value of 1 / 6 of 20 ?
Options: a ) 14 , b ) 15 , c ) 20 , d ) 22 , e ) 25
Rationale: "b 15"
Answer: b
Problem: working together , a and b can do a job in 6 days . b and c can do the same job in 10 days , while c and a can do it in 7.5 days . how long will it take if all a , b and c work together to complete the job ?
Options: a ) 4 days , b ) 5 days , c ) 8 days , d ) 9 days , e ) 10 days
Rationale: a and b 1 day work = 1 / 6 b and c 1 day work = 1 / 10 c and a 1 day work = 1 / 7.5 a , b , c 1 day work = ( 1 / 6 + 1 / 10 + 1 / 7.5 ) * 1 / 2 = 1 / 5 so a . b . c completes work in 5 days answer : b
Answer: b
Problem: from below option 49 is divisible by which one ?
Options: a ) a ) 2 , b ) b ) 3 , c ) c ) 4 , d ) d ) 5 , e ) e ) 7
Rationale: 49 / 7 = 7 e
Answer: e
Problem: ramesh purchased a refrigerator for rs . 12500 after getting a discount of 20 % on the labelled price . he spent rs . 125 on transport and rs . 250 on installation . at what price should it be sold so that the profit earned would be 12 % if no discount was offered ?
Options: a ) 17608 , b ) 17920 , c ) 17604 , d ) 17600 , e ) 117601
Rationale: "price at which the tv set is bought = rs . 12,500 discount offered = 20 % marked price = 12500 * 100 / 80 = rs . 15625 the total amount spent on transport and installation = 125 + 250 = rs . 375 \ total price of tv set = 15625 + 375 = rs . 16000 the price at which the tv should be sold to get a profit of 10 % if no discount was offered = 16000 * 112 / 100 = rs . 17920 . answer : b"
Answer: b
Problem: if x / ( 12 p ) is an even prime number , where x is a positive integer and p is a prime number , what is the least value of x ?
Options: a ) 22 , b ) 33 , c ) 44 , d ) 48 , e ) 99
Rationale: x / ( 12 p ) = even prime number x = even prime number * 11 p least value of x = lowest even prime number * 12 * lowest value of p = 2 * 12 * 2 = 48 answer d
Answer: d
Problem: there are 8 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 10 , b ) 30 , c ) 28 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 8 c 2 = 8 * 7 / 2 = 28 so option c is correct"
Answer: c
Problem: a driver just filled the car ' s gas tank with 45 liters of gasohol , a mixture consisting of 5 % ethanol and 95 % gasoline . if the car runs best on a mixture consisting of 10 % ethanol and 90 % gasoline , how many liters of ethanol must be added into the gas tank for the car to achieve optimum performance ?
Options: a ) 1.3 , b ) 1.7 , c ) 2.1 , d ) 2.5 , e ) 2.9
Rationale: "let x be the number of liters of ethanol added to the gas tank . 0.05 ( 45 ) + x = 0.1 ( 45 + x ) 0.9 x = 4.5 - 2.25 = 2.25 x = 2.5 liters the answer is d ."
Answer: d
Problem: think of a number , divide it by 5 and add 23 to it . the result is 42 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 267 , e ) 95
Rationale: "explanation : 42 - 23 = 19 19 x 5 = 95 answer : e"
Answer: e
Problem: ms . lopez deposits $ 100 in an account that pays 20 % interest , compounded semiannually . how much money will there be in the account at the end of one year ?
Options: a ) $ 118.00 , b ) $ 120.00 , c ) $ 121.00 , d ) $ 122.00 , e ) $ 140.00
Rationale: "et me explain the concept for those who are not familiar with compounded semi annually / quarterly etc . . it basically means , here , that the interest will be paid twice , after 6 months and at the end of year . . so twice . . but interest is 20 % , which will get distributed semiannually that is 10 % . . . so the q literally means . . after 6 months . . 100 * 10 / 100 + 100 = 110 . . at the end of year 110 * 10 / 100 + 110 = 121 . . or we put it in compound interest formula . . where ci = 10 % , t is 2 and p = 100 . . so amount = 100 ( 1 + 10 / 100 ) ^ 2 = 100 * 1.1 * 1.1 = 121 . . answer : c"
Answer: c
Problem: here ' s an easy question of averages , but let ' s try to see innovative ways of solving this . a class has 12 boys and x girls . average score of boys and girls is 84 and 92 respectively . the average of the whole class is 86 , what is the value of x ?
Options: a ) a ) 6 , b ) b ) 4 , c ) c ) 8 , d ) d ) 10 , e ) e ) 12
Rationale: 12 ( 84 ) + 92 x / 12 + x = 86 1008 + 92 x / 12 + x = 86 1008 + 92 x = 86 ( 12 + x ) 1008 + 92 x = 1032 + 86 x x ' s one side , numbers one side we get , 92 x - 86 x = 1032 - 1008 6 x = 24 hence , x = 4 answer b
Answer: b
Problem: the present population of a town is 1000 . population increase rate is 20 % p . a . find the population of town after 2 years ?
Options: a ) 1440 , b ) 1220 , c ) 1400 , d ) 1500 , e ) 1620
Rationale: "p = 1000 r = 20 % required population of town = p * ( 1 + r / 100 ) ^ t = 1000 * ( 1 + 20 / 100 ) ^ 2 = 1000 * ( 6 / 5 ) ^ 2 = 1440 ( approximately ) answer is a"
Answer: a
Problem: if rs . 7500 are borrowed at c . i at the rate of 4 % per annum , then after 4 years the amount to be paid is ?
Options: a ) 3377 , b ) 2688 , c ) 2688 , d ) 8774 , e ) 1268
Rationale: "a = 7500 ( 26 / 25 ) ^ 4 = 8774 answer : d"
Answer: d
Problem: kim can do a work in 3 days while david can do the same work in 2 days . both of them finish the work together and get rs . 150 . what is the share of kim ?
Options: a ) 77 , b ) 60 , c ) 99 , d ) 26 , e ) 21
Rationale: kim ' s wages : david ' s wages = kim ' s 1 day work : david ' s 1 day work = 1 / 3 : 1 / 2 = 2 : 3 kim ' s share = 2 / 5 * 150 = rs . 60 answer : b
Answer: b
Problem: at what price must an article costing rs . 51.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 60.5 , b ) 69.5 , c ) 67.5 , d ) 67.7 , e ) 22.5
Rationale: "cp = 51.50 sp = 51.50 * ( 125 / 100 ) = 64.375 mp * ( 95 / 100 ) = 64.375 mp = 67.7 answer : d"
Answer: d
Problem: 4,7 , 11,18 , 29,47 , . . . ? . . , 123,199
Options: a ) 84 , b ) 102 , c ) 76 , d ) 70 , e ) none of the above
Rationale: "the addition of difference between each no . is equal to latter no . so , difference between 47 and 76 is 29 which is previous no . of 47 answer c"
Answer: c
Problem: there are two cars . one is 60 miles north of the other . simultaneously , the car to the north is driven westward at 15 miles per hour and the other car is driven eastward at 25 miles per hour . how many miles apart are the cars after 2 hours ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "here , drawing a quick sketch of the ' actions ' described will end in a diagonal line that you canbuilda right triangle around : the right triangle will have a base of 60 and a height of 80 . the hidden pattern here is a 3 / 4 / 5 right triangle ( the 60 lines up with the ' 3 ' and the 80 lines up with the ' 4 ' ) . in this way , you can deduce that each side is ' 20 times ' bigger than it ' s corresponding side : 3 / 4 / 5 becomes 60 / 80 / 100 thus the distance between the two cars is the length of the hypotenuse of this larger right triangle . . . final answer : c"
Answer: c
Problem: the diluted wine contains only 8 liters of wine and the rest is water . a new mixture whose concentration is 30 % , is to be formed by replacing wine . how many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: explanation : wine water 8 l 32 l 1 : 4 20 % 80 % ( original ratio ) 30 % 70 % ( required ratio ) in ths case , the percentage of water being reduced when the mixture is being replaced with wine . so the ratio of left quantity to the initial quantity is 7 : 8 therefore , \ frac { 7 } { 8 } = \ left [ 1 - \ frac { k } { 40 } \ right ] \ rightarrow \ frac { 7 } { 8 } = \ left [ \ frac { 40 - k } { 40 } \ right ] \ rightarrow k = 5 l answer : b ) 5
Answer: b
Problem: the length of the side of a square is represented by x + 2 . the length of the side of an equilateral triangle is 2 x . if the square and the equilateral triangle have equal perimeter , then the value of x is ?
Options: a ) 5 , b ) 7 , c ) 4 , d ) 8 , e ) 6
Rationale: since the side of the square is x + 2 , its perimeter = 4 ( x + 2 ) = 4 x + 8 since the side of the equilateral triangle is 2 x , its perimeter = 3 * 2 x = 6 x also , the perimeters of both are equal . ( i . e . ) 4 x + 8 = 6 x ( i . e . ) 2 x = 8 è x = 4 . answer : c
Answer: c
Problem: the cost price of 8 articles is equal to the selling price of 5 articles . what is the profit percent ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: "5 * sp = 8 * cp sp = 1.6 * cp the profit percent is 60 % . the answer is d ."
Answer: d
Problem: a man is 30 years older than his son . in two years , his age will be twice the age of his son . the present age of the son is ?
Options: a ) 16 , b ) 19 , c ) 15 , d ) 20 , e ) 28
Rationale: "let the son ' s present age be x years . then , man ' s present age = ( x + 30 ) years . ( x + 30 ) + 2 = 2 ( x + 2 ) x + 32 = 2 x + 4 = > x = 28 . answer : e"
Answer: e
Problem: in what ratio should a variety of rice costing rs . 7 per kg be mixed with another variety of rice costing rs . 8.75 per kg to obtain a mixture costing rs . 7.50 per kg ?
Options: a ) 5 / 6 , b ) 5 / 2 , c ) 5 / 1 , d ) 5 / 3 , e ) 7 / 6
Rationale: "let us say the ratio of the quantities of cheaper and dearer varieties = x : y by the rule of allegation , x / y = ( 8.75 - 7.50 ) / ( 7.50 - 7 ) = 5 / 2 answer : b"
Answer: b
Problem: q and r are two - digit positive integers that have the same digits but in reverse order . if the positive difference between q and r is less than 20 , what is the greatest possible value of q minus r ?
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "a two - digit integer ` ` ab ' ' can be expressed algebraically as 10 a + b . q - r = ( 10 a + b ) - ( 10 b + a ) = 9 ( a - b ) < 20 . the greatest multiple of 9 which is less than 20 is 18 . the answer is d ."
Answer: d
Problem: a 600 meter long train crosses a signal post in 50 seconds . how long will it take to cross a 3 kilometer long bridge , at the same speed ?
Options: a ) 4 min , b ) 2 min , c ) 8 min , d ) 9 min , e ) 5 min
Rationale: "s = 600 / 50 = 12 mps s = 3600 / 12 = 300 sec = 5 min answer : e"
Answer: e
Problem: a cistern is normally filled in 6 hrs , but takes 2 hrs longer to fill because of a leak on its bottom , if cistern is full , how much time citern would empty ?
Options: a ) 24 hours , b ) 20 hours , c ) 30 hours , d ) 40 hours , e ) 50 hours
Rationale: "if leakage / hour = 1 / x , then 1 / 6 - 1 / x = 1 / 8 , solving 1 / x = 1 / 24 so in 24 hours full cistern will be empty . answer : a"
Answer: a
Problem: a number x is multiplied with itself and then added to the product of 4 and x . if the result of these two operations is - 8 , what is the value of x ?
Options: a ) - 4 , b ) - 2 , c ) 2 , d ) 4 , e ) can not be determined .
Rationale: "a number x is multiplied with itself - - > x ^ 2 added to the product of 4 and x - - > x ^ 2 + 4 x if the result of these two operations is - 4 - - > x ^ 2 + 4 x = - 8 i . e x ^ 2 + 4 x + 8 = 0 is the quadratic equation which needs to be solved . no solution imo e"
Answer: e
Problem: if the sum of two positive integers is 20 and the difference of their squares is 40 , what is the product of the two integers ?
Options: a ) 108 , b ) 99 , c ) 128 , d ) 135 , e ) 143
Rationale: "let the 2 positive numbers x and y x + y = 20 - - 1 x ^ 2 - y ^ 2 = 40 = > ( x + y ) ( x - y ) = 40 - - 2 using equation 1 in 2 , we get = > x - y = 2 - - 3 solving equation 1 and 3 , we get x = 11 y = 9 product = 11 * 9 = 99 answer b"
Answer: b
Problem: 8 men can do a piece of work in 12 days . 4 women can do it in 48 days and 10 children can do it in 24 days . in how many days can 10 men , 20 women and 10 children together complete the piece of work ?
Options: a ) 5 days , b ) 15 days , c ) 28 days , d ) 4 days , e ) 7 days
Rationale: "explanation : 1 man ’ s 1 day ’ s work = 1 / 8 × 12 = 1 / 96 10 men ’ s 1 day ’ s work = 1 × 10 / 96 = 5 / 48 1 woman ’ s 1 day ’ s work = 1 / 192 20 women ’ s 1 day ’ s work = 1 / 192 × 20 = 5 / 48 1 child ’ s 1 day ’ s work = 1 / 240 10 children ’ s 1 day ’ s work = 1 / 24 therefore , ( 10 men + 20 women + 10 children ) ’ s 1 day ’ s work = 5 / 48 + 5 / 48 + 1 / 24 = 1 / 4 the required no . of days = 4 days answer : option d"
Answer: d
Problem: what is the remainder when 3 ^ 86 is divided by 5 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 0 , e ) 3
Rationale: "3 ^ 0 = 1 3 ^ 1 = 3 3 ^ 2 = 9 3 ^ 3 = 27 3 ^ 4 = . . . 1 3 ^ 5 = . . . . 3 3 ^ 6 = . . . . . . 9 and so on . 86 / 4 = 21 ( with a remainder 2 ) so the last number is a 9 . so when 3 ^ 86 is divided by 5 the remainder is 4 , ans = c"
Answer: c
Problem: if the ratio of two number is 2 : 5 and lcm of the number is 160 then what is the number .
Options: a ) 15 , b ) 20 , c ) 16 , d ) 30 , e ) 35
Rationale: "product of two no = lcm * hcf 2 x * 5 x = 160 * x x = 16 answer : c"
Answer: c
Problem: the moon revolves around the earth at a speed of approximately 1.03 kilometers per second . this approximate speed is how many kilometers per hour ?
Options: a ) 60 , b ) 61.2 , c ) 62.5 , d ) 3,708 , e ) 3,672
Rationale: "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 = 1.03 * 3600 = 3708 kilometers per hour . option d is correct"
Answer: d
Problem: the average marks obtained by 100 candidates in an examination is 50 . find how many candidates have passed in the examination , if the average marks of candidates who passed is 70 and that of failed candidates is 20 .
Options: a ) 33 , b ) 77 , c ) 60 , d ) 29 , e ) 11
Rationale: explanation : let the number of students who passed the examination be x number of students failed = ( 100 - x ) total marks of students who have passed = 70 x total marks of 100 students = 100 * 50 = 5000 total marks of students who have failed = 20 ( 100 – x ) 20 ( 100 – x ) + 70 x = 5000 2000 – 20 x + 70 x = 5000 50 x = 3000 x = 60 answer : c
Answer: c