regisss/math_qa huggingface dataset:
Problem: in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 1 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 2 / 7
Rationale: "there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssds ∘ sssibl ∈ g ∘ ssand ∘ ssviceversa ) ∘ ss ( c ∘ ssis ∘ ssdssibl ∈ gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 3 people who have exactly 1 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 1 people out of 7 is 7 c 1 = 7 first sibling pair - - - - ( a and b ) - - selecting 1 people - - 1 c 1 = 1 second sibling pair ( c and d ) - - selecting 1 people - - 1 c 1 = 1 third sibling pair ( e f g ) - - selecting 1 out of 3 - - 3 c 1 = 3 total = 1 + 1 + 3 = 5 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 1 people who are siblings = 5 / 7 ( 7 is 7 c 1 ) = 1 - 5 / 7 = 2 / 7 ans e"
Answer: e
Problem: a mixture of 150 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 7 liters , b ) 15 liters , c ) 10 liters , d ) 9 liters , e ) none of these
Rationale: "explanation : number of liters of water in 150 liters of the mixture = 20 % of 150 = 20 / 100 * 150 = 30 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 30 + p ) and total volume of mixture is ( 150 + p ) . ( 30 + p ) = 25 / 100 * ( 150 + p ) 120 + 4 p = 150 + p = > p = 10 liters . answer is c"
Answer: c
Problem: a factory producing tennis balls stores them in either big boxes , 25 balls per box , or small boxes , 20 balls per box . if 126 freshly manufactured balls are to be stored , what is the least number of balls that can be left unboxed ?
Options: a ) 2 , b ) 4 , c ) 1 , d ) 5 , e ) 3
Rationale: "we have to work with multiples of 20 and 25 . first , we must know the limits of this multiples , so : 126 / 25 = 5 . . . . so the max is 5 126 / 20 = 6 . . . so the max is 6 126 - 125 = 1 ( 5 big box or 5 small box + 1 big box ) answer : c"
Answer: c
Problem: how many seconds will a 900 metre long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 54
Rationale: "relative speed of the train = 63 - 3 = 60 kmph = 60 * 5 / 18 = 50 / 3 m / sec t = 900 * 3 / 50 = 54 sec answer : e"
Answer: e
Problem: what will be the vulgar fraction of 0.8
Options: a ) 3 / 5 , b ) 4 / 5 , c ) 3 / 2 , d ) 3 / 7 , e ) 3 / 8
Rationale: "explanation : 0.8 = 80 / 100 = 4 / 5 option b"
Answer: b
Problem: jenny can divide her sweets equally to 5 people and also to 6 people equally but not to 12 people . what could be the number ?
Options: a ) 120 , b ) 134 , c ) 127 , d ) 30 , e ) 650
Rationale: option ( b ) and ( c ) are ruled out as they are not divisilble by 5 and 6 . 120 is both divisible by 5 and 6 but also by 12 , so it wrong . 650 is divisible by 5 but not by 6 . hence , ( d ) is the answer , as it is both divisible by 5 or 6 but not by 12
Answer: d
Problem: one pipe can fill a pool 1.5 times faster than a second pipe . when both pipes are opened , they fill the pool in five hours . how long would it take to fill the pool if only the slower pipe is used ?
Options: a ) 11.25 , b ) 11.52 , c ) 12.5 , d ) 9 , e ) 7.2
Rationale: "say the rate of the slower pipe is r pool / hour , then the rate of the faster pipe would be 1.5 r = 3 r / 2 . since when both pipes are opened , they fill the pool in five hours , then their combined rate is 1 / 5 pool / hour . thus we have that r + 3 r / 2 = 1 / 5 - - > r = 2 / 25 pool / hour - - > time is reciprocal of rate thus it ' s 25 / 2 = 12.5 hours . answer : c ."
Answer: c
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 35 % profit on the cost of the item ?
Options: a ) 18 , b ) 21.6 , c ) 22 , d ) 22.5 , e ) 27.7
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 35 % of the final price - - > ( final price ) * 0.65 = $ 18 - - > ( final price ) = $ 27.7 . answer : e ."
Answer: e
Problem: at a certain committee meeting only associate professors and assistant professors are present . each associate professor has brought 2 pencils and 1 chart to the meeting , while each assistant professor has brought 1 pencil and 2 charts . if a total of 10 pencils and 11 charts have been brought to the meeting , how many people are present ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: "say there are ' a ' associate professors . so we have 2 a pencils and a charts . say there are ' b ' assistant professors . so we have b pencils and 2 b charts . total pencils are 10 so 2 a + b = 10 total charts are 11 so a + 2 b = 11 add both : 3 a + 3 b = 21 so a + b = 7 total number of people = 7 answer : b"
Answer: b
Problem: a reduction of 20 % in the price of oil enables a house wife to obtain 4 kgs more for rs . 684 , what is the reduced price for kg ?
Options: a ) 72 , b ) 27 , c ) 34 , d ) 28 , e ) 20
Rationale: "684 * ( 20 / 100 ) = 136 - - - - 4 ? - - - - 1 = > rs . 34 answer : c"
Answer: c
Problem: if 522 x is a 3 digit no . with as a digit x . if the no . is divisible by 6 , what is the value of the digit x is ?
Options: a ) 1 , b ) 6 , c ) 4 , d ) 7 , e ) 9
Rationale: if a number is divisible by 6 , it must be divisible by both 2 and 3 in 522 x , to this number be divisible by 2 , the value of x must be even . so it can be 2,4 or 6 from given options 552 x is divisible by 3 , if sum of its digits is a multiple of 3 . 5 + 5 + 2 + x = 12 + x , if put x = 2 , 12 + 2 = 14 not a multiple of 3 if put x = 4 , 12 + 6 = 18 is a multiple of 3 if put x = 6 , 12 + 2 = 14 not a multiple of 3 the value of x is 6 . b
Answer: b
Problem: what is the value of ( p + q ) / ( p - q ) if p / q is 8 ?
Options: a ) 4 / 3 , b ) 2 / 3 , c ) 2 / 6 , d ) 7 / 8 , e ) 9 / 7
Rationale: "( p + q ) / ( p - q ) = [ ( p / q ) + 1 ] / [ ( p / q ) - 1 ] = ( 8 + 1 ) / ( 8 - 1 ) = 9 / 7 answer : e"
Answer: e
Problem: cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 5 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 3 : 5 , c ) 4 : 7 , d ) 2 : 6 , e ) 1 : 4
Rationale: "2 % is 3 % - points below 5 % and 10 % is 5 % - points above 5 % . the ratio of a : b should be 3 : 5 . the answer is b ."
Answer: b
Problem: the side of a rhombus is 28 m and length of one of its diagonals is 12 m . the area of the rhombus is ?
Options: a ) 326.2 , b ) 324.2 , c ) 328.2 , d ) 338.2 , e ) 328.9
Rationale: "area of the rhombus = 1 / 2 * p * √ 4 ( a ) 2 - ( p ) 2 a = 28 ; p = 12 a = 1 / 2 * 12 * √ 4 ( 28 ) 2 - ( 12 ) 2 = 1 / 2 * 12 * √ 3136 - 144 = 1 / 2 * 12 * √ 2992 a = 328.2 answer : c"
Answer: c
Problem: what is the remainder when 14,456 × 15,657 × 16,788 is divided by 10 ?
Options: a ) 6 , b ) 8 , c ) 4 , d ) 3 , e ) 2
Rationale: "only the unit ' s digit of the product will decide the remainder when divided by 10 . hence , 6 * 7 * 8 = will give units digit as 6 so , whatever be the number , if it ends in 6 , the remainder after dividing with 10 will be 6 . optiona"
Answer: a
Problem: the product of two numbers is 2028 and their hcf is 13 . what are the number of such pairs ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 23 , e ) 25
Rationale: "let the numbers be 13 x and 13 y ( hcf of the numbers = 13 ) 13 x × 13 y = 2028 xy = 12 co - primes with product 12 are ( 1 , 12 ) and ( 3 , 4 ) ( we need to take only co - primes with product 12 . if we take two numbers with product 12 , but not co - prime , the hcf will not remain as 13 ) hence the numbers with hcf 13 and product 2028 = ( 13 × 1 , 13 × 12 ) and ( 13 × 3 , 13 × 4 ) = ( 13 , 156 ) and ( 39 , 52 ) so , there are 2 pairs of numbers with hcf 13 and product 2028 answer is b"
Answer: b
Problem: a hall is 24 meters long and 12 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
Options: a ) 1896
b ) 1912
c ) 2108
d ) 2304
e ) 2524
Rationale: 2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 2304 the answer is d .
Answer: d
Problem: at deluxe paint store , fuchsia paint is made by mixing 6 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 24 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: in 24 liters , red = 6 / 9 * 24 = 16 and blue = 8 so , 16 / ( 8 + x ) = 4 / 5 or , x = 12 ( answer b )
Answer: b
Problem: if x is a positive integer with fewer than 3 digits , what is the probability w that x * ( x + 1 ) is a multiple of either 4 or 5 ?
Options: a ) 4 / 99 , b ) 2 / 25 , c ) 8 / 99 , d ) 49 / 100 , e ) 86 / 99
Rationale: "interesting question ! also one that we should be able to answer very quickly be keeping an eye on our best friends , the answer choices . we know that x belongs to the set { 1 , 2 , 3 , . . . , 99 } . we want to know the probability w that x ( x + 1 ) is a multiple of either 4 or 5 . when will this happen ? if either x or ( x + 1 ) is a multiple of 4 or 5 . since 4 * 5 is 20 , let ' s look at the first 20 numbers to get a rough idea of how often this happens . out of the numbers from 1 to 20 : 4 , 5 , 6 , 8 , 9 , 10 , 11 , 12 , 13 , 15 , 16 , 17 , 20 so , 14 out of the first 20 numbers match our criteria . since : probability = ( # of desired outcomes ) / ( total # of possibilities ) , we guesstimate the answer to be 14 / 20 . since ( e ) is the only answer greater than 1 / 2 , we go with ( e ) ."
Answer: e
Problem: because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 2 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 22.5 % , d ) 33.3 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindys income is 2 * 100 = 200 so tax paid is 30 % * 200 = 60 total tax paid = 40 + 60 = 100 . combined tax % will be 100 / 100 + 200 = 33.3 %"
Answer: d
Problem: two employees m and n are paid a total of rs . 550 per week by their employer . if m is paid 120 percent of the sum paid to n , how much is n paid per week ?
Options: a ) rs . 220 , b ) rs . 250 , c ) rs . 280 , d ) rs . 300 , e ) rs . 320
Rationale: let the amount paid to m per week = x and the amount paid to n per week = y then x + y = 550 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 550 ⇒ y [ 12 / 10 + 1 ] = 550 ⇒ 22 y / 10 = 550 ⇒ 22 y = 5500 ⇒ y = 5500 / 22 = 500 / 2 = rs . 250 b )
Answer: b
Problem: a certain bag of gemstones is composed of two - thirds diamonds and one - third rubies . if the probability of randomly selecting two diamonds from the bag , without replacement , is 5 / 12 , what is the probability of selecting two rubies from the bag , without replacement ?
Options: a ) 5 / 36 , b ) 5 / 24 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: 2 / 3 * ( 2 x - 1 ) / ( 3 x - 1 ) = 5 / 12 = > x = 3 so total gems = 9 and probability of ruby = 1 / 3 * 2 / 8 = 1 / 12 answer 1 / 12 c
Answer: c
Problem: one man adds 5 liters of water to 10 liters of milk and another 4 liters of water to 20 liters of milk . what is the ratio of the strengths of milk in 2 mixtures ?
Options: a ) 4 : 5 , b ) 9 : 11 , c ) 2 : 3 , d ) 4 : 7 , e ) 3 : 7
Rationale: strength of milk in the mixture = quantity of milk / total quantity of mixture strength of milk in the 1 st mixture = 10 / 15 strength of the milk 2 nd mixture = 20 / 24 the ratio of their strengths = 10 / 15 : 20 / 24 = 4 : 5 answer is b
Answer: b
Problem: the average of 9 observations was 6 , that of the 1 st of 5 being 10 and that of the last 5 being 8 . what was the 5 th observation ?
Options: a ) 36 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "explanation : 1 to 9 = 9 * 6 = 54 1 to 5 = 5 * 10 = 50 5 to 9 = 5 * 8 = 40 5 th = 50 + 40 = 90 – 54 = 36 option a"
Answer: a
Problem: in a certain school , 20 % of students are below 8 years of age . the number of students above 8 years of age is 2 / 3 of the number of students of 8 years of age which is 60 . what is the total number of students in the school ?
Options: a ) 72 , b ) 80 , c ) 125 , d ) 150 , e ) 100
Rationale: explanation : let the number of students be x . then , number of students above 8 years of age = ( 100 - 20 ) % of x = 80 % of x . 80 % of x = 60 + 2 / 3 of 60 80 / 100 x = 100 x = 125 . answer : option c
Answer: c
Problem: two pipes a and b can fill a tank in 24 and 48 minutes respectively . if both the pipes are used together , then how long will it take to fill the tank ?
Options: a ) 12 , b ) 16 , c ) 19 , d ) 20 , e ) 22
Rationale: "part filled by a in 1 min . = 1 / 24 part filled by b in 1 min . = 1 / 48 part filled by ( a + b ) in 1 min . = 1 / 24 + 1 / 48 = 1 / 16 . both the pipes can fill the tank in 16 minutes . answer : b"
Answer: b
Problem: rohan spends 40 % of his salary on food , 20 % on house rent , 10 % on entertainment and 10 % on conveyance . if his savings at the end of a month are rs . 1000 . then his monthly salary is
Options: a ) rs . 5000 , b ) rs . 6000 , c ) rs . 4000 , d ) rs . 3000 , e ) rs . 2000
Rationale: "sol . saving = [ 100 - ( 40 + 20 + 10 + 10 ] % = 20 % . let the monthly salary be rs . x . then , 20 % of x = 1000 â ‡ ” 20 / 100 x = 1000 â ‡ ” x = 1000 ã — 5 = 5000 . answer a"
Answer: a
Problem: the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 36 kmph , find the speed of the stream ?
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 36 / 3 = 12 kmph . answer : a"
Answer: a
Problem: find the average of first 7 multiples of 5 ?
Options: a ) 10 , b ) 15 , c ) 12.5 , d ) 13 , e ) 20
Rationale: "average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 ) / 7 = 20 answer is e"
Answer: e
Problem: robert ' s salary was decreased by 40 % and subsequently increased by 40 % . how much percentage does he lose ?
Options: a ) 16 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 40 % = 100 - 100 x 40 / 100 = $ 60 salary after increasing 40 % on $ 60 = 60 + 60 x 40 / 100 = $ 84 percentage of loss = 100 - 84 = 16 % answer : a"
Answer: a
Problem: rs . 1560 is divided so that 4 times the first share , thrice the 2 nd share and twice the third share amount to the same . what is the value of the third share ?
Options: a ) s . 528 , b ) s . 542 , c ) s . 528 , d ) s . 720 , e ) s . 549
Rationale: "a + b + c = 1560 4 a = 3 b = 2 c = x a : b : c = 1 / 4 : 1 / 3 : 1 / 2 = 3 : 4 : 6 6 / 13 * 1560 = rs . 720 answer : d"
Answer: d
Problem: the average runs of a cricket player of 12 innings was 48 . how many runs must he make in his next innings so as to increase his average of runs by 10 ?
Options: a ) 12 , b ) 142 , c ) 164 , d ) 178 , e ) 84
Rationale: "explanation : average after 13 innings = 58 required number of runs = ( 58 * 13 ) – ( 48 * 12 ) = 754 – 576 = 178 answer d"
Answer: d
Problem: find the area , diameter = 10 m .
Options: a ) 78.24 square meter , b ) 78.57 square meter , c ) 78.26 square meter , d ) 24.24 square meter , e ) 24.43 square meter
Rationale: "diameter = 10 meter . radius = diameter / 2 . = 10 / 2 . = 5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 5 . area of a circle = 3.14 ã — 5 ã — 5 . . = 3.14 ã — 25 . = 78.57 square meter answer : b"
Answer: b
Problem: tickets numbered from 1 to 22 are mixed and then a ticket is selected randomly . what is the probability that the selected ticket bears a number which is a multiple of 3 ?
Options: a ) 1 / 5 , b ) 2 / 5 , c ) 3 / 10 , d ) 3 / 7 , e ) 7 / 22
Rationale: "here , s = [ 1 , 2 , 3 , 4 , … . , 19 , 20 , 21 , 22 ] let e = event of getting a multiple of 3 = [ 3 , 6 , 9 , 12 , 15 , 18 , 21 ] p ( e ) = n ( e ) / n ( s ) = 7 / 22 the answer is e ."
Answer: e
Problem: a present value of a machine is $ 900 . its value depletiation rate is 25 % per annum then find the machine value before 2 years ?
Options: a ) $ 1500 , b ) $ 1200 , c ) $ 1600 , d ) $ 1000 , e ) $ 1350
Rationale: "p = $ 900 r = 25 % t = 2 years machine value before 2 years = p / [ ( 1 - r / 100 ) ^ t ] = 900 * 4 / 3 * 4 / 3 = $ 1600 answer is c"
Answer: c
Problem: how many positive integers less than 100 are neither multiples of 3 or 5 .
Options: a ) a ) 30 , b ) b ) 31 , c ) c ) 32 , d ) d ) 53 , e ) e ) 34
Rationale: "to answer this q we require to know 1 ) multiples of 5 till 100 = 100 / 5 = 20 2 ) multiples of 3 till 100 = 100 / 3 = 33.33 = 33 add the two 20 + 33 = 53 ; subtract common terms that are multiple of both 5 and 3 . . lcm of 5 and 3 = 15 multiples of 15 till 100 = 100 / 15 = 6 so total multiples of 5 and 3 = 53 - 6 = 47 ans = 100 - 47 = 53 d"
Answer: d
Problem: 122 * 252 - 12234 = ?
Options: a ) 15310 , b ) 18870 , c ) 24510 , d ) 18510 , e ) 42510
Rationale: "d ? = 122 * 252 - 12234 = 30744 - 12234 = 18510"
Answer: d
Problem: a company has two models of computers , model x and model y . operating at a constant rate , a model x computer can complete a certain task in 72 minutes and a model y computer can complete the same task in 36 minutes . if the company used the same number of each model of computer to complete the task in 1 minute , how many model x computers were used ?
Options: a ) 22 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: let ' s say 1 work is processing 72 gb of data . model x : 1 gb per min model y : 2 gb per min working together , 1 x and 1 y = 3 gb per min so , 24 times as many computers would work at 72 gb per min . so no . of x = 24 answer is c
Answer: c
Problem: a fruit seller had some oranges . he sells 40 % oranges and still has 360 oranges . how many oranges he had originally ?
Options: a ) 700 , b ) 710 , c ) 600 , d ) 730 , e ) 740
Rationale: "60 % of oranges = 360 100 % of oranges = ( 360 × 100 ) / 6 = 600 total oranges = 700 answer : c"
Answer: c
Problem: of the goose eggs laid at a certain pond , 1 / 2 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 800 , b ) 840 , c ) 880 , d ) 920 , e ) 960
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 2 ) x = 120 ( 6 / 40 ) x = 120 x = 800 the answer is a ."
Answer: a
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 34 % , b ) 24 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "et 100 be the total volume . total salt = 10 salt taken out = 10 / 4 = 2.5 to make solution 16 % , total salt = 16 salt added = 16 - 7.5 = 8.5 solution had = 8.5 / 25 * 100 = 34 % sugar answer : a"
Answer: a
Problem: if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 420 , what is the least possible value of n ?
Options: a ) 5 , b ) 7 , c ) 9 , d ) 11 , e ) 12
Rationale: "420 = 2 * 2 * 3 * 5 * 7 , so n must be at least 7 . the answer is b ."
Answer: b
Problem: if x = 5 - q and y = 3 q - 1 , then for what value of q , x is three times to y ?
Options: a ) 0 , b ) 1 , c ) - 1 , d ) - 8 , e ) 8
Rationale: "explanation : x = 3 y < = > 5 - q = 3 ( 3 q - 1 ) < = > 5 - q = 9 q - 3 < = > 8 q = 8 < = > q = 1 . answer : b"
Answer: b
Problem: express a speed of 16 kmph in meters per second ?
Options: a ) 10 mps , b ) 8 mps , c ) 4 mps , d ) 7 mps , e ) 2 mps
Rationale: "16 * 5 / 18 = 4 mps answer : c"
Answer: c
Problem: xavier starts from p towards q at a speed of 90 kmph and after every 12 mins increases his speed by 10 kmph . if the distance between p and q is 51 km , then how much time does he take to cover the distance ?
Options: a ) 30 , b ) 32 , c ) 30 , d ) 36 , e ) 40
Rationale: "first 12 min = 90 * 12 / 60 = 18 km 2 nd 12 min = 100 * 12 / 60 = 20 km 3 rd 12 min = 110 * 12 / 60 = 22 km total time 12 * 3 = 36 min d"
Answer: d
Problem: a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 63 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 245
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 63 35 - - - ? = > 245 answer : e"
Answer: e
Problem: how many multiples of 2 are there between 0 and 100 , exclusive ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 45 , e ) 49
Rationale: "2 * 50 = 100 total multiples = ( 50 - 1 ) + 1 = 50 exclude 0 and 100 = 50 - 1 = 49 answer is e ."
Answer: e
Problem: the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 68 kg . what is the correct weight ?
Options: a ) 58 kgs , b ) 58.85 kgs , c ) 58.95 kgs , d ) 59 kgs , e ) 59.85 kgs
Rationale: "actual total weight is ( 20 x 58.4 - 56 + 68 ) = 1180 kgs actual average weight is 1180 / 20 = 59 kgs d"
Answer: d
Problem: what is the probability that a two digit number selected at random will be a multiple of ' 3 ' and not a multiple of ' 5 ' ?
Options: a ) 2 / 15 , b ) 4 / 15 , c ) 1 / 15 , d ) 4 / 90 , e ) 5 / 60
Rationale: solution : there are a total of 90 two digit numbers . every third number will be divisible by ' 3 ' . therefore , there are 30 of those numbers that are divisible by ' 3 ' . of these 30 numbers , the numbers that are divisible by ' 5 ' are those that are multiples of ' 15 ' . i . e . numbers that are divisible by both ' 3 ' and ' 5 ' . there are 6 such numbers - - 15 , 30,45 , 60,75 and 90 . we need to find out numbers that are divisible by ' 3 ' and not by ' 5 ' , which will be : 30 â ˆ ’ 6 = 24 24 out of the 90 numbers are divisible by ' 3 ' and not by ' 5 ' . the required probability is therefore , = 24 / 90 = 4 / 15 answer is b
Answer: b
Problem: tom , working alone , can paint a room in 12 hours . peter and john , working independently , can paint the same room in 6 hours and 2 hours , respectively . tom starts painting the room and works on his own for two hour . he is then joined by peter and they work together for two hour . finally , john joins them and the three of them work together to finish the room , each one working at his respective rate . what fraction of the whole job was done by peter ?
Options: a ) 5 / 3 , b ) 1 / 3 , c ) 7 / 3 , d ) 4 / 9 , e ) 3 / 5
Rationale: let the time when all three were working together be t hours . then : tom worked for t + 4 hour and has done 1 / 12 * ( t + 4 ) part of the job ; peter worked for t + 2 hour and has done 1 / 6 * ( t + 2 ) part of the job ; john worked for t hours and has done 1 / 2 * t part of the job : 1 / 12 * ( t + 4 ) + 1 / 6 * ( t + 2 ) + 1 / 2 * t = 1 - - > multiply by 12 - - > ( t + 4 ) + ( 2 t + 2 ) + 6 t = 12 - - > t = 2 / 3 ; hence peter has done 1 / 6 * ( 2 / 3 + 2 ) = 1 / 6 * 8 / 3 = 8 / 18 = 4 / 9 answer : d
Answer: d
Problem: p and q started a business investing rs 50000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 12 : 5 , b ) 17 : 3 , c ) 10 : 6 , d ) 17 : 7 , e ) 10 : 3
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 50000 : 15000 = 50 : 15 = 10 : 3 option e"
Answer: e
Problem: there are many numbers that can be expressed as the sum of 3 squares in 3 different ways . can you find out the smallest of such number ?
Options: a ) 87 , b ) 54 , c ) 29 , d ) 30 , e ) 70
Rationale: b 54 7 ^ 2 + 2 ^ 2 + 1 ^ 1 6 ^ 2 + 3 ^ 2 + 3 ^ 2 2 ^ 2 + 5 ^ 2 + 5 ^ 2
Answer: b
Problem: the speed at which a man can row a boat in still water is 15 kmph . if he rows downstream , where the speed of current is 3 kmph , what time will he take to cover 100 metres ?
Options: a ) 16 seconds , b ) 20 seconds , c ) 14 seconds , d ) 12 seconds , e ) 15 seconds
Rationale: "speed of the boat downstream = 15 + 3 = 18 kmph = 18 * 5 / 18 = 5 m / s hence time taken to cover 100 m = 100 / 5 = 20 seconds . answer : b"
Answer: b
Problem: in a mayoral election , candidate x received 1 / 5 more votes than candidate y , and candidate y received 1 / 2 fewer votes than z . if z received 20,000 votes how many votes did candidate x received ?
Options: a ) 12000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 20 - - > y received 1 / 2 fewer votes than z - - > y = z - 1 / 2 * z = 10 ; x received 1 / 5 more votes than y - - > x = y + 1 / 5 * y = 12 . answer : a ."
Answer: a
Problem: ages of two persons differ by 22 years . if 6 year ago , the elder one be 3 times as old the younger one , find their present age
Options: a ) 12,28 , b ) 14,30 , c ) 17,39 , d ) 18,34 , e ) 19,34
Rationale: "explanation : let the age of younger person is x , then elder person age is ( x + 22 ) = > 3 ( x - 6 ) = ( x + 22 - 6 ) [ 6 years before ] = > 3 x - 18 = x + 16 = > x = 17 . so other person age is x + 22 = 39 answer : option c"
Answer: c
Problem: a basket of 1430 apples is divided equally among a group of apple lovers . if 45 people join the group , each apple lover would receive 9 apples less . how many w apples did each person get before 45 people joined the feast ?
Options: a ) 20 . , b ) 21 . , c ) 22 . , d ) 23 . , e ) 24 .
Rationale: "before solving it algebraically , let us prime factorize 1430 = 2 * 5 * 11 * 13 . since number of apples per person * total persons w = 1430 , the answer should be a factor of 1430 . only c is . and that ' s your answer . c"
Answer: c
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 280 more , there would have been a gain of 4 % . what is the cost price ?
Options: a ) s : 2000 , b ) s : 1067 , c ) s : 1278 , d ) s : 1028 , e ) s : 1027
Rationale: "90 % 104 % - - - - - - - - 14 % - - - - 280 100 % - - - - ? = > rs : 2000 answer : a"
Answer: a
Problem: a man can row his boat with the stream at 18 km / h and against the stream in 8 km / h . the man ' s rate is ?
Options: a ) 5 kmph , b ) 2 kmph , c ) 7 kmph , d ) 8 kmph , e ) 3 kmph
Rationale: "ds = 18 us = 8 s = ? s = ( 18 - 8 ) / 2 = 5 kmph answer : a"
Answer: a
Problem: free notebooks were distributed equally among children of a class . the number of notebooks each child got was one - eighth of the number of children . had the number of children been half , each child would have got 16 notebooks . how many notebooks were distributed in all ?
Options: a ) 432 , b ) 640 , c ) 256 , d ) 512 , e ) none of these
Rationale: "in case i : let the no . of children = x . hence , total no . of notebooks distributed 1 ⁄ 8 x . x or x 2 ⁄ 8 . . . . . . . ( i ) in case ii : no . of children = x ⁄ 2 now , the total no . of notebooks = 16 × x ⁄ 2 . . . . . . . ( ii ) comparing ( i ) & ( ii ) , we get x 2 ⁄ 8 = 8 x or , x = 64 hence , total no . of notebooks = 64 × 64 / 8 = 512 answer d"
Answer: d
Problem: one pipe can fill a tank 3 times as fast as another pipe . if together the two pipes can fill tank in 40 min , then the slower pipe alone will be able to fill the tank in ?
Options: a ) 160 , b ) 787 , c ) 144 , d ) 128 , e ) 121
Rationale: let the slower pipe alone fill the tank in x min . then , faster pipe will fill it in x / 3 min . 1 / x + 3 / x = 1 / 40 4 / x = 1 / 40 = > x = 160 min . answer : a
Answer: a
Problem: 1500 is increased by 20 % . find the final number .
Options: a ) 1500 , b ) 1800 . , c ) 1900 , d ) 1700 , e ) 1660
Rationale: final number = initial number + 20 % ( original number ) = 1500 + 20 % ( 1500 ) = 1500 + 300 = 1800 . answer b
Answer: b
Problem: the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 50 , then how long is the base of isosceles triangle ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "the base of the isosceles triangle is 50 - 20 - 20 = 10 units the answer is b ."
Answer: b
Problem: a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 1 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 120 , c ) 289 , d ) 270 , e ) 927
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 1 = 120 answer : b"
Answer: b
Problem: ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + 0.05 + ( 0.1 ) ( power 2 ) is :
Options: a ) 0.8 , b ) 0.4 , c ) 0.96 , d ) 0.69 , e ) 0.76
Rationale: "given expression = ( 0.5 ) ( power 3 ) - ( 0.1 ) ( power 3 ) / ( 0.5 ) ( power 2 ) + ( 0.5 x 0.1 ) + ( 0.1 ) ( power 2 ) = a ( power 3 ) - b ( power 3 ) / a ( power 2 ) + ab + b ( power 2 ) = ( a - b ) = ( 0.5 - 0.1 ) = 0.4 answer is b"
Answer: b
Problem: if p is a prime number greater than 3 , find the remainder when p ^ 2 + 17 is divided by 12 .
Options: a ) 6 , b ) 1 , c ) 0 , d ) 8 , e ) 7
Rationale: "take any prime number greater than 3 and check - say p = 5 so , p ^ 2 + 17 = 25 + 17 = > 42 42 / 12 will have remainder as 6 say p = 7 so , p ^ 2 + 17 = 49 + 17 = > 66 66 / 12 will have remainder as 6 so answer will be ( a ) 6"
Answer: a
Problem: 9.8 , 9.8 , 9.9 , 9.9 , 10.0 , 10.0 , 10.1 , 10.5 the mean and the standard deviation of the 8 numbers shown above is 10 and 0.212 respectively . what percent of the 8 numbers are within 1 standard deviation of the mean ?
Options: a ) 90.5 % , b ) 87.5 % , c ) 80.5 % , d ) 77.5 % , e ) 70.5 %
Rationale: within 1 standard deviation of the mean - means in the range { mean - 1 * sd ; mean + 1 * sd } = { 10 - 1 * 0.212 ; 10 + 0.3 } = { 9.788 ; 10.212 } . from the 8 listed numbers , 7 are within this range so 6 / 8 = 87.5 % . answer : b .
Answer: b
Problem: at the opening of a trading day at a certain stock exchange , the price per share of stock m was $ 25 . if the price per share of stock m was $ 28 at the closing of the day , what was the percent increase in the price per share of stock m for that day ?
Options: a ) 1.4 % , b ) 5.9 % , c ) 12 % , d ) 12.5 % , e ) 23.6 %
Rationale: "opening = 25 closing = 28 rise in price = 3 so , percent increase = 3 / 25 * 100 = 12 answer : c"
Answer: c
Problem: the average of 13 numbers is 60 . average of the first 7 of them is 57 and that of the last 7 is 61 . find the 8 th number ?
Options: a ) 43 , b ) 30 , c ) 35 , d ) 45 , e ) 50
Rationale: "sum of all the 13 numbers = 13 * 60 = 780 sum of the first 7 of them = 7 * 57 = 399 sum of the last 7 of them = 7 * 61 = 427 so , the 8 th number = 427 + 399 - 780 = 46 . answer a"
Answer: a
Problem: martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 19.20 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 2
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 19.2 0.4 x = 3.2 = > x = 8 discounted tickets = 10 - x = 2 ans : e"
Answer: e
Problem: the length of a rectangular field is 7 / 5 its width . if the perimeter of the field is 360 meters , what is the width of the field ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 75
Rationale: "let l be the length and w be the width . l = ( 7 / 5 ) w perimeter : 2 l + 2 w = 360 , 2 ( 7 / 5 ) w + 2 w = 360 solve the above equation to find : w = 75 m and l = 105 m . correct answer e ) 75"
Answer: e
Problem: the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 2090 . what was his original salary ?
Options: a ) 2277 , b ) 2999 , c ) 1000 , d ) 2651 , e ) 2000
Rationale: "x * ( 110 / 100 ) * ( 95 / 100 ) = 2090 x * ( 11 / 10 ) * ( 1 / 100 ) = 22 x = 2000 answer : e"
Answer: e
Problem: given f ( x ) = 2 x – 3 , for what value of x does 2 * [ f ( x ) ] – 21 = f ( x – 4 ) ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "2 ( 2 x - 3 ) - 21 = 2 ( x - 4 ) - 3 2 x = 16 x = 8 the answer is e ."
Answer: e
Problem: a train passes a platform in 40 seconds . the same train passes a man standing on the platform in 20 seconds . if the speed of the train is 54 km / hr , the length of the platform is
Options: a ) 280 meter , b ) 240 meter , c ) 200 meter , d ) 300 meter , e ) none of these
Rationale: "explanation : speed of the train = 54 km / hr = ( 54 × 10 ) / 40 m / s = 15 m / s length of the train = speed × time taken to cross the man = 15 × 20 = 300 m let the length of the platform = l time taken to cross the platform = ( 300 + l ) / 15 = > ( 300 + l ) / 15 = 40 = > 300 + l = 15 × 40 = 600 = > l = 600 - 300 = 300 meter answer : option d"
Answer: d
Problem: a rectangular window is twice as long as it is wide . if its perimeter is 18 feet , then what are its dimensions in feet ?
Options: a ) 3 / 2 by 7 / 2
b ) 5 / 3 by 10 / 3
c ) 2 by 4
d ) 3 by 6
e ) 10 / 3 by 20 / 3
Rationale: let x be the width of the window . then the length is 2 x . x + 2 x + x + 2 x = 18 6 x = 18 x = 18 / 6 = 3 the width is 3 and the length is 6 . the answer is d .
Answer: d
Problem: a train running at the speed of 40 km / hr crosses a pole in 27 seconds . what is the length of the train ?
Options: a ) 250 , b ) 300 , c ) 350 , d ) 400 , e ) 450
Rationale: "speed = ( 40 * 5 / 18 ) m / sec = ( 100 / 9 ) m / sec length of the train = ( speed x time ) = ( 100 / 9 * 29 ) m = 300 m . answer : b"
Answer: b
Problem: find the least number of 5 digits , which is exactly divisible by 89 .
Options: a ) 27 , b ) 37 , c ) 932 , d ) 12 , e ) 91
Rationale: answer : a
Answer: a
Problem: a rope of which a calf is tied is increased from 16 m to 23 m , how much additional grassy ground shall it graze ?
Options: a ) 1217 , b ) 1219 , c ) 1210 , d ) 1212 , e ) 858
Rationale: "π ( 232 – 162 ) = 858 answer : e"
Answer: e
Problem: the edges of a cuboid are 4 cm , 4 cm and 6 cm . find the volume of the cuboid ?
Options: a ) 90 , b ) 60 , c ) 96 , d ) 80 , e ) 72
Rationale: "4 * 4 * 6 = 96 answer : c"
Answer: c
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure m in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 m = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = 10 ans e ."
Answer: e
Problem: the sum of all consecutive odd integers from − 23 to 31 , inclusive , is
Options: a ) 96 , b ) 112 , c ) 158 , d ) 192 , e ) 235
Rationale: the sum of the odd numbers from - 23 to + 23 is 0 . let ' s add the remaining numbers . 25 + 27 + 29 + 31 = 112 the answer is b .
Answer: b
Problem: david obtained 76 , 65 , 82 , 67 and 85 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
Options: a ) 75 , b ) 37 , c ) 26 , d ) 97 , e ) 27
Rationale: "average = ( 76 + 65 + 82 + 67 + 85 ) / 5 = 375 / 5 = 75 . answer : a"
Answer: a
Problem: in a kilometer race , a beats b by 80 meters or 8 seconds . what time does a take to complete the race ?
Options: a ) 77 sec , b ) 92 sec , c ) 67 sec , d ) 16 sec , e ) 76 sec
Rationale: time taken by b run 1000 meters = ( 1000 * 8 ) / 80 = 100 sec . time taken by a = 100 - 8 = 92 sec . answer : b
Answer: b
Problem: the least number which when divided by 5 , 6 , 7 and 8 leaves a remainder 3 , but when divided by 9 leaves no remainder , is
Options: a ) 1677 , b ) 1683 , c ) 2523 , d ) 3363 , e ) none of these
Rationale: explanation : l . c . m of 5 , 6 , 7 , 8 = 840 therefore required number is of the form 840 k + 3 . least value of k for which ( 840 k + 3 ) is divisible by 9 is k = 2 therefore required number = ( 840 x 2 + 3 ) = 1683 . answer : b
Answer: b
Problem: a policeman noticed a criminal from a distance of 240 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 3 minutes ?
Options: a ) 100 m , b ) 120 m , c ) 190 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 3 / 60 ) km = 1 / 20 km = 50 m . . ' . distance between the criminal and policeman = ( 240 - 50 ) m = 190 m . answer : c"
Answer: c
Problem: what least number must be added to 1120 , so that the sum is completely divisible by 23 ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "49 * 23 = 1127 1127 - 1120 = 7 answer : e"
Answer: e
Problem: 24 men can complete a work in 16 days . 32 women can complete the same work in 24 days . 16 men and 16 women started working and worked for 12 days . how many more men are to be added to complete the remaining work in 2 days ?
Options: a ) 16 , b ) 24 , c ) 36 , d ) 48 , e ) 49
Rationale: explanation : 1 man ’ s 1 day work = 1 / 384 1 woman ’ s 1 day work = 1 / 768 work done in 12 days = 12 ( 16 / 384 + 16 / 768 ) = 12 * 3 / 48 = 3 / 4 remaining work = 1 / 4 ( 16 men + 16 women ) ’ s 2 day work = 2 ( 16 / 384 + 16 / 768 ) = 1 / 8 remaining work = 1 / 4 - 1 / 8 = 1 / 8 1 / 384 work is done in 1 day by 1 man 1 / 8 work will be done in 2 days by 384 x 1 / 8 x 1 / 2 = 24 men answer : option b
Answer: b
Problem: at an elementary school , 60 % of the faculty members are women and 60 % of the faculty members are married . if 3 / 4 of the men are single , what fraction of the women are married ?
Options: a ) 5 ⁄ 7 , b ) 7 ⁄ 10 , c ) 1 ⁄ 3 , d ) 7 ⁄ 30 , e ) 5 ⁄ 6
Rationale: "2 x 2 table works perfect : - - - - - - - - - - - - - - - - - - - - m - - - - - - w - - - - - - - - total marrried - - - - - - - - - 10 - - - - - 50 - - - - - - - - - 60 not married - - - - - 30 - - - - - 10 - - - - - - - - - 40 total - - - - - - - - - - - - - 40 - - - - - 60 - - - - - - - - 100 need married woman / total woman , so 50 / 60 = 5 / 6 e"
Answer: e
Problem: the manager of a produce market purchased a quantity of tomatoes for $ 0.80 per pound . due to improper handling , 10 percent of the tomatoes , by weight , were ruined and discarded . at what price per pound should the manager sell the remaining tomatoes if she wishes to make a profit on the sale of the tomatoes equal to 8 percent of the cost of the tomatoes .
Options: a ) $ 0.94 , b ) $ 0.96 , c ) $ 0.98 , d ) $ 1.00 , e ) $ 1.20
Rationale: "assume the manager bought 100 tomatoes . cost price = 80 given : 10 % are damaged - - > available tomatoes to sell = 90 90 * x - 80 = 0.08 * 80 90 x - 80 = 6.4 90 x = 86.64 x = 86.64 / 90 = 87 / 90 ( approx ) = 29 / 30 = 0.966 x is slightly under 0.9666 = 0.96 answer : b"
Answer: b
Problem: a group of men decided to do a work in 50 days , but 10 of them became absent . if the rest of the group did the work in 60 days , find the original number of men ?
Options: a ) 60 , b ) 50 , c ) 40 , d ) 100 , e ) 25
Rationale: "original number of men = 10 * 60 / ( 60 - 50 ) = 60 answer is a"
Answer: a
Problem: 30 % of a number is more than 60 % of 50 by 30 . find the number ?
Options: a ) 120 , b ) 200 , c ) 180 , d ) 300 , e ) 140
Rationale: "( 30 / 100 ) * x – ( 60 / 100 ) * 50 = 30 2 / 7 x = 60 x = 200 answer : b"
Answer: b
Problem: operation # is defined as adding a randomly selected two digit multiple of 8 to a randomly selected two digit prime number and reducing the result by half . if operation # is repeated 10 times , what is the probability that it will yield at least two integers ?
Options: a ) 0 % , b ) 10 % , c ) 20 % , d ) 30 % , e ) 40 %
Rationale: any multiple of 8 is even . any two - digit prime number is odd . ( even + odd ) / 2 is not an integer . thus # does not yield an integer at all . therefore p = 0 . answer : a .
Answer: a
Problem: right triangle abc is the base of the prism in the figure above . if ab = ac = â ˆ š 10 and the height of the prism is 4 , what is the volume of the prism ?
Options: a ) 40 , b ) 85 , c ) 20 , d ) 60 , e ) 45
Rationale: "volume of prism = area of base * height = 1 / 2 * ( square root of 10 ) * ( square root of 10 ) * 4 = 20 answer : c"
Answer: c
Problem: a woman swims downstream 54 km and upstream 6 km taking 6 hours each time , what is the speed of the woman in still water ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "54 - - - 6 ds = 9 ? - - - - 1 6 - - - - 6 us = 1 ? - - - - 1 m = ? m = ( 9 + 1 ) / 2 = 5 answer : d"
Answer: d
Problem: what is the least number which when divided by 7 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 230 , b ) 240 , c ) 236 , d ) 256 , e ) 266
Rationale: "explanation : lcm of 7 , 9 , 12 and 18 is 252 required number = 252 + 4 = 256 answer : option d"
Answer: d
Problem: how many points ( x , y ) lie on the line segment between ( 15 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?
Options: a ) 1 , b ) 5 , c ) 7 , d ) 8 , e ) 9
Rationale: slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 15 ) = - 5 / 8 y = mx + b = > 12 2 / 3 = - 15 * 5 / 8 + b = > b = 1 y = - 75 x / 8 + 22 only integer values work , and the only multiples of 8 between 7 and 15 for x value is 8 , thus 1 point . a
Answer: a
Problem: a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 per cent is cut away . in the second week 20 per cent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 145 kg , c ) 165 kg , d ) 115 kg , e ) 100 kg
Rationale: "a 105 kg = 250 ã — 0.7 ã — 0.8 ã — 0.75 ."
Answer: a
Problem: a bowl was filled with 10 ounces of water , and 0.008 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 40 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 008 * 50 = . 008 * 100 / 2 = . 8 / 2 = . 4 percent of the original amount of water evaporated during this period = ( . 4 / 10 ) * 100 % = 4 % answer d"
Answer: d
Problem: a goods train runs at the speed of 72 km / hr and crosses a 260 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 260 , e ) 109
Rationale: speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 260 ) / 26 = 20 x = 260 m . answer : d
Answer: d
Problem: when positive integer n is divided by positive integer j , the remainder is 12 . if n / j = 134.08 , what is value of j ?
Options: a ) 22 , b ) 56 , c ) 78 , d ) 112 , e ) 150
Rationale: "1 ) we know that decimal part of decimal quotient = { remainder / divisor } so 0.08 , the decimal part of the decimal quotient , must equal the remainder , 12 , divided by the divisor j . 0.08 = 12 / j 0.08 * j = 12 j = 12 / 0.08 = 1200 / 8 = 300 / 2 = 150 so j = 150 , answer = e ."
Answer: e
Problem: q is a set of 8 distinct prime numbers . if the sum of the integers in q is even and the number x is a member of q , then what is the least value that x can be ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 7
Rationale: 2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 = 77 ( discard as sum is odd ) 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 = 98 ( sum is even ) least number = 3 b
Answer: b
Problem: in a fuel station the service costs $ 1.75 per car , every liter of fuel costs 0.65 $ . assuming that a company owns 12 cars and that every fuel tank contains 58 liters and they are all empty , how much money total will it cost to fuel all cars ?
Options: a ) 320.40 $ , b ) 383.40 $ , c ) 420.40 $ , d ) 450.40 $ , e ) 473.40 $
Rationale: "total cost = ( 1.75 * 12 ) + ( 0.65 * 12 * 58 ) = 473.40 hence answer will be ( e )"
Answer: e
Problem: in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,7 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 4 / 7 , b ) 2 / 3 , c ) 3 / 5 , d ) 3 / 7 , e ) 1 / 2
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 7 = 14 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 14 = 4 / 7 the answer is a ."
Answer: a
Problem: ( 565945 x 121 ) = ?
Options: a ) 68463812 , b ) 68463813 , c ) 68479345 , d ) 68463814 , e ) 68463814
Rationale: 565945 * 121 = 68479345 ans c
Answer: c
Problem: mixture a is 20 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 3 gallons , b ) 4 gallons , c ) 5 gallons , d ) 10 gallons , e ) 12 gallons
Rationale: let a = number of gallons on mixture a in 15 gallon mixture b = number of gallons on mixture b in 15 gallon mixture ( 20 / 100 ) a + ( 50 / 100 ) b = ( 30 / 100 ) ( a + b ) - - 1 a + b = 15 - - 2 on solving equations 1 and 2 , we get a = 10 b = 5 answer d 10 gallons
Answer: d
Problem: sum of two numbers prime to each other is 14 and their l . c . m . is 45 . what are the numbers ?
Options: a ) 6 and 5 , b ) 8 and 5 , c ) 9 and 5 , d ) 8 and 5 , e ) 3 and 5
Rationale: "as two numbers are prime , satisfies all but option c will make the product of numbers i . e 45 answer : c"
Answer: c
Problem: if 5 is one solution of the equation x ^ 2 + 3 x + k = 10 , where k is a constant , what is the other solution ?
Options: a ) - 8 , b ) - 4 , c ) - 3 , d ) 1 , e ) 6
Rationale: "the phrase “ 5 is one solution of the equation ” means that one value of x is 5 . thus , we first must plug 5 for x into the given equation to determine the value of k . so we have 5 ^ 2 + ( 3 ) ( 5 ) + k = 10 25 + 15 + k = 10 40 + k = 10 k = - 30 next we plug - 30 into the given equation for k and then solve for x . x ^ 2 + 3 x – 30 = 10 x ^ 2 + 3 x – 40 = 0 ( x + 8 ) ( x - 5 ) = 0 x = - 8 or x = 5 thus , - 8 is the other solution . answer a ."
Answer: a
Problem: if 350 ! / 10 ^ n is an integer , what is the largest possible value of n ?
Options: a ) 88 , b ) 82 , c ) 86 , d ) 87 , e ) 80
Rationale: "the question actually asks the highest power of 10 which divides 350 ! ( for a number to be an integer - without any remainder all the trailing zeroe ' s must be divided by the denominator ) 10 = 2 x 5 350 factorial will have 86 as - 350 / 5 = 70 70 / 5 = 14 14 / 5 = 2 so answer will be ( c ) 86"
Answer: c
Problem: a person decided to build a house in 100 days . he employed 100 men in the beginning and 100 more after 80 days and completed the construction in stipulated time . if he had not employed the additional men , how many days behind schedule would it have been finished ?
Options: a ) 40 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "200 men do the rest of the work in 100 - 80 = 20 days 100 men can do the rest of the work in 20 * 200 / 100 = 40 days required number of days = 40 - 80 = 40 days answer is a"
Answer: a