regisss/math_qa huggingface dataset:
Problem: how many seconds will a 200 m 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 ) 26 sec , b ) 30 sec , c ) 12 sec , d ) 19 sec , e ) 12 sec
Rationale: "speed of train relative to man = 63 - 3 = 60 km / hr . = 60 * 5 / 18 = 50 / 3 m / sec . time taken to pass the man = 200 * 3 / 50 = 12 sec . answer : c"
Answer: c
Problem: the radius of a cone is 4 m , height 5 m . find the curved surface area ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "cone curved surface area = π rl = 22 / 7 × 4 × 5 = 440 / 7 = 62 6 / 7 slant height ( l ) = √ r ( power 2 ) + h ( power 2 ) = √ 16 + 9 = √ 25 = 5"
Answer: c
Problem: a constructor estimates that 8 people can paint mr khans house in 3 days . if he uses 4 people instead of 8 , how long will they take to complete the job ?
Options: a ) 6 , b ) 8 , c ) 3 , d ) 4 , e ) 0
Rationale: "explanation : use formula for a work members ã — days = constant 8 ã — 3 = 4 ã — a a = 6 so answer is 6 days answer : a"
Answer: a
Problem: the radius of a semi circle is 70 cm then its perimeter is ?
Options: a ) 32.8 , b ) 32.4 , c ) 360 , d ) 32.2 , e ) 32.9
Rationale: "diameter = 140 cm 1 / 2 * 22 / 7 * 140 + 140 = 360 answer : c"
Answer: c
Problem: a cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.3 m and its walls are 5 cm thick . the thickness of the bottom is :
Options: a ) 90 cm , b ) 3 dm , c ) 1 m , d ) 1.1 cm , e ) none of these
Rationale: "explanation : let the thickness of the bottom be x cm . then , [ ( 330 - 10 ) × ( 260 - 10 ) × ( 130 - x ) ] = 8000 × 1000 = > 320 × 250 × ( 130 - x ) = 8000 × 1000 = > ( 130 - x ) = 8000 × 1000 / 320 = 100 = > x = 30 cm = 3 dm . answer : b"
Answer: b
Problem: operation # is defined as adding a randomly selected two digit multiple of 12 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 12 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: running at their respective constant rate , machine x takes 2 days longer to produce w widgets than machines y . at these rates , if the two machines together produce 5 w / 4 widgets in 3 days , how many days would it take machine x alone to produce 6 w widgets .
Options: a ) 4 , b ) 36 , c ) 8 , d ) 10 , e ) 12
Rationale: i am getting 12 . e . hope havent done any calculation errors . . approach . . let y = no . of days taken by y to do w widgets . then x will take y + 2 days . 1 / ( y + 2 ) + 1 / y = 5 / 12 ( 5 / 12 is because ( 5 / 4 ) w widgets are done in 3 days . so , x widgets will be done in 12 / 5 days or 5 / 12 th of a widget in a day ) solving , we have y = 4 = > x takes 6 days to doing x widgets . so , he will take 36 days to doing 6 w widgets . answer : b
Answer: b
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1230 , find the loss % ?
Options: a ) 18 % , b ) 19 % , c ) 68 % , d ) 19 % , e ) 38 %
Rationale: "1500 - - - - 270 100 - - - - ? = > 18 % answer : a"
Answer: a
Problem: among the two clocks , clock a gains 20 seconds per minute . if clock a and b are set at 2 0 ' clock , when clock a is at 7 : 20 , what does clock b show ?
Options: a ) 5 : 30 , b ) 6 : 00 , c ) 5 : 45 , d ) 6 : 20 , e ) 3 : 30
Rationale: clock a gains 20 seconds per minute , 1200 seconds per hour or 20 minutes per hour . the two clocks show 2 : 00 at 2 0 ' clock at 3 : 00 - clock b is at 3 : 00 clock a is at 3 : 20 ( 1 hour + gains 20 minutes ) at 4 : 00 - clock b is at 4 : 00 clock a is at 4 : 40 ( 2 hours + gains 40 minutes ) in 4 hours the clock a gains 4 * 20 = 80 minutes or 1 hour 20 minutes if clock a is at 7 : 20 the clock b is at 6 : 00 answer is b
Answer: b
Problem: the sale price sarees listed for rs . 500 after successive discount is 10 % and 5 % is ?
Options: a ) 427.5 , b ) 277 , c ) 342 , d ) 882 , e ) 212
Rationale: "500 * ( 90 / 100 ) * ( 95 / 100 ) = 427.5 answer : a"
Answer: a
Problem: the number of timeshare condos available at sunset beach is 2 / 5 the number of timeshare condos available at playa del mar . if the total number of timeshare condos available at the two beaches combined is 350 , what is the difference between the number of condos available at sunset beach and the number of condos available at playa del mar ?
Options: a ) 60 , b ) 90 , c ) 120 , d ) 150 , e ) 240
Rationale: let x be the number of timeshare condos available at playa del mar . then number of timeshare condos available at sunset beach = 3 / 5 x we know , x + 2 / 5 x = 350 hence , x = 250 . so , number of timeshare condos available at playa del mar = 250 the difference between the number of condos available at sunset beach and the number of condos available at playa del mar = x - 2 / 5 x = 3 / 5 x = 3 / 5 ( 250 ) = 150 the correct answer is d
Answer: d
Problem: a can do a piece of work in 8 days and b alone can do it in 12 days . how much time will both take to finish the work ?
Options: a ) a ) 4.8 , b ) b ) 6.333 , c ) c ) 7.333 , d ) d ) 8.5 , e ) e ) 9
Rationale: "this question can be solved by different methods . we need to conserve time in exams so solving this problem using equations is the good idea . time taken to finish the job = xy / ( x + y ) = 8 x 12 / ( 8 + 12 ) = 96 / 20 = 4.8 days answer : a"
Answer: a
Problem: the measurement of a rectangular box with lid is 25 cmx 6 cmx 18 cm . find the volume of the largest sphere that can be inscribed in the box ( in terms of π cm 3 ) . ( hint : the lowest measure of rectangular box represents the diameter of the largest sphere )
Options: a ) 288
b ) 48
c ) 36
d ) 864
e ) 964
Rationale: d = 6 , r = 2 ; volume of the largest sphere = 4 / 3 π r 3 = 4 / 3 * π * 3 * 3 * 3 = 36 π cm 3 answer : c
Answer: c
Problem: a and b go around a circular track of length 150 m on a cycle at speeds of 36 kmph and 54 kmph . after how much time will they meet for the first time at the starting point ?
Options: a ) 30 sec , b ) 198 sec , c ) 178 sec , d ) 665 sec , e ) 276 sec
Rationale: "time taken to meet for the first time at the starting point = lcm { length of the track / speed of a , length of the track / speed of b } = lcm { 150 / ( 36 * 5 / 18 ) , 150 / ( 54 * 5 / 18 ) } = lcm ( 15 , 10 ) = 30 sec . answer : a"
Answer: a
Problem: maxwell leaves his home and walks toward brad ' s house at the same time that brad leaves his home and runs toward maxwell ' s house . if the distance between their homes is 50 kilometers , maxwell ' s walking speed is 4 km / h , and brad ' s running speed is 6 km / h , what is the distance traveled by brad ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 24 , e ) 30
Rationale: "time taken = total distance / relative speed total distance = 50 kms relative speed ( opposite side ) ( as they are moving towards each other speed would be added ) = 6 + 4 = 10 kms / hr time taken = 50 / 10 = 5 hrs distance traveled by brad = brad ' s speed * time taken = 6 * 5 = 30 kms . . . answer - e"
Answer: e
Problem: two trains of length 150 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively . in what time will they be clear of each other from the moment they meet ?
Options: a ) 22 sec , b ) 77 sec , c ) 76 sec , d ) 21.5 sec , e ) 66 sec
Rationale: "relative speed = ( 42 + 30 ) * 5 / 18 = 4 * 5 = 20 mps . distance covered in passing each other = 150 + 280 = 430 m . the time required = d / s = 430 / 20 = 21.5 sec . answer : d"
Answer: d
Problem: source : knewton a cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . what is the maximum distance , in miles , that the cyclist could travel in 5 hours ?
Options: a ) 42 , b ) 56 , c ) 70 , d ) 98 , e ) 140
Rationale: we are told that : generallya cyclist ' s speed varies , depending on the terrain , between 6.0 miles per hour and 14.0 miles per hour , inclusive . is it possible the cyclist to travel with maximum speed for some time ? why not , if there is right terrain for that . so , if there is long enough terrain for the maximum speed of 14 mph then the maximum distance , in miles , that the cyclist could travel in 5 hours would be 5 * 14 = 70 miles . answer : c .
Answer: c
Problem: elena purchased brand x pens for $ 4.00 apiece and brand y for $ 2.40 apiece . if elena purchased a total of 12 of these pens for $ 42.00 , how many brand x pens did she purchase ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "4 x + 2.8 y = 42 - - > multiply by 2.5 ( to get the integers ) - - > 10 x + 7 y = 105 - - > only one positive integers solutions x = 5 and y = 5 ( how to solve : 7 y must have the last digit of 5 in order the last digit of the sum to be 5 ) . answer : b ."
Answer: b
Problem: the length of a rectangle is two - seventh of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 5929 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 25 units ?
Options: a ) 660 sq . units
b ) 440 sq . units
c ) 770 sq . units
d ) 550 sq . units
e ) 220 sq . units
Rationale: given that the area of the square = 5929 sq . units = > side of square = â ˆ š 5929 = 77 units the radius of the circle = side of the square = 77 units length of the rectangle = 2 / 7 * 77 = 22 units given that breadth = 25 units area of the rectangle = lb = 22 * 25 = 550 sq . units answer : d
Answer: d
Problem: if 20 men take 15 days to to complete a job , in how many days can 25 men finish that work ?
Options: a ) 12 , b ) 66 , c ) 77 , d ) 8 , e ) 6
Rationale: ans . 12 days
Answer: a
Problem: carl is facing very difficult financial times and can only pay the interest on a $ 30,000 loan he has taken . the bank charges him a quarterly compound rate of 5 % . what is the approximate interest he pays annually ?
Options: a ) $ 1200 , b ) $ 2000 , c ) $ 2150 , d ) $ 6000 , e ) $ 12000
Rationale: "usually , you are given the annual rate of interest and it is mentioned that it is annual rate . the bank charges him a quarterly compounded annual rate of 20 % . here you find per quarter rate as ( 20 / 4 ) % = 5 % i have actually never seen a question with quarter rate given but since this question did not mentionannual rate of interestand since the options did not make sense with 5 % annual rate of interest , it is apparent that the intent was a 5 % quarterly rate . so the bank charges 5 % every quarter and compounds it in the next quarter . had it been a simple quarterly rate , we would have just found 4 * 5 % of 30,000 = $ 6000 as our answer . but since , the interest is compounded , it will be a bit more than $ 6000 . option ( d ) looks correct ."
Answer: d
Problem: on a certain transatlantic crossing , 20 percent of a ship ’ s passengers held round - trip tickets and also took their cars abroad the ship . if 50 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ’ s passengers held round - trip tickets ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 65 %
Rationale: "let t be the total number of passengers . let x be the number of people with round trip tickets . 0.2 t had round trip tickets and took their cars . 0.5 x had round trip tickets and took their cars . 0.5 x = 0.2 t x = 0.4 t the answer is b ."
Answer: b
Problem: the pinedale bus line travels at an average speed of 60 km / h , and has stops every 5 minutes along its route . yahya wants to go from his house to the pinedale mall , which is 7 stops away . how far away , in kilometers , is pinedale mall away from yahya ' s house ?
Options: a ) 20 km , b ) 35 km , c ) 40 km , d ) 50 km , e ) 60 km
Rationale: "number of stops in an hour : 60 / 5 = 12 distance between stops : 60 / 12 = 5 km distance between yahya ' s house and pinedale mall : 5 x 7 = 35 km imo , correct answer is ` ` b . ' '"
Answer: b
Problem: if p represents the product of the first 18 positive integers , then p is not a multiple of
Options: a ) 99 , b ) 84 , c ) 72 , d ) 65 , e ) 95
Rationale: "answer is e . since prime factor of 95 is 5 x 19 . 19 is a prime number and not part of the first 18 positive integers . a ) 9 x 11 b ) 12 x 7 c ) 12 x 6 d ) 13 x 5 e ) 3 x 19"
Answer: e
Problem: the fuel indicator in a car shows 1 / 5 th of the fuel tank as full . when 22 more liters of fuel are poured in to the tank , the indicator rests at the 3 / 4 of the full mark . find the capacity of the tank .
Options: a ) 25 litres , b ) 35 litres , c ) 30 litres , d ) 40 litres , e ) none of these
Rationale: x / 5 + 22 = 3 x / 4 = > x = 40 litres answer : d
Answer: d
Problem: a salesman sold twice as much pears in the afternoon than in the morning . if he sold $ 450 kilograms of pears that day , how many kilograms did he sell in the afternoon ?
Options: a ) 120 , b ) 180 , c ) 300 , d ) 280 , e ) 320
Rationale: 3 x = 450 x = 150 therefore , the salesman sold 150 kg in the morning and 2 ⋅ 150 = 300 kg in the afternoon . so answer is c .
Answer: c
Problem: a and b together can complete work in 10 days . a alone starts working and leaves it after working for 6 days completing only half of the work . in how many days it can be completed if the remaining job is undertaken by b ?
Options: a ) 4 , b ) 8 , c ) 5 , d ) 6 , e ) 30
Rationale: "explanation : ( a + b ) one day work = 1 / 10 now a does half of the work in 6 days so a can complete the whole work in 12 days a ’ s one day work = 1 / 12 b ’ s one day work = 1 / 10 - 1 / 12 = 2 / 120 = 1 / 60 b alone can complete the work in 60 days so half of the work in 30 days answer : option e"
Answer: e
Problem: set a consists of the integers from 4 to 16 , inclusive , while set b consists of the integers from 6 to 20 , inclusive . how many distinct integers do belong to the both sets at the same time ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 9 , e ) 11
Rationale: "a = { 4 , 5,6 , 7,8 , 9,10 , 11,12 , . . . 16 } b = { 6 , 7,8 , 9,10 , 11,12 . . . } thus we see that there are 11 distinct integers that are common to both . e is the correct answer ."
Answer: e
Problem: find large no . from below question the difference of two numbers is 1365 . on dividing the larger number by the smaller , we get 6 as quotient and the 30 as remainder
Options: a ) 1235 , b ) 1456 , c ) 1567 , d ) 1632 , e ) 1635
Rationale: "let the smaller number be x . then larger number = ( x + 1365 ) . x + 1365 = 6 x + 30 5 x = 1335 x = 267 large number = 267 + 1365 = 1632 d"
Answer: d
Problem: the sum of the ages of 5 children born at the intervals of 3 years each is 50 years . what is the age of the youngest child ?
Options: a ) 4 years , b ) 8 years , c ) 10 years , d ) 12 years , e ) none of these
Rationale: "let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 5 x = 20 = > x = 4 . age of youngest child = x = 4 years . answer : a"
Answer: a
Problem: paul sells encyclopedias door - to - door . he earns $ 150 on every paycheck , regardless of how many sets he sells . in addition , he earns commission as follows : commission sales 10 % $ 0.00 - $ 10 , 000.00 5 % $ 10 , 000.01 - - - > he does not earn double commission . that is , if his sales are $ 12,000 , he earns 10 % on the first $ 10,000 and 5 % on the remaining $ 2,000 . his largest paycheck of the year was $ 1,320 . what were his sales for that pay period ?
Options: a ) 13,400 , b ) 14,800 , c ) 16,400 , d ) 15,800 , e ) 19,600
Rationale: his pay check was $ 1320 . out of this , $ 150 was his fixed salary so the total commission he earned was $ 1320 - $ 150 = $ 1170 he earns 10 % on the sales of first $ 10,000 which gives a commission of $ 1000 . he earns 5 % on every subsequent dollar . since he earns another $ 170 , he must have had sales of another 170 * ( 100 / 5 ) = 3400 so his total sales must have been $ 10,000 + $ 3400 = $ 13,400 a
Answer: a
Problem: a rectangle with width 8 and diagonal 30 . find the area ?
Options: a ) 240 square units
b ) 180 square units
c ) 100 square units
d ) 150 square units
e ) 160 square units
Rationale: then the area is : 8 ' ' x 30 ' ' = 240 square inches , or 240 square units hence a
Answer: a
Problem: train a leaves the station traveling at 30 miles per hour . two hours later train в leaves the same station traveling in the same direction at 35 miles per hour . how many miles from the station was train a overtaken by train b ?
Options: a ) 420 , b ) 450 , c ) 480 , d ) 510 , e ) 540
Rationale: "after two hours , train a is ahead by 60 miles . train b can catch up at a rate of 5 miles per hour . the time to catch up is 60 / 5 = 12 hours . in 12 hours , train a travels another 30 * 12 = 360 miles for a total of 420 miles . the answer is a ."
Answer: a
Problem: a box contains 25 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 3 / 10 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 95 , e ) none
Rationale: "solution p ( none is defective ) = 21 c 2 / 25 c 2 = 7 / 10 p ( at least one is defective ) = ( 1 - 7 / 10 ) = 3 / 10 . answer a"
Answer: a
Problem: how many prime numbers are between 28 / 3 and 86 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "28 / 3 = 9 . xxx 86 / 6 = 14 . xxx so we need to find prime numbers between 9 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Problem: in a school of 800 students , 44 % wear blue shirts , 28 % wear red shirts , 10 % wear green shirts , and the remaining students wear other colors . how many students wear other colors ( not blue , not red , not green ) ?
Options: a ) 120 , b ) 132 , c ) 144 , d ) 156 , e ) 168
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 800 * 18 / 100 = 144 the answer is c ."
Answer: c
Problem: a man whose speed is 6 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph , find his average speed for the total journey ?
Options: a ) 7 , b ) 5.6 , c ) 6 , d ) 9 , e ) 3
Rationale: "m = 6.0 s = 1.5 ds = 7.5 us = 4.5 as = ( 2 * 7.5 * 4.5 ) / 12 = 5.6 answer : b"
Answer: b
Problem: in what ratio must rice of rs . 25 per kg be mixed with rice of rs . 12 per kg so that cost of mixture is rs . 20 per kg ?
Options: a ) 8 : 5 , b ) 5 : 8 , c ) 20 : 25 , d ) 12 : 20 , e ) 25 : 12
Rationale: "( 20 - 12 ) / ( 25 - 20 = 8 / 5 = 8 : 5 answer : a"
Answer: a
Problem: 10 men and 15 women together can complete a work in 4 days . it takes 100 days for one man alone to complete the same work . how many days will be required for one woman alone to complete the same work ?
Options: a ) 100 days , b ) 667 days , c ) 177 days , d ) 187 days , e ) 225 days
Rationale: "1 man ' s 1 day work = 1 / 100 ( 10 men + 15 women ) ' s 1 day work = 1 / 4 15 women ' s 1 day work = ( 1 / 4 - 10 / 100 ) = 3 / 20 1 woman ' s 1 day work = 1 / 100 1 woman alone can complete the work in 100 days . answer : a"
Answer: a
Problem: if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 4 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 100 , b ) $ 175 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 4 people . so $ 100 . but , he also has to put in the average for himself ( the fiveth person ) , so add $ 75 . so $ 175 is your answer . answer b
Answer: b
Problem: if 0.5 : x : : 5 : 8 , then x is equal to :
Options: a ) a ) 1.12 , b ) b ) 1.2 , c ) c ) 1.25 , d ) d ) 0.9 , e ) e ) 0.8
Rationale: "( x * 5 ) = ( 0.5 * 8 ) x = 4 / 5 x = 0.8 answer = e"
Answer: e
Problem: the average weight of 8 people increases by 2.5 kg when a new person comes in place of one of them weighing 75 kg . what is the weight of the new person ?
Options: a ) 75 kg , b ) 85 kg , c ) 95 kg , d ) 65 kg , e ) 55 kg
Rationale: "the total weight increase = ( 8 x 2.5 ) kg = 20 kg weight of new person = ( 75 + 20 ) kg = 95 kg the answer is c ."
Answer: c
Problem: the radius of a wheel is 12.6 cm . what is the distance covered by the wheel in making 200 resolutions ?
Options: a ) 158.210 m , b ) 704 m , c ) 153.256 m , d ) 158.256 m , e ) 204 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 200 resolutions . = 200 * 2 * 22 / 7 * 12.6 = 15825.6 cm = 158.256 m answer : d"
Answer: d
Problem: simplify : 250 x 250 - 100 x 100
Options: a ) 761200 , b ) 761400 , c ) 52500 , d ) 761500 , e ) none of them
Rationale: "( 250 ) ^ 2 - ( 100 ) ^ 2 = ( 250 + 100 ) ( 250 - 100 ) = 350 x 150 = 52500 . answer is c ."
Answer: c
Problem: on my sister ' s birthday , she was 143 cm in height , having grown 10 % since the year before . how tall was she the previous year ?
Options: a ) 140 cm , b ) 136 cm , c ) 130 cm , d ) 127 cm , e ) 125 cm
Rationale: "let the previous year ' s height be x . 1.1 x = 143 x = 130 the answer is c ."
Answer: c
Problem: if the selling price of 50 articles is equal to the cost price of 35 articles , then the loss or gain percent is :
Options: a ) 45 % , b ) 23 % , c ) 30 % , d ) 60 % , e ) 56 %
Rationale: "c . p . of each article be re . 1 . then , c . p . of 50 articles = rs . 50 ; s . p . of 50 articles = rs . 35 . loss % = 15 / 50 * 100 = 30 % answer c"
Answer: c
Problem: the length of each side of an equilateral triangle having an area of 4 â ˆ š 3 cm 2 is ?
Options: a ) 4 / 3 cm
b ) 3 / 4 cm
c ) 3 cm
d ) 4 cm
e ) 5 cm
Rationale: explanation : â ˆ š 3 / 4 a 2 = 4 â ˆ š 3 - > a = 4 answer is d
Answer: d
Problem: if the sides of a rectangle are increased by 25 % , what is the percentage increase in the area ?
Options: a ) 54.25 % , b ) 56.25 $ , c ) 53.25 % , d ) 55.25 % , e ) 58.25 %
Rationale: "if sides are a and b , after increase sides would be 1.25 a and 1.25 b . percentage increase in area = ( 1.25 a * 1.25 b - ab ) * 100 / ab = 56.25 % answer : b"
Answer: b
Problem: the charge for a single room at hotel p is 30 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 28 % , b ) 20 % , c ) 40 % , d ) 50 % , e ) 150 %
Rationale: "let rate in r = 100 x then p = 70 x g = 100 y p = 90 y thus 70 x = 90 y or x = 1.28 y ans r = 128 y so increase = 28 % answer : a"
Answer: a
Problem: a trader marked the selling price of an article at 11 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 10.5 % , c ) 9.9 % , d ) 12.5 % , e ) none
Rationale: "sol . let c . p . = rs . 100 . then , marked price = rs . 110 , s . p . = rs . 99 . ∴ discount % = [ 11 / 111 * 100 ] % = 9.9 % answer c"
Answer: c
Problem: bottle r contains 250 capsules and costs $ 5.25 . bottle t contains 130 capsules and costs $ 2.99 . what is the difference between the cost per capsule for bottle r and the cost per capsule for bottle t ?
Options: a ) $ 0.25 , b ) $ 0.12 , c ) $ 0.05 , d ) $ 0.03 , e ) $ 0.002
Rationale: cost per capsule in r is 5.25 / 250 = 0.525 / 25 = 0.021 cost per capsule in t is 2.99 / 130 = 0.023 the difference is 0.002 the answer is e
Answer: e
Problem: sushil got thrice as many marks in english as in science . his total marks in english , science and maths are 162 . if the ratio of his marks in english and maths is 4 : 5 , find his marks in science ?
Options: a ) 10.9 , b ) 20.9 , c ) 30.9 , d ) 35 , e ) 45
Rationale: "s : e = 1 : 3 e : m = 4 : 5 - - - - - - - - - - - - s : e : m = 4 : 12 : 15 4 / 31 * 162 = 20.9 answer : b"
Answer: b
Problem: solve the equation for x : 21 ( x + y ) + 5 = 21 ( - x + y ) + 47
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 2 , e ) 1
Rationale: "e 1 21 ( x + y ) + 5 = 21 ( - x + y ) + 47 21 x + 21 y + 5 = - 21 x + 21 y + 47 21 x + 5 = - 21 x + 47 42 x = 42 = > x = 1"
Answer: e
Problem: area of four walls of a room is 99 m 2 . the length and breadth of the room are 7.5 m and 3.5 m respectively . the height of the room is :
Options: a ) 2.5 m
b ) 3.5 m
c ) 1.5 m
d ) 4.5 m
e ) 5.5 m
Rationale: 2 ( 7.5 + 3.5 ) × h = 99 2 ( 11 ) h = 99 22 h = 99 h = 99 / 22 = 9 / 2 = 4.5 m answer is d .
Answer: d
Problem: x is a positive integer less than 300 . when x is divided by 7 , the remainder is 1 ; when x is divided by 3 , the remainder is 2 . how many x are there ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "the nubmer which when divided by 7 leaves remainder 1 should be of the form 7 k + 1 this number when divided by 3 leaves remainder 2 . so , ( 7 k + 1 ) - 2 should be divisible by 3 or 7 k - 1 should be divisible by 3 . we now put the values of k starting from 0 to find first number divisible by 3 we find 1 st number at k = 1 thus smallest number will be 7 ( 1 ) + 1 = 8 now , next number will be = 8 + lcm of 37 i . e 29 now we will find number of all such values less than 500 by using the formula for last term of an a . p 8 + ( n - 1 ) 21 = 300 n = 22.13 or n = 22 answer : - b"
Answer: b
Problem: how many different ways can 2 students be seated in a row of 4 desks , so that there is always at least one empty desk between the students ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "total cases : 12 ( student one has 4 options and student two has three options , 4 x 3 = 12 ) non - favourable cases : 6 ( when two students sit together . students in desk 1 and desk 2 , in desk 2 and desk 3 , in desk 3 and desk 4 ) for each of these cases there are two possibilities because the positions can be interchanged . hence 2 x 3 = 6 . so favourable cases : 12 - 6 = 6 . answer : d"
Answer: d
Problem: if each side of a square is increased by 25 % , find the percentage change in its area ?
Options: a ) 56.29 % , b ) 56.25 % , c ) 56.95 % , d ) 53.25 % , e ) 36.25 %
Rationale: "let each side of the square be a , then area = a x a new side = 125 a / 100 = 5 a / 4 new area = ( 5 a x 5 a ) / ( 4 x 4 ) = ( 25 a ² / 16 ) increased area = = ( 25 a ² / 16 ) - a ² increase % = [ ( 9 a ² / 16 ) x ( 1 / a ² ) x 100 ] % = 56.25 % answer : b"
Answer: b
Problem: a dishonest dealer professes to sell goods at the cost price but uses a weight of 720 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 25 % , c ) 38.9 % , d ) 45 % , e ) 35 %
Rationale: "explanation : 720 - - - 280 100 - - - ? = > 38.9 % answer : c"
Answer: c
Problem: if the mean of numbers 28 , x , 42 , 78 , 82 and 104 is 62 , then what is the mean of 128 , 255 , 511 , 1023 and x ?
Options: a ) 395 , b ) 275 , c ) 391 , d ) 415 , e ) 365
Rationale: "the mean of numbers 28 , x , 42 , 78 and 104 is 62 : 28 + x + 42 + 78 + 82 + 104 = 62 * 6 - - > x = 38 ; so , the mean of 128 , 255 , 511 , 1023 and x is ( 128 + 255 + 511 + 1023 + 38 ) / 5 = 391 . answer : c ."
Answer: c
Problem: machine a produces 100 parts twice as fast as machine b does . machine b produces 100 parts in 80 minutes . if each machine produces parts at a constant rate , how many parts does machine a produce in 20 minutes ?
Options: a ) 60 , b ) 80 , c ) 70 , d ) 40 , e ) 50
Rationale: machine b produces 100 part in 80 minutes . machine a produces 100 parts twice as fast as b , so machine a produces 100 parts in 80 / 2 = 40 minutes . now , machine a produces 100 parts in 40 minutes which is 100 / 40 = 10 / 4 parts / minute . 10 / 4 parts x a total of 20 minutes = 10 / 4 * 20 = 50 e
Answer: e
Problem: if x and y are integers such that | y + 3 | ≤ 3 and 2 y – 3 x + 6 = 0 , what is the least possible value t of the product xy ?
Options: a ) - 12 , b ) - 3 , c ) 0 , d ) 2 , e ) none of the above
Rationale: "how to deal with inequalities involving absolute values ? first example shows us the so callednumber case in this case we have | y + 3 | ≤ 3 which is generalized | something | ≤ some number . first we solve as if there were no absolute value brackets : y + 3 ≤ 3 y ≤ 0 so y is 0 or negative second scenario - remove the absolute value brackets . put a negative sign around the other side of the inequality , andflip the sign : y + 3 > = - 3 y > = - 6 therefore we have a possible range for y : - 6 = < y < = 0 ok , so far so good , we ' re half way through . what about x ? here ' s the formula : 2 y – 3 x + 6 = 0 , rewrite it as 2 y + 6 = 3 x . you can say that 2 y + 6 is a multiple of 3 ( = 3 x ) . so all values which must be integer must also satisfy this constraint . i ' m just saying that , so it ' s easier to evaluate all the possible numbers ( - 6 , - 3 , 0 ) . if you plug in y = 0 , x will be 2 and xy = 0 as the lowest possible value t . hence , answer choice c is the one to go ."
Answer: c
Problem: a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 66 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 83 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 66 % is one st . dev , then on either side of m we have 66 / 2 = 33 % . so , 33 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 33 = 83 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 83 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c"
Answer: c
Problem: in a class of 54 students , 12 enrolled for both english and german . 22 enrolled for german . if the students of the class enrolled for at least one of the two subjects , then how many students enrolled for only english and not german ?
Options: a ) 30 , b ) 10 , c ) 18 , d ) 28 , e ) 32
Rationale: "total = english + german - both + neither - - > 54 = english + 22 - 12 + 0 - - > english = 44 - - > only english = english - both = 44 - 12 = 32 . answer : e ."
Answer: e
Problem: usc invited each south carolina high school to send up to 39 students to watch a football game . a section which has 199 seats in each row is reserved for those students . what is the least number of rows needed to guarantee that if 2006 students show up , then all students from the same high school can be seated in the same row ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: the answer is 12 rows . if 59 schools send 34 students each , then we can sit at most 5 groups of students in the same row , so we will need 12 rows . next , 12 rows are sufficient . assume that this is not the case . suppose the groups of students are seated like this : first the largest group , then the second largest group , then the third largest group , etc . suppose we run out of space - there are not enough seats in any row to seat together the next group . suppose the first group that can not be seated together is the kth group and it consists of n students . then k 61 since any row fits at least 5 groups . also , n 2006 / k 2006 / 61 < 33 ( all groups already seated are no smaller than the kth group ) . so , n 32 . since there is not enough space in any of the 12 rows to seat the kth group , then there must be at least 168 students seated in each of the 12 rows . now , 12 × 168 = 2016 > 2006 a contradiction . so , 12 rows are sufficient . correct answer b
Answer: b
Problem: a rectangular photograph is surrounded by a border that is 1 inch wide on each side . the total area of the photograph and the border is m square inches . if the border had been 3 inches wide on each side , the total area would have been ( m + 64 ) square inches . what is the perimeter of the photograph , in inches ?
Options: a ) 16
b ) 24
c ) 32
d ) 40
e ) 48
Rationale: let x and y be the width and length of the photograph . ( x + 2 ) ( y + 2 ) = m and so ( 1 ) xy + 2 x + 2 y + 4 = m ( x + 6 ) ( y + 6 ) = m and so ( 2 ) xy + 6 x + 6 y + 36 = m + 64 let ' s subtract equation ( 1 ) from equation ( 2 ) . 4 x + 4 y + 32 = 64 2 x + 2 y = 16 , which is the perimeter of the photograph . the answer is a .
Answer: a
Problem: a “ palindromic integer ” is an integer that remains the same when its digits are reversed . so , for example , 43334 and 516615 are both examples of palindromic integers . how many 6 - digit palindromic integers are both even and greater than 300,000 ?
Options: a ) 200 , b ) 216 , c ) 300 , d ) 400 , e ) 2,500
Rationale: "the first digit and last digit are the same so the 3 possibilities are 4 , 6 , or 8 . the second and third digits can be any digit from 0 to 9 . the total number of palindromic integers is 3 * 10 * 10 = 300 the answer is c ."
Answer: c
Problem: the unit digit in the product 4556 * 3432 * 4581 * 2784 is ?
Options: a ) 8 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: unit digit in the given product = unit digit in 6 * 2 * 1 * 4 = 8 answer is a
Answer: a
Problem: for any positive number x , the function [ x ] denotes the greatest integer less than or equal to x . for example , [ 1 ] = 1 , [ 1.367 ] = 1 and [ 1.996 ] = 1 . if k is a positive integer such that k ^ 2 is divisible by 45 and 80 , what is the units digit of k ^ 3 / 4000 ?
Options: a ) 0 , b ) 1 , c ) 0 , d ) 54 , e ) can not be determined
Rationale: "k = [ lcm of 80 and 45 ] * ( any integer ) however minimum value of k is sq . rt of 3 ^ 2 * 4 ^ 2 * 5 ^ 2 = 60 * any integer for value of k ( 60 ) * any integer unit value will be always zero . c"
Answer: c
Problem: a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 276 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 184 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: "explanation : let the length of train be l m . acc . to question ( 276 + l ) / 20 = l / 8 2208 + 8 l = 20 l l = 2208 / 12 = 184 m answer a"
Answer: a
Problem: to be considered for “ movie of the year , ” a film must appear in at least 1 / 4 of the top - 10 - movies lists submitted by the cinematic academy ’ s 760 members . what is the smallest number of top - 10 lists a film can appear on and still be considered for “ movie of the year ” ?
Options: a ) 191 , b ) 190 , c ) 193 , d ) 212 , e ) 213
Rationale: "total movies submitted are 760 . as per question we need to take 1 / 4 of 760 to be considered for top 10 movies = 190 approximate the value we 190 . imo option b is the correct answer . . ."
Answer: b
Problem: each child has 4 crayons and 14 apples . if there are 9 children , how many crayons are there in total ?
Options: a ) 22 , b ) 65 , c ) 12 , d ) 36 , e ) 10
Rationale: 4 * 9 = 36 . answer is d .
Answer: d
Problem: a man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes . if the ratio between the length and breadth of the park be 3 : 2 , then its area is :
Options: a ) 1536 m 2
b ) 15360 m 2
c ) 153600 m 2
d ) 163600 m 2
e ) none of these
Rationale: perimeter = distance covered in 8 min = ( 12000 / 60 * 8 ) m = 1600 m let , length = 3 x meters and breadth = 2 x meters then , 2 ( 3 x + 2 x ) = 1600 or x = 160 therefore , length = 480 m and breadth = 320 m therefore , area = ( 480 * 320 ) m 2 = 153600 m 2 answer : c
Answer: c
Problem: find the value of m 12519 x 9999 = m ?
Options: a ) 125177481 , b ) 353654655 , c ) 545463251 , d ) 725117481 , e ) 477899932
Rationale: "12519 x 9999 = 12519 x ( 10000 - 1 ) = 12519 x 10000 - 12519 x 1 = 125190000 - 12519 = 125177481 a"
Answer: a
Problem: a is twice as good a workman as b and they took 9 days together to do the work b alone can do it in .
Options: a ) 17 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 27 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 9 x = 1 / 27 = > 27 days answer : e"
Answer: e
Problem: find the value of ( 875 233 / 899 ) × 899
Options: a ) 786845 , b ) 786857 , c ) 786858 , d ) 786859 , e ) 786860
Rationale: "( 875 233 / 899 ) × 899 ( 786625 + 233 ) / 899 × 899 786858 / 899 × 899 786858 c"
Answer: c
Problem: a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 2.00 , what total number of pens and pencils did the customer purchase ?
Options: a ) 6 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "answer : aalgebraically , the question looks like this : 2.5 = 0.35 x + 0.25 ythere are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 and 1 pencils for $ 0.25 each . that ' s 5 pens and 1 pencils for a total of 6 pens and pencils . choice ( a ) is correct ."
Answer: a
Problem: the length of the bridge , which a train 130 metres long and travelling at 108 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 245 m , d ) 170 m , e ) 240 m
Rationale: "speed = [ 108 x 5 / 18 ] m / sec = 30 m / sec time = 10 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 10 = > 130 + x = 300 = > x = 170 m . answer : d"
Answer: d
Problem: what is the smallest number which , when increased by 9 , is divisible by 7 , 8 , and 24 ?
Options: a ) 143 , b ) 150 , c ) 159 , d ) 168 , e ) 177
Rationale: "lcm ( 7 , 8,24 ) = 24 x 7 = 168 so the least divisible number is 168 , and the number we are looking for is 168 - 9 = 159 . the answer is c ."
Answer: c
Problem: what is the sum of all the prime numbers greater than 50 but less than 70 ?
Options: a ) 249 , b ) 248 , c ) 246 , d ) 240 , e ) 241
Rationale: "required sum = ( 53 + 59 + 61 + 67 ) = 240 note : 1 is not a prime number answer d"
Answer: d
Problem: the length of a rectangular floor is more than its breadth by 200 % . if rs . 150 is required to paint the floor at the rate of rs . 2 per sq m , then what would be the length of the floor ?
Options: a ) 65 , b ) 15 , c ) 18 , d ) 16 , e ) 14
Rationale: "let the length and the breadth of the floor be l m and b m respectively . l = b + 200 % of b = l + 2 b = 3 b area of the floor = 150 / 2 = 75 sq m l b = 75 i . e . , l * l / 3 = 75 l 2 = 225 = > l = 15 answer : b"
Answer: b
Problem: a car traveled from san diego to san francisco at an average speed of 66 miles per hour . if the journey back took twice as long , what was the average speed of the trip ?
Options: a ) 24 . , b ) 32 . , c ) 36 . , d ) 42 . , e ) 44 .
Rationale: "let the time taken be = x one way distance = 66 x total distance traveled = 2 * 66 x = 132 x total time taken = x + 2 x = 3 x average speed = 132 x / 3 x = 44 answer : e"
Answer: e
Problem: a cube of side 5.5 meter length is cut into small cubes of side 110 cm each . how many such small cubes can be obtained ?
Options: a ) 125 , b ) 127 , c ) 152 , d ) 140 , e ) 190
Rationale: "along one edge , the number of small cubes that can be cut = 550 / 110 = 5 along each edge 5 cubes can be cut . ( along length , breadth and height ) . total number of small cubes that can be cut = 5 * 5 * 5 = 125 answer : a"
Answer: a
Problem: rates for having a manuscript typed at a certain typing service are $ 5 per page for the first time a page is typed and $ 2 per page each time a page is revised . if a certain manuscript has 100 pages , of which 40 were revised only once , 10 were revised twice , and the rest required no revisions , what was the total cost of having the manuscript typed ?
Options: a ) $ 430 , b ) $ 620 , c ) $ 650 , d ) $ 680 , e ) $ 770
Rationale: "for 100 - 40 - 10 = 50 pages only cost is 5 $ per page for the first time page is typed - 50 * 5 = 250 $ ; for 40 pages the cost is : first time 5 $ + 2 $ of the first revision - 40 * ( 5 + 2 ) = 280 $ ; for 10 pages the cost is : first time 5 $ + 2 $ of the first revision + 2 $ of the second revision - 10 ( 5 + 2 + 2 ) = 90 $ ; total : 250 + 280 + 90 = 620 $ . answer : b ."
Answer: b
Problem: some persons can do a piece of work in 32 days . two times the number of these people will do half of that work in ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 8
Rationale: 32 / ( 2 * 2 ) = 8 days answer : e
Answer: e
Problem: what is the units digit of 33 ^ 2 * 17 ^ 3 * 39 ^ 2 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 39 ^ 2 is the units digit of 9 * 9 = 81 which is 1 . the units digit of 9 * 3 * 1 = 27 is 7 . the answer is d ."
Answer: d
Problem: a department of 10 people - 6 men and 4 women - needs to send a team of 5 to a conference . if they want to make sure that there are no more than 3 members of the team from any one gender , how many distinct groups are possible to send ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 210 , e ) 240
Rationale: they can make a team of 3 men and 2 women . the number of ways to do this is 6 c 3 * 4 c 2 = 20 * 6 = 120 they can make a team of 2 men and 3 women . the number of ways to do this is 6 c 2 * 4 c 3 = 15 * 4 = 60 the total number of distinct groups is 180 . the answer is c .
Answer: c
Problem: an error 3 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 9.09 % , b ) 4.02 % , c ) 4 % , d ) 3 % , e ) 2 %
Rationale: "percentage error in calculated area = ( 3 + 3 + ( 3 ã — 3 ) / 100 ) % = 9.09 % answer : a"
Answer: a
Problem: uncle bruce is baking chocolate chip cookies . he has 40 ounces of dough ( with no chocolate ) and 20 ounces of chocolate . how much chocolate is left over if he uses all the dough but only wants the cookies to consist of 25 % chocolate ?
Options: a ) 8.5 , b ) 9.5 , c ) 10.5 , d ) 6.7 , e ) 6.5
Rationale: "first , you must find the total weight of the mixture given that 80 % of it will be dough . 75 % * total = 40 = > ( 75 / 100 ) total = 40 = > total = 4000 / 75 = > total = 53.33 oz , from there , you must find 25 % of the total 53.33 oz of the mixture . 25 % * total = > ( 25 / 100 ) ( 53.33 ) = 13.33 oz choclate used , not forgetting that the question asks how much chocolate is left over we must subtract the chocolate used from the initial chocolate . 20 - 13.3 = 6.7 oz chocolate left over . answer : d"
Answer: d
Problem: two pipes a and b can separately fill a tank in 10 and 15 minutes respectively . a third pipe c can drain off 20 liters of water per minute . if all the pipes are opened , the tank can be filled in 15 minutes . what is the capacity of the tank ?
Options: a ) 150 liters , b ) 540 liters , c ) 200 liters , d ) 560 liters , e ) 580 liters
Rationale: "1 / 10 + 1 / 15 - 1 / x = 1 / 15 x = 10 10 * 20 = 200 answer : c"
Answer: c
Problem: a and b started a business investing rs . 90,000 and rs 25,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 2 , c ) 18 : 20 , d ) 18 : 5 , e ) 17 : 4
Rationale: "a : b = 90000 : 25000 = 90 : 25 = 18 : 5 answer : d"
Answer: d
Problem: we invested a total of $ 1,000 . we invested one part of the money at 3 % and the rest of the money at 4 % . the total investment with interest at the end of the year was $ 1 , 036.70 . how much money did we invest at 3 % ?
Options: a ) $ 300 , b ) $ 330 , c ) $ 360 , d ) $ 390 , e ) $ 420
Rationale: "let x be the money invested at 3 % . 1.03 x + 1.04 ( 1000 - x ) = 1036.70 . 0.01 x = 1040 - 1036.70 . 0.01 x = 3.30 . x = 330 . the answer is b ."
Answer: b
Problem: how many positive integers less than 400 can be formed using the numbers 1 , 2 , 3 and 5 for the digits ?
Options: a ) 48 , b ) 52 , c ) 66 , d ) 84 , e ) 68
Rationale: "notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero : 0 1 1 1 2 2 2 3 3 3 5 5 number of possibilities = 4 * 4 * 4 = 64 . then , just add up the number of 1 digits numbers = 4 , so total is 64 + 4 = 68 . answer : e"
Answer: e
Problem: forks , spoons , and knives in drawer are in the ratio of 4 : 4 : 3 . if there are 16 forks , the number of knives in the drawer is :
Options: a ) 8 , b ) 4 , c ) 12 , d ) 16 , e ) 14
Rationale: explanation : let forks = 4 x , spoons = 4 x & knives = 3 x . now , 4 x = 16 hence x = 4 . number of knives = 3 x = 12 . answer : c
Answer: c
Problem: what is the smallest positive integer x such that 450 x is the cube of a positive integer ?
Options: a ) 2 , b ) 15 , c ) 30 , d ) 60 , e ) 120
Rationale: "450 = 2 x 3 ^ 2 x 5 ^ 2 now we need two 2 s , one 3 and one 5 to make it perfect cube . so x = 2 ^ 2 x 3 x 5 = 60 . answer is c ."
Answer: c
Problem: in an election between two candidates , one got 55 % of the total valid votes , 20 % of the votes were invalid . if the total number of votes was 6000 , the number of valid votes that the other candidate got , was :
Options: a ) 2800 , b ) 2700 , c ) 2160 , d ) 2200 , e ) 2300
Rationale: "c number of valid votes = 80 % of 6000 = 4800 . valid votes polled by other candidate = 45 % of 4800 = ( 45 / 100 x 4800 ) = 2160 ."
Answer: c
Problem: 10 : 4 seconds : : ? : 6 minutes
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "10 * 6 = 4 * x x = 15 answer : b"
Answer: b
Problem: a train passes a platform in 36 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 ) 240 , b ) 250 , c ) 260 , d ) 230 , e ) 220
Rationale: "speed of the train = 54 km / hr = ( 54 × 10 ) / 36 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 = 36 = > 300 + l = 15 × 36 = 540 = > l = 540 - 300 = 240 meter answer is a ."
Answer: a
Problem: rs . 6000 is lent out in two parts . one part is lent at 2 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 11 , b ) 5 : 6 , c ) 5 : 2 , d ) 5 : 8 , e ) 5 : 2
Rationale: "let the amount lent at 2 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 2 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 3 x / 100 = > 600 - 3 / 100 x = 450 = > x = 1875 amount lent at 10 % = 4125 required ratio = 5 : 11 answer : a"
Answer: a
Problem: if two dice are thrown together , the probability of getting a doublet on the dice is
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting doublet on the dies is 6 / 36 = 1 / 6 p ( e ) = 1 / 6 . a )"
Answer: a
Problem: how many different positive integers are factors of 64 ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "8 × 8 = 4 ^ 2 × 2 ^ 2 so total factors = ( 3 + 1 ) ( 3 + 1 ) = 16 answer : d"
Answer: d
Problem: the ratio of the volumes of two cubes is 343 : 512 . what is the ratio of their total surface areas ?
Options: a ) 12 : 24 , b ) 8 : 16 , c ) 45 : 25 , d ) 18 : 56 , e ) 49 : 64
Rationale: "ratio of the sides = â ³ â ˆ š 343 : â ³ â ˆ š 512 = 7 : 8 ratio of surface areas = 49 : 64 answer : e"
Answer: e
Problem: a 6 % stock yields 9 % . the market value of the stock is :
Options: a ) rs 66.55 , b ) rs 68.55 , c ) rs 69.55 , d ) rs 65.55 , e ) rs 66.66
Rationale: "explanation : for an income of rs . 9 , investment = rs . 100 . for an income of rs 6 , investment = rs . 100 / 9 x 6 = rs 66.66 market value of rs . 100 stock = rs . 66.66 answer is e"
Answer: e