regisss/math_qa huggingface dataset:
Problem: what is the least number which when divided by 5 , 9 , 12 and 18 leaves remainder 4 in each care ?
Options: a ) 130 , b ) 140 , c ) 136 , d ) 184 , e ) 196
Rationale: "explanation : lcm of 5 , 9 , 12 and 18 is 180 required number = 180 + 4 = 184 answer : option d"
Answer: d
Problem: abhinav and bhupathi together have rs . 1210 . if 4 / 15 of abhinav ' s amount is equal to 2 / 5 of bhupathi ' s amount , how much amount does bhupathi have ?
Options: a ) rs 460 , b ) rs 484 , c ) rs 550 , d ) rs 664 , e ) none of these
Rationale: explanation : let a = abhinav , b = bhupathi . 4 / 15 a = 2 / 5 b = > a = ( 2 / 515 / 4 ) b = > a = 3 / 2 b = > a / b = 3 / 2 = > a : b = 3 : 2 b ' s share = rs . ( 12102 / 5 ) = rs . 484 . answer : b
Answer: b
Problem: difference of two numbers is 1620 . if 7.5 % of the number is 12.5 % of the other number , find the number ?
Options: a ) 2660 , 1000 , b ) 3660 , 2000 , c ) 3000 , 4160 , d ) 2430 , 4050 , e ) 4660 , 3000
Rationale: "let the numbers be x and y . then , 7.5 % of x = 12.5 % of y x = 125 * y / 75 = 5 * y / 3 . now , x - y = 1620 5 * y / 3 – y = 1620 2 * y / 3 = 1620 y = [ ( 1620 * 3 ) / 2 ] = 2430 . one number = 2430 , second number = 5 * y / 3 = 4050 . answer d ."
Answer: d
Problem: a shirt goes on sale for 60 % of its original price . one week later , the sale price is marked down 10 % . the final price is what percent of the original price ?
Options: a ) 72 % , b ) 70 % , c ) 52 % , d ) 50 % , e ) 28 %
Rationale: "just assume original price is 100 . sale price = 60 then it is marked down by 10 % = 60 - 6 = 52 . hence it is 52 % od the original price . hence answer is c ."
Answer: c
Problem: two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 9 hours and 16 hours respectively the ratio of their speeds is
Options: a ) 2 : 3 , b ) 4 : 3 , c ) 6 : 7 , d ) 9 : 16 , e ) none
Rationale: "solution let us name the trains as a and b . = ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 16 : √ 9 = 4 : 3 answer b"
Answer: b
Problem: 61 small identical cubes are used to form a large cube . how many more cubes are needed to add one top layer of small cube all over the surface of the large cube ?
Options: a ) 64 , b ) 128 , c ) 152 , d ) 155 , e ) 256
Rationale: "61 small cube will make a large cube with 4 cubes in each line i . e . adding one layer will require one cube at each end and hence new cube will have 6 cubes in each line . total number of small cubes in new cube = 6 ^ 3 = 216 extra cube required = 216 - 61 = 155 hence , d is the answer ."
Answer: d
Problem: pipe a can fill a tank in 5 hr , pipe b in 10 hr and pipe c in 30 hr . if all the pipes are open in how many hours will tank be filled ?
Options: a ) 1 hr , b ) 2 hr , c ) 3 hr , d ) 4 hr , e ) 5 hr
Rationale: "part filled by ( a + b + c ) in 1 hour = 1 / 5 + 1 / 10 + 1 / 30 = 1 / 3 all the 3 pipes together will fill the tank in 3 hours answer is c"
Answer: c
Problem: a pipe takes a hours to fill the tank . but because of a leakage it took 5 times of its original time . find the time taken by the leakage to empty the tank
Options: a ) 50 min , b ) 60 min , c ) 90 min , d ) 80 min , e ) 75 min
Rationale: "pipe a can do a work 60 min . lets leakage time is x ; then 1 / 60 - 1 / x = 1 / 300 x = 75 min answer : e"
Answer: e
Problem: the average weight of 19 students is 15 kg . by the admission of a new student the average weight is reduced to 14.7 kg . the weight of the new student is ?
Options: a ) 10.6 kg , b ) 10.8 kg , c ) 11 kg , d ) 14.9 kg , e ) none
Rationale: "answer weight of new student = total weight of all 20 students - total weight of initial 19 students = ( 20 x 14.7 - 19 x 15 ) kg = 9 kg . correct option : e"
Answer: e
Problem: sandy walked 20 meters towards south . then sandy turned to her left and walked 20 meters . she then turned to her left and walked 20 meters . she then turned to her right and walked 20 meters . what distance is she from the starting point and in which direction ?
Options: a ) 20 m east , b ) 40 m north , c ) 30 m west , d ) 40 m east , e ) 20 m west
Rationale: "the net distance is 20 + 20 = 40 meters to the east . the answer is d ."
Answer: d
Problem: the following questions are based on the information given . choose the appropriate answer that suits the question based on the information . a cube is cut in two equal parts along a plane parallel to one of its faces . one piece is then colored red on the two larger faces and green on remaining . while the other is colored green on two smaller adjacent faces and red on the remaining . each is then cut into 32 cubes of same size and mixed up . 21 . how many cubes have only one colored face each ?
Options: a ) 32
b ) 8
c ) 16
d ) 24
e ) 0
Rationale: 16 = 2 ^ 3 each cube will have 2 ^ 3 cubes painted 1 side . answer : c
Answer: c
Problem: the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 2 years ?
Options: a ) 3277 , b ) 2977 , c ) 22500 , d ) 6077 , e ) 17112
Rationale: explanation : 40,000 * ( 3 / 4 ) ^ 2 answer : c
Answer: c
Problem: a committee is reviewing a total of 20 x black - and - white films and 6 y color films for a festival . if the committee selects y / x % of the black - and - white films and all of the color films , what fraction e of the selected films are in color ?
Options: a ) 1 / 130 , b ) 1 / 5 , c ) 3 / 13 , d ) 10 / 13 , e ) 30 / 31
Rationale: "it ' s y / xpercentnot y / x . if x = 20 and y = 10 . then : 20 x = 400 black - and - white films ; 6 y = 60 color films . y / x % = 10 / 20 % = 0.5 % of the black - and - white films , so 2 black - and - white films and all 60 color films , thus total of 62 films were selected . color films thus compose e = 60 / 62 = 30 / 31 of the selected films . answer : e ."
Answer: e
Problem: a wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 4 cm x 7 cm x 6 cm . the maximum number ofboxes that can be carried in the wooden box , is
Options: a ) 9800000 , b ) 1000000 , c ) 7500000 , d ) 2000000 , e ) none of these
Rationale: explanation : number = ( 800 * 700 * 600 ) / 8 * 7 * 6 = 2000000 answer : d
Answer: d
Problem: a searchlight on top of the watch - tower makes 3 revolutions per minute . what is the probability that a man appearing near the tower will stay in the dark for at least 10 seconds ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "3 revolutions per minute = 1 revolution every 20 seconds so no matter what anybody appearing at the tower can not stay in the dark for more than 20 seconds . this will be our total number of possibilities i . e the denominator . p ( man in dark for at least 5 seconds ) = 1 - p ( man in dark for max of 10 seconds ) = 1 - 10 / 20 = 1 - 1 / 2 = 1 / 2 or the other way would be : p ( man in dark for at least 5 seconds ) is like saying he can be in dark for 5 , 6,7 . . . all the way to 20 seconds because that is the max . in this approach it would be 10 / 20 seconds = 1 / 2 . answer is c"
Answer: c
Problem: the time it took car p to travel 750 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 40 , b ) 56 , c ) 60 , d ) 70 , e ) 80
Rationale: let speed of car r be = x then speed of car p = x + 10 a / q , ( 750 / x ) - ( 750 / ( x + 10 ) ) = 2 solving for x = 56 miles \ hr . b
Answer: b
Problem: if 5 % more is gained by selling an book for $ 350 than by selling it for $ 340 , the cost of the book is :
Options: a ) 500 , b ) 400 , c ) 200 , d ) 300 , e ) 100
Rationale: "c 200 let c . p . be $ x . then , 5 % of x = 350 - 340 = 10 x / 20 = 10 = > x = 200"
Answer: c
Problem: find the number which when added to itself 13 times , gives 112 .
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "let the number be x . then , x + 13 x = 112 14 x = 112 x = 8 . answer : b"
Answer: b
Problem: there are 6 red shoes & 4 green shoes . if two of red shoes are drawn what is the probability of getting red shoes
Options: a ) 1 / 3 , b ) 1 / 4 , c ) 1 / 2 , d ) 1 / 5 , e ) 1 / 6
Rationale: "taking 2 red shoe the probablity is 6 c 2 from 10 shoes probablity of taking 2 red shoe is 6 c 2 / 10 c 2 = 1 / 3 answer : a"
Answer: a
Problem: a batsman makes a score of 200 runs in the 17 th inning and thus increases his averages by 10 what is his average after 17 th inning ?
Options: a ) 39 , b ) 35 , c ) 42 , d ) 40 , e ) 41.5
Rationale: "let the average after 16 th inning = x then total run after 16 th inning = 16 x then total run after 17 th inning = 16 x + 200 then average run after 17 th inning = ( 16 x + 200 ) / 17 ( 16 x + 200 ) / 17 = x + 10 = > 16 x + 200 = 17 x + 170 x = 30 ; average after 17 th inning = 30 + 10 = 40 answer : d"
Answer: d
Problem: a certain number when divided by 110 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "explanation : 110 + 25 = 135 / 15 = 9 ( remainder ) e"
Answer: e
Problem: if w and y are both odd prime numbers and w < y , how many distinct positive integer factors does 2 wy have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: since 2 wy prime factors are w ^ 1 * y ^ 1 * 2 ^ 1 , its total number or factors must be ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 2 ^ 3 = 8 . thus , i think d would be the correct answer . d
Answer: d
Problem: in goshawk - eurasian nature reserve 30 percent of the birds are hawks , and 40 percent of the non - hawks are paddyfield - warblers . if there are 25 percent as many kingfishers as paddyfield - warblers in the reserve , then what percent of the birds r in the nature reserve are not hawks , paddyfield - warblers , or kingfishers ?
Options: a ) 25 % , b ) 35 % , c ) 45 % , d ) 70 % , e ) 80 %
Rationale: 1 . we are given the following percentages : 30 ( 70 ) , 40 ( 60 ) , 25 ( 75 ) . there are two threads from here . first starts at 30 % and finishes there . second one starts at 70 , then 40 , and then 25 . we need a value that is divisible by 7 , 2 , and 5 at least once . lets pick a number now , say 700 . so say if non hawks are 700 ( this is 70 % of the total , so total = 1000 ) , then paddy warbs are 2 / 5 x 700 = 1400 / 5 = 280 . kingfishers , therefore , are 280 / 4 = 70 . lets add them up . 300 hawks + 280 peddy warbs + 70 kingsifhers = 650 . so all others are 1000 - 650 = 350 or 35 % of total birds . the main job here to to identify the smart number to start the question with . this can be time consuming , but once identified , this question can be solved fairly quickly . 2 . another method : if x is total - - > non hawks = 0.7 x - - > warbs = 0.4 ( 0.7 x ) - - > kfs = 0.25 ( 0.4 ( 0.7 x ) ) . our job is to find out r : ( 0.3 x + 0.28 x + 0.07 x ) / x . or 0.65 x / x = 0.65 . we need to find 1 - 0.65 = 0.35 or 35 % . b
Answer: b
Problem: what is the remainder when 8 ^ 1 + 8 ^ 2 + 8 ^ 3 + . . . + 8 ^ 9 is divided by 4 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 5 , e ) none of the above
Rationale: "notice that in the brackets we have the sum of 9 even multiples of 4 , hence the sum in the brackets will be even multiple of 4 ( the sum of 9 even numbers is even ) . which yields remainder of 0 upon division by 4 . answer : e"
Answer: e
Problem: the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8112 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50 , b ) rs . 67.50 , c ) rs . 86.50 , d ) rs . 91.00 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 7600 ⇔ 12 x 2 = 8112 ⇔ x 2 = 676 ⇔ x = 26 so , length = 78 m and breadth = 104 m . perimeter = [ 2 ( 78 + 104 ) ] m = 364 m . ∴ cost of fencing = rs . ( 0.25 × 364 ) = rs . 91 . answer d"
Answer: d
Problem: a sum was put at simple interest at a certain rate for 5 years had it been put at 6 % higher rate , it would have fetched 90 more . find the sum .
Options: a ) 90 , b ) 100 , c ) 200 , d ) 300 , e ) 400
Rationale: "difference in s . i . = p × t / 100 ( r 1 − r 2 ) ⇒ 90 = p × 5 x 6 / 100 ( ∵ r 1 - r 2 = 2 ) ⇒ p = 90 × 100 / 5 x 6 = 300 answer d"
Answer: d
Problem: a can complete a project in 20 days and b can complete the same project in 30 days . if a and b start working on the project together and a quits 5 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 27 days , c ) 26.67 days , d ) 15 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 30 ) . ( 1 / 20 ) * ( x - 5 ) + ( 1 / 30 ) * ( x ) = 1 ( x / 20 ) + ( x / 30 ) - ( 5 / 20 ) = 1 5 x / 60 = 5 / 4 x = 60 / 4 x = 15 therefore , the answer is d : 15 ."
Answer: d
Problem: sides of a rectangular park are in the ratio 3 : 2 and its area is 3750 sq m , the cost of fencing it at 90 ps per meter is ?
Options: a ) 287 , b ) 369 , c ) 225 , d ) 279 , e ) 361
Rationale: "3 x * 2 x = 3750 = > x = 25 2 ( 75 + 50 ) = 250 m 250 * 0.9 = rs . 225 answer : c"
Answer: c
Problem: if 30 % of a number is equal to one - third of another number , what is the ratio of first number to the second number ?
Options: a ) 2 : 5 , b ) 3 : 7 , c ) 10 : 9 , d ) 7 : 3 , e ) none of these
Rationale: "explanation : let 30 % of a = 1 / 3 b then , 30 a / 100 = 1 b / 3 = > 3 a / 10 = b / 3 = > a : b = 10 : 9 answer : c"
Answer: c
Problem: every year an amount increases by 1 / 8 th of itself . how much will it be after two years if its present value is rs . 32000 ?
Options: a ) 81000 , b ) 33888 , c ) 77678 , d ) 200988 , e ) 40500
Rationale: "32000 * 9 / 8 * 9 / 8 = 40500 answer : e"
Answer: e
Problem: out of 450 students of a school , 325 play football , 175 play cricket and 50 neither play football nor cricket . how many students play both football and cricket ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 150 , e ) none of these
Rationale: "explanation : students who play cricket , n ( a ) = 325 students who play football , n ( b ) = 175 total students who play either or both games , = n ( a ∪ b ) = 450 − 50 = 400 required number , n ( a ∩ b ) = n ( a ) + n ( b ) − n ( a ∪ b ) = 325 + 175 − 400 = 100 option b"
Answer: b
Problem: a number is doubled and 7 is added . if resultant is trebled , it becomes 99 . what is that number
Options: a ) 8 , b ) 10 , c ) 14 , d ) 13 , e ) 16
Rationale: "explanation : = > 3 ( 2 x + 7 ) = 99 = > 2 x + 7 = 33 = > x = 13 option d"
Answer: d
Problem: a bag holds 3 red marbles and 3 green marbles . if you removed two randomly selected marbles from the bag , without replacement , what is the probability that both would be green ?
Options: a ) 1 / 10 , b ) 1 / 6 , c ) 3 / 10 , d ) 1 / 5 , e ) 1 / 2
Rationale: "given : 3 r and 3 g marbles required : probability that 2 marbles removed without replacement are both red initially we have to pick one red from a total of 3 red and 3 green marbles after one green has been picked , we need to pick 1 green from a total of 2 greenand 3 red marbles . p ( both green ) = ( 3 / 6 ) * ( 2 / 5 ) = 1 / 5 option d"
Answer: d
Problem: in a 200 m race , a covers the distance in 45 seconds and b in 60 second . in this race a beats b by :
Options: a ) 20 m , b ) 50 m , c ) 45 m , d ) 60 m , e ) none of these
Rationale: "solution distance covered by b in 15 sec . = ( 200 / 60 x 15 ) m = 50 m . ∴ a beats b by 50 metres . answer b"
Answer: b
Problem: find the value of a / b + b / a , if a and b are the roots of the quadratic equation x 2 + 8 x + 4 = 0 ?
Options: a ) 15 , b ) 14 , c ) 13 , d ) 12 , e ) 11
Rationale: "a / b + b / a = ( a 2 ] / ab a + b = + b 2 ) / ab = ( a 2 + b 2 + a + b ) / ab = [ ( a + b ) 2 - 2 ab - 8 / 1 = - 8 ab = 4 / 1 = 4 hence a / b + b / a = [ ( - 8 ) 2 - 2 ( 4 ) ] / 4 = 56 / 4 = 14 . answer : b"
Answer: b
Problem: 20 ^ 10 / 120 ^ 5 = ?
Options: a ) 6 ^ 5 , b ) 5 ^ 6 , c ) ( 10 / 3 ) ^ 5 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "20 ^ 10 / 120 ^ 5 = ? a . 6 ^ 5 b . 5 ^ 6 c . ( 10 / 3 ) ^ 5 d . 6 ^ 3 e . 15 ^ 3 - > 20 ^ 10 / 120 ^ 5 = ( 20 ^ 10 ) / ( 6 ^ 5 ) ( 20 ^ 5 ) = ( 20 ^ 5 ) / ( 6 ^ 5 ) = ( 2 ^ 5 ) ( 10 ^ 5 ) / ( 2 ^ 5 ) ( 3 ^ 5 ) = ( 10 / 3 ) ^ 5 . thus , c is the answer ."
Answer: c
Problem: darren bought 5 packs of white t - shirts and 3 packs of blue t - shirts for his basketball team . the white t - shirts come in packs of 6 , and the blue t - shirts come in packs of 9 . how many t - shirts did darren buy in all ?
Options: a ) 77 , b ) 57 , c ) 34 , d ) 65 , e ) 21
Rationale: step 1 : find the number of white t - shirts . 5 × 6 = 30 step 2 : find the number of blue t - shirts . 3 × 9 = 27 step 3 : find the total number of t - shirts . 30 + 27 = 57 darren bought 57 t - shirts . answer is b .
Answer: b
Problem: car a is 10 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.25 , c ) 2.75 , d ) 2.5 , e ) 3.5
Rationale: "relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 10 miles and drive 8 miles ahead so to drive 18 miles it ' ll need 18 / 8 = 2.25 hours . answer : b"
Answer: b
Problem: in a 400 m race , a covers the distance in 60 seconds and b in 100 second . in this race a beats b by :
Options: a ) 20 m , b ) 125 m , c ) 120 m , d ) 160 m , e ) none of these
Rationale: "solution distance covered by b in 40 sec . = ( 400 / 100 x 40 ) m = 160 m . ∴ a beats b by 160 metres . answer d"
Answer: d
Problem: a business executive and his client are charging their dinner tab on the executive ' s expense account . the company will only allow them to spend a total of 50 $ for the meal . assuming that they will pay 7 % in sales tax for the meal and leave a 20 % tip , what is the most their food can cost ?
Options: a ) 39.55 $ , b ) 40.63 $ , c ) 38.63 $ , d ) 37.88 $ , e ) 35.15 $
Rationale: let x is the cost of the food 1.07 x is the gross bill after including sales tax 1.20 * 1.07 x = 50 x = 37.88 hence , the correct option is c
Answer: c
Problem: the h . c . f . of two numbers is 11 and their l . c . m . is 693 . if one of the number is 77 , find the other ?
Options: a ) 88 , b ) 99 , c ) 76 , d ) 55 , e ) 66
Rationale: "other number = 11 * 693 / 77 = 99 answer is b"
Answer: b
Problem: p , q and r can do a work in 6 , 9 and 12 days respectively . they completed the work and got rs . 195 . what is the share of p ?
Options: a ) 80 , b ) 70 , c ) 85 , d ) 90 , e ) 95
Rationale: "the ratio of their working rates = 1 / 6 : 1 / 9 : 1 / 12 = 6 : 4 : 3 . since , they work together , the share of p = 6 / 13 * 195 = rs . 90 answer : d"
Answer: d
Problem: machine a and machine b are each used to manufacture 220 sprockets . it takes machine a 10 hours longer to produce 220 sprockets than machine b . machine b produces 10 percent more sprockets per hour than machine a . how many sprockets per hour does machine a produces ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "machine b : takes x hours to produce 220 sprockets machine a : takes ( x + 10 ) hours to produce 220 sprockets machine b : in 1 hour , b makes 220 / x sprockets machine a : in 1 hour , a makes 220 / ( x + 10 ) sprockets equating : 1.1 ( 220 / ( x + 10 ) ) = 220 / x 242 / ( x + 10 ) = 220 / x 242 x = 220 x + 2200 22 x = 2200 x = 100 a makes 220 / ( 110 ) = 2 sprockets per hour answer : a"
Answer: a
Problem: a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 30 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 30 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 130 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 130 - 90 ) / 90 * 100 = 30 % answer : d ."
Answer: d
Problem: a cricket bat is sold for $ 900 , making a profit of $ 300 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 50 % , e ) 40 %
Rationale: "300 / ( 900 - 300 ) = 50 % . answer : d"
Answer: d
Problem: each of the integers from 1 to 15 is written on the a seperate index card and placed in a box . if the cards are drawn from the box at random without replecement , how many cards must be drawn to ensure that the product of all the integers drawn is even ?
Options: a ) 9 , b ) 12 , c ) 11 , d ) 10 , e ) 3
Rationale: "out of the 15 integers : 8 are odd and 7 are even . if we need to make sure that the product of all the integers withdrawn is even then we need to make sure that we have at least one even number . in the worst case : 1 . we will end up picking odd numbers one by one , so we will pick all 8 odd numbers first 2 . 9 th number will be the first even number so we need to withdraw at least 9 numbers to make sure that we get one even number and the product of all the integers picked is even . so , answer will be 9 . ( a )"
Answer: a
Problem: a student chose a number , multiplied it by 7 , then subtracted 150 from the result and got 130 . what was the number he chose ?
Options: a ) 40 , b ) 42 , c ) 44 , d ) 46 , e ) 48
Rationale: "let x be the number he chose , then 7 ⋅ x − 150 = 130 7 x = 280 x = 40 correct answer a"
Answer: a
Problem: average monthly income of a family of 4 earning members was rs . 735 . one of the earning members died and therefore , the average income came down to rs 550 . the income of the deceased was ?
Options: a ) rs . 692.80 , b ) rs . 820 , c ) rs . 990 , d ) rs . 1385 , e ) none
Rationale: "answer income of the deceased = total income of 4 members - total income of remaining 3 members . = 735 x 4 - 550 x 3 rs . = 1290 rs . correct option : e"
Answer: e
Problem: evaluate : ( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 )
Options: a ) 5 / 100 , b ) 6 / 100 , c ) 7 / 100 , d ) 8 / 100 , e ) 9 / 100
Rationale: ( 1 - 1 / 10 ) ( 1 - 1 / 11 ) ( 1 - 1 / 12 ) . . . ( 1 - 1 / 99 ) ( 1 - 1 / 100 ) = ( 9 / 10 ) ( 10 / 11 ) ( 11 / 12 ) . . . ( 98 / 99 ) ( 99 / 100 ) = 9 / 100 : simplify correct answer e
Answer: e
Problem: when a person aged 39 is added to a group of n people , the average age increases by 2 . when a person aged 15 is added instead , the average age decreases by 1 . what is the value of w ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "a simple and elegant solution . as addition of 39 , shifts mean by 2 , and addition of 15 , shifts mean by 1 to the other side , we have the mean lying between 3915 , and in a ratio of 2 : 1 39 - 15 = 24 24 divide by 3 is 8 . meaning mean of the n terms is 15 + 8 = 39 - 16 = 23 now , from first statement , when a person aged 39 is added to a group of n people , the average age increases by 2 . w * 23 + 39 = 25 * ( w + 1 ) w = 7 ans . ( a )"
Answer: a
Problem: 210 college students were asked in a survey if they preferred windows or mac brand computers . 90 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 60 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: "210 = 90 ( mac ) + x ( window ) + 60 ( both ) = > x = 60 answer : d"
Answer: d
Problem: 210 school students were asked in a survey if they preferred windows or mac brand computers . 60 students claimed that they preferred mac to windows brand computers . one third as many of the students who preferred mac to windows , equally preferred both brands . 90 of the students had no preference . how many of the students in the survey preferred windows to mac brand computers ?
Options: a ) 25 , b ) 40 , c ) 50 , d ) 60 , e ) 75
Rationale: we are told that 60 students claimed that they preferred mac to windows , which means that 60 preferred mac but not windows , so # of students who preferred mac ( p ( a ) as you wrote ) , does not equal to 60 , it equals to 60 + 20 ( 20 is # of students who equally preferred both brands ) . also we are asked to find # of the students who preferred windows to mac , so if you denote x as those who prefer windows then you should calculate x - 20 . so , if we use your formula it should be : 210 = { mac } + { windows } - { both } + { neither } = ( 60 + 20 ) + x - 20 + 90 - - > x = 60 ( # of student who prefer windows ) - - > # of the students who preferred windows to mac is x - 20 = 40 .
Answer: b
Problem: speed of a boat in standing water is 11 kmph and speed of the stream is 2.5 kmph . a man can rows to a place at a distance of 105 km and comes back to the starting point . the total time taken by him is ?
Options: a ) 21.12 hours , b ) 20.12 hours , c ) 19.12 hours , d ) 18.12 hours , e ) 17.12 hours
Rationale: "speed upstream = 8.5 kmph speed downstream = 13.5 kmph total time taken = 105 / 8.5 + 105 / 13.5 = 20.12 hours answer is b"
Answer: b
Problem: a train 650 m long is running at a speed of 81 km / hr . in what time will it pass a bridge 340 m long ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 46
Rationale: "speed = 81 * 5 / 18 = 45 / 2 m / sec total distance covered = 650 + 340 = 990 m required time = 990 * 2 / 45 = 44 sec answer : c"
Answer: c
Problem: what is the probability that carol and bernie will get selected for a job they both applied for in a company , given that their chances of getting selected is 4 / 5 and 3 / 5 respectively ?
Options: a ) 8 / 25 , b ) 11 / 24 , c ) 12 / 25 , d ) 12 / 25 , e ) 12 / 23
Rationale: explanation : p ( carol ) = 4 / 5 p ( bernie ) = 3 / 5 e = { carol and bernie both get selected } p ( e ) = p ( carol ) * p ( bernie ) = 4 / 5 * 3 / 5 = 12 / 25 answer : d
Answer: d
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 5 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6
Rationale: "5 b = 7 c and so b = 7 c / 5 7 a = 2 b and so a = 2 b / 7 = 2 c / 5 a + b = 2 c / 5 + 7 c / 5 = 9 c / 5 b + c = 7 c / 5 + c = 12 c / 5 the ratio of a + b : b + c = 9 : 12 = 3 : 4 the answer is c ."
Answer: c
Problem: a certain bag contains 100 balls â € ” 10 white , 30 green , 10 yellow , 47 red , and 3 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.9 , b ) 0.75 , c ) 0.6 , d ) 0.8 , e ) 0.5
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 10 + 30 + 10 ) / 100 = 50 / 100 = 0.5 . answer is e"
Answer: e
Problem: how many bricks , each measuring 25 cm x 11 cm x 6 cm , will be needed to build a wall of 8 m x 1 m x 5 cm ?
Options: a ) 5600 , b ) 6000 , c ) 242 , d ) 7200 , e ) 8600
Rationale: "number of bricks = volume of the wall / volume of 1 brick = ( 800 x 100 x 5 ) / ( 25 x 11 x 6 ) = 242 . answer : option c"
Answer: c
Problem: the breadth of a rectangular field is 60 % of its length . if the perimeter of the field is 800 m , find out the area of the field .
Options: a ) 37500 , b ) 38000 , c ) 38500 , d ) 39000 , e ) 39500
Rationale: "given that breadth of the rectangular field is 60 % of its length . ⇒ b = 60 l 100 = 3 l 5 perimeter of the field = 800 m ⇒ 2 ( l + b ) = 800 ⇒ 2 ( l + 3 l 5 ) = 800 ⇒ l + 3 l 5 = 400 ⇒ 8 l 5 = 400 ⇒ l 5 = 50 ⇒ l = 5 × 50 = 250 m b = 3 l 5 = 3 × 2505 = 3 × 50 = 150 m area = lb = 250 × 150 = 37500 m 2 answer is a ."
Answer: a
Problem: if the number is divided by 3 , it reduced by 30 . the number is
Options: a ) a ) 51 , b ) b ) 50 , c ) c ) 45 , d ) d ) 40 , e ) e ) 36
Rationale: "explanation : let the number be x . then , x - ( x / 3 ) = 30 = > 2 x / 3 = 30 = > x = 45 answer : option c"
Answer: c
Problem: among 400 students , 51 % study sociology , 46 % study mathematics and 40 % study biology . if 34 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
Options: a ) 30 , b ) 90 , c ) 148 , d ) 172 , e ) 188
Rationale: i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 136 using your analysis : we see that the total number of students who study either maths or sociology = 184 + 204 - 136 = 252 so , in the image we know that the number of students in the zone with the black boundary = 252 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 252 + b + w = 400 or , b + w = 400 - 252 = 148 that is , b = 148 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 148 c
Answer: c
Problem: in the third grade of windblown school there are 102 students , one third of them failed the math test and 1 / 6 failed that literature test . at least how many students failed both tests ?
Options: a ) 0 . , b ) 6 . , c ) 8 . , d ) 10 . , e ) 12 .
Rationale: "total = 102 failed in math = 102 / 3 = 34 failed in literature = 108 / 6 = 17 the least failed in both can be 0 while max can be 17 answer a"
Answer: a
Problem: the principal that amounts to rs . 5913 in 3 years at 6 1 / 4 % per annum c . i . compounded annually , is ?
Options: a ) s . 3096 , b ) s . 4076 , c ) s . 4085 , d ) s . 4096 , e ) s . 5096
Rationale: "principal = [ 4913 / ( 1 + 25 / ( 4 * 100 ) ) 3 ] = 5913 * 16 / 17 * 16 / 17 * 16 / 17 = rs . 5096 . answer : e"
Answer: e
Problem: if 2805 / 2.55 = 1100 , then 280.5 / 25.5 is equal to ?
Options: a ) 1.01 , b ) 1.1 , c ) 0.11 , d ) 11 , e ) none
Rationale: "answer given expression 280.5 / 25.5 = 2805 / 255 = 2805 / ( 2.55 x 100 ) = 1100 / 100 = 11 correct option : d"
Answer: d
Problem: a and b complete a work in 50 days . a alone can do it in 40 days . if both together can do the work in how many days ?
Options: a ) 1.075 days , b ) 0.185 days , c ) 0.065 days , d ) 0.045 days , e ) 0.0775 days
Rationale: "1 / 50 + 1 / 40 = 0.045 days answer : d"
Answer: d
Problem: a sum of rs . 2769 is lent into two parts so that the interest on the first part for 8 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) 1642 , b ) 1640 , c ) 1632 , d ) 2789 , e ) 1704
Rationale: "( x * 8 * 3 ) / 100 = ( ( 2769 - x ) * 3 * 5 ) / 100 24 x / 100 = 41535 / 100 - 15 x / 100 39 x = 41535 = > x = 1065 second sum = 2769 – 1065 = 1704 answer : e"
Answer: e
Problem: ( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) =
Options: a ) 0.099 , b ) 0.0099 , c ) 9.9 , d ) 990 , e ) 99
Rationale: "( 0.0077 ) ( 3.6 ) / ( 0.04 ) ( 0.1 ) ( 0.007 ) = 0.0077 * 360 / 4 * ( 0.1 ) ( 0.007 ) = 0.077 * 90 / 1 * 0.007 = 77 * 90 / 7 = 11 * 90 = 990 answer : d"
Answer: d
Problem: in a certain candy store , 22 % of the customers are caught sampling the candy and are charged a small fine , but 12 % of the customers who sample the candy are not caught . what is the total percent of all customers who sample candy ?
Options: a ) 22 % , b ) 23 % , c ) 24 % , d ) 25 % , e ) 34 %
Rationale: "since 12 % of the customers who sample the candy are not caught , then 88 % of the customers who sample the candy are caught : { % of customers who sample candy } * 0.88 = 0.22 ; { % of customers who sample candy } = 0.25 . answer : d ."
Answer: d
Problem: a lent rs . 5000 to b for 2 years and rs . 3000 to c for 4 years on simple interest at the same rate of interest and received rs . 1760 in all from both of them as interest . the rate of interest per annum is ?
Options: a ) 16 % , b ) 12 % , c ) 74 % , d ) 10 % , e ) 8 %
Rationale: "let the rate be r % p . a . then , ( 5000 * r * 2 ) / 100 + ( 3000 * r * 4 ) / 100 = 1760 100 r + 120 r = 1760 r = 8 % answer : e"
Answer: e
Problem: out of 4 numbers , the average of first 3 is 20 and that of the last 3 is 15 . if the last number is 18 , the first number is :
Options: a ) 22 , b ) 33 , c ) 77 , d ) 99 , e ) 27
Rationale: explanation : let the numbers be a , b , c , d given , a + b + c = 60 , b + c + d = 45 now , d = 18 thus , b + c + 18 = 45 ⇒ b + c = 27 putting the value of b + c in a + b + c = 60 a + 27 = 60 ⇒ a = 33 answer : b
Answer: b
Problem: 4 car rental agencies a , b , c and d rented a plot for parking their cars during the night . a parked 15 cars for 12 days , b parked 12 cars for 20 days , c parked 18 cars for 18 days and d parked 16 cars for 15 days . if a paid rs . 1125 as rent for parking his cars , what is the total rent paid by all the 4 agencies ?
Options: a ) rs . 6152 , b ) rs . 6159 , c ) rs . 6156 , d ) rs . 6150 , e ) rs . 6196
Rationale: the ratio in which the four agencies will be paying the rents = 15 * 12 : 12 * 20 : 18 * 18 : 16 * 15 = 180 : 240 : 324 : 240 = 45 : 60 : 81 : 60 let us consider the four amounts to be 45 k , 60 k , 81 k and 60 k respectively . the total rent paid by the four agencies = 45 k + 60 k + 81 k + 60 k = 246 k it is given that a paid rs . 1125 45 k = 1125 = > k = 25 246 k = 246 ( 25 ) = rs . 6150 thus the total rent paid by all the four agencies is rs . 6150 . answer : d
Answer: d
Problem: harry started a 7 - mile hike with a full 9 - cup canteen of water and finished the hike in 2 hours with 3 cup of water remaining in the canteen . if the canteen leaked at the rate of 1 cup per hour and harry drank 2 cups of water during the last mile , how many cups did he drink per mile during the first 6 miles of the hike ?
Options: a ) 1 / 6 , b ) 2 / 6 , c ) 3 / 6 , d ) 4 / 6 , e ) 5 / 6
Rationale: "no of cups leaked during the trip = 2 cups . no of cups harry drank = 6 cups . no of cups harry drank during the first 6 miles = 4 . drink / mile = 4 / 6 answer d"
Answer: d
Problem: the banker ' s gain on a sum due 6 years hence at 12 % per annum is rs . 900 . what is the banker ' s discount ?
Options: a ) 1240 , b ) 1120 , c ) 1190 , d ) 2150 , e ) none of these
Rationale: "explanation : td = ( bg × 100 ) / tr = ( 900 × 100 ) / ( 6 × 12 ) = rs . 1250 bg = bd – td = > 900 = bd - 1250 = > bd = 2150 answer : option d"
Answer: d
Problem: 8 ^ 100 is divisible by 17 . find the remainder for this ?
Options: a ) 10 , b ) 12 , c ) 16 , d ) 17 , e ) 19
Rationale: "this is an extremely difficult problem to solve with out fermat ' s little theorem . by applying fermat ' s little theorem , we know that 816 when divided by 17 , the remainder is 1 . so divide 100 by 16 and find the remainder . remainder = 4 therefore , 100 = ( 16 × 6 ) + 4 now this problem can be written as 810017 = 816 × 6 + 417 = ( 816 ) 6 × 8417 now this problem simply boils down to ( 1 ) 6 × 8417 = 8417 84 = 82 × 82 , we need to find the remainder when 64 × 64 is divisible by 17 . or 13 × 13 = 169 . when 169 is divided by 17 , remainder is 16 . c"
Answer: c
Problem: a shopkeeper sold an book offering a discount of 5 % and earned a profit of 42.5 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 140 , b ) 120 , c ) 130 , d ) 110 , e ) 150
Rationale: "let c . p . be $ 100 . then , s . p . = $ 142.50 let marked price be $ x . then , 95 / 100 x = 142.5 x = 14250 / 95 = $ 150 now , s . p . = $ 150 , c . p . = $ 100 profit % = 50 % . e"
Answer: e
Problem: a driver would have reduced the time it took to drive from home to the store by 1 / 4 if the average speed had been increased by 10 miles per hour . what was the actual average speed , in miles per hour , when the driver drove from home to the store ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: since the distance remains the same ( we ' re just changing the rate and time ) , any increase in rate or time is met with a decrease in the other term . decreasing the time by 1 / 4 would give us : d = ( r ) ( t ) = ( 3 t / 4 ) ( x * r ) x = 4 / 3 since ( 3 t / 4 ) ( 4 r / 3 ) = ( r ) ( t ) = d 4 r / 3 = r + 10 r / 3 = 10 r = 30 the answer is e .
Answer: e
Problem: a can do a job in 15 days and b can do it in 30 days . a and b working together will finish twice the amount of work in - - - - - - - days ?
Options: a ) 14 days , b ) 16 days , c ) 20 days , d ) 11 days , e ) 19 days
Rationale: "c 1 / 15 + 1 / 30 = 1 / 10 10 * 2 = 20 days"
Answer: c
Problem: at a supermarket , john spent 1 / 2 of his money on fresh fruits and vegetables , 1 / 3 on meat products , and 1 / 10 on bakery products . if he spent the remaining $ 10 on candy , how much did john spend at the supermarket ?
Options: a ) $ 60 , b ) $ 80 , c ) $ 90 , d ) $ 120 , e ) $ 150
Rationale: "let ' s let t = total number of dollars spent at the supermarket . with this variable we can set up an equation and determine t . we are given that john spent 1 / 2 of his money on fresh fruits and vegetables , or ( 1 / 2 ) t , 1 / 3 on meat products , or ( 1 / 3 ) t , and 1 / 10 on bakery products , or ( 1 / 10 ) t . we are also given that he spent the remaining $ 10 on candy . since we know where all his money was allocated , we can sum these values together and set the sum to t . so we have : ( 1 / 2 ) t + ( 1 / 3 ) t + ( 1 / 10 ) t + 10 = t to get rid of the fractions we can multiply the entire equation by 30 , and we obtain : 15 t + 10 t + 3 t + 300 = 30 t 28 t + 300 = 30 t 300 = 2 t t = 150 john spent $ 90 at the supermarket . answer : e"
Answer: e
Problem: the h . c . f . of two numbers is 12 and their l . c . m . is 600 . if one of the number is 120 , find the other ?
Options: a ) 100 , b ) 60 , c ) 120 , d ) 200 , e ) 150
Rationale: "other number = 12 * 600 / 120 = 60 answer is b"
Answer: b
Problem: 66.2 is what percent of 1000 ?
Options: a ) 6.62 , b ) 66.2 , c ) 662 , d ) 0.662 , e ) 0.0662
Rationale: "we assume that 1000 is 100 % assume ' x ' is value we looking for here , 1000 = 100 % and x % = 66.2 therefore , 100 / x = 1000 / 66.2 100 / x = 15.105 x = 6.62 a"
Answer: a
Problem: if the sum and difference of two numbers are 5 and 10 respectively , then the difference of their square is :
Options: a ) 50 , b ) 28 , c ) 160 , d ) 180 , e ) 18
Rationale: "let the numbers be x and y . then , x + y = 5 and x - y = 10 x 2 - y 2 = ( x + y ) ( x - y ) = 5 * 10 = 50 . answer : a"
Answer: a
Problem: find the least number which when divided by 56 , 78 leaves a remainder 3 but when divided by 9 leaves no remainder
Options: a ) 9632 , b ) 7896 , c ) 8741 , d ) 1683 , e ) 8523
Rationale: l . c . m of 5,6 , 7,8 = 840 required number is of the form of 840 k + 3 least value of k for which ( 840 k + 3 ) is divided by 9 is k = 2 required number = ( 840 * 2 + 3 ) = 1683 answer ( d )
Answer: d
Problem: what is the average of first 21 multiples of 8 ?
Options: a ) a ) 70 , b ) b ) 77 , c ) c ) 79 , d ) d ) 81 , e ) e ) 88
Rationale: "required average = 8 ( 1 + 2 + . . . . + 21 ) / 21 ( 8 / 21 ) x ( ( 21 x 22 ) / 2 ) ( because sum of first 21 natural numbers ) = 88 e"
Answer: e
Problem: a invested $ 150 in a business after 6 months b invested $ 200 in the business . end of the year if they got $ 100 as profit . find a shares ?
Options: a ) $ 100 , b ) $ 75 , c ) $ 20 , d ) $ 120 , e ) $ 60
Rationale: "a : b = 150 * 12 : 200 * 6 a : b = 3 : 2 a ' s share = 100 * 3 / 5 = $ 60 answer is e"
Answer: e
Problem: for any number y , y * is defined as the greatest positive even integer less than or equal to y . what is the value of 9.2 – 9.2 * ?
Options: a ) 0.2 , b ) 1.2 , c ) 1.8 , d ) 2.2 , e ) 4.0
Rationale: "since y * is defined as the greatest positive even integer less than or equal to y , then 9.2 * = 8 ( the greatest positive even integer less than or equal to 9.2 is 4 ) . hence , 9.2 – 9.2 * = 9.2 - 8 = 1.2 answer : b ."
Answer: b
Problem: the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1.40 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 932.4 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1.4 = 932.4 answer : c"
Answer: c
Problem: $ 400 is divided amongst a , b and c so that a may get 2 / 3 as much as b and c together , b may get 6 / 9 as much as a and c together , then the share of a is
Options: a ) $ 100 , b ) $ 150 , c ) $ 160 , d ) $ 200 , e ) $ 250
Rationale: "a : ( b + c ) = 2 : 3 a ' s share = 400 * 2 / 5 = $ 160 answer is c"
Answer: c
Problem: 2 . the value of x + x ( xx ) when x = 2 is :
Options: a ) 5 , b ) 10 , c ) 8 , d ) 15 , e ) 20
Rationale: x + x ( xx ) put the value of x = 2 in the above expression we get , 2 + 2 ( 22 ) = 2 + 2 ( 2 × 2 ) = 2 + 2 ( 4 ) = 2 + 8 = 10 answer : b
Answer: b
Problem: find the value of x from the below equation ? : x ^ 2 + 5 x + 25 = 0
Options: a ) no answer , b ) 25 , c ) 1 , d ) 0 , e ) - 2
Rationale: "a = 1 , b = 5 , c = 25 x 1,2 = ( - 5 â ± â ˆ š ( 5 ^ 2 - 4 ã — 1 ã — 25 ) ) / ( 2 ã — 1 ) = ( - 5 â ± â ˆ š ( 25 - 100 ) ) / 2 = ( - 5 â ± â ˆ š - 75 ) / 2 no real roots a"
Answer: a
Problem: a doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 75 pounds . if the typical dosage is 2 cubic centimeters per 15 pounds of the body weight , by what percent was the prescribed dosage greater than the typical dosage ?
Options: a ) 8 % , b ) 9 % , c ) 11 % , d ) 12.5 % , e ) 20 %
Rationale: "typical dosage is dose : weight : : 2 : 15 . now if weight is 75 : ( 75 / 15 ) ) then typical dosage would be 2 * 5 = 10 cc . dosage = 18 cc . dosage is greater by 2 cc . % dosage is greater : ( 2 / 10 ) * 100 = 20 % e is the answer ."
Answer: e
Problem: if two positive numbers are in the ratio 1 / 7 : 1 / 5 , then by what percent is the second number more than the first ?
Options: a ) 70 % , b ) 90 % , c ) 60 % , d ) 40 % , e ) 65 %
Rationale: "given ratio = 1 / 7 : 1 / 5 = 5 : 7 let first number be 5 x and the second number be 7 x . the second number is more than first number by 2 x . required percentage = 2 x / 5 x * 100 = 40 % . answer : d"
Answer: d
Problem: 30.5 % of 2000
Options: a ) 556 , b ) 612.5 , c ) 756.8 , d ) 610 , e ) 820
Rationale: 1 % of 2000 = 20 30 % of 2000 = 30 * 20 = 600 0.5 % of 2000 = 0.5 * 2000 = 10 total = 610 answer : d
Answer: d
Problem: if the operation x is defined by a x b = ( b - a ) ^ 2 / a ^ 2 for all numbers a and b , and a ≠ 0 , then − 1 x ( 1 x − 1 ) =
Options: a ) − 1 , b ) 0 , c ) 1 , d ) 25 , e ) 29
Rationale: on solving the inner bracket we get 4 . then we get equation as - 1 x 4 where b = 4 and a = - 1 answer d
Answer: d
Problem: the two lines y = x and x = - 3 intersect on the coordinate plane . if z represents the area of the figure formed by the intersecting lines and the x - axis , what is the side length of a cube whose surface area is equal to 6 z ?
Options: a ) 16 , b ) 3 / √ 2 , c ) 8 , d ) 2 √ 2 , e ) ( √ 2 ) / 3
Rationale: 800 score official solution : the first step to solving this problem is to actually graph the two lines . the lines intersect at the point ( - 3 , - 3 ) and form a right triangle whose base length and height are both equal to 4 . as you know , the area of a triangle is equal to one half the product of its base length and height : a = ( 1 / 2 ) bh = ( 1 / 2 ) ( 3 × 3 ) = 9 / 2 ; so z = 9 / 2 . the next step requires us to find the length of a side of a cube that has a face area equal to 9 / 2 . as you know the 6 faces of a cube are squares . so , we can reduce the problem to finding the length of the side of a square that has an area of 9 / 2 . since the area of a square is equal to s ² , where s is the length of one of its side , we can write and solve the equation s ² = 9 / 2 . clearly s = √ 9 / 2 = 3 / √ 2 , oranswer choice ( b ) .
Answer: b
Problem: subtracting 4 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.96 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 4 % of a = ab . ⇒ ( 96 x a ) / 100 = ab ∴ b = 0.96 correct option : a"
Answer: a
Problem: each of the integers from 0 to 9 , inclusive , is written on a separate slip of blank paper and the ten slips are dropped into a hat . if 5 of the slips are the drawn , without replacement , what is the probability that all 5 have a even number written on it ?
Options: a ) 1 / 252 , b ) 1 / 10 , c ) 1 / 8 , d ) 1 / 2 , e ) 5 / 9
Rationale: "key is that there is no replacement , so each successive choice will become more skewed towards picking a neg ( i . e . the pool of positives decreases , while the pool of negatives stay the same ) p ( + on 1 st pick ) = 5 / 10 p ( + on 2 nd pick ) = 4 / 9 p ( + on 3 rd pick ) = 3 / 8 p ( + on 4 rd pick ) = 2 / 7 p ( + on 5 rd pick ) = 1 / 6 5 / 10 * 4 / 9 * 3 / 8 * 2 / 7 * 1 / 6 = 1 / 252 a"
Answer: a
Problem: if a and b are integers and ( a * b ) ^ 5 = 32 y , y could be :
Options: a ) 16 , b ) 1 , c ) 8 , d ) 12 , e ) 24
Rationale: "distribute the exponent . a ^ 5 * b ^ 5 = 32 y find the prime factorization of 32 . this is 2 ^ 5 * 1 . we need 1 the answer is b ."
Answer: b
Problem: it was calculated that 100 men could complete a piece of work in 20 days . when work was scheduled to commence , it was found necessary to send 50 men to another project . how much longer will it take to complete the work ?
Options: a ) 45 days . , b ) 40 days . , c ) 38 days . , d ) 35 days . , e ) 30 days .
Rationale: one day work = 1 / 20 one man ’ s one day work = 1 / ( 20 * 100 ) now : no . of workers = 50 one day work = 50 * 1 / ( 20 * 100 ) the total no . of days required to complete the work = ( 100 * 20 ) / 50 = 40 answer : b
Answer: b
Problem: if a is thrice as fast as b and together can do a work in 15 days . in how many days a alone can do the work ?
Options: a ) 36 , b ) 20 , c ) 28 , d ) 54 , e ) 45
Rationale: "a ’ s one day ’ s work = 1 / x b ’ s one day ’ s work = 1 / 3 x a + b ’ s one day ’ s work = 1 / x + 1 / 3 x = 1 / 15 = 3 + 1 / 3 x = 4 / 3 x = 1 / 15 x = 15 * 4 / 3 = 20 answer : b"
Answer: b
Problem: average of 5 numbers is - 10 , and the sum of 3 of the numbers is 16 , wat is the average of the other 2 numbers ?
Options: a ) - 33 , b ) 33 , c ) 35 , d ) 36 , e ) - 35
Rationale: let the five numbers be a , b , c , d , e . then their average is ( a + b + c + d + e 5 ) = 10 . ( a + b + c + d + e 5 ) = 10 . now three of the numbers have a sum of 16 , say , a + b + c = 16 a + b + c = 16 . so substitute 16 for a + b + ca + b + c in the average above : ( 16 + d + e 5 ) = 10 . ( 16 + d + e 5 ) = 10 . solving this equation for d + ed + e gives d + e = − 66 d + e = − 66 . finally , dividing by 2 ( to form the average ) gives ( d + e 2 ) = − 33 . ( d + e 2 ) = − 33 . hence , the answer is a : - 33
Answer: a
Problem: a number when divided by 296 leaves 75 as remainder when the same number is divided by 37 then the remainder will be ?
Options: a ) 2 , b ) 9 , c ) 6 , d ) 5 , e ) 1
Rationale: "let x = 296 q + 75 = ( 37 * 8 q + 37 * 2 ) + 1 37 * ( 8 q + 2 ) + 1 thus when the number is divided by 37 the remainder is 1 answer ( e )"
Answer: e
Problem: if | 4 x + 6 | = 50 , what is the sum of all the possible values of x ?
Options: a ) 2 , b ) - 2 , c ) 4 , d ) - 3 , e ) 6
Rationale: "there will be two cases 4 x + 6 = 50 or 4 x + 6 = - 50 = > x = 11 or x = - 14 sum of both the values will be - 14 + 11 = - 3 answer is d"
Answer: d