mathewhe/aqua_rat huggingface dataset:
Question: Of the 8 members of flight crew, 7 are trained to serve economic class customer, 5 are trained to serve business class customer, and 4 can serve both. If one member is chosen at random, what is the probability that the member chosen will be someone who can serve either type of customer?
(A) a) 1/9
(B) b) 0
(C) c) 1/6
(D) d) 1/4
(E) e) 1/3
Rationale: You know how to solve for Total number of people who can serve at least one type of customer:
Total = n(A) + n(B) - n(A and B)
Total people who can serve at least one type of customer = 7 + 5 - 4 = 8
So All 8 people know how to serve at least one type of customer. Hence, if you pick anyone, the probability is 0 that he/she wouldn't know how to serve any type of customer
Answer (B)
Answer: (B) b) 0
Question: In a certain city, 70 percent of the households have cable television, and 50 percent of the households have videocassette recorders. If there are 150,000 households in the city, then the number of households that have both cable television and videocassette recorders could be any number from:
(A) 30,000 to 75,000 inclusive
(B) 30,000 to 90,000 inclusive
(C) 60,000 to 75,000 inclusive
(D) 60,000 to 90,000 inclusive
(E) 90,000 to 120,000 inclusive
Rationale: The maximum percentage with both is 50% which is 75,000 households.
This means that every household with a recorder also has cable television.
The minimum percentage with both is 20% which is 30,000 households.
This means that 30% of households have only recorders but not cable television.
The other 20% of households with recorders have cable television.
The answer is A.
Answer: (A) 30,000 to 75,000 inclusive
Question: A present value of a machine is $700. Its value depletion rate is 10% per annum then find the machine value after 2 years?
(A) $900
(B) $810
(C) $915
(D) $715
(E) $567
Rationale: P= $700
R = 10%
T = 2 years
Machine value after 2 years = P[(1-R/100)^T]
=700*9/10 * 9/10
=$567
Answer is E
Answer: (E) $567
Question: After 2 games, team B had an average of 61.5 points per game. If it got only 47 points in game 3, how many more points does it need to score to get its total above 500?
(A) 805
(B) 740
(C) 670
(D) 530
(E) 330
Rationale: (2*61.5) + 47 +x >500
123+47+x > 500
170+x >500
=> x>330
Option E
Answer: (E) 330
Question: 12 men can complete a piece of work in 25 days. In how many days can 20 men complete that piece of work?
(A) 55 days
(B) 77 days
(C) 20 days
(D) 88 days
(E) 15 days
Rationale: 12 * 25 = 20 * x => x
= 15 days
Answer: E
Answer: (E) 15 days
Question: In a series of six consecutive even numbers, the sum of the second and sixth numbers is 24. What is the fourth number?
(A) 12
(B) 66
(C) 87
(D) 88
(E) 66
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 2) + (x + 10) = 24
=> 2x + 12 = 24 => x = 6
The fourth number = x + 6 = 6 + 6 = 12.
Answer: A
Answer: (A) 12
Question: Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?
(A) 18
(B) 20
(C) 23
(D) 24
(E) 26
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
Option 'D'
Answer: (D) 24
Question: In an office, 50 percent of the workers have at least 5 years of service, and a total of 16 workers have at least 10 years of service. If 90 percent of the workers have fewer than 10 years of service, how many of the workers have at least 5 but fewer than 10 years of service?
(A)  8
(B)  64
(C)  50
(D)  144
(E)  160
Rationale: (10/100)Workers = 16 = > number of workers = 160
(50/100)*Workers = x+16 = > x = 8
Answer A
Answer: (A)  8
Question: At a florist shop on a certain day, all corsages sold for either $40 or $45. If 8 of the corsages that sold for $30 had instead sold for $20, then the store's revenue from corsages that day would have been reduced by 20 percent. What was the store's actual revenue from corsages that day?
(A) $200
(B) $400
(C) $600
(D) $800
(E) $1000
Rationale: I am doing it elaborately, hope it will help you.
Let, No. of corsages @ $40 = x, no. of corsages @ $45 = y and revenue= r
so, 40 x+45 y=r.........(1)
Now,
Given the situation, 40(x+8) + 45(y-8)= r-.2r
=> 40 x+320+45 y-360 = .8r
=> 40x+45y = .8r+40............(2)
so, r = .8r+40
=> r = 200
The answer is A.
Answer: (A) $200
Question: Ten percent of Country Y's yearly exports come from fruit exports. One-fifth of all fruit exports from Country Y are orange exports. If country Y generates $400 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $127.5m
(E) $20000m
Rationale: 10/100*1/5*(total) = 400
1/50*(total) = 400
(total) = 400*50 = 20000
Answer: E
Answer: (E) $20000m
Question: In how many ways 8 different tickets Q can be distributed between Jane and Bill if each is to receive any even number of tickets and all 8 tickets to be distributed.
(A) From 2 to 6 inclusive.
(B) From 98 to 102 inclusive.
(C) From 122 to 126 inclusive.
(D) From 128 to 132 inclusive.
(E) From 196 to 200 inclusive.
Rationale: Possibilities
J 8 6 4 2 0
B 0 2 4 6 8
# of ways 8C8 8C6 8C4 8C2 8C0
Q=1+28+70+28+1 = 128 Answer is D.
Answer: (D) From 128 to 132 inclusive.
Question: If a is an integer larger than 1, and x=60a, then x must be a multiple of which of the following?
(A) 8
(B) 9
(C) 12
(D) 18
(E) 120
Rationale: X must be divisible by 60 .
a , an integer less than 1 means a could be 0,-1,-2,....... and x = 60a
so if a= 0, x = 0*60=0 is divisible by 12 ( recall 0 is divisible by any integer)
if a= -1, then -60 is divisible by 12 but not 8,9,18 and 120 , if a-2 , then -120 is divisible by 60 and so on
Answer is C
Answer: (C) 12
Question: Out of 8 consonants and 4 vowels, how many words of 3 consonants and 1 vowels can be formed?
(A) 21005
(B) 10500
(C) 25200
(D) 5376
(E) None of these
Rationale: Solution
Number of ways of selecting (3 consonants out of 8) and (1 vowels out of 4)
8c3 x 4c1= (8x7x6/3x2x1)x(4/1) =224
Number of group,each having 3 consonants and 1 vowels = 224 .
Each group contains 4 letter.
Number of ways of arranging 5 letters among themselves
= 4 ! = (4 × 3 × 2 × 1) = 24 .
So, Required number of words = (24 × 224) = 5376 .Answer D
Answer: (D) 5376
Question: The unit digit in the product (784x618x917x463) is
(A) 2
(B) 3
(C) 4
(D) 5
(E) None of them
Rationale: Unit digit in the given product = Unit digit in (4x8x7x3)=2
Answer is A
Answer: (A) 2
Question: A toy factory stores its toys in either a big box or a small box. The big box can store 35 toys while the small box can store 14 toys. If the factory is to store 86 newly manufactured toys, what is the least number of toys that will be left unboxed?
(A) 2
(B) 1
(C) 3
(D) 5
(E) 4
Rationale: Total toys to be stored 86
The big box can store 35
small box can store 14
storing 85 toys in big box 85/35 =2 r 16
store remainder in small box 16/14=1 r 2
least number of toys that will be left unboxed=2
Answer: A
Answer: (A) 2
Question: Which of these lines in the xy-plane does not contain any point with two negative coordinates?
(A) y = 2x
(B) y = x + 9
(C) y = x^2 - 3
(D) y = x^3 + x
(E) y = x^4
Rationale: x^4 is 0 when x is 0 and positive for all other values of x.
The answer is E.
Answer: (E) y = x^4
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 10 kmph, then the speed in downstream is?
(A) 25
(B) 378
(C) 20
(D) 27
(E) 121
Rationale: M = 15
S = 10
DS = 15 + 10 = 25
Answer: A
Answer: (A) 25
Question: An association of mathematics teachers has 1,260 members. Only 640 of these members cast votes in the election for president of the association. What percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast?
(A) 30.47%
(B) 58%
(C) 42%
(D) 34%
(E) 25%
Rationale: Total Number of members = 1260
Number of members that cast votes = 640
Since , winning candidate received 60 percent of the votes cast
Number of votes for winning candidate = (60/100)*640 = 384
Percent of total membership that voted for winning candidate = (384/1260)*100 = 30.47%
Answer A
Answer: (A) 30.47%
Question: John purchased a fridge and a mobile for Rs. 15000 &Rs. 8000 respectively. He sold the fridgeat a loss of 4% and the mobile phone at a profit of 10%. Overall how much he make a profit.
(A) Rs. 100
(B) Rs. 120
(C) Rs. 200
(D) Rs. 240
(E) Rs. 250
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
C
Answer: (C) Rs. 200
Question: If m is an integer such that (-2)^2m=2^(15-m) then m=?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: (-2)^(2m) = 4^m
and
2^(15-m) = 4^((15-m)/2)
Therefore,
m = (15-m)/2
2m = 15 - m
m = 5
Answer D
Answer: (D) 5
Question: Denise is trying to open a safe whose combination she does not know. IF the safe has 3000 possible combinations,and she can try 75 different possibilities,what is the probability that she does not pick the one correct combination.
(A) 1
(B) 159/160
(C) 157/160
(D) 0.875
(E) 0.975
Rationale: If Denise does not pick the correct combination in first 75 try, then the correct combination is one of remaining 2925. So Probability = 2925/3000 = 0.975.
answer is E
Answer: (E) 0.975
Question: Two goods trains each 1250 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 228
(B) 278
(C) 48
(D) 27
(E) 120
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 1250 + 1250 = 2500 m.
Required time = 2500 * 6/125 = 120 sec.
Answer:E
Answer: (E) 120
Question: A triangle has a perimeter 13. The two shorter sides have integer lengths equal to x and x + 1. Which of the following could be the length of the other side?
(A) 8
(B) 6
(C) 1
(D) 5
(E) 4
Rationale: The measure of the third side of a triangle must lie between the sum and the difference of the other two sides. Using this fact along with the answer choices, we can eliminate the wrong answers.
cannot be correct because 4 would not be the longest side.(sides 4, 5, and 4)
could be correct because the other two sides would be 3 and 4.
cannot be correct because this third side would be greater than the sum of the other two sides.
Answer: B
Answer: (B) 6
Question: An athlete runs 100 meters race in 12sec. His speed is?
(A) 30km/hr
(B) 15km/hr
(C) 25km/hr
(D) 20km/hr
(E) 32km/hr
Rationale: speed = 100/12 = 25/3 m/sec
= 25/3 * 18/3 km/hr = 30km/hr
Answer is A
Answer: (A) 30km/hr
Question: If A : B = 4 : 7 and B : C = 5 : 8 then A : B : C is :
(A) 20 : 35 : 56
(B) 35 : 36 : 63
(C) 30 : 35 : 65
(D) 25 :34: 68
(E) None of these
Rationale: Expl : A : B = 4 : 7
B : C = 5 :8 = 5*7/5 : 8 *7/5 = 7 : 56/5
A : B : C = 4 : 7 : 56/5 = 20 : 35 : 56
Answer: A
Answer: (A) 20 : 35 : 56
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
(A) 1/15
(B) 1/20
(C) 1/21
(D) 3/14
(E) 2/7
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
B
Answer: (B) 1/20
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different E arrangements of plays can be run, if the same play can’t be run more than once?
(A) 24
(B) 125
(C) 243
(D) 504
(E) 729
Rationale: Number of E ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: (D) 504
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 283
(B) 240
(C) 883
(D) 379
(E) 123
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x
= 240 m.
Answer: B
Answer: (B) 240
Question: Because of the economic slowdown, a multinational company curtailed some of the allowances of its employees. John, the marketing manager of the company whose monthly salary has been reduced to Rs.42,000 is unable to cut more on his expenditure. He finds that there is a deficit of Rs.2,000 between his earning and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. John has a saving of Rs 60,000 which will be used to fill the deficit. After his savings get exhausted, John would start borrowing from his friends. How soon will he start borrowing?
(A) 12th months
(B) 11th months
(C) 10th months
(D) 8th months
(E) 13th months
Rationale: Let the Rashid 's savings will last till 'nn' months.
⇒n2[2×2000+(n−1)500]=60,000⇒n2[2×2000+(n−1)500]=60,000
[Expenditure every month increases by 500 rupees]
⇒n2+7n−200=0⇒n2+7n−200=0
n=12.38n=12.38
⇒ Rashid after Kartik's mother asked him to get the vegetables, milk and butter from the market and gave him the money in the denominator of 1 Rupee, 2 Rupee and 5 Rupee coins.
Kartik first goes to the grocery shop to buy vegetables. At the grocery shop he gives half of his 5 Rupee coins in return receives the same number of 1 Rupee coins.
Next he goes to the dairy shop to buy milk and butter and gives all 2 Rupee coins and in return get thirty 5 Rupee coins, which increase the number of five rupee coins by 75% more than the original number.
If the number of 1 rupee coins now is 50, the number of 1 rupee and 5 rupee coins originally were will start borrowing money from his friends.
E
Answer: (E) 13th months
Question: What value will come in place of question mark in the following equation? 0.006 +? = 0.6
(A) 0.01
(B) 0.05
(C) 0.03
(D) 0.07
(E) 0.02
Rationale: Let 0.006 / x = 0.6, Then, x = (0.006 / 0.6) = (0.006*10) / (0.6*10) = 0.06/6 = 0.01
Answer is A.
Answer: (A) 0.01
Question: How many seconds will a 500 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?
(A) 22
(B) 30
(C) 99
(D) 77
(E) 62
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 = 500 * 3/50 = 30 sec.
Answer:B
Answer: (B) 30
Question: Find the positive number which when increased by 17 is equal to 60 times the reciprocal of the number
(A) 4
(B) 3
(C) 2
(D) 9
(E) 7
Rationale: Let the number be x
x+17=60/x
x^2+17x-60=0
(x+20)(x-3)=0
x=3
correct answer B
Answer: (B) 3
Question: If after 400 grams of water were added to the 24%-solution of alcohol, the strength of the solution decreased by one-third, how much of the 24%-solution was used?
(A) 180 grams
(B) 220 grams
(C) 250 grams
(D) 350 grams
(E) 800 grams
Rationale: I too think 800 grams should be the answer.
My reasoning is
The h20 content in 200 gms of water is 1
h20 content in 24% solution is 0.76
Resulting new solution's concentration decreases by one third means. Now it becomes 16% solution which means h20 content is 0.84
Let amount of solution be X
Then the equation can be set up
400*1 + 0.76X = 0.84 (X+400)
0.08X = 64
8X = 6400
X = 800 (ANS E)
Answer: (E) 800 grams
Question: a is an integer greater than 19 but less than 32, b is an integer greater than 29 but less than 42, what is the range of a/b?
(A) 1/4
(B) 1/2
(C) 3/4
(D) 1
(E) 5/4
Rationale: min value of a/b will be when b is highest and a is lowest ---> a=20 and b=40
So, a/b = 1/2
max value of a/b will be when b is lowest and a is highest ---> a=30 and b=30
So, a/b = 1
Range is 1-(1/2) = 1/2.
Answer should be B
Answer: (B) 1/2
Question: If A is 25 kms east of B, which is 12 kms south of C, which is 9 kms west of D. A person starts walking at 3 kms/hr from A towards D. Calculate the distance of the point from A where he is going to meet a person from D walking towards A at 2 kms / hr.
(A) 20
(B) 12
(C) 8
(D) 20 sqrt (12*8)
(E) none
Rationale: 2,3=common factor
hence 20
ANSWER:A
Answer: (A) 20
Question: 10 years ago Neha's mother was 4 times older than Neha. After 10 years Neha's mother will be twice Neha's age. How old is Neha now?
(A) 10 years
(B) 15 years
(C) 17 years
(D) 20 years
(E) 23 years
Rationale: Let us assume m = mother and n = neha
m-10 = 4(n-10) => 4n-m = 30 this is equation 1
m+10 = 2(n+10 => -2n+m = 10 this is equation 2
By equations 1 and 2
n=20
n means Neha age = 20 years
ANSWER:D
Answer: (D) 20 years
Question: Find the compound ratio of (2:3), (6:11) and (11:2) is
(A) 3:2
(B) 2:1
(C) 1:2
(D) 4:5
(E) 2:3
Rationale: Required ratio = 2/3 * 6/11 * 11/2 = 2/1 = 2:1
Answer is B
Answer: (B) 2:1
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 13 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 51 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
(A) A)11
(B) B)18
(C) C)24
(D) D)25
(E) D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 52..
Not W = 52 -31= 21..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=21 or x=9..
so who won Nobel but not Wolf = x+3 = 12..
But people who won BOTH W and N = 13..
so total who won N = 12+13 = 25..
D
Answer: (D) D)25
Question: there is one designed bedsheets having length 6m and breadth 4m.in the middle there is square shape design with 3m side.calculate the % of bedsheet which do not have any design.
(A) 62
(B) 60
(C) 75
(D) 62.5
(E) 65
Rationale: area of bedsheet=24m2.
area of square shape design=9m2.
undesigned area=24-9=15m2.
%of undesigned area=15/24*100=62.5%
answer D
Answer: (D) 62.5
Question: There are 18 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 288
(B) 267
(C) 261
(D) 211
(E) 380
Rationale: The total number of stations = 20
From 20 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in ²⁰P₂ ways.
²⁰P₂ = 20 * 19 = 380.
Answer: E
Answer: (E) 380
Question: Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 3 carpenters build in 4 hours?
(A) 2.4.
(B) 4.8.
(C) 4.2.
(D) 5.5.
(E) 6.4
Rationale: W = 2 desks
T = 2.5 hrs
Rate of 2 carpenters = 2×R
Rate = work done/ time
2xR = 2/2.5
R = 1/2.5 = 2/5 (this is the rate of each carpenter)
Work done by 3 carpenters in 4 hrs = 3 × rate of each carpenter x time = 3× 2/5 × 4 = 4.8 desks
B is the correct answer.
Answer: (B) 4.8.
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 39
(B) 35
(C) 42
(D) 40.5
(E) 41
Rationale: Explanation:
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
=> 16(x-3) + 87 = 17x
=> 16x - 48 + 87 = 17x
=> x = 39
Answer: Option A
Answer: (A) 39
Question: A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12300 after a year?
(A) 3630
(B) 3690
(C) 2887
(D) 9977
(E) 2212
Rationale: 6300:4200:10500
3:2:5
3/10 * 12300 = 3690.Answer: B
Answer: (B) 3690
Question: If the length of the sides of two cubes are in the ratio 2:1, what is the ratio of their total surface area?
(A) 2:1
(B) 3:1
(C) 4:1
(D) 6:1
(E) 8:1
Rationale: Let x be the length of the small cube's side.
The total surface area of the small cube is 6x^2.
The total surface area of the large cube is 6(2x)^2=24x^2.
The ratio of surface areas is 4:1.
The answer is C.
Answer: (C) 4:1
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 6m
(B) 9m
(C) 3m
(D) 2m
(E) 1m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 = 2m.
Answer:D
Answer: (D) 2m
Question: If n is a negative integer and p is a positive integer, which of the options below must be positive?
(A) (n + p)^2
(B) np
(C) n/p
(D) p/n
(E) none of the above
Rationale: A.(n + p)^2
will be positive irrespective of the absolute values of x and y
will be positive always
B. np
-ve*+ve=-ve
will be negative
C. n/p
-ve*/ve=-ve
D.+ve/-ve=-ve
+ve/-ve=-ve
Answer A
Answer: (A) (n + p)^2
Question: A 75-liter solution of cool-drink is made from 8% jasmine water. If 3 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine?
(A) 10.3%
(B) 11.5%.
(C) 10%.
(D) 12.2%
(E) 12%.
Rationale: Denominator
75+3+12
90
Numerator
75*0.08=6--->Jasmine water
6+3=9--->New content of Jasmine water in new solution
Ratio
9/90
Answer: C
Answer: (C) 10%.
Question: A train 100 m long crosses a platform 125 m long in 30 sec; find the speed of the train?
(A) 36
(B) 77
(C) 27
(D) 33
(E) 99
Rationale: D = 100 + 125 = 225
T = 30
S = 225/30 * 18/5 = 27 kmph
Answer: C
Answer: (C) 27
Question: A certain fraction has the same ratio to 1/18, as 2/5 does to 7/9. What is this certain fraction?
(A) 1/20
(B) 1/25
(C) 1/30
(D) 1/35
(E) 1/40
Rationale: x / (1/18) = (2/5) / (7/9)
x = 2*9*1 / 18*5*7 = 1/35
The answer is D.
Answer: (D) 1/35
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 9
(B) 7
(C) 8
(D) 12
(E) 10
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
ANSWER C
Answer: (C) 8
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 110. If legs are counted, there are 580. The number of hares in the zoo is?
(A) 120
(B) 182
(C) 190
(D) 137
(E) 180
Rationale: 110*2 = 220
580
-----
360
1----2
?----360 = 180
Answer:E
Answer: (E) 180
Question: A certain city with a population of 120,000 is to be divided into 11 voting districts , and no district is to have a population that is more than 10 percent greater than the population of any other district What is the minimum possible population that the least populated district could have ?
(A) a) 10,700
(B) b) 10,000
(C) c) 10,900
(D) d) 11,000
(E) e) 11,100
Rationale: Let x = number of people in smallest district
x*1.1 = number of people in largest district
x will be minimised when the number of people in largest district is maximised
10*x*1.1 = 11x = total number of people in other districts
So we have 11x + x = 120k
x = 10,000
Answer : B
Answer: (B) b) 10,000
Question: The length of the bridge, which a train 120 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 239
(B) 277
(C) 255
(D) 88
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (120 + X)/30
= 25/2 ==> 2(120 + X) = 750 ==> X = 255 m.
Answer: C
Answer: (C) 255
Question: Using all the letters of the word "THURSDAY", how many different words can be formed?
(A) 9
(B) 8!
(C) 2
(D) 7
(E) 5
Rationale: Total number of letters = 8
Using these letters the number of 8 letters words formed is 8P8
= 8!.
Answer: B
Answer: (B) 8!
Question: If 10,000 microns = 1 decimeter, and 10,000,000,000 angstroms = 1 decimeter, how many angstroms equal 1 micron?
(A) 0.01
(B) 1,000,000
(C) 0.001
(D) 1,000
(E) 1.0e-05
Rationale: Given that 10,000 microns = 1 decimeter =10,000,000,000 angstroms
So, 1 micron = 10,000,000,000/10,000
=1,000,000
Answer : B
Answer: (B) 1,000,000