mathewhe/aqua_rat huggingface dataset:
Question: If Mel saved more than $10 by purchasing a sweater at a 15 percent discount, what is the smallest amount the original price of the sweater could be, to the nearest dollar?
(A) 45
(B) 67
(C) 75
(D) 83
(E) 150
Rationale: We are told that 15 percent discount from the original price is more than $10:
0.15*{price} > 10;
{price} > 1,000/15;
{price} > 66 2/3.
Answer: B.
Answer: (B) 67
Question: If the average marks of three batches of 45, 60 and 45 students respectively is 50, 55 and 60, then the average marks of all the students is
(A) 53.33
(B) 54.68
(C) 55
(D) 57
(E) None
Rationale: Sol.
Required average = [55x50 + 60x55 + 45x60 / 45 + 60 + 45]
= [2250 + 3300 + 2700 / 150]
= 8250 / 150 = 55
Answer C
Answer: (C) 55
Question: Raj has bought the product and sold it for a profit of Rs.30. His cost of buying and selling is in the ratio of 8:9 respectively. How much did Raj spent for buying A?
(A) 200
(B) 240
(C) 250
(D) 270
(E) 300
Rationale: Let cost of buying of product A be x, (x+30/x)=9/8
Up on cross multiplication and solving for x, we get x=240
Answer: B
Answer: (B) 240
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
(A) 1/14
(B) 1/7
(C) 2/7
(D) 3/7
(E) 1/2
Rationale: P=Favorable outcomes / Total # of outcomes
Favorable outcomes: 2 women and 2 men = C^2/5∗C^2/3=30
Total # of outcomes: 4 people out of 5+3=8 = C^4/8=70
P=30/70=3/7
Answer: D.
Answer: (D) 3/7
Question: A truck owner will refuel his vehicle at a rate of 2 gallons of diesel fuel every 5 seconds. If diesel fuel costs $ 2 per gallon, how long will it take for the truck owner to refuel his vehicle with $ 100 worth of diesel fuel?
(A) 20 seconds
(B) 2 minute 5 seconds
(C) 1 minute 20 seconds
(D) 20 minutes
(E) 1 hour 20 minutes
Rationale: 2 gal / 5 sec
$2 / gal
$100/$2 = 502 gal
2 gal / 5 sec with 50 gal = 125 sec
B. 2 minute 5 seconds
Answer: (B) 2 minute 5 seconds
Question: Arabica coffee costs $0.4 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.36 per ounce, what is the share of Arabica in this blend?
(A) 20%
(B) 24%
(C) 30%
(D) 33%
(E) 60%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.4a + .3(1-a) = .36
.4a + .3 - .3a = .36
a= .6
therefore: .6/1 ounce = 60%. Therefore, the answer should be E
Answer: (E) 60%
Question: Which one of the fractions has the highest value?
(A) A)23/77
(B) B)23/78
(C) C)23/84
(D) D)23/87
(E) E)23/25
Rationale: 23/25
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: (E) E)23/25
Question: If a is an odd integer and b is an odd integer which of the following must not be an odd integer :
(A) a/b
(B) ab
(C) 2a+b
(D) 2(a+b)
(E) 3a/b
Rationale: only when two odd number added then we get even number.
Therefore answer is D
Answer: (D) 2(a+b)
Question: Jane started baby-sitting when she was 16 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 10 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
(A) 20
(B) 21
(C) 22
(D) 23
(E) 24
Rationale: Check two extreme cases:
Jane = 16, child = 8, years ago = 32-16 = 16 --> child's age now = 8+16 = 24;
Jane = 22, child = 11, years ago = 32-22 = 10 --> child's age now = 11+10 = 21.
Answer: E.
Answer: (E) 24
Question: A jogger running at 9 kmph alongside a railway track in 240 metres ahead of the engine of a 120 metres long train running at 45 kmph in the same direction.In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 18 sec
(C) 36 sec
(D) 72 sec
(E) none
Rationale: speed of the train relative to jogger = (45-9)km/hr=36km/hr.
(36*5/8)m/sec.
10m/sec.
Distance to be covered = (240 + 120) m = 360 m.
time taken =(360/10)sec=36sec.
Answer: C
Answer: (C) 36 sec
Question: Two people measure each other's height, the height of the taller person is H and the height of the other person is L. If the difference in their heights is equal to the average height, what is the Value of H/L
(A) 1/3.
(B) 1/2.
(C) 2.
(D) 3.
(E) 6.
Rationale: Difference = Average
H - L = (H + L)/2,
Solving for H/L gives 3. A quick check, H be 21 and L be 7, 21- 7= (21 + 7 )/2
D
Answer: (D) 3.
Question: Of the films Empty Set Studios released last year, 60% were comedies and the rest were horror films. 75% of the comedies were profitable, but 75% of the horror moves were unprofitable. If the studio made a total of 60 films, and broke even on none of them, how many of their films were profitable?
(A) 18
(B) 19
(C) 20
(D) 21
(E) 59
Rationale: After fiddling some more, this is how I got to answer choice E...but did I get here using voodoo math or is it sound?
(.60*.75) + (.40*.25) = .44 + .10 = .55
55/100 = 11/20
Then subtract from 60:
60 - 11/20 = 59 (answer E)
Answer: (E) 59
Question: 10 business executives and 7 chairmen meet at a conference. If each business executive shakes the hand of every other business executive and every chairman once, and each chairman shakes the hand of each of the business executives but not the other chairmen, how many handshakes would take place?
(A) 144
(B) 131
(C) 115
(D) 90
(E) 45
Rationale: there are 10 business exec and in each handshake 2 business execs are involved.
hence 10C2=45
Also, each of 10 exec will shake hand with every 7 other chairmen for total of 70 handshake.
total=45+70=115
ANS: C
Answer: (C) 115
Question: For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 90 Θ 33 ) Θ 17 ) - ( 97 Θ (33 Θ 17)) ?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: (( 90 Θ 33 ) Θ 17 )
The remainder of 90 divided by 33 is 24;
The remainder of 24 divided by 17 is 7;
( 97 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 97 divided by 16 is 1.
7 - 1 = 6.
Answer: D.
Answer: (D) 6
Question: Two trains A and B are 150 m and 150 m long and are moving at one another at 54 Km/hr and 36 Km/hr respectively. Arun is sitting on coach B1 of train A. Calculate the time taken by Arun to completely cross Train B.
(A) 10 s
(B) 6 s
(C) 4 s
(D) 8 s
(E) 12 s
Rationale: DETAILED SOLUTION
Speed of A = 54∗1000/60∗60 = 15 m/s
Speed of B = 36∗1000/60∗60 = 10 m/s
Relative speed = S1 + S2 = 15 + 10 m/s = 25 m/s
The length that needs to be crossed = length of train B = 150 m. Therefore time taken = 150/25 = 6s.
What is the time taken for trains to completely cross each other? The length that needs to be crossed = 150 + 150 = 300 m. Time taken = 300/25 = 12 s.
CORRECT ANSWER E.
Answer: (E) 12 s
Question: At what time, in minutes, between 3 o'clock and 4 o'clock, both the needles will coincide each other?
(A) 16 4/19
(B) 16 4/18
(C) 16 4/10
(D) 16 4/11
(E) 16 4/14
Rationale: Formula : θ=∣∣∣30h−112m∣∣∣θ=|30h−112m|
Here angle is 0. So
11/2 m – 30 h = 0
11/2 m – 30 × 3 = 0
m = 180/11
= 16 4/11
Ans:: D
Answer: (D) 16 4/11
Question: In a barrel of juice there is 60 liters; in a barrel of beer there are 80 liters. If the price ratio between barrels of juice to a barrel of beer is 3:4, what is the price ratio between one liter of juice and one liter of beer?
(A) 3:2.
(B) 1:1.
(C) 3:1.
(D) 4:3.
(E) 3:4.
Rationale: Juice barrel : beer Barrel = 60:80 i.e. 3:8
price of Juice : Price of Beer = 3 : 4
so for 6/8 costs 3/4, ie 6J / 8B = 3/4.
Solving for J/B, we get 2:2=1:1
Answer B.
Answer: (B) 1:1.
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required?
(A) 34
(B) 40
(C) 68
(D) 88
(E) None
Rationale: Solution
We have:L =20 ft and lb = 680 sq.ft	b = 34ft
Length of fencing	= (l + 2b)
= (20 + 68)ft
= 88 ft.
Answer D
Answer: (D) 88
Question: A river 2m deep and 45 m wide is flowing at the rate of 3 kmph the amount of water that runs into the sea per minute is?
(A) 4500 M3
(B) 4580 M3
(C) I8500 M3
(D) 4900 M3
(E) 4700 M3
Rationale: Explanation:
(3000 * 2 * 5)/60 = 4500 M3
Answer: Option A
Answer: (A) 4500 M3
Question: You and your friend spent a total of $19 for lunch. Your friend spent $3 more than you. How much did your friend spend on their lunch?
(A) $9
(B) $3
(C) $4
(D) $6
(E) $11
Rationale: My lunch = l, my friends lunch = l+3
(l)+(l+3)=19
l+l+3-3=19-3
2l=16
l=8
My friends lunch l+3 = 8+3=$11, the answer is E
Answer: (E) $11
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations F are possible?
(A) 3
(B) 4
(C) 5
(D) 6
(E) F=8
Rationale: The combinations could be F{(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8..E
Answer: (E) F=8
Question: Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each is riding at 6 MPH. They live 36 miles apart. One of them has a pet carrier pigeon and it starts flying the instant the friends start traveling. The pigeon flies back and forth at 21 MPH between the 2 friends until the friends meet. How many miles does the pigeon travel?
(A) 54
(B) 66
(C) 68
(D) 60
(E) 63
Rationale: E
63
It takes 3 hours for the friends to meet; so the pigeon flies for 3 hours at 21 MPH = 63 miles
Answer: (E) 63
Question: Two wheels are connected via a conveyor belt. The larger wheel has a 36cm diameter and the smaller wheel has a 24cm diameter. In order for the conveyor belt to work smoothly, each wheel must rotate the exact same number of centimetres per minute. If the larger wheel makes r revolution per minute, how many revolutions does the smaller wheel make per hour in terms of r?
(A) 1280π
(B) 75r
(C) 48r
(D) 90r
(E) (64π)/3
Rationale: Interesting to note that the larger wheel has a diameter of 36 (6*6) while the smaller one has a diameter of 24 (6*4)...
If the large wheel has a diameter of 36 and the small wheel, 24, then their circumferences are 36pi and 24pi respectively. In order for them to move the conveyor belt at the same rate, the smaller wheel would need to rotate 1.5 times as fast as the larger wheel. Lets say the large wheel makes 10 revolutions per minute, the smaller wheel would need to make 10*1.5 = 15 revolutions per minute. If the large wheel makes 10 revolutions per minute it makes 600 per hour. Therefore, the smaller wheel would need to make 600*1.5 = 900 revolutions per hour.
If r = 10, then the answer choice must be d.
D. 90r
Answer: (D) 90r
Question: Ramesh can finish a work in 20 days and Sushil in 25 days. They both work together for 5 days and then Sushil goes away. In how many days will Ramesh complete the remaining work?
(A) 12 days
(B) 5 days
(C) 8 days
(D) 11 days
(E) 6 days
Rationale: Answer: Option D
(5 + x)/20 + 5/25 = 1 => x = 11 days
Answer: (D) 11 days
Question: Ajay can complete a piece of work in 4 days. Balu takes double the time taken by Ajay, Charan takes double that of Balu, and Danush takes double that of Charan to complete the same task. They are paired in groups of two each. One pair takes two thirds the time needed by the second pair-to complete the work. Which is the first pair?
(A) A, B
(B) A, C
(C) B, C
(D) A, D
(E) None of these
Rationale: Time taken by Ajay, Balu, Charan, Dhanush is 4 days, 8 days, 16 days and 32 days respectively.
Therefore, grouping Ajay and Dhanush work will be two third of the work that will be completed by grouping Balu and Charan.
ANSWER:D
Answer: (D) A, D
Question: A Bell Curve (Normal Distribution) has a mean of − 1 and a standard deviation of 1/8 . How many integer values M are within three standard deviations of the mean?
(A) 0
(B) 1
(C) 3
(D) 6
(E) 7
Rationale: Got the question correctly -- the second item -- [highlight]bthe list of elements in the set is required.[/highlight] is not required.
With the new information, there is only one integer value (-1) that is between (-1.375, -0.625) i.e., falls within the three 3 SD range.B
Answer: (B) 1
Question: What is the units digit of 2222^(555)*3333^(222)?
(A) 0
(B) 2
(C) 4
(D) 6
(E) 8
Rationale: Each of the other explanations to this question has properly explained that you need to break down the calculation into pieces and figure out the repeatingpatternof the units digits.
Here's another way to organize the information.
We're given [(2222)^333][(3333)^222]
We can 'combine' some of the pieces and rewrite this product as....
([(2222)(3333)]^222) [(2222)^111]
(2222)(3333) = a big number that ends in a 6
Taking a number that ends in a 6 and raising it to a power creates a nice pattern:
6^1 = 6
6^2 = 36
6^3 = 216
Etc.
Thus, we know that ([(2222)(3333)]^222) will be a gigantic number that ends in a 6.
2^111 requires us to figure out thecycleof the units digit...
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
2^5 = 32
2^6 = 64
2^7 = 128
2^8 = 256
So, every 4powers, the pattern of the units digits repeats (2, 4, 8, 6.....2, 4, 8, 6....).
111 = 27 sets of 4 with a remainder of 3....
This means that 2^111 = a big number that ends in an 8
So we have to multiply a big number that ends in a 6 and a big number that ends in an 8.
(6)(8) = 48, so the final product will be a gigantic number that ends in an 2.
Final Answer:
B
Answer: (B) 2
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
(A) 7
(B) 8
(C) 5
(D) 2
(E) 4
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
Answer:B
Answer: (B) 8
Question: A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.20. For each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total for a book on the third day it is overdue?
(A) $0.60
(B) $0.70
(C) $0.80
(D) $0.90
(E) $1.00
Rationale: 1st day fine - 0.2
2nd day fine - 0.2*2 = 0.4 (as doubling gives lower value)
3rd day fine - 0.4+3 = 0.7 (as doubling gives higher value)
Answer: B.
Answer: (B) $0.70
Question: The sides of a rectangle are in the ratio of 6 : 5 and its area is 1331 sq.m. Find the perimeter of rectangle.
(A) 121
(B) 123
(C) 125
(D) 122
(E) 126
Rationale: Let 6x and 5x be sides of the rectangle
6x × 5x = 1331
11xpower2 = 1331
xpower2 = 1331/11 = 121 => x = 11
Length = 6x = 6 × 11 = 66
Breadth = 5x => 5 × 11 = 55
Perimeter = 2 (l+b) => 2 (66+55) = 121 m
Answer is A.
Answer: (A) 121
Question: A CAN FINISH A WORK IN 21 DAYS AND B CAN DO THE SAME WORK IN15 DAYS. B WORKED FOR 10 DAYS AND LEFT THE JOB. IN HOW MANY DAYS, A ALONE CAN FINISH THE REMAINING WORK?
(A) 5
(B) 5 1/2
(C) 7
(D) 8
(E) NONE OF THESE
Rationale: B'S 10 DAY'S WORK=(1/15*10)=2/3 REMAINING WORK = (1-2/3)=1/3
NOW, 1/18 WORK IS DONE BY A IN 1 DAY
1/3 WORK IS DONE BY A IN (21*1/3)=7 DAYS.
CORRECT OPTION:C
Answer: (C) 7
Question: The volume of a large cube is 125 cubic inches. A new
shape is formed by removing a smaller cube from one
corner of the large cube. The surface area of this new
shape in square inches is
(A) 120
(B) 150
(C) 180
(D) 225
(E) 250
Rationale: Note that the surface area of the shape is the same as the surface area of the
large cube. Also, the large cube has side 5, and surface area 6 × 5-2round = 150.
correct answer B
Answer: (B) 150
Question: The first four numbers in a regular sequence are 4, 10, 22, and 46. What is the next number in the sequence?
(A) 94
(B) 54
(C) 176
(D) 82
(E) 190
Rationale: it is a good Q to learn to pick up number properties in the given set, even if we do not get a Q on these line in actuals..
when we see the sequence 4, 10, 22, 46, we see that each succeeding number is some value more than twice the previous number..
10=2*4+2..
22=2*10+2..
and so on..
so next number= 2*46+2=94..
A
Answer: (A) 94
Question: What least number must be added to 1056, so that the sum is completely divisible by 23 ?
(A) 23
(B) 24
(C) 12
(D) 2
(E) 6
Rationale: 23) 1056 (45
92
---
136
115
---
21
---
Required number = (23 - 21)
= 2
ANSWER D
Answer: (D) 2
Question: A cricketer has a certain average for 10 innings. In the eleventh inning, he scored 108 runs, there by increasing his average by 6 runs. His new average is:
(A) 46
(B) 50
(C) 52
(D) 54
(E) 30
Rationale: Let average for 10 innings be x. Then,
(10x + 108)/11 = x + 6
= 11x + 66 = 10x + 108
= x = 42.
New average = (x + 6) = 48 runs.
ANSWER A
Answer: (A) 46
Question: How many four-digit numbers that do not contain the digits 2, 3, 4, 5, 6, 7, or 8 are there?
(A) 30
(B) 36
(C) 42
(D) 48
(E) 54
Rationale: The 1st digit can be filled up by the numbers: {1,9} = 2 ways
The 2nd digit can be filled up by the numbers: {0,1,9} = 3 ways
The 3rd digit can be filled up by the numbers: {0,1,9} = 3 ways
The 4th digit can be filled up by the numbers: {0,1,9} = 3 ways
The total number of such four-digit numbers is 2*3*3*3 = 54
The answer is E.
Answer: (E) 54
Question: How many three letter words are formed using the letters of the word THREE?
(A) A)117
(B) B)118
(C) C)119
(D) D)120
(E) E)121
Rationale: The number of letters in the given word is five.
The number of three letter words that can be formed using these four letters is 5P4
= 5 * 4 * 3*2 = 120.
Answer:D
Answer: (D) D)120
Question: In a pair of fractions, fraction A is twice the fraction B and the product of two fractions is 2/25. What is the value of fraction A?
(A) 1/5
(B) 1/25
(C) 2/5
(D) Data inadequate
(E) None of these
Rationale: A = 2B => B = 1/2 A, so, AB = 2/25
1/2 A2 = 2/25
A2 = 4/25
A = 2/5
ANSWER:C
Answer: (C) 2/5
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
(A) 28882
(B) 27772
(C) 23123
(D) Rs.13500
(E) 28811
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer: D
Answer: (D) Rs.13500
Question: What is the maximum number Q of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
(A) 36
(B) 32
(C) 24
(D) 21
(E) 15
Rationale: 27 cubic centimetre cubes gives side = 3cm
so if:
L*W*H is 9*12*8, then max. cube we can have are 3*4*2 = 24
L*W*H is 9*8*12, then max. cube we can have are 3*2*4 = 24
L*W*H is 12*8*9, then max. cube we can have are 4*2*3 = 24
L*W*H is 12*9*8, then max. cube we can have are 4*3*2 = 24
L*W*H is 8*12*9, then max. cube we can have are 2*4*3 = 24
L*W*H is 8*9*12, then max. cube we can have are 2*3*4 = 24
In all cases we get Q=24 cubes.
Ans. C
Answer: (C) 24
Question: In a can, there is a mixture of milk and water in the ratio 3:2. If the can is filled with an additional 6 liters of milk, the can would be full and the ratio of milk and water would become 2:1. Find the capacity of the can?
(A) 36
(B) 34
(C) 32
(D) 30
(E) 28
Rationale: Let C be the capacity of the can.
(3/5)*(C-6)+6=(2/3)*C
9C-54+90=10C
C=36
The answer is A.
Answer: (A) 36
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:8
(C) 2:4
(D) 2:1
(E) 2:2
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer: A
Answer: (A) 2:5
Question: To mail a package, the rate is 40 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 20 cents
(B) Combined, with a saving of 35 cents
(C) Separately, with a saving of 5 cents
(D) Separately, with a saving of 15 cents
(E) Combined, with a saving of 25 cents
Rationale: 4 pounds cost = 40+3*5 = 55
6 pounds cost = 40+5*5 = 65
Total = 120
10 pounds cost = 40+ 9*5 =85 dif. 35
Answer : B
Answer: (B) Combined, with a saving of 35 cents
Question: Twenty eight years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
(A) 120
(B) 176
(C) 168
(D) 105
(E) 86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-28)=3 (x-28)
x=56.
Required sum =(2x+x)=3x=168 years.
Answer is C
Answer: (C) 168
Question: In an election between two candidates A and B, the number of valid votes received by A exceeds those received by B by 15% of the total number of votes polled. If 20% of the votes polled were invalid and a total of 8720 votes were polled, then how many valid votes did B get?
(A) 1888
(B) 2999
(C) 2834
(D) 2777
(E) 2991
Rationale: Let the total number of votes polled in the election be 100k.
Number of valid votes = 100k - 20% (100k) = 80k
Let the number of votes polled in favour of A and B be a and b respectively.
a - b = 15% (100k) => a = b + 15k
=> a + b = b + 15k + b
Now, 2b + 15k = 80k and hence b = 32.5k
It is given that 100k = 8720
32.5k = 32.5k/100k * 8720 = 2834
The number of valid votes polled in favour of B is 2834.
Answer: C
Answer: (C) 2834
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.04. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.053. What is the value of x?
(A) 0.05
(B) 0.055
(C) 0.07
(D) 0.1
(E) 0.2
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.04*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.053=(x*40+0.06*35+0.04*25)/100
=> 40x+2.1+1=5.3
=>40x = 2.2
>x=2.2/40=0.055
Ans B
Answer: (B) 0.055
Question: Rachel drove 40 1/4 kilometres in 45 minutes. What was her average rate of speed in kilometres per hour?
(A) 52
(B) 52 2/3
(C) 53
(D) 53 2/3
(E) 54 1/3
Rationale: D = 40(1/4) = 161/4
T = 3/4
S = D/T = 53 2/3
Answer = D
Answer: (D) 53 2/3
Question: What number must be added to 6, 16 and 8 to get an average of 13?
(A) 23
(B) 22
(C) 44
(D) 33
(E) 55
Rationale: B
22
Answer: (B) 22
Question: A box contains four silver coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 3/5
(B) 4/5
(C) 2/5
(D) 1/5
(E) 3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
B
Answer: (B) 4/5
Question: There are 3 fictions and 6 non-fictions. How many cases are there such that 2 fictions and 2 non-fictions are selected from them?
(A) 90
(B) 120
(C) 45
(D) 180
(E) 200
Rationale: Number of ways of selecting 2 fiction books = 3C2
Number of ways of selecting 2 non fiction books = 6C2
3C2 * 6C2 = 3 * 15 = 45
Answer: C
Answer: (C) 45
Question: total 85 matches are conducted in Knockout match type. How many players will be participated in that tournament?
(A) 85
(B) 81
(C) 53
(D) 82
(E) 84
Rationale: 84 players
ANSWER:E
Answer: (E) 84