mathewhe/aqua_rat huggingface dataset:
Question: The average (arithmetic mean) monthly income of four workers is $2,000. After one worker’s income increases by 25 percent the new average income is $2,250. What was the original income of the worker whose monthly income increased?
(A) $3,000
(B) $2,000
(C) $4,000
(D) $5,000
(E) $6,000
Rationale: Increase in total income was 250*4=$1000, we know that this increase was 25% (1/4th) of the workers original income, thus his/her original income was 1000*4=$4,000
Answer: C
Answer: (C) $4,000
Question: Four packages have an average weight of 12.5 pounds. What is the minimum possible weight of the heaviest package in pounds if the median is 12 pounds?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: Let us denote the weights of the packages in pounds by a, b, c, d naming from the lightest one to the heaviest one. The median is 12 pounds. Therefore (b + c) / 2 = 12.
b + c = 24
The average is 12.5 pounds. Therefore (a + b + c + d) / 4 = 12.5.
a + (b + c) + d = 50
a + 24 + d = 50
a + d = 26
The weight a must be no greater than 12, since 12 is the median. Therefore the minimum possible weight of the heaviest package is 26 – 12 = 14 pounds (all the other packages would weigh 12 pounds in this case).
Answer: C
Answer: (C) 14
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 27
(B) 23
(C) 20
(D) 28
(E) 12
Rationale: M = 15
S = 5
DS = 15 + 5 = 20
Answer: C
Answer: (C) 20
Question: In the city of San Durango, 60 people own cats, dogs, or rabbits. If 40 people owned cats, 40 owned dogs, 10 owned rabbits, and 12 owned exactly two of the three types of pet, how many people owned all three?
(A) 2
(B) 4
(C) 8
(D) 9
(E) 32
Rationale: Total = C + D + R - (CD + DR + CR) - 2CDR
60 = 40 + 40 + 10 - (12) - 2x
x = 9
So, answer will be D
Answer: (D) 9
Question: There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?
(A) 1/13
(B) 4/13
(C) 3/13
(D) 5/13
(E) 6/13
Rationale: If 1 green and 1 blue ball are taken from the box, then there are 7 green, 3 blue and 3 white balls, a total of 13 balls. If one ball is selected at random, the probability that it is blue is given by 3 / 13
correct answer C
Answer: (C) 3/13
Question: A credit card company has a cash back option for their customers which is based on the annual amount that they charge on their credit cards. The customer receives 1.5% cash on their first $5000 of purchase, 2.5% on the next $5000 of purchase and a 3% on cash back on portion that exceeds $10,000. If a customer receives a cash back of 2.5% on their total annual charges made on the credit card, then what was the customer's annual charge?
(A) $17,500
(B) $20,000
(C) $22,500
(D) $25,000
(E) $27,500
Rationale: The customer receives $75 for the first $5000.
The customer receives $125 for the next $5000.
Let x be the total amount of the customer's annual charge.
$200 + 0.03(x-10,000)=0.025x
0.005x=100
x=20,000
The answer is B.
Answer: (B) $20,000
Question: If a = 1 and b = -2, then (2a^2 + b)(q + y) + (a + b)(q - y) =
(A) 0
(B) 2x
(C) y - q
(D) x - y
(E) x + y
Rationale: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(q+y)=y-q => Smash C
Answer: (C) y - q
Question: f a card is drawn from a well shuffled pack of cards, the probability of drawing a spade or a king is -.
(A) 4/15
(B) 4/10
(C) 4/18
(D) 4/13
(E) 4/11
Rationale: P(SᴜK) = P(S) + P(K) - P(S∩K), where S denotes spade and K denotes king.
P(SᴜK) = 13/52 + 4/52 - 1/52 = 4/13
Answer:D
Answer: (D) 4/13
Question: In a series of seven football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 7 draws in the series?
(A) 24/576
(B) 125/864
(C) 1/25
(D) 1/16384
(E) 1/5
Rationale: Since the probability of a draw is 1/4, then the probability of 7 draws in 7 matches is (1/4)^7=1/16384.
Answer: D.
Answer: (D) 1/16384
Question: 150 ml of 30% sulphuric acid was added to approximate 400 ml of 12% sulphuric acid solution. Find the approximate concentration R of the acid in the mixture?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/6
(E) 1/5
Rationale: Do not need any computation
30%-----------21%---------12%
if volume of both sol. were equal the concentration R would be 21%=1/5, but 12% is more than 3 times
only possibility is 1/6
D
Answer: (D) 1/6
Question: P can do the work in 10 days and Q can do the same work in 12 days. If they work together for 4 days, what is the fraction of work that is left?
(A) 1/3
(B) 1/5
(C) 2/5
(D) 4/15
(E) 7/15
Rationale: 4/10 + 4/12 = 44/60 = 11/15 (completed work)
The work that is left is 1 - 11/15 = 4/15
The answer is D.
Answer: (D) 4/15
Question: A fort had provision of food for 150 men for 60 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 29 1/5
(B) 37 1/4
(C) 42
(D) 54
(E) 60
Rationale: After 10 days : 150 men had food for 50 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 50 : x <=> 125 x x = 150 x 50
=> x =150 x 50/125
=> x = 60.
Correct answer is E
Answer: (E) 60
Question: m and n are the x and y coordinates, respectively, of a point in the coordinate plane. If the points (m, n) and (m + p, n + 9) both lie on the line defined by the equation x = (y/3) - (2/5), what is the value of p?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: x = (y/3) - (2/5), and so y = 3x + 6/5. The slope is 3.
(n+9-n) / (m+p-m) = 3
p = 3
The answer is C.
Answer: (C) 3
Question: In a group of 25 factory workers, 16 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes.
(A) 10
(B) 9
(C) 8
(D) 7
(E) 4
Rationale: Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 16
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 8 are men. (B - 8= 16 - 8= 8)
So 8 out of 11 men have brown eyes.
C
Answer: (C) 8
Question: Length of a rectangular plot is 20 mtr more than its breadth. If the cost of fencing the plot at 26.50 per meter is Rs. 5300, what is the length of the plot in mtr?
(A) 59 m
(B) 60 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let breadth = x metres.
Then, length = (x + 18) metres.
Perimeter = 5300 m = 200 m.
26.50
2[(x + 18) + x] = 200
2x + 18 = 100
2x = 82
x = 41.
Hence, length = x + 18 = 59 m
A
Answer: (A) 59 m
Question: For the positive numbers, n, n + 1, n + 2, n + 7, and n +10, the mean is how much greater than the median?
(A) 0
(B) 1
(C) n+l
(D) 2
(E) n+3
Rationale: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + n + 1 + n + 2 + n + 7 + n +10)/5
mean = (5n + 20)/5
mean = n + 4
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n, n + 1, n + 2, n + 7, n +10
The median is n + 2.
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 4 – (n + 2) = n + 4 – n – 2 = 2
The answer is D
Answer: (D) 2
Question: A Cistern is filled by pipe A in 9 hrs and the full Cistern can be leaked out by an exhaust pipe B in 10 hrs. If both the pipes are opened in what time the Cistern is full?
(A) 45
(B) 90
(C) 1/10
(D) 1/90
(E) 60
Rationale: Explanation :
Work down by the inlet in 1 hr = 1 /9
Work done by outlet in 1 hr 1/10
Net part filled in 1 hr = 1/9 - 1/10 = 1/90
The Cistern will be full in 90 hrs.
Hint: Take the reciprocals.
Answer : B
Answer: (B) 90
Question: By selling 14 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 28
(B) 26
(C) 25
(D) 23
(E) 21
Rationale: 80% --- 14
120% --- ?
80/120 * 14 = 21
Answer:E
Answer: (E) 21
Question: A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond?
(A) 1/52
(B) 1/26
(C) 2/37
(D) 1/14
(E) 1/27
Rationale: Let n(S) = sample space and here n(s) = 52
n(E) = event of getting the 3 diamond = 1
therefore probability = p = n(E) / n(S)
=1/52
My answer is (A)
Answer: (A) 1/52
Question: The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 22
(B) 30
(C) 99
(D) 28
(E) 17
Rationale: Explanation:
Total age increased = (8 * 2) years = 16 years.
Sum of ages of two new men = (21 + 23 + 16) years = 60 years
Average age of two new men = (60/2) years = 30 years
Answer: B
Answer: (B) 30
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 158
(B) 159
(C) 155
(D) 112
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer: E
Answer: (E) 150
Question: AB
+BA
___
161
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
(A) 6
(B) 13
(C) 9
(D) 11
(E) 14
Rationale: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
only 13 fits in..
B
Answer: (B) 13
Question: How many numbers between 0 and 1270 have a prime tens digit and a prime units digit?
(A) 186
(B) 192
(C) 198
(D) 204
(E) 210
Rationale: From 1-9 there are 4 prime numbers {2, 3, 5, 7}. The 10s and 1s of the number must be made with these numbers. The total number of combinations is 4*4 = 16. Thus every set of 100 consecutive positive integers has 16 such numbers.
From 0 to 1200, there 16*12 = 192 such numbers.
From 1201 to 1270, the 10s units can only use 3 numbers {2, 3, 5}. 3*4 =12.
The total number is then 192+12 = 204
The answer is D.
Answer: (D) 204
Question: In an office, totally there are 1800 employees and 60% of the total employees are males. 30% of the males in the office are at-least 50 years old. Find the number of males aged below 50 years?
(A) 756
(B) 750
(C) 600
(D) 760
(E) None of these
Rationale: Number of male employees = 1800* 60/100 = 1080
Required number of male employees who are less than 50 years old = 1080* (100 - 30)%
= 1080* 70/100 = 756.
ANSWER:A
Answer: (A) 756
Question: A can complete a project in 20 days while B can complete same project in 30 days. If A and B start working together and A leaves the work 5 days before completion of project, then in how many days the project will be completed?
(A) 15
(B) 19
(C) 20
(D) 21
(E) 22
Rationale: A's 1day work=1/20;
B's 1day work=1/30;
(A+B) 1day work=(1/20+1/30)=1/12;
It is given that A leaves the work 5 days before completion of the project..
Thus,B alone does the remaining job in 5 days.
So,In 5 days ,B can do 1/6 w ..
Thus,(A+B) have worked (1-1/6)=5/6 w..
(A+B)can do 1/12 work in 1 day...
They did 5/6 w in 10 days.
Total days=(10+5) = 15
ANSWER:A
Answer: (A) 15
Question: Charles walks over a railway-bridge. At the moment that he is just ten meters away from the middle of the bridge, he hears a train coming from behind. At that moment, the train, which travels at a speed of 90 km/h, is exactly as far away from the bridge as the bridge measures in length. Without hesitation, Charles rushes straight towards the train to get off the bridge. In this way, he misses the train by just four meters! If Charles had rushed exactly as fast in the other direction, the train would have hit him eight meters before the end of the bridge.
What is the length of the railway-bridge?
(A) 37
(B) 44
(C) 73
(D) 52
(E) 48
Rationale: B
44 m
Let the length of the bridge be x meters.
Running towards the train, Charles covers 0.5x-10 meters in the time that the train travels x-4 meters. Running away from the train, Charles covers 0.5x+2 meters in the time that the train travels 2x-8 meters.
Because their speeds are constant, the following holds:
(0.5x-10) / (x-4) = (0.5x+2) / (2x-8)
which can be rewritten to
0.5x2 - 24x + 88 = 0
Using the quadratic formula we find that x=44, so the railway-bridge has a length of 44 meters.
Answer: (B) 44
Question: The averge score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42. Then find the average for the last four matches?
(A) 33.25
(B) 33.5
(C) 34.25
(D) 35
(E) 36
Rationale: sum of last 4 matches = (10 × 38.9) – (6 × 42)
= 389 – 252 = 137
Average =
137/4
= 34.25
ANSWER:C
Answer: (C) 34.25
Question: When positive integer q is divided by 13, the remainder is 2. When n is divided by 8, the remainder is 5. How many such values are less than 180?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  4
Rationale: the equation that can be formed q is 13x+2=8y+5..
13x-3=8y...
as we can see x can take only odd values as the RHS will always be even..
Also x can take values till 13 as 13*14>180..
now we have to substitue x as 1,3,5,7,9,11,13...
once we find 7 fitting in , any other value need not be checked as every 4th value will give us answer so next value will be 15..
ans 1.. B
Answer: (B)  1
Question: If Rs.20 is the True Discount on Rs260due after a certain time.What wil be true discount on the same sum due after half of the former time, the rate of interest being the same?
(A) Rs.9.40
(B) Rs.10.14
(C) Rs.10.40
(D) Rs.9.14
(E) None of these
Rationale: Explanation:
Simple Interest on Rs. (260-20) for a gven time= Rs.20
Simple Interest on Rs. (260-20) for a half time = Rs.10
True Discount on Rs.250 = Rs.10
True Discount on Rs.260 = R(s10/250x260 ) = Rs. 10.40
Answer: C
Answer: (C) Rs.10.40
Question: Gasoline varies in cost from $0.94 to $1.14 per gallon. If a car’s mileage varies from 16 to 24 miles per gallon, what is the difference between the most and least that the gasoline for a 480-mile trip will cost?
(A) $15.20
(B) $15.30
(C) $15.40
(D) $15.50
(E) $15.60
Rationale: Solution:
We know that the per gallon cost of gasoline varies from $0.94 - $1.14.
Now we want to find the MAXIMUM difference between the least amount of money spent on gasoline and the largest amount of money spent i.e. to calculate max. trip cost - min. trip cost.
Mileage is given to be 16 to 24 miles per gallon, thus to travel 480 miles you will need gasoline in the range 480/24 to 480/16 which is 20 to 30 gallons.
So, for these 20 gallons and 30 gallons of gasoline the cost is as follows: (divide this task into 2 parts, 1 for 30 gallons and 2nd one for 20 gallons).
Case 1: for 30 gallons the cost is 30*0.94 to 30*1.14 which is $28.20 to $34.20
Case 2: for 20 gallons the cost is 20*0.94 to 20*1.14 which is $18.80 to $22.80
Thus, the maximum cost of the 480 mile trip is $34.20 and minimum is $18.80
so the difference is $34.20 - $18.80 = $15.40
Answer: C
Answer: (C) $15.40
Question: -20 , -16 , -12 , -8 ....
In the sequence above, each term after the first is 6 greater than the preceding term. Which of the following could not be a term in the sequence?
(A) 0
(B) 200
(C) 444
(D) 660
(E) 780
Rationale: Ans :B
Since 200 is not divisible by 6 , all the other options are divisible by 6
Answer: (B) 200
Question: A man swims downstream 70 km and upstream 30 km taking 10 hours each time; what is the speed of the current?
(A) 1
(B) 4
(C) 2
(D) 6
(E) 8
Rationale: 70 --- 10 DS = 7
? ---- 1
30 ---- 10 US = 3
? ---- 1 S = ?
S = (7 - 3)/2 = 2
Answer: C
Answer: (C) 2
Question: A mixture contains milk and water in the ratio 3:2. On adding 10 liters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it?
(A) 30
(B) 40
(C) 20
(D) 10
(E) 25
Rationale: milk:water = 3:2
after adding 10 liters of water
milk:water = 2:3
Olny water patrs increase when mixture of water
milk:wate = 3:2 = 2*(3:2) = 6:4
after adding 10 liters of water
milk:water = 2:3 = 3*(2:3) = 6:9
Option 'C'
Answer: (C) 20
Question: The average of first 50 non-zero positive integers is
(A) 11.5
(B) 25.5
(C) 22
(D) 25
(E) 27
Rationale: Explanation :
Sum of first n non-zero positive integers n(n + 1)/2
So, average of first n non-zero positive integers n(n + 1)/2n = (n + 1)/2
=> (50 + 1)/2 = 25.5
Answer : B
Answer: (B) 25.5
Question: Alan buys 4 TVs, a 26 inch, a 28 inch, a 30 inch, and a 32 inch, for his new house. Each TV costs $200 more than the size below it. Alan spends a total of $4,600. How much would he have spent if he had bought only the 28 inch and 30 inch TVs?
(A) 850
(B) 1,100
(C) 1,700
(D) 2,550
(E) 2,300
Rationale: Assume the cost of the least sized (26 Inch) TV = x
Cost of 28 inches TV = x + 200
Cost of 30 inches TV = x + 400
Cost of 32 inches TV = x + 600
Total cost = 4x + 1200 = 4600
Therefore x = 3400/4 = 850
Price of 28inch + 30 inch = 1050 + 1250 = 2300
Option E
Answer: (E) 2,300
Question: Triangle STV has sides ST = TV = 5, and SV = 6. What is the area?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Let the base B of the triangle be SV = 6. Then we need to find the height H.
H^2 = 5^2 - 3^2 = 16 and then H = 4.
The area is (1/2)*B*H = 3*4 = 12
The answer is C.
Answer: (C) 12
Question: A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. Find the time required by the first pipe to fill the tank ?
(A) 10 hours
(B) 15 hours
(C) 17 hours
(D) 18 hours
(E) 19 hours
Rationale: Explanation:
Suppose, first pipe alone takes x hours to fill the tank .
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
As per question, we get
1/X + 1/X-5 =1/X-9
=>xâˆ’5+x/ X(xâˆ’5)=1/X-9
=>(2xâˆ’5)(xâˆ’9)=x(xâˆ’5)
=>x2âˆ’18x+45=0
After solving this euation, we get
(x-15)(x+3) = 0,
As value can not be negative, so x = 15
ANSWER IS B
Answer: (B) 15 hours
Question: The probability that a number selected at random from the first 50 natural numbers is a composite number is
(A) 17/20
(B) 17/25
(C) 17/29
(D) 17/27
(E) 17/21
Rationale: The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25.
Answer:B
Answer: (B) 17/25
Question: Ages of two persons differ by 14 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
(A) 12,28
(B) 13,27
(C) 16,32
(D) 18,34
(E) 19,34
Rationale: Explanation:
Let the age of younger person is x,
Then elder person age is (x+14)
=> 3(x-6) = (x+14-6) [6 years before]
=> 3x-18 = x+8
=> x = 13
So other person age is x + 14 = 27
Answer: Option B
Answer: (B) 13,27
Question: A foreign language club at Washington Middle School consists of n students, 2/5 of whom are boys. All of the students in the club study exactly one foreign language. 1/3 of the girls in the club study Spanish and 3/4 of the remaining girls study French. If the rest of the girls in the club study German, how many girls in the club, in terms of n, study German?
(A) 2n/5
(B) n/3
(C) n/5
(D) 2n/15
(E) n/10
Rationale: 2/5 of the students are boys, thus 3/5 of the students are girls.
1/3 of the girls in the club study Spanish and 3/4 of the remaining girls study French.
Thus 1/4 of 2/3 = 1/6 of the girls study German.
Since girls comprise 3/5 of the students, then 3/5*1/6=1/10 of students are girls who study German.
The answer is E.
Answer: (E) n/10
Question: A semicircular cubicle has a radius of 14. What is the approximate perimeter of the cubicle?
(A) 55
(B) 86
(C) 25
(D) 72
(E) 35
Rationale: perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*14 + 2*14 = 71.96 approximately 72
answer D
Answer: (D) 72
Question: Jack went on a diet 6 months ago when he weighed 222 pounds. If he now weighs 198 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 180 pounds?
(A) 3
(B) 3,5
(C) 4
(D) 4,5
(E) 5
Rationale: Joe lost his weigh 24 pounds during 6 months. That means that he lost 4 pounds per month. He should lose more 18 pounds to be 180 pounds.
So it would take 18/4=4.5 months.
Correct answer is D
Answer: (D) 4,5
Question: Seven different books (A, B, C, D,E,F,G and H) are to be arranged on a shelf. Books A and B are to be arranged first and second starting from the right of the shelf. The number of different orders in which books C, D,E,F and G may be arranged is
(A) 9!
(B) 12!
(C) 5!
(D) 25!
(E) 18!
Rationale: Solution
Since books A and B are arranged first and second, only books C,D,E,F and G will change order. Therefore it an arrangement problem involving 5 items and the number of different order is given by
5!
Answer C
Answer: (C) 5!
Question: If two resistors, A(R1) and B(R2) stand in parallel with each other in electrical wire, the total resistor appears as R1R2/(R1+R2). If three resistors, A(R1), B(R2), and C(2R2) stand in parallel in electrical wire, what is the ratio Q of the resistors’ sum of A and C to the resistors’ sum of A and B?
(A) 2(R1+R2):(R1+2R2)
(B) (R1+R2):(R1+2R2)
(C) (2R1+R2):(R1+2R2)
(D) 2(R1+R2):(2R1+R2)
(E) 2(R1-R2):(R1+2R2)
Rationale: two resistors A (r1) and B (r2).
total or sum of two resistors appear as
r1r2/r1+r2. It is looks like inversion of sum of rates.
1/r1+1/r2= r1+r2/r1r2.
same way sum of A(r1) and c(2r2)=1/r1+1/2r2
=2r2+r1/r12r2.
inversion rate = r12r2/2r2+r1.
ratio of sum of a and c/sum of a and b=2r2r1/2r2+r1*r1+r2/r1r2
Q=2(r1+r2)/2r2+r1.A
Answer: (A) 2(R1+R2):(R1+2R2)
Question: What is the median from the below series
5, 8, 11, 6, 10, 4, 18, 16, 13, 12 and 14
(A) 11
(B) 5
(C) 12
(D) 13
(E) 10
Rationale: Ordering the data from least to greatest, we get:
4, 5, 6, 8, 10, 11, 12, 13, 14, 16, 18
The median number was 11. (Five numbers were higher than 11 and five were lower.)
A
Answer: (A) 11
Question: A and B invests Rs.8000 and Rs.9000 in a business. After 4 months, A withdraws half of his capital and 2 months later, B withdraws one-third of his capital. In what ratio should they share the profits at the end of the year?
(A) 32:48
(B) 32:49
(C) 32:45
(D) 32:42
(E) 32:41
Rationale: A : B
(8000*4)+(4000*8) : (9000*6)+(6000*6)
64000 : 90000
32 : 45.Answer:C
Answer: (C) 32:45
Question: Of the 800 employees of Company X, 80 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 50 percent ?
(A) 200
(B) 160
(C) 112
(D) 480
(E) 56
Rationale: The # oflong-termemployees is 80%*800=640.
After y of them retire new # oflong-termemployees would become 640-y.
Total # of employees would become 800-y.
We want 640-y to be 60% of 800-y --> 640-y=(800 -y)*50% --> y = 480.
Answer: D.
Answer: (D) 480
Question: boring a well 60 m depth, the cost is
Rs.4/– for the first meter. The cost of each successive meter
increases by Rs.3/–. What is the cost of boring the entire well?
(A) 5550
(B) 5450
(C) 5650
(D) 5780
(E) 5980
Rationale: as it is increased by 3 rupees so
4+7+10+13........
first term a=4
difference=d=3 then
60th term=a+59d=181
total cost=n/2(a+l)=60/2(4+181)=5550
ANSWER:A
Answer: (A) 5550
Question: 7 people (A, B, C, D, E, F and G) go to a movie and sit next to each other in 7 adjacent seats in the front row of the theater.
How many different arrangements are possible? If A will not sit to the left of F and F will not sit to the left of E. How many different arrangements are possible.
(A) 7!/2
(B) 7!/3
(C) 7!/4
(D) 7!/5
(E) 7!/6
Rationale: 7 people can be arranged in a row in 7! ways.
Now, three people among those 7 can be arranged in 3! = 6 ways:
AFE
AEF
EAF
EFA
FAE
FEA
From the 6 arrangements above only EFA is possible (A is not to the left of F and F is not to the left of E), so out of total 7! ways only in 1/6th of the arrangements they are sitting as they want.
Answer: E (7!/6).
Answer: (E) 7!/6