mathewhe/aqua_rat huggingface dataset:
Question: Three boys, two girls, and two women are to be seated on a bench. If one specific boy must be seated on one of the end seats, and one specific girl must me seated exactly in the middle, find the number of possible arrangements R.
(A) a) 48
(B) b) R=144
(C) c) R=240
(D) d) R=288
(E) e) 120
Rationale: One specific boy is seated to either of end seat, lets call him b1
One specific girl is seated in the middle, lets call her g1
Note the question says *specific girl* and *specific boy*, so we do not consider for example the other girl , g2, being seated on seat #4. Same goes with the specific boy, b1.
b1 can be seated 2 different seats : 2!
g1 is seated on the seat #4, fixed (no other alternative) : 1
the remaining 5 seats can be filled with the remaining people b2,b3,g2,w1,w2: 5!
2! x 1 x 5! = 240
Answer C
Answer: (C) c) R=240
Question: A watch was sold at a loss of 10%. If it was sold for Rs.140 more, there would have been a gain of 4%. What is the cost price?
(A) 1000
(B) 2881
(C) 2771
(D) 1111
(E) 7121
Rationale: 90%
104%
--------
14% ---- 140
100% ---- ? => Rs.1000
Answer: A
Answer: (A) 1000
Question: What is the greatest prime factor of 42^2+75^2+6300
(A) 3
(B) 7
(C) 11
(D) 13
(E) 79
Rationale: 42^2 = (50-8)(50-8) = 1764
75^2 = (100-25)(100-25) = 5625
1764+5625+6300 = 13689
this number is divisible by 3 and 9
divide by 9 and get 1521, the sum of this number is again a multiple of 9, thus we can divide it one more time by 9. we get 169, and 169 is 13^2. thus the answer is 13.
ANSWER:D
Answer: (D) 13
Question: If 5 machines can produce 20 units in 10 hours, how long would it take 20 machines to produce 180 units?
(A) 50 hours
(B) 40 hours
(C) 22.5 hours
(D) 12 hours
(E) 8 hours
Rationale: Here, we're told that 5 machines can produce 20 units in 10 hours....
That means that EACH machine WORKS for 10 hours apiece. Since there are 5 machines (and we're meant to assume that each machine does the same amount of work), then the 5 machines equally created the 20 units.
20 units/5 machines = 4 units are made by each machine every 10 hours
Now that we know how long it takes each machine to make 4 units, we can break THIS down further if we choose to...
10 hours/4 units = 2.5 hours per unit when 1 machine is working.
The prompt asks us how long would it take 20 machines to produce 180 units.
If 20 machines each work for 2.5 hours, then we'll have 20 units. Since 180 units is '9 times' 20, we need '9 times' more TIME.
(2.5 hours)(9 times) = 22.5 hours
Final Answer:
[Reveal]Spoiler:
C
Answer: (C) 22.5 hours
Question: The ratio of males to females in a class is 2:3. The career preferences of the students in the class are represented in a circle graph. If the area of the graph allocated to each career preference is proportional to the number of students who have that career preference, how many degrees of the circle should be used to represent a career that is preferred by one-fourth of the males and three-fourths of the females in the class?
(A) 186
(B) 192
(C) 198
(D) 204
(E) 210
Rationale: 1/4*2/5 + 3/4*3/5 = 2/20 + 9/20 = 11/20
The number of degrees is 11/20 * 360 = 198 degrees
The answer is C.
Answer: (C) 198
Question: When a number is divided by 6 &then multiply by 12 the answer is 18 what is the no.?
(A) 4.5
(B) 5
(C) 5.6
(D) 5.7
(E) 9
Rationale: if $x$ is the number, x/6 * 12 = 18
=> 2x = 18
=> x = 9
E
Answer: (E) 9
Question: A cube has four of its faces painted half red and half white. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
(A) 1:4
(B) 1:3
(C) 1:2
(D) 2:5
(E) 2:11
Rationale: Let x be the area of each face of the cube.
The area painted red is 4(x/2) = 2x
The area painted white is 4(x/2) + 2x = 4x
The ratio of red to white is 2x:4x which is 1:2.
The answer is C.
Answer: (C) 1:2
Question: If the range W of the six numbers 4,3,14,7,10 and x is 12, what is the difference between the greatest possible value of x and least possible value of x?
(A) 	0
(B) 	2
(C) 	12
(D) 	13
(E) 	15
Rationale: The range W of a set is the difference between the largest and smallest elements of a set.
Without x, the difference between the largest and smallest elements of a set is 14-3=11<12, which means that in order 12 to be the range of the set x must be either the smallest element so that 14-x=12 ---> x=2 OR x must the largest element so that x-3=12 --> x=15.
The the difference between the greatest possible value of x and least possible value of x is 15-2=13.
Answer: D.
Answer: (D) 	13
Question: A man can row 4 kmph is still water. If the river is running at 2 kmph it takes 90 min to row to a place and back. How far is the place
(A) 2 km
(B) 4 km
(C) 5 km
(D) 2.25 km
(E) None of these
Rationale: Explanation :
Speed in still water = 4 kmph
Speed of the stream = 2 kmph
Speed upstream = (4-2)= 2 kmph
Speed downstream = (4+2)= 6 kmph
Total time = 90 minutes = 90⁄60 hour = 3⁄2 hour
Let L be the distance. Then
(L/6) + (L/2) = 32
=> L + 3L = 9
=> 4L = 9
=> L = 9⁄4= 2.25 km. Answer : Option D
Answer: (D) 2.25 km
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:
(A) × 108 miles
(B) × 1010 miles
(C) × 10-10 miles
(D) × 1012 miles
(E) × 10-12 miles
Rationale: Solution:
The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer : D
Answer: (D) × 1012 miles
Question: Aravind had $ 2100 left after spending 30 % of the money he took for shopping. How much money did he
take along with him?
(A) 4000
(B) 3000
(C) 4500
(D) 5000
(E) 5500
Rationale: Let the money he took for shopping be m.
Money he spent = 30 % of m
= 30/100 × m
= 3/10 m
Money left with him = m – 3/10 m = (10m – 3m)/10 = 7m/10
But money left with him = $ 2100
Therefore 7m/10 = $ 2100
m = $ 2100× 10/7
m = $ 21000/7
m = $ 3000
Therefore, the money he took for shopping is $ 3000.
B)
Answer: (B) 3000
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 100, the runs scored by A are?
(A) 11
(B) 18
(C) 13
(D) 16
(E) 12
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
4/25 * 100 = 16
Answer:D
Answer: (D) 16
Question: A single discount equivalent to the discount series of 20%, 10% and 5% is?
(A) 31.7
(B) 31.21
(C) 31.6
(D) 31.37
(E) 31.25
Rationale: 100*(80/100)*(90/100)*(95/100)
= 68.4
100 - 68.4
= 31.6
Answer:C
Answer: (C) 31.6
Question: A number exceeds by 20 from its 3/8 part. Then the number is?
(A) A)32
(B) B)35
(C) C)39
(D) D)40
(E) E)45
Rationale: x – 3/8 x = 20
x = 32
ANSWER:A
Answer: (A) A)32
Question: A and B can do a piece of work in 3 days, B and C in 4 days, C and A in 6 days. How long will C take to do it?
(A) 24
(B) 18
(C) 20
(D) 30
(E) 15
Rationale: 2c = Â¼ + 1/6 â€“ 1/3 = 1/12
c = 1/24 => 24 days
ANSWER A
Answer: (A) 24
Question: Out of 4 fruits in a basket, 2 are rotten. If two fruits are drawn at random from the basket, the probability of both being rotten is
(A) 1/6
(B) 10/21
(C) 20/21
(D) 11/16
(E) 2/21
Rationale: The number of exhaustive events = 4C2 =6.
Let E be event of the 2 fruits being rotten. The number of favourable cases are
2C2 = 1 way.
Required probability = 1/6
ANSWER:A
Answer: (A) 1/6
Question: Of 15 applicants for a job, 7 had at least 4 years' experience, 9 had degrees, and 1 had less than 4 years' experience and did not have a degree.How many of the applicants had at least 4 years' experience and a degree?
(A) 14
(B) 13
(C) 9
(D) 7
(E) 2
Rationale: 15 - 1 = 14
14 - 7 - 9= -2
Then 2 are in the intersection between 4 years experience and degree.
Answer : E
Answer: (E) 2
Question: 0.002 x 0.5 = ?
(A) 0.0001
(B) 1.0
(C) 0.1
(D) 0.01
(E) 0.001
Rationale: 2 x 5 = 10.
Sum of decimal places = 4
0.002 x 0.5 = 0.001
Answer is E.
Answer: (E) 0.001
Question: A number is four less than two times the other number. If their difference is 21, what is the greater number?
(A) 50
(B) 46
(C) 31
(D) 21
(E) 15
Rationale: A = one number
B = other number
A = -4 + 2B
A - B = 21
solve for A by adding B to each side
A = B + 21
Substitute (B + 21) for A in A = -4 + 2B
(B + 21) = -4 + 2B
add -B to each side
21 = -4 + B
add 4 to each side
25 = B
Since A = B + 21 , A = 25 + 21 , A = 46
ANSWER:B
Answer: (B) 46
Question: How many positive integers less than 600 can be formed using the numbers 1, 2, 3 and 5 for the digits?
(A)  48
(B)  52
(C)  66
(D)  68
(E)  84
Rationale: Notice that we can find the number of 2 and 3 digit numbers by just assuming the first digit can also be zero:
0 1 1
1 2 2
2 3 3
3 5 5
5 5 5
Number of possibilities = 5*4*4 = 80.
Then, just add up the number of 1 digits numbers = 4, so total is 80+4 = 84.
Answer:E
Answer: (E)  84
Question: A Man travelled a distance of 48 km in 7 hours. He travelled partly on foot at 4 km/hr and partly on
bicycle at 9 km/hr. What is the distance travelled on foot?
(A) 16 km
(B) 20 km
(C) 12 km
(D) 10 km
(E) None of these
Rationale: Explanation:
Let the time in which he travelled on foot = x hour
Time for travelling on bicycle = (9 - x) hr
Distance = Speed * Time, and Total distance = 48 km
So,
4x + 7(9-x) = 48
=> 3x = 15
=> x = 5
So distance traveled on foot = 4(5) = 20 km
Answer: Option B
Answer: (B) 20 km
Question: Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $8.00 each, what was Company C’s gross profit?
(A)  $2,250
(B)  $2,500
(C)  $2,100
(D)  $2,150
(E)  $2,700
Rationale: Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900
Revenue : 500 * 8 = $4000
Profit: 4000 - 1900 = $ 2100
Option C is correct
Answer: (C)  $2,100
Question: A boat covers a certain distance downstream in 1 hour, while it comes back in 1.30 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water?
(A) 10
(B) 13
(C) 11
(D) 08
(E) 15
Rationale: Let the speed of the water in still water =x
Given that speed of the stream = 3 kmph
Speed downstream =(x+3) kmph
Speed upstream =(x−3) kmph
He travels a certain distance downstream in 1 hour and come back in 1 1⁄2 hour.
i.e., distance travelled downstream in 1 hour = distance travelled upstream in 1 1⁄2 hour
Since distance = speed × time, we have
(x+3)×1=(x−3)3/2
⇒2(x+3)=3(x−3)
⇒2x+6=3x−9
⇒x=6+9=15 kmph
Answer is E.
Answer: (E) 15
Question: Steve traveled the first 2 hours of his journey at 30 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
(A) 60 mph
(B) 56.67 mph
(C) 53.33 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 30 = 60 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 60 = 300m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 300/5 = 60 mph
Answer: A
Answer: (A) 60 mph
Question: Find the no.of ways of arranging the boy and 5 guests at a circular table so that the boy always sits in a particular seat?
(A) 7!
(B) 5!
(C) 9!
(D) 10!
(E) 11!
Rationale: Ans.(B)
Sol. Total number of persons = 6 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 5 places in 5P5 = 5! Ways ... The number of required arrangements = 5! x 1= 5! = 5! ways
Answer: (B) 5!
Question: Use distributive property to solve the problem below:
Maria bought 10 notebooks and 5 pens costing 2 dollars each.How much did Maria pay?
(A) 30 dollars
(B) 40 dollars
(C) 50 dollars
(D) 60 dollars
(E) 70 dollars
Rationale: Solution
2 × (10 + 5) = 2 × 10 + 2 × 5 = 20 + 10 = 30 dollars
Answer A
Answer: (A) 30 dollars
Question: A person X working alone can complete a work in 5 days. A person Y completes the same amount of work in 20 days, and a person Z when working alone can complete the same amount of work in 30 days. All three people work together for 2 days but then X and Y leave. How many more days does Z need to complete the work after X and Y leave?
(A) 13
(B) 14
(C) 15
(D) 16
(E) 17
Rationale: The fraction of work completed in two days is 2/5 + 2/20 + 2/30 = 17/30
The fraction of work remaining is 1 - 17/30 = 13/30
The number of days required for Z is 13 days.
The answer is A.
Answer: (A) 13
Question: We can rent a canoe for x cents per minute for the first 30 minutes and then y cents for each additional minute. How much will it cost to rent a canoe for z minutes, where z>30?
(A) 30y+(z-30)x
(B) 30x + zy
(C) 30x+(z-30)y
(D) 30x + 30y
(E) x + (z-30)y
Rationale: The first 30 minutes cost 30x.
The next (z-30) minutes cost (z-30)y.
The total cost is 30x+(z-30)y.
The answer is C.
Answer: (C) 30x+(z-30)y
Question: If d is the standard deviation x, y, and z, what is the standard deviation of 2x, 2y, 2z ?
(A) d
(B) 2d
(C) 15d
(D) d + 5
(E) d + 15
Rationale: If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.
If we increase or decrease each term in a set by the same percent (multiply by a constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.
So in our case SD will change by same multiple (% increase) as we are multiplying each number in a set by 2--> SD=2d.
Answer: B.
Answer: (B) 2d
Question: In traveling from a dormitory to a certain city, a student went 1/5 of the way by foot, 2/3 of the way by bus, and the remaining 10 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 30
(B) 45
(C) 60
(D) 75
(E) 120
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/5x + 2/3x + 10
x - 13/15x = 10
2/15x = 10=> so x = (15/2)*10 = 75Km
Answer D
Answer: (D) 75
Question: If 1 tic equals 5 tacs and 2 tacs equal 8 tocs, what is the ratio of one tic to one toc?
(A) 15/2
(B) 20/1
(C) 5/6
(D) 3/10
(E) 1/15
Rationale: Tic=5*Tac and 2*Tac=8*Toc;
2*Tic=10*Tac and 10*Tac=40*Toc --> 2*Tic=40*Toc --> Tic/Toc=40/2=20/1.
Answer: B.
Answer: (B) 20/1
Question: Harriet planned to complete a certain task on Wednesday, January 1, but because of illness the completion date was postponed 44 days. On which day of the week in February was the task completed?
(A) Monday
(B) Tuesday
(C) Wednesday
(D) Thursday
(E) Friday
Rationale: This type of story problem is essentially just about a repeating pattern and a 'remainder.'
We're told that Harriet planned to complete a certain task on WEDNESDAY, January 1, but because of illness the completion date was postponed 44 DAYS. We're asked on what day of the week the task was actually completed on.
Since the task was supposed to be completed on a Wednesday....
A 1 day postponement would be Thursday
A 2 day postponement would be Friday
A 3 day postponement would be Saturday
A 4 day postponement would be Sunday
A 5 day postponement would be Monday
A 6 day postponement would be Tuesday
A 7 day postponement would be Wednesday
A 8 day postponement would be Thursday
Etc.
So this question is ultimately asking how many 'groups of 7' are there, and how many 'leftover days' are there, when you postpone 44 days.
44/7 = 6 remainder 2
This means that there are 6 full weeks AND 2 extra days after a Wednesday....Thus, the task was completed on a Friday.
E
Answer: (E) Friday
Question: On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.3, what is the probability that Malachi will return home at the end of the day on the following Monday?
(A) 0.008
(B) 0.125
(C) 0.147
(D) 0.512
(E) 0.64
Rationale: Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.3
Therefore, probability of no rain = 0.7
0.7*0.7*0.3 = 0.147
Hence C
Answer: (C) 0.147
Question: A motor cyclist participant of a race says "We drove with the speed of 10 miles an hour one way, but while returning because of less traffic we drove on the same route with 18 miles per hour." What was their average speed in the whole journey?
(A) 10 miles/hour
(B) 12 miles/hour
(C) 11 miles/hour
(D) 13 miles/hour
(E) 12.9 miles/hour
Rationale: 2xy/x+y=12.9 miles/hour
ANSWER:E
Answer: (E) 12.9 miles/hour
Question: How much 60% of 50 is greater than 34% of 30?
(A) 18
(B) 19.8
(C) 11
(D) 17
(E) 12
Rationale: (60/100) * 50 – (34/100) * 30
30 - 10.2 = 19.8
Answer: B
Answer: (B) 19.8
Question: Two trains are moving at 50 kmph and 70 kmph in opposite directions. Their lengths are 150 m and 100 m respectively. The time they will take to pass each other completely is?
(A) 6 ½ sec
(B) 9 ½ sec
(C) 3 ½ sec
(D) 7 ½ sec
(E) 2 ½ sec
Rationale: \70 + 50 = 120 * 5/18 = 100/3 mps
D = 150 + 100 = 250 m
T = 250 * 3/100 = 15/2 = 7 ½ sec
Answer:D
Answer: (D) 7 ½ sec
Question: A train 360 m long is running at a speed of 36 km/hr. In what time will it pass a bridge 140 m long?
(A) 40 sec
(B) 50 sec
(C) 88 sec
(D) 19 sec
(E) 10 sec
Rationale: Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/10 = 50 sec
Answer: B
Answer: (B) 50 sec
Question: In the faculty of Reverse-Engineering, 226 second year students study numeric methods, 450 second year students study automatic control of airborne vehicles and 134 second year students study them both. How many students are there in the faculty if the second year students are approximately 80% of the total?
(A) 515.
(B) 678.
(C) 618.
(D) 644.
(E) 666.
Rationale: Answer is B :678
Solution : Total number of students studying both are 450 + 226 - 134 = 542 (Subtracting the 134 since they were included in the both the other numbers already).
So 80% of total is 542, so 100% is approx. 678.
Answer: (B) 678.
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
(A) 5!
(B) 8!
(C) 9!
(D) 10!
(E) 12!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: (B) 8!
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 6?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: 6
To be divisible by six the sum of the digits must be divisible by 3 and be even. Use same logic as finding all divisible by three but strike all odd answers. Highest number becomes 72 and we select from the divisible by 3 answers the even numbers.
72 -yes
54 -yes
42 - yes
36 - yes
24 - yes
12 - yes
Correct answer is B.
Answer: (B) 6
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 7200 interest. The principal amount borrowed by him was.
(A) Rs 14000
(B) Rs 15000
(C) Rs 16000
(D) Rs 20000
(E) None of these
Rationale: Explanation:
S.I.=Pâˆ—Râˆ—T/100
=>P=S.I.âˆ—100/Râˆ—T
=>P=7200âˆ—100/12âˆ—3=Rs 20000
Option D
Answer: (D) Rs 20000
Question: What approximate value should come in place of the question mark (?) in each of the following equations ?
(9.009)1/2 + (16.0001)1/4 = (?)% of 50.5
(A) 7
(B) 8
(C) 5
(D) 10
(E) 11
Rationale: Explanation :
92 + 162 = (?)% of (50.5) 3 + 2 = (2)% of (50.5) 5 = 10% of (50.5)
Answer : Option D
Answer: (D) 10
Question: The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is?
(A) Rs.4078
(B) Rs.4000
(C) Rs.4029
(D) Rs.4027
(E) Rs.4020
Rationale: Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (ii) from (iv), we get, P = 4000.
P's monthly income = Rs.4000.
Answer: B
Answer: (B) Rs.4000
Question: At a dinner party, 6 people are to be seated around a circular table. Two seating arrangements are considered different only when the positions of the people are different relative to each other. What is the total number of different possible seating arrangements for the group?
(A) 1) 5
(B) 2) 10
(C) 3) 24
(D) 4) 32
(E) 5) 120
Rationale: for number of distinct arrangements of 'n' items around a circular table, we get the arrangements by way of (n-1)!
in this case, there are 6 guests, so number of distinct arrangements = 5! = 120
Answer : E
Answer: (E) 5) 120
Question: How many 7's are there in the following series which are preceded by 6 which is not preceded by 8 ?
8 7 6 7 8 6 7 5 6 7 9 7 6 1 5 7 7 6 8 8 6 9 7 6 8 7
(A) 2
(B) 1
(C) 5
(D) 3
(E) None
Rationale: total 2 are there
ANSWER:A
Answer: (A) 2
Question: Rahul's Mathematics test had 75 problems, 10 arithmetic, 30 algebra, 35 geometry problems. Although he answered 70% of arithmetic, 40% of arithmetic and 60% of geometry problems correctly, still he got less than 60% problems right. How many more questions he would have to answer more to get passed
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: Explanation:
Number of questions attempted correctly = (70% of 10 + 40% of 30 + 60% of 35)
= 7 + 12 + 21 = 40.
Questions to be answered correctly for 60% = 60% of total quations
= 60 % of 75 = 45.
He would have to answer 45 - 40 = 5
Answer: Option A
Answer: (A) 5
Question: Ram professes to sell his goods at the cost price but he made use of 950 grms instead of a kg, what is the gain percent?
A. 11%
(A) 11 1/9%
(B) 5.26%
(C) 11 9/9%
(D) 11 5/9%
(E) 11 1/5%
Rationale: 950 --- 50
100 --- ? => 5.26%
Answer:B
Answer: (B) 5.26%
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
(A) 4
(B) 4/7
(C) 4/11
(D) 5
(E) 5/7
Rationale: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
Option B
Answer: (B) 4/7
Question: Evaluate 75% of 450 + 45% of 750
(A) 632
(B) 642
(C) 652
(D) 675
(E) 572
Rationale: Explanation:
= (75/100) * 450 + (45/100) * 750
= 675
Option E
Answer: (E) 572
Question: In a group of hens and cows, the total number of legs are 24 more than twice the number of heads. How many cows are there in the group?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Explanation :
Let the number of cows be x and the number of hens be y.
Then,
=> 4x + 2y = 2(x + y) + 24
=> 2x = 24
=> x = 12.
Answer : C
Answer: (C) 12
Question: Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 16 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: If the average of 10-pound and 20-pound boxes is 18, the ratio of 10-pound boxes:20-pound boxes is 1:4.
So out of 30 boxes, 6 are 10-pound boxes and 24 are 20-pound boxes.
If the average of 10 and 20-pound boxes is to be 16, the ratio of 10-pound boxes:20-pound boxes should be 2:3.
The number of 10 pound boxes remain the same so we still have 6 of them.
To get a ratio of 2:3, the number of 20-pound boxes must be 9.
We need to remove 15 of the 20-pound boxes.
The answer is C.
Answer: (C) 15
Question: Lines y=4√7·x−3 and y=3√7·x−1 intersect at what height above the x axis?
(A) 7√5
(B) 12
(C) 5√7
(D) 0
(E) 5
Rationale: Solve two equations for y
y=4√7·x−3
y=3√7·x−1
Set the two equations equal to each other and solve for x
4√7·x − 3=3√7·x−1
√7·x = 2
x = 2/√7
Plug x = 2/√7 into any one of the original equations to find the y value (height above x axis) where the two lines intersect
y=4√7·x−3
y=(4√7)·(2/√7)−3
y=4·2 - 3
y = 8 - 3
y = 5
Final answer:
E) 5
Answer: (E) 5