RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Find the perimeter and area of the rectangle of length 17 cm and breadth 13 cm.
A.221 cm2
B.211 cm2
C.231 cm2
D.236 cm2
Answer: A.221 cm2
Explanation: Given: length = 17 cm, breadth = 13 cm
Perimeter of rectangle = 2 (length + breadth)
= 2 (17 + 13) cm
= 2 × 30 cm
= 60 cm
We know that the area of rectangle = length × breadth
= (17 × 13) cm22
= 221 cm2 ANSWER :A
Question: A can do a piece of work in 4 days. B can do it in 5 days. With the assistance of C they completed the work in 2 days. Find in how many days can C alone do it?
A.87 days
B.20 days
C.66 days
D.77 days
Answer: B.20 days
Explanation: C = 1/2 - 1/4 - 1/5 = 1/20
=> 20 days
Answer: B
Question: What is the total number of prime numbers less than 50?
A.17
B.18
C.19
D.15
Answer: D.15
Explanation: Solution
Prime numbers less than 50 are	=15.
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47
Their number is 15.
Answer D
Question: What will be the compound interest on Rs. 30000 after 3 years at the rate of 12 % per annum
A.Rs 10123.20
B.Rs 12147.84
C.Rs 10123.40
D.Rs 10123.50
Answer: B.Rs 12147.84
Explanation: Explanation:
(30000×(1+12/100)3)
=>30000×28/25×28/25×28/25
=>42147.84
So Compound interest will be 42147.84 - 30000
= Rs 12147.84
Option B
Question: A high school has 400 students 1/2 attend the airthmetic club, 5/8 attend the physics club and 3/4 attend the chemistry club. 3/8 attend all 3 clubs. If every student attends at least one club how many students attend exactly 2 clubs.
A.80
B.70
C.60
D.50
Answer: D.50
Explanation: A-Club has 200 members (1/2 of 400)
B-Club has 250 members (5/8 of 400)
C-Club has 300 members (3/4 of 400)
We can create an equation to solve this:
200+250+300 = n + x + 2y
where n is the number of students, x is the number of students in two clubs, and y is the number of students in three clubs.
The question provides y for us (150).
750 = 400 + x + 300
x = 50
D
Question: In how many different ways can the letter of the word 'JUDGE ' be arranged in such a way that the vowels always come together?
A.48
B.89
C.56
D.74
Answer: A.48
Explanation: It has 5 different letters.
when the vowels UE are always together, they can be supposed to form one letter.
then we have to arrange the letter JD
now 4 letters can be arranged in 4!=24ways
the vowels UE can be arranged amoung themselves in 2!=2 ways
required number of ways =24*2=48
Answer(A)
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 2000, the number of valid votes that the other candidate got, was:
A.900
B.750
C.250
D.600
Answer: A.900
Explanation: Number of valid votes = 80% of 2000 = 1600
Valid votes polled by other candidate = 45% of 2000
=(45/100)X2000 =900
ANSWER = A
Question: if the ratio of s.i earned on certain amount on same rate is 4:5.what is the ratio of time?
A.1:2
B.6:9
C.4:5
D.2:3
Answer: C.4:5
Explanation: s.i1/s.i2=[(p*r*t1)/100]/[(p*r*t2)/100]
4/5=t1/t2
ratio=4:5
answer C
Question: A man sitting in a train which is traveling at 36 kmph observes that a goods train, traveling in opposite direction, takes 10 seconds to pass him. If the goods train is 240 m long, find its speed
A.50 kmph
B.56 kmph
C.58 kmph
D.62 kmph
Answer: A.50 kmph
Explanation: Explanation:
Relative speed = 240/10 m / sec = ((240/10)×(18/5)) kmph = 86 kmph.
Speed of goods train = (86 - 36) kmph = 50 kmph
Answer: Option A
Question: If P and Q are positive integers and P = 10Q + 3, what is the remainder when P is divided by 5?
A.0
B.1
C.2
D.3
Answer: D.3
Explanation: This question asks what IS...(the answer), so we know that the answer will be consistent. As such, we can TEST VALUES to quickly get the solution.
We're told that P and Q are POSITIVE INTEGERS and P = 10Q + 3. We're asked for the REMAINDER when X is divided by 5.
IF....
Q = 1
P= 13
13/5 = 3 remainder 3
Final Answer:
D
Question: John invested part of his savings into a investment X that earned a profit of 10% and the rest of the savings into an investment Q that lost 15%. If John neither made a profit nor a loss, then what fraction of his savings was invested in investment X?
A.a. 3/5
B.b.2/3
C.c.7/10
D.d.3/4
Answer: A.a. 3/5
Explanation: X(10) --- Net(0) --- Q(-15) = -15/-10 = 3/2.
So, John invested 3/3+2 = 3/5 of his savings in investment X. Ans (A).
Question: Three partners A , B , C start a business . B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital . If the total profit is Rs 16500 at the end of a year ,Find out B's share in it.
A.Rs. 4000
B.Rs. 5000
C.Rs. 6000
D.Rs. 7000
Answer: C.Rs. 6000
Explanation: Solution: Suppose C's capital = x then
B's capital = 4x (Since B's Capital is four times C's capital)
A's capital = 6x ( Since twice A's capital is equal to thrice B's capital)
A:B:C =6 x : 4x : x
= 6 : 4 : 1
B's share = 16500 * (4/11) = 1500*4 = 6000.
Answer: Option C
Question: The length of a rectangle is two third of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 4761 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 13 units?
A.598 sq.units
B.556 sq.units
C.589 sq.units
D.958 sq.units
Answer: A.598 sq.units
Explanation: Given that the area of the square = 4761sq.units
=> Side of square = âˆš4761 = 69 units
The radius of the circle = side of the square = 69 units
Length of the rectangle = 2/3 * 69 =46units
Given that breadth = 13 units
Area of the rectangle = lb = 46 * 13= 598 sq.units
Answer:A
Question: A man is 12 years older than his brother. In two years, his age will be twice the age of his brother. The present age of his brother is:
A.10
B.21
C.22
D.23
Answer: A.10
Explanation: Let the brother's present age be x years. Then, man's present age = (x + 12) years.
(x + 12) + 2 = 2(x + 2)
x + 14 = 2x + 4
x = 10.
Answer:A
Question: P alone can complete a piece of work in 14 days. Work done by Q alone in one day is equal to one-third of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
A.6 (1/4) days
B.21/2 days
C.7 (3/4) days
D.8/5 days
Answer: B.21/2 days
Explanation: Work done by P alone in one day = 1/14th of the total work done by Q alone in one day = 1/3(of that done by P in one day) = 1/3(1/14 of the total) = 1/42 of the total.
Work done by P and Q, working together in one day = 1/14 + 1/42 = 4/42 of the total
They would take 42/4 days = 21/2 days to complete the work working together.
ANSWER:B
Question: If 20% of a number = 400, then 120% of that number will be?
A.20
B.120
C.360
D.2400
Answer: D.2400
Explanation: Let the number x. Then,
20% of x = 400
x = (400 * 100)/20 = 2000
120% of x = (120/100 * 2000) = 2400.
ANSWER:D
Question: The profit earned by selling an article for Rs. 832 is equal to the loss incurred when the same article is sold for Rs. 448. What should be the sale price for making 50% profit ?
A.Rs. 660
B.Rs. 560
C.Rs. 1060
D.Rs. 960
Answer: D.Rs. 960
Explanation: Explanation:
Let C.P. = Rs. C.
Then, 832 - C = C - 448
2C = 1280 => C = 640
Required S.P. = 150% of Rs. 640 = 150/100 x 640 = Rs. 960.
ANSWER IS D
Question: Mohan has 8 pairs of shoes; each pair is a different color. If Kim randomly selects 2 shoes without replacement from the 16 shoes, what is the probability that she will select 2 shoes of the same color?
A.2/5
B.1/15
C.1/9
D.1/10
Answer: B.1/15
Explanation: Can be tackled in this way as well: Probability of selecting any 1 out of 16 shoes = 16/16 = 1
Probability of selecting the next shoe (out of 16 available) having the same color = 1/16 (as after selecting the 1st one, there is only 1 another shoe left with the same color).
Thus the total probability = 1*1/15=1/15.
B is the correct answer.
Question: Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What is the average score of classes A, B, C ?
A.81.8
B.81.1
C.81.2
D.81.5
Answer: D.81.5
Explanation: Let the number of students in classes A, B and C be P, Q and R respectively.
Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R.
Also given that,
(83P + 76Q) / (P + Q) = 79
=>4P = 3Q.
(76Q + 85R)/(Q + R) = 81
=>4R = 5Q,
=>Q = 4P/3 and R = 5P/3
Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5
Answer: D
Question: In a class of students, the ratio of girls to boys is 1:2. If 2 more girls joined the class, the ratio would be 2:3. How many students are in the class?
A.18
B.20
C.22
D.24
Answer: A.18
Explanation: Let x be the number of students in the class.
(1/3)*x=(2/5)(x+2)-2
5x=6x+12-30
x=18
The answer is A.
Question: A dozen eggs and 10 pounds of oranges are currently at the same price. If the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 %. How much more will it cost to buy a dozen eggs and 10 pounds of oranges .
A.5%
B.10%
C.15%
D.20%
Answer: C.15%
Explanation: Say currently both a dozen eggs and 10 pounds of oranges cost $100 (they are at the same price). So, to buy a dozen eggs and 10 pounds of oranges we need $100.
After the increase, the price of a dozen eggs will be $109 and the price of 10 pounds of oranges will be $106. So after the increase, to buy a dozen eggs and 10 pounds of oranges we'll need $215.
Increase = 15%.
Answer: C.
Question: Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.
A.99:61
B.99:160
C.61:160
D.61:99
Answer: A.99:61
Explanation: Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;
Vessel A + B = 800 gallons --> milk = 495, water 305.
The ratio = 495/305 --> reduce by 5 = 99/61.
Answer: A.
Question: One-third of Rahul's savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 1,50,000 as total savings, how much has he saved in Public Provident Fund ?
A.Rs. 30,000
B.Rs. 50,000
C.Rs. 60,000
D.Rs. 90,000
Answer: C.Rs. 60,000
Explanation: Let savings in N.S.C and P.P.F. be Rs. x and Rs. (150000 - x) respectively. Then,
(1/3)x= (1/2)(150000-x)
x/3+x/2=75000
5x/6=75000
x=75000*6/5= 90000
Therefore, Savings in Public Provident Fund = Rs. (150000 - 90000) = Rs. 60000
ANSWER:C
Question: If 1/12 of the passengers on a ship are from North America, 1/8 are Europeans, 1/3 are from Africa, 1/6 are from Asia and the remaining 35 people are citizens of other continents, then how many passengers are on board the ship?
A.110
B.115
C.120
D.125
Answer: C.120
Explanation: 1/12 + 1/8 + 1/3 + 1/6 = (2+3+8+4)/24 = 17/24
Let x be the number of passengers on the ship.
35 = (7/24)x
x = 120
The answer is C.
Question: The avg age of an adult class is 40years. 12new students with an avg age of 32years join the class. Therefore decreasingthe avg by 4year. Find what was the original strength of class?
A.8
B.12
C.15
D.16
Answer: B.12
Explanation: Let original strength = y
Then , 40y + 12 x 32 = ( y + 12) x 36
⇒ 40y + 384 = 36y + 432
⇒ 4y = 48
∴ y = 12
B
Question: In a survey about potential presidential candidates A and B, 37% of the public like A and 55% like B. If the percentage of the public who like one candidate only is twice the percentage of the public who like both candidates, then what is the percentage of the public that like neither?
A.27%
B.31%
C.41%
D.22%
Answer: B.31%
Explanation: Let x be the percentage of people who like both.
Then the percentage of people who like only 1 but not both is 2x.
37% + 55% = 2x + 2(x) because the percentage who like both are counted twice.
Then x = 23% and 2x = 46%
100% = 23% + 46% + Neither
Neither = 31%
The answer is B.
Question: On a baseball team, 7 players including Alice want to play 1st base, 2nd base, or 3rd base. Before every game, the coach chooses a name randomly from a bag and this person plays 1st base. Then the coach chooses the next name randomly and this person plays 2nd base. The coach then chooses a third name randomly and this person plays 3rd base. What is the probability that Alice plays 1st, 2nd, or 3rd base?
A.2/3
B.3/5
C.4/5
D.3/7
Answer: D.3/7
Explanation: The total number of ways to choose three players is 7C3=35.
Excluding Alice, the number of ways to choose three players is 6C3=20.
P(Alice is not chosen)=20/35=4/7.
P(Alice is chosen)=1 - 4/7 = 3/7.
The answer is D.
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
A.2
B.4
C.6
D.8
Answer: C.6
Explanation: five letters -> 5 blanks ....
First and last--> N and A
remaining three blanks --> remaining 3 letters in 3!
req no of words ==>6
ANSWER C
Question: Catherina works 5 hours per day on Monday, Wednesday and Friday, and 10 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $420 per week. How much does she earn in dollars per hour?
A.14
B.15
C.16
D.12
Answer: D.12
Explanation: So, she works 15 hours in 3 days
So, she works 20 hours in 2 days
So in a week she works 35 hours ( 15 + 20 ) and earns $420
So, Hourly wage is 420/35 => 12
Hence answer will be (D) 12
Question: If a, b, and c are consecutive odd positive integers and a < b < c, which of the following could be equal to c - b - a+3 ?
A.4
B.-4
C.-1
D.-2
Answer: A.4
Explanation: let we put values. a=1, b=3, c=5
5-3-1=1
1+3 =4
Answer :A
Question: A 300 m long train crosses a platform in 40 sec while it crosses a signal pole in 18 sec. What is the length of the platform?
A.288
B.350
C.889
D.367
Answer: D.367
Explanation: Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/40 = 50/3
3x + 900 = 2000 => x = 367 m.
Answer:D
Question: A circular racetrack is 3 miles in length and has signs posted to indicate each 1/10 mile increment. If a race car starts at a random location on the track and travels exactly one half mile, what is the probability that the car ends within a half mile of the sign indicating 2 1/2 miles?
A.1/6
B.3/10
C.1/3
D.1/2
Answer: C.1/3
Explanation: The car ends within a half mile of the sign indicating 2 1/2 miles means that the car will end in one mile interval, between the signs indicating 2 and 3 miles.
Now, it doesn't matter where the car starts or what distance it travels, the probability will be P=(favorable outcome)/(total # of outcomes)=1/3 (as the car starts at random point end travels some distance afterwards we can consider its end point as the point where he randomly appeared, so the probability that the car appeared within 1 mile interval out of total 3 miles will be 1/3).
Answer: C.
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 48 years now, the son's age five years back was:
A.14 years
B.19 years
C.33 years
D.38 years
Answer: B.19 years
Explanation: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
Answer:B
Question: If the average of 5 positive integers is 70 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
A.50
B.52
C.69
D.78
Answer: D.78
Explanation: Sum of 5 Integer (a, b, c, d, e) = 5*70 = 350
e - a = 10
i.e. e = a+10
For e to be maximum remaining 4 MUST be as small as possible
Since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers
i.e. a+a+a+a+(a+10) = 350
i.e. 5a = 340
i.e. a = 68
i.e. Largest e = 68+10 = 78
Answer: option D
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.2:9
C.2:2
D.2:9
Answer: A.2:5
Explanation: 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
Question: A courtyard is 24 meter long and 14 meter board is to be paved with bricks of dimensions 25 cm by 15 cm. The total number of bricks required is :
A.6000
B.8000
C.8960
D.2000
Answer: C.8960
Explanation: Explanation:
Number of bricks =Courtyard area /1 brick area
=(2400Ã—1400 /25Ã—15)=8960
Option C
Question: A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After six months, C joined them with Rs.20,000. What will be B's share in the total profit of Rs.27,000 earned at the end of 2 years from the starting of the business?
A.Rs.8100
B.Rs.9000
C.Rs.9500
D.Rs.10,000
Answer: A.Rs.8100
Explanation: Solution
A : B : C	=(20000×24):(15000×24):(20000×18)
=4 :3 :3
B's share	=Rs.(27000×3/10)
= Rs.8100.
Answer A
Question: How much is 80% of 40 is greater than 4/5 of 25?
A.22
B.77
C.15
D.12
Answer: D.12
Explanation: (80/100) * 40 – (4/5) * 25
32 - 20 = 12
Answer: D
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
A.Rs.488
B.Rs.480
C.Rs.482
D.Rs.487
Answer: B.Rs.480
Explanation: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640
= Rs.160
SP = CP - Loss
= 640 - 160
= Rs.480
Answer: B
Question: The North-South Express is a pair of trains between Jammu and Chennai. A train leaves Jammu for Chennai exactly at 12 noon everyday of the week. Similarly, there's a train that leaves Chennai bound for Jammu on everyday of the week exactly at 12 noon. The time required by a train to cover the distance between Chennai and Jammu is exactly 7 days and 1 minute. Find the number of trains from Chennai to Jammu which a train from Jammu to Chennai would cross in completing its journey, assuming all the trains are on time.
A.7
B.8
C.15
D.16
Answer: C.15
Explanation: Explanation :
Let a train from Chennai to Jammu starts on Day 1 and it reaches jammu on day 8 at 12:01 Hrs
The train which starts from Jammu on Day 8 at 12:00 will cross this Day 1 train (from Chennai) at approx. 12:00:30 Hrs and this train will reach Chennai on day 15 at 12:01 Hrs so it will cross the train which started from Chennai at 12:00 Hrs on day 15 (in between 12:00 Hrs and 12:01 Hrs).
So it will cross a total of 15 trains.
Answer : C
Question: 0.99998+0.11112=?
A.1
B.1.0001
C.1.0021
D.1.1111
Answer: D.1.1111
Explanation: 0.99998 + 0.11112
= 0.99998 + 0.1111 + 0.00002
= (0.99998 + 0.00002) + 0.1111
= 1 + 0.1111
= 1.1111
D
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
A.120 gallons
B.200 gallons
C.170 gallons
D.180 gallons
Answer: A.120 gallons
Explanation: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
ANSWER A
Question: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is:
A.24
B.26
C.42
D.46
Answer: A.24
Explanation: Let the ten's digit be x. Then, unit's digit = x + 2. Number = 10x + (x + 2) = 11x + 2
Sum of digits = x + (x + 2) = 2x + 2
(11x + 2)(2x + 2) = 144
2x2 + 26x - 140 = 0
(x - 2)(11x + 35) = 0
x = 2
Hence, required number = 11x + 2 = 24.
ANSWER:A
Question: At present the ratio between the ages of Arun and Deepak is 2:5. After 10 years Arun's age will be 30 years. What is the age of the Deepak?
A.20
B.40
C.50
D.60
Answer: C.50
Explanation: Let the present age of Arun and Deepak be 4x and 3x
2x+10 = 30
2x = 20
x = 10
Deepak's age = 5x = 50 years
Answer is C
Question: Fifthty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 10 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club?
A. 60
B. 80
C. 100
D. 120
Answer: B. 80
Explanation: 50% of the members have passed the test, thus 50% have not passed the test.
We also know that 30+10=40 members have not passed the test, thus 0.5*Total=40 --> Total=80.
Answer: B.
Question: How many words of 3 letters can be formed from the letters "AABBCC"?
A.18
B.21
C.24
D.27
Answer: C.24
Explanation: There are 3 distinct letters: A, B, C
There are repetition: 2A, 2B, 2C
1. All 3 letters are different: 3!=6
2. Two letters are similar, third is different:
- choose 1 out of 3 letters: 3C1
- choose 1 out of remaining 2 letters: 2C1
- count in repetitions: 3!/2!
3C1x2C1x3!/2! = 18
Total: 18+6=24 ANSWER:C
Question: Which of the following numbers is not prime?
A.79+52
B.33+88
C.166-3
D.100+67
Answer: B.33+88
Explanation: The number 11 can be factored out of Choice B which shows that it can not be a prime number. --> 33+11= 11*(3+8). The correct answer is B.
Question: Which of the following triples of numbers have the same standard deviation as the numbers u, v and w?
I. u-2, v-2, w-2
II. 0, u-v, w-v
III. u-4, v+5, w-1
A.I only
B.II only
C.I and III only
D.II and I only
Answer: D.II and I only
Explanation: If we add or subtract a constant to each term in a set the standard deviation will not change.
Set {u-2, v-2, w-2} is obtained by subtracting 2 from each term of {u, v, w}.
Set {0, u-v, w-v} is obtained by subtracting s from each term of {u, v, w}.
Set {u-4, v+5, w-1} is totally different from {u, v, w}.
Thus the answer is I and II only.
Answer: D.
Question: AAA manufacturing owns 2 plants. Tikon plant and Mikon plant. The policy is that 50% of all workers get bonuses every year. If the ratio of employees at the plants is 3:2, respectively, and the percentage of employees getting bonuses at Tikon is 55%, what percentage of employees at Mikon get bonuses?
A.42.5%
B.56%
C.25.5%
D.55%
Answer: A.42.5%
Explanation: Let T and M be number employees at Tikon and Mikon, respectively, and b represent bonus.
T + M = total employees.
T:M = 3:2
Tb/T = 55%
Mb/M = ?
[(3)(Tb/T) + (2)(Mb/M)]/(3 + 2) = 50%
[(3)(55%) + (2)(Mb/M)]/5 = 50%
Mb/M = 42.5%
Answer: A
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
A.6! * 7P7
B.6! * 7P6
C.6! * 7P1
D.6! * 7P5
Answer: B.6! * 7P6
Explanation: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in 7P6 ways.
Hence required number of ways = 6! * 7P6
Answer: B
Question: A ferry can transport 50 tons of vehicles. Automobiles range in weight from 1,800 to 3,200 pounds. What is the greatest number of automobiles that can be loaded onto the ferry?
A.23
B.55
C.48
D.62
Answer: B.55
Explanation: to get maximum vehicles we must take into consideration the minimum weight i.e 1800 pounds here
since , 1 ton = 2000 pounds
50 tons will be 100,000 pounds
from the answer choices:
let max number of vehicles be
total weight will be = 55*1800 = 99000 pounds , which is lesser than the maximum weight allowed .
Ans: B
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 99 km/hr. What is the length of the platform?
A.440
B.488
C.477
D.426
Answer: A.440
Explanation: Speed = 99 * 5/18 = 27.5 m/sec.
Length of the train = 27.5 * 20 = 550 m.
Let the length of the platform be x m . Then,
(x + 550)/36 = 27.5 => x = 440 m.
Answer: A
Question: A certain rectangular crate measures 6 feet by 8 feet by 10 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?
A.4
B.4
C.6
D.8
Answer: B.4
Explanation: Ans is "B".
For max volume of cylinder (pi*r^2*h) we need to max out r^2*h. We don't know what the dimensions of the crate refer to. . Therefore for max vol base should be 8x10 i.e. of radius 8/2 = 4
B