Explanation : 

A is 16th from the left end in a row

Q is 3rd from V towards the right, so position of Q = 18 – 3 = 15th from right end.
Q is 11th from A towards the right, so position of Q = 16 + 11 = 27th from left end.
Hence, total number of boys in the row = 27 + 15 – 1 = 41 (we subtract one because Q has been counted twice)

Explanation : 

(5,1) (7,3) (3,9) (5,7) (3,1) (1,5)

Explanation : 

All cats are dogs. All cats are black.

The two given statements are “All cats are dogs” and “All cats are black.” From these statements, we can’t conclude anything about the color of dogs. The first conclusion “All dogs are black” assumes that all dogs are cats, which is not stated in the given statements.

The second conclusion “Some dogs are not black” also assumes something about the color of dogs that is not stated in the given statements. Therefore, neither conclusion logically follows from the two given statements disregarding commonly known facts.

So the correct answer is © Neither Conclusion-I nor Conclusion-II.

Explanation : 

Conclusion-I states that all numbers are divisible by 6. This conclusion is true because 6 is the least common multiple of 2 and 3. Therefore, any number that is divisible by both 2 and 3 must also be divisible by 6.

Conclusion-II All numbers are divisible by 4.

All numbers that are divisible by 2 and 3 may not be divisible by 4. For example, 6 is divisible by 2 and 3 but not divisible by 4.

Explanation : 

A man walks down

The man starts at the back of his house facing East. He then walks 25 meters straight down the backside of his house. Since he is walking away from the house and the house faces East, he is now facing West.

He then turns to his right and walks 50 meters. Since he was originally facing West and turned right, he is now facing North.

Finally, he turns left and walks another 25 meters. Since he was originally facing North and turned left, he is now facing West again.

So from his starting point at the back of his house, the man has walked in a rectangular path and ended up to the North-West of where he started. So the correct answer is (d) North-west.

Explanation :

Product & Sum of two numbers

Let the two numbers be x and y. Then, we have:

S1: xy = 21
S2: x + y = 10

From statement S1, we can express one of the variables in terms of the other. For example, we can write y = 21/x. Substituting this value of y in statement S2, we get:

x + 21/x = 10

Multiplying both sides by x, we get:

x^2 + 21 = 10x

Bringing all the terms to one side, we get:

x^2 – 10x + 21 = 0

This is a quadratic equation that can be factored as (x – 7)(x – 3) = 0. Therefore, the two values of x that satisfy this equation are 7 and 3.

Using statement S1, we can find the corresponding values of y as follows:

If x = 7, then y = 21/x = 3.
If x = 3, then y = 21/x = 7.

Hence, the two numbers that satisfy both statements are 3 and 7. Therefore, the correct answer is (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

Explanation : 

Let’s consider statement S2 first. If n leaves a remainder of 1 when divided by 4, then n must be of the form 4k + 1, where k is an integer.

Let’s list down the numbers between 10 and 20 that are of the form 4k + 1:
11, 13, 15, 17, 19

Out of these numbers, only 11 and 17 are prime. So, if we consider statement S1 alone, we get two possible values of n, i.e., 11 and 17.

However, if we consider both statements S1 and S2 together, we cannot determine the unique value of n. Both 11 and 17 satisfy both statements S1 and S2. Hence, the correct answer is (d) S1 and S2 together are not sufficient to answer the Question.

Explanation : 

First, let’s consider S1. It tells us that R is greater than both P and Q. However, this statement alone does not provide us with enough information to determine which of the four numbers is the largest, as R could be either the largest or the second-largest number.

Next, let’s consider S2. It tells us that S is not the largest number. This statement is also not sufficient on its own to determine which of the four numbers is the largest, as S could be either the second-largest, third-largest, or smallest number.

However, if we combine both statements, we can deduce that either R is the largest number.
Therefore, the correct answer is (c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

Explanation : 

12th January is a Sunday

No. of days in February is 29 if it is a leap year.

No. of days left in January = 31 – 12 = 19

Total no. of days till 12th July = (19 + 29 + 31 + 30 + 31 + 30 + 12) = 182

No. of odd days = 182 ÷ 7 = 26 weeks and 0 odd days.

So, 12th July is a Sunday if the year is a leap year.

Explanation : 

Family of two generations

From the given information, we know that U is P’s daughter and Q is R’s mother-in-law. This means that R is married to one of Q’s children.
We also know that T is an unmarried male and S is a male. Since there are two married couples in the family and T is unmarried, S must be married.
Since R is married to one of Q’s children and S is married, it follows that R must be married to S. Therefore, (b) R is S’s wife.