Explanation

 8 – even number  

- 22 – even number  

- 27 – odd number  

- 7 – odd number  

So based on even/odd, 8 and 22 are even; 27 and 7 are odd → not helpful.

Now check prime numbers:

- 7 – prime  

- 8 – not prime  

- 22 – not prime  

- 27 – not prime  

So 7 is the only prime number.

Explanation

Explanation

Statement 1: Mangoes cost more than apples.  

Statement 2: Mangoes cost less than apples.

These two statements contradict each other — both cannot be true at the same time.

So if both are claimed to be true, we cannot trust the information.

Statement 3: Peaches cost more than Apples and Mangoes.

But since we don't know the actual relation between Mangoes and Apples (because 1 and 2 contradict), we can’t determine if statement 3 is true or false.

Explanation

Look closely at Set A:

1. All shapes are geometric (circle, pentagon, triangle, hexagon).

2. Each shape is divided into 3 parts using straight white lines.

   - Circle: 3 equal sectors

   - Pentagon: 3 segments

   - Triangle: 3 segments

   - Hexagon: 3 segments

There is a clear pattern:  

Different shapes, but always divided into 3 parts.

Explanation

Set A shows shapes divided into exactly 3 parts using white lines.

- Circle → 3 parts  

- Pentagon → 3 parts  

- Triangle → 3 parts  

- Hexagon → 3 parts  

This shows consistency in pattern.

Set B, however, has:

- Triangle → 4 parts  

- Others with 2, 3, or more divisions (not consistent)  

- Different logic in division

So, Set A follows a clear, consistent rule.

Explanation

Explanation

- Brightest 20% = 20 students, mean score = 80  

- Dullest 25% = 25 students, mean score = 31  

- Remaining 55% = 55 students, mean score = x (to find)  

- Overall mean = 52

Using weighted average:

(20 × 80) + (25 × 31) + (55 × x) = 100 × 52  

1600 + 775 + 55x = 5200  

55x = 5200 - 2375  

55x = 2825  

x = 2825 / 55  

x = 51.36 approx.

Explanation

Let the original number of boys be n.

Original average = 30 kg  

New average after adding boy = 31 kg  

Weight of new boy = 35 kg

Total weight originally = 30n  

Total weight after adding = 30n + 35

New average = (30n + 35) / (n + 1) = 31

So,  

(30n + 35) = 31(n + 1)  

30n + 35 = 31n + 31  

35 - 31 = 31n - 30n  

4 = n

Explanation

Given: Time downstream is half the time upstream.

Let:

- Speed of boat in still water = b

- Speed of current = c

Speed downstream = b + c  

Speed upstream = b - c

Time ∝ 1 / Speed

Given: Time downstream = (1/2) × Time upstream  

=> 1/(b + c) = (1/2) × 1/(b - c)  

=> 2/(b + c) = 1/(b - c)  

=> 2(b - c) = b + c  

=> 2b - 2c = b + c  

=> 2b - b = c + 2c  

=> b = 3c  

=> b : c = 3 : 1

Explanation

Initially, the total weight of four boys is:

Total weight = Average weight * Number of boys

= 24 * 4

= 96 kg

When the fifth boy's weight is included, the new total weight is:

New total weight = New average weight * New number of boys

= 24.6 * 5

= 123 kg

The weight of the fifth boy is:

Weight of fifth boy = New total weight - Initial total weight

= 123 - 96

= 27 kg