model 2 divisibility, multiples, add and subtract based number system Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Let the total number of members be X.

Then, each member's contribution =Rs. 2X

Given, X × 2X = 3042

⇒ 2X² = 3042

⇒ X² = 1521

⇒ X = 39

Answer: (d)

The expression 2⁶ⁿ − 4²ⁿ = (2⁶)ⁿ − (4²)ⁿ

= 64ⁿ − 16ⁿ

Which is divisible by 64 –16= 48

Therefore the required answer is 48.

Answer: (b)

Let the number be p.

According to the question,

∴ $\text"p + 12"/6 = 112$

⇒   p + 12 = 672

⇒   p = 672 – 12 = 660

∴  Correct answer = $\text"600"/6 = 112$

Correct answer =  110 + 12 = 122

Answer: (c)

Answer: (c)

$a^4 - b^4 = (a - b) (a + b) (a^2 + b^2)$,

Where a and b are odd positive integers.

If two positive integers are odd, then their sum, difference and sum of their squares are always even.

∴ (a - b) (a + b) and $(a^2 + b^2)$ are divisible by 2.

Hence (a - b) (a + b) x $(a^2 + b^2) = a^4 - b^4$ is always divisible by $2^3 = 8$

Answer: (d)

As we know, xⁿ – aⁿ is exactly divisible by (x – a) if n is odd.

∴ (49)¹⁵ – (1 )¹⁵ is exactly divisible by 49 – 1 = 48, that is a multiple of 8.

Hence required answer is 8.