Question

Summation of 4A3 and 984 is equal to 13B7 and if 13B7 is divisible by 11 then find 3A + 4B.

• A. 29
• B. 39
• C. 49
• D. NOT

Answer 1

Answer:

B. 39

Given:

4A3 + 984 = 13B7      ----(i)

13B7 is divisible by 11

Concept Used:

Divisibility by 11:

The difference between both the pairs of sum of alternate digits should be either 0 or a multiple of 11.

Calculation:

From equation (i), we get:

A + 8 = B      ----(ii)

Also, for 13B7 to be divisible by 11, we should have:

(1 + B) – (3 + 7) = multiple of 11 

⇒ B – 9 = 0 or a multiple of 11      ----(ii)

Equation(ii) is satisfied only when B = 9

On substituting B = 9 in the equation(ii), we get:

A = 9 – 8 = 1

⇒ 3A + 4B = (3 $\times$ 1) + (4 $\times$ 9) = 39

∴ The required value of (3A + 4B) is 39