If a number 2x64y is completely divisible by 88, then what is the value of 6x - 5y?

Question

Question

This question was previously asked in

SSC CHSL Tier-I Exam 2022 Official Paper (Held On: 10 March, 2023 Shift 4)

Answer 1

Given:

The nine-digit number = 2x64y

Divisible by = 88

Concept used:

Divisibility rule of 8 - The last three digits of a number are divisible of 8

Divisibility rule of 11 - If the difference between the sum of the digits at odd places and even places equals 0 or divisible by 11

Calculation:

We know that the last three digits of a number are divisible of 8

⇒ The number made from the last three digits without altering their position will be divisible by 8

⇒ Possible values of y = 8

Now, check the divisibility rule of 11

⇒ (2 + 6 + 8) - (x + 4) = 0 or 11

⇒ 12 - x = 0 or 11

Then, x = (12 – 11) = 1

Now,

⇒ (6x - 5y)

⇒ (6 × 1) - (5 × 8)

⇒ 6 - 40

⇒ - 34

∴ The required value is -34