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Consider the following assumption and two statements Assumption: A number ‘PQRSTU’ is divisible by 33. Statement 1: U – T + S – R + Q – P is divisible by 11. Statement 2: P + Q + R + S + T + U is divisible by 3. Which one of the following is correct?

Consider the following assumption and two statements Assumption: A number ‘PQRSTU’ is divisible by 33. Statement 1: U – T + S – R + Q – P is divisible by 11. Statement 2: P + Q + R + S + T + U is divisible by 3. Which one of the following is correct? Correct Answer Both the statements are together sufficient to prove the assumption 

Concept:

If the difference of the sum of odd digits and sum of even digits is either 0 or multiple of 11, then the number is divisible by 11.

If the sum of digits of a number is divisible by 3, then the number is also divisible by 3.

Calculation:

The number ‘PQRSTU’

Statement 1

The sum of odd digits = P + R + T

The sum of even digits = Q + S + U

The difference of the sum of odd and even digits = (P + R + T) – (Q + S + U)

⇒ P – Q + R – S + T – U

It follows the divisibility rule of 11.

Statement 2

Sum of all the digits = P + Q + R + S + T + U

It follows the divisibility rule of 3.

∴ Both the statements are together sufficient to prove the assumption.

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