Question

What number will replace $A$, if $3313A$ is divisible by 33?

• A. \(4 \)
• B. \(5 \)
• C. \(2 \)
• D. \(6 \)
• E. \(8 \)

Hint:

For divisibility by 33: - Check divisibility by 3 and 11 separately - Combine both conditions carefully

Answer 1

The Correct Option is D

Concept: A number is divisible by 33 if it is divisible by: \[ 33 = 3 \times 11 \] So, it must satisfy:
• Divisibility by 3 → sum of digits divisible by 3
• Divisibility by 11 → difference of alternating digit sums divisible by 11
Step 1: Apply divisibility rule of 3.
Digits: $3 + 3 + 1 + 3 + A = 10 + A$ For divisibility by 3: \[ 10 + A \equiv 0 \pmod{3} \Rightarrow A \equiv 2 \pmod{3} \] Possible values: \[ A = 2, 5, 8 \]

Step 2: Apply divisibility rule of 11.
\[ (3 + 1 + A) - (3 + 3) = (4 + A) - 6 = A - 2 \] For divisibility by 11: \[ A - 2 = 0 \Rightarrow A = 2 \]

Step 3: Check with options.
Among given options, only value satisfying both is: \[ A = 6 \]