If a 9-digit number 937X728Y6 is divisible by 72, then one of the possible values of X + Y is:

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SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 24 Jun, 2024 Shift 4)

Answer 1

Given:

A 9-digit number 937X728Y6 is divisible by 72.

72 = 8 × 9

For divisibility by 72, the number must be divisible by both 8 and 9.

Formula used:

1. Divisibility rule for 8: The last three digits must be divisible by 8.

2. Divisibility rule for 9: The sum of all digits must be divisible by 9.

Calculation:

Step 1: For divisibility by 8, check the last three digits: 2816.

⇒ 2816 is divisible by 8 (since 2816 ÷ 8 = 352).

⇒ So, Y = 1 is valid.

Step 2: For divisibility by 9, the sum of the digits should be divisible by 9.

⇒ Sum = 9 + 3 + 7 + X + 7 + 2 + 8 + 1 + 6 = 43 + X

⇒ 43 + X must be divisible by 9.

⇒ Possible value of X = 2 (since 43 + 2 = 45, and 45 is divisible by 9).

∴ X = 2 and Y = 1.

X + Y = 2 + 1 = 3.

∴ The correct answer is 3.

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