Question

A number G236G0 can be divided by 36 if G is:

• A. 8
• B. 6
• C. 1
• D. More than one value is possible

Hint:

36 = 9 × 4; use the digit-sum rule for 9 on 11 + 2G to narrow G down to a single value.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept.
Since \(36=9\times4\) and 9 and 4 are co-prime, a number is divisible by 36 exactly when it is divisible by both 9 and 4.

Step 2: Apply the divisibility rule for 4.
For G236G0, the last two digits are “G0”, which must be divisible by 4. Checking G = 0, 2, 4, 6, 8, all of “00, 20, 40, 60, 80” are divisible by 4, so every even digit for G survives this test.

Step 3: Apply the divisibility rule for 9.
The digit sum is \(G+2+3+6+G+0=11+2G\), which must be a multiple of 9.

Step 4: Test the surviving values of G.
G=0: 11, not a multiple of 9. G=2: 15, not a multiple of 9. G=4: 19, not a multiple of 9. G=6: 23, not a multiple of 9. G=8: \(11+16=27\), which is a multiple of 9.

Step 5: Final Answer.
Only G = 8 satisfies both conditions, so option A is correct.