Question

If a seven-digit number 876p37q is divisible by 225, then the values of p and q respectively are:

• A. 0 and 9
• B. 5 and 0
• C. 3 and 9
• D. 0 and 5
• E. 9 and 0

Hint:

For divisibility by 25, check last two digits. For divisibility by 9, check sum of digits.

Answer 1

The Correct Option is D

Step 1: 225 = $9 \times 25$. For a number to be divisible by 225, it must be divisible by both 9 and 25.
Step 2: Divisibility by 25: Last two digits must be 00, 25, 50, or 75. Here last two digits are 7q? Actually the number is 876p37q, so last two digits are 7q? Wait, the digits: 8,7,6,p,3,7,q. So the number ends with 7q. For divisibility by 25, last two digits must be 00, 25, 50, or 75. So 7q must be one of these: 75 is possible if q=5. So q=5.
Step 3: Divisibility by 9: Sum of digits must be divisible by 9. Sum = 8+7+6+p+3+7+q = 31 + p + q. With q=5, sum = 36 + p. For this to be divisible by 9, p must be 0 or 9 (since 36 is divisible by 9, so p must be multiple of 9: 0 or 9).
Step 4: Check optionss: p=5? Not from our calculation. p=0 gives q=5? But options says 5 and 0 (p=5, q=0). That doesn't match. Try q=0? Then last two digits 70, not a multiple of 25. q=5 gives 75, works. Then p=0 or 9. options 0 and 9? That gives p=0, q=9? No, q must be 5. options 5 and 0 gives p=5, q=0, invalid. options 3 and 9? No. options 0 and 5 gives p=0, q=5. That works.
Step 5: Final Answer: 0 and 5.