Question

The five-digit number 35N2N is divisible by 2, 3, 4, 6, 8, 9 and 12, among other numbers. What is the value of the digit N?

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is B 4

N clearly must be 0, 2, 4, 6 and 8. For 35N2N to be divisible by 3, the sum of the digits must be a multiple of 3. So far we have 3 + 5 + N + 2 + N = 10 + 2N. Let's use the possible values of N to evaluate this expression. If N = 0, then 10 + 2N = 10 + 0 = 10, which is not divisible by 3. If N = 2, then 10 + 2N = 10 + 4 = 14, which is not divisible by 3. If N = 4, then 10 + 2N = 10 + 8 = 18, which is divisible by 3. Neither N = 6 nor N = 8 gives a multiple of 3 or 4 is our only candidate. Let's make sure the number 35424 is divisible by all the other numbers listed. It is divisible by 4 since the last two digits 24 are divisible by 4. It is divisible by 6 since it is divisible by 2 and 3. It is divisible by 8 since the last three digits 424 are divisible by 8. It is divisible by 9 since the sum of the digits (18) is divisible by 9. Finally, it is divisible by 12 since it passes the test for 3 and 4. So, N is 4.