A six-digit number 4ABBSA is a multiple of 35 for non-zero digits A and B which of the following could be the possible values of A and B ?

Options

A. A = 3, B = 2
B. A = 6, B = 3
C. A = 6, B = 2
D. A = 3, B = 6

Answer

To determine the possible values of A and B in the six-digit number 4ABB8A that is a multiple of 35, we need to check the conditions for divisibility by both 5 and 7, since 35 = 5 × 7.

### Step 1: Check for divisibility by 5
A number is divisible by 5 if its last digit is either 0 or 5. In our case, the last digit is A. Since A is a non-zero digit, the only possible value for A is 5.

**Hint:** Check the last digit of the number for divisibility by 5.

### Step 2: Substitute A = 5
Now, we substitute A with 5 in the number 4ABB8A, which becomes 458B5.

**Hint:** Replace A with the value found in the previous step.

### Step 3: Check for divisibility by 7
Next, we need to check if 458B5 is divisible by 7. To do this, we can test different values of B (which can be any digit from 1 to 9 since B is also a non-zero digit).

**Hint:** Use the divisibility rule for 7 or simply divide the number by 7 to check for divisibility.

### Step 4: Testing values of B
We will test values of B from 1 to 9:

- For B = 1: 45815 ÷ 7 = 6552.14 (not divisible)
- For B = 2: 45825 ÷ 7 = 6553.57 (not divisible)
- For B = 3: 45835 ÷ 7 = 6554.71 (not divisible)
- For B = 4: 45845 ÷ 7 = 6555.86 (not divisible)
- For B = 5: 45855 ÷ 7 = 6557.00 (divisible)
- For B = 6: 45865 ÷ 7 = 6558.14 (not divisible)
- For B = 7: 45875 ÷ 7 = 6559.29 (not divisible)
- For B = 8: 45885 ÷ 7 = 6560.43 (not divisible)
- For B = 9: 45895 ÷ 7 = 6561.57 (not divisible)

From our tests, we find that when B = 5, the number 45855 is divisible by 7.

**Hint:** Test each value systematically to find which one makes the number divisible by 7.

### Conclusion
The possible values of A and B that make the six-digit number 4ABB8A a multiple of 35 are A = 5 and B = 5.

**Final Answer:** A = 5, B = 5.