When a is divided by b the remainder...

LUANDATO wrote:When a is divided by b the remainder is 13. When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b*d?

1)100
2)121
3)144
4)169
5)196

The OA is E.

Can any expert help me with this PS question please? I don't have it clear. Thanks.

Rule: The remainder must be less than the divisor.
If a/b yields a remainder of 13, then b, the divisor, must be greater than 13. So the smallest possible value of b is 14.
If c/d yields a remainder of 12, then d, the divisor, must be great than 12. So the smallest possible value of d is 13.

Smallest possible value of b * d = 14 * 13. Answer choice D is 169 = 13 * 13, so the correct answer must be greater than this value. That leaves us with E

BTGmoderatorLU wrote:When a is divided by b the remainder is 13. When c is divided by d the remainder is 12.
If a,b,c,d are all positive integers then which of these may be the value of b*d?

1)100
2)121
3)144
4)169
5)196

Recall that the remainder from any division of positive integers must be less than the divisor.

Since, when a is divided by b, the remainder is 13, then b must be at least 14.

Since, when c is divided by d, the remainder is 12, then d must be at least 13.

Thus, b*d is least 14*13 = 182. We see that only 196 could be the value of b*d.

Answer: E/5