Minimum Divisor for Remainder Problem

[ShaneK]

a, b, c, d are positive integers. If a/b has a remainder of 9 and c/d has a remainder of 10, what is the minimum possible value of b*d?

Answer key says 110.. I disagree, can someone explain why the following is not true:

If a = 1, c = 1
b = 9, d = 10 for an answer of 90.

1/9 = remainder of 9
1/10 = remainder of 10

Why, "the remainder must always be smaller than the divisor"? If the numerator is smaller than the divisor, doesn't the divisor = the remainder?

[Brent@GMATPrepNow]

a, b, c, d are positive integers. If a/b has a remainder of 9 and c/d has a remainder of 10, what is the minimum possible value of b*d?

Answer key says 110.. I disagree, can someone explain why the following is not true:

If a = 1, c = 1
b = 9, d = 10 for an answer of 90.

1/9 = remainder of 9
1/10 = remainder of 10

Why, "the remainder must always be smaller than the divisor"? If the numerator is smaller than the divisor, doesn't the divisor = the remainder?

The problem is above, in green.

1 divided by 9 equals 0 with remainder 1 (not 9)
1 divided by 10 equals 0 with remainder 1 (not 10)

Cheers,
Brent

[Brent@GMATPrepNow]

a, b, c, d are positive integers. If a/b has a remainder of 9 and c/d has a remainder of 10, what is the minimum possible value of b*d?

If a=9 and b=10, then a divided by b = 0 with remainder 9.
If c=10 and d=11, then c divided by d = 0 with remainder 10.

So, bd = (10)(11) = 110

Cheers,
Brent

[ShaneK]

I'm embarrassed that I asked in public.

Thanks Brent

[Brent@GMATPrepNow]

That's an easy (and common) mistake to make.
The best thing is that you made it before test day.

Cheers,
Brent