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Minimum Divisor for Remainder Problem

Expert replies
by ShaneK » Sat Feb 09, 2013 7:56 am
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?
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Source: — Problem Solving |

by Brent@GMATPrepNow » Sat Feb 09, 2013 8:06 am
ShaneK wrote: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 Hanneson - Creator of GMATPrepNow.com
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by Brent@GMATPrepNow » Sat Feb 09, 2013 8:10 am
ShaneK wrote: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
Brent Hanneson - Creator of GMATPrepNow.com
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by ShaneK » Sat Feb 09, 2013 8:12 am
I'm embarrassed that I asked in public.

Thanks Brent ;)
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by Brent@GMATPrepNow » Sat Feb 09, 2013 11:30 am
That's an easy (and common) mistake to make.
The best thing is that you made it before test day.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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