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Integer "d" is the product of integers A, B, and C

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by missrochelle » Tue Aug 03, 2010 7:30 pm
Integer "d" is the product of Integers A,B and C. 1<a<b<c. If the remainder when 233 is divided by "d" is 79? What is A+C?

A. 7
B. 9
C. 13
D. 14
E. 18

Source: Kaplan 1,012 Gmat math questions.

Please help. Where to start!
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by Rahul@gurome » Tue Aug 03, 2010 7:44 pm
Now 233 - 79 = 154 should be divisible by a*b*c.

Now 154 = 2*7*11.

So a = 2 and c = 11.
Or a+c = 13.
The correct answer is C.
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by missrochelle » Wed Aug 04, 2010 4:57 am
thanks! you made it so easy :)
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by sanju09 » Wed Aug 04, 2010 5:00 am
missrochelle wrote:Integer "d" is the product of Integers A,B and C. 1<a<b<c. If the remainder when 233 is divided by "d" is 79? What is A+C?

A. 7
B. 9
C. 13
D. 14
E. 18

Source: Kaplan 1,012 Gmat math questions.

Please help. Where to start!

We can take

233 = d q + 79, or d q = 154, where q is the quotient obtained when 233 is divided by d.

But remember that d is the product of 3 distinct integers each greater than 1, and 154 = 2 × 7 × 11, all primes! No room for q, which means that q = 1 and d = 154.

Since, 1 < A < B < C, therefore A = 2 and C = 11; and hence [spoiler]A + C = 13

C[/spoiler]
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