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MathRevolution
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MathRevolution
[Math Revolution GMAT math practice question]

A store sold \(72\) watches for \($a2,34b,\) where \(a2,34b\) is a \(5\)-digit integer. What is the value of \(a + b\)?

\(A. 5\)
\(B. 6\)
\(C. 7\)
\(D. 8\)
\(E. 9\)

Assuming the price of each watch is the same, we see that a2,34b must be a multiple of 72. That is, it must be a multiple of 8 and 9 since 72 = 8 x 9. We know that for a number to be a multiple of 8, the last 3 digits must be divisible by 8 and for a number to be a multiple of 9, the sum of the digits must be divisible by 9. So here, we need 34b to be divisible by 8 and a + 2 + 3 + 4 + b = a + b + 9 to be divisible by 9.

If 34b is divisible by 8, then b = 4 only. In that case a must be 5 so that a + b + 9 = 18 will be divisible by 9. So a + b = 5 + 4 = 9.

Answer: E
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Dear MathRevolution
shouldn't the question stated that : 1- each watch sold for the same price
2- that price is an integer
Thanks
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I saw that the question is asking for a+b so I used the rule of multiple of 9

Since a2,34b must be divisible by 9 -> sum of digits = a+b+9 must also be divisible by 9 -> so a+b must be divisible by 9
Only choice E gives this answer
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