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Difficulty:   55% (hard)

Question Stats: 57% (02:05) correct 43% (02:05) wrong based on 70 sessions

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[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 $$a + b$$?

$$A. 5$$
$$B. 6$$
$$C. 7$$
$$D. 8$$
$$E. 9$$

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Manager  S
Joined: 17 Jul 2017
Posts: 191

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Can somebody help me with this problem?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42 GPA: 3.82

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MathRevolution wrote:
[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.

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Manager  B
Joined: 09 Jun 2017
Posts: 105
GMAT 1: 640 Q44 V35 Show Tags

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 Re: A store sold 72 watches for $a2,34b, where a2,34b is a 5-digit integer [#permalink] 18 Apr 2019, 04:27 Display posts from previous: Sort by A store sold 72 watches for$a2,34b, where a2,34b is a 5-digit integer

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