Call 911: Some Digits are Missing

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Tue May 19, 2009 12:33 pm

Given that 29a031 × 342 = 100900b02 where a and b denote two missing
digits, what is the value of a + b ?
(a) 7
(b) 8
(c) 9
(d) 10
(e) 11

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Source: Beat The GMAT — Problem Solving | Tue May 19, 2009 12:33 pm

dumb.doofus: Master | Next Rank: 500 Posts; Posts: 435; Joined: Sat Sep 27, 2008 2:02 pmFollowed by: 1 member; Location: San Jose, CA; Thanked: 43 times; GMAT Score:720

by dumb.doofus » Tue May 19, 2009 1:43 pm

I just used basic multiplication to deduce a = 5 and b = 6

so a + b = 11

any other methods??

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dtweah: Master | Next Rank: 500 Posts; Posts: 487; Joined: Fri Mar 27, 2009 5:49 am; Thanked: 36 times

by dtweah » Wed May 20, 2009 5:26 am

dumb.doofus wrote:I just used basic multiplication to deduce a = 5 and b = 6

so a + b = 11

any other methods??

I did the same but here is what they say in the OA

Recall the tests for divisibility by 9 and by 11. Since 342 is divisible by 9, the number 100900b02 is as well. So b has to be 6. But then 100900b02 is divisible by 11. Since 342 is not divisible by 11, we deduce 29a031 must be divisible by 11. So a has to be 5, and a + b = 11.

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