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# Number prop I #5

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Director
Joined: 11 Jun 2007
Posts: 914

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22 Sep 2009, 21:26
If $$a$$ and $$b$$ are positive integers, is $$10^a + b$$ divisible by 3?

1. $$\frac{b}{2}$$ is an odd integer.
2. the remainder of $$\frac{b}{10}$$ is $$b$$ .

(C) 2008 GMAT Club - Number properties - I#5

* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient
* Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient
* BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
* EACH statement ALONE is sufficient
* Statements (1) and (2) TOGETHER are NOT sufficient

can someone explain the second statement?

[Reveal] Spoiler:
Statements (1) and (2) combined are insufficient. Consider $$b = 2$$ (the answer is "yes") and $$b = 6$$ (the answer is "no").
Intern
Joined: 23 Sep 2009
Posts: 12
Re: Number prop I #5 [#permalink]

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24 Sep 2009, 00:55
For the expression 10^a + b to be divisible by 3, the sum of the digits should be divisible by 3.

Statement 1:
For b/2 to be odd, b must be a multiple of 2 for odd numbers 1, 3, 5, 7, ... ; so b can be 2, 6, 10, 14... But we have no way of knowing what b is.
INSUFFICIENT

Statement 2:
If the remainder of b/10 is b, that means b < 10. But it could be any positive number less than 10.
INSUFFICIENT

Put together:
WIth Statements 1 and 2, we would know that b can be either 2 or 6. If b = 2, sum of digits of 10^a + 2 is 3 (divisible by 3). If b = 6, sum of digits of 10^a + 6 is 7 (NOT divisible by 3)

I would say answer is E, both statements insufficient.
SVP
Joined: 29 Aug 2007
Posts: 2473
Re: Number prop I #5 [#permalink]

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24 Sep 2009, 20:56
beckee529 wrote:
If $$a$$ and $$b$$ are positive integers, is $$10^a + b$$ divisible by 3?

1. $$\frac{b}{2}$$ is an odd integer.
2. the remainder of $$\frac{b}{10}$$ is $$b$$

1. If b/2 is an odd integer, b is equal to (2+4n) where n is an integer. n >= 0 so n could be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, & so on........

(10^a + b)/3 has reminder 0 if n is divisible by 3.
(10^a + b)/3 has reminder 1 if n is not divisible by 3.

Not sufff.....

2. The remainder of b/10 is b means b < 10.

Togather: B is either 2 or 6. NSF and E..
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Re: Number prop I #5   [#permalink] 24 Sep 2009, 20:56
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# Number prop I #5

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