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What is the remainder when positive integer x is divided by

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What is the remainder when positive integer x is divided by [#permalink] New post 05 Mar 2013, 08:11
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What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2
(2) When x is divided by 15, the remainder is 2


What's a good approach to a problem like this. This was the first problem I got on my OG Test
[Reveal] Spoiler: OA

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Re: What is the remainder when positive integer x is divided by [#permalink] New post 05 Mar 2013, 09:47
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manimgoindowndown wrote:
What is the remainder when positive integer x is divided by 3?
1) When x is divided by 6, the remainder is 2
2) When x is divided by 15, the remainder is 2




From F.S 1, we have that x = 6k+2, where k is a non-negative integer constant. Required to find x = 3p+r, where p= again a non-negative integer constant. We can see that for some value, 6k =3*(2k) = 3p. Thus, the remainder when divided by 3 will also be 2. Sufficient.

Similarly, from F.S 2 , we have that x = 15t+2. Just as above, for some integer, 15t = 3*(5t) = 3p. Thus, the remainder is 2.Sufficient.

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Re: What is the remainder when positive integer x is divided by [#permalink] New post 06 Mar 2013, 01:48
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What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2 --> x=6q+2=3(2q)+2 --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> x=15p+2=3(5p)+2 --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

For more on remainders check here: remainders-144665.html

Hope it helps.
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Re: What is the remainder when positive integer x is divided by [#permalink] New post 06 Mar 2013, 05:45
Bunuel wrote:
What is the remainder when positive integer x is divided by 3?

(1) When x is divided by 6, the remainder is 2 --> x=6q+2=3(2q)+2 --> the remainder upon division x by 3 is 2. Sufficient.

(2) When x is divided by 15, the remainder is 2 --> x=15p+2=3(5p)+2 --> the remainder upon division x by 3 is 2. Sufficient.

Answer: D.

For more on remainders check here: remainders-144665.html

Hope it helps.

Thanks even though it's my off day I'm going to run through that thread. Thanks for sorting the problems by difficulty. Your work and its contribution has been immense to my preparation Bunuel
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Re: What is the remainder when positive integer x is divided by   [#permalink] 06 Mar 2013, 05:45
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