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# What is the remainder when the positive integer x is divided

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Joined: 13 Apr 2010
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What is the remainder when the positive integer x is divided [#permalink]

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14 Apr 2010, 07:04
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What is the remainder when the 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.

If m,r,x and y are positive, the ratio of m to r equal to the ratio x to y?

(1) the ratio of m to y is equal to the ratio of x to r
(2) the ratio of m + x to r + y is equal to the ratio of x to y
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Joined: 02 Oct 2009
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GMAT 1: 530 Q47 V17
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Re: need explanation for DS question thank you thank you! [#permalink]

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14 Apr 2010, 08:02
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Quote:
What is the remainder when the 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.

Dont know whether this is a very long method to solve.

1) when x is divided by 6, the remainder is 2

so the number will be form of 6*Y+2(k=0,1,2,3,....)

(2) when x is divided by 15, the remainder is 2
so the number will be form of 15*Z+2(k=0,1,2,3,....)

Both 1,2

Last edited by RaviChandra on 14 Apr 2010, 08:54, edited 1 time in total.
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Re: need explanation for DS question thank you thank you! [#permalink]

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14 Apr 2010, 08:29
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Expert's post
What is the remainder when the positive integer x is divided by 3

(1) when x is divided by 6, the remainder is 2 --> $$x=6p+2$$ --> dividing this by 3 --> 6p is divisible by 3 and 2 divided by 3 leaves remainder of 2. Sufficient.
(2) when x is divided by 15, the remainder is 2 --> $$x=15q+2$$ --> dividing this by 3 --> 15q is divisible by 3 and 2 divided by 3 leaves remainder of 2. Sufficient.

If m,r,x and y are positive, the ratio of m to r equal to the ratio x to y?

Is $$\frac{m}{r}=\frac{x}{y}$$? Is $$my=rx$$?

(1) the ratio of m to y is equal to the ratio of x to r --> $$\frac{m}{y}=\frac{x}{r}$$ --> $$mr=xy$$. Not sufficient.

(2) the ratio of m + x to r + y is equal to the ratio of x to y --> $$\frac{m+x}{r+y}=\frac{x}{y}$$ --> cross multiply --> $$my+xy=rx+xy$$ --> $$my=rx$$. Sufficient.

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Re: need explanation for DS question thank you thank you!   [#permalink] 14 Apr 2010, 08:29
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# What is the remainder when the positive integer x is divided

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