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# If x is a positive number

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If x is a positive number [#permalink]  26 Aug 2012, 06:24
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If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.
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Re: If x is a positive number [#permalink]  26 Aug 2012, 06:42
If x is a positive number, is x an even integer?

Notice that we are not told that x is an integer.

(1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.

(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.

(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x-3x=even-even --> 2x=even --> x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.

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Re: If x is a positive number [#permalink]  26 Aug 2012, 09:13
syog wrote:
If x is a positive number, is x an even integer?

(1) 3x is an even integer.

(2) 5x is an even integer.

Neither (1) nor (2) alone is sufficient.

(1) and (2) together:

From (1) 3x=2k, where k is a positive integer.
From (2) 5x=2m, where m is some positive integer. Necessarily \frac{2k}{3}=\frac{2m}{5} from which 5k=3m.
k and m being integers, necessarily k must be a multiple of 3 (because 5 is not divisible by 3), so k=3a for some positive integer a.
It follows that x=\frac{2k}{3}=2a so x is even.

Sufficient.

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Re: If x is a positive number [#permalink]  30 Aug 2012, 04:53
Bunuel wrote:
If x is a positive number, is x an even integer?

Notice that we are not told that x is an integer.

(1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.

(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.

(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x-3x=even-even --> 2x=even --> x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.

My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer?
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Re: If x is a positive number [#permalink]  30 Aug 2012, 05:18
ziko wrote:
Bunuel wrote:
If x is a positive number, is x an even integer?

Notice that we are not told that x is an integer.

(1) 3x is an even integer. x could be ANY even number or some fraction (for example 2/3), so this statement is NOT sufficient.

(2) 5x is an even integer. The same here, x could be ANY even number or some fraction (for example 2/5). Not sufficient.

(1)+(2) We have that 3x=even and 5x=even. Subtract one from another: 5x-3x=even-even --> 2x=even --> x=even/2=integer. Now, x=integer and 3x=even (from 1) means that x must be an even integer. Sufficient.

My answer to this question was D, both sufficient, however my assumption was that in GMAT number and integer are interchangible words, but as i see i was wrong. Bunuel could you please remind what word was interchangible with word integer?

I think you refer to Natural Numbers, which are non-negative (or positive) integers but GMAT doesn't use words "Natural Number" in their questions.

So, there is no interchangeable word for "integer" on the GMAT.
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Re: If x is a positive number [#permalink]  30 Aug 2012, 19:50
great job
great way to solve this problem..

i didnt reach the answer as you did

ds has been troubling me like anything
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Re: If x is a positive number   [#permalink] 30 Aug 2012, 19:50
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