If x is a positive number : GMAT Data Sufficiency (DS)
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# If x is a positive number

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If x is a positive number [#permalink]

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26 Aug 2012, 05:24
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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]

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26 Aug 2012, 05:42
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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]

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26 Aug 2012, 08:13
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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]

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30 Aug 2012, 03:53
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]

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30 Aug 2012, 04:18
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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]

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30 Aug 2012, 18:50
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]

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02 Sep 2013, 07:23
Bunuel wrote:
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.

I am a little confused.
1) 3x is an even integer.
Let x=4/3; then 3x=4. But in this case x is not an even integer. Hence INSUFFICIENT.

2) 5x is an even integer.
Let x=4/5; then 5x=4. But in this case x is not an even integer. Hence INSUFFICIENT.

(1+2): 15x is an integer.
Let x=4/15; then 15x=4. But in this case x is not an even integer. Hence INSUFFICIENT.
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Re: If x is a positive number [#permalink]

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02 Sep 2013, 07:42
domfrancondumas wrote:
Bunuel wrote:
ziko 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.

I am a little confused.
1) 3x is an even integer.
Let x=4/3; then 3x=4. But in this case x is not an even integer. Hence INSUFFICIENT.

2) 5x is an even integer.
Let x=4/5; then 5x=4. But in this case x is not an even integer. Hence INSUFFICIENT.

(1+2): 15x is an integer.
Let x=4/15; then 15x=4. But in this case x is not an even integer. Hence INSUFFICIENT.

Notice that x cannot be 4/15, because in this case 3x=12/15 which is NO an even integer and 5x=20/15 which is also NOT an even integer, so in this case both statements are violated.
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Re: If x is a positive number [#permalink]

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10 Oct 2014, 09:16
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Re: If x is a positive number [#permalink]

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24 Aug 2016, 12:05
Hello from the GMAT Club BumpBot!

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