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(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.

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.

Answer C
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PhD in Applied Mathematics Love GMAT Quant questions and running.

(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.

Answer: C.

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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If you found my post useful and/or interesting - you are welcome to give kudos!

(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.

Answer: C.

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.
_________________

(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.

Answer: C.

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.

(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.

Answer: C.

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.
_________________

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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