# Thread: How many of the numbers x, y, and z are positive?

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## How many of the numbers x, y, and z are positive?

How many of the numbers x, y, and z are positive? x, y, and z are all less than 30.
(1) x + y + z = 61
(2) x + y = 35

A) Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.

B) Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.

C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.

D) Either statement BY ITSELF is sufficient to answer the question.

E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question

2. Good post? |

## Re: How many of the numbers x, y, and z are positive?

I believe the answer is A. Is that correct?

If we take 1) x+y+z = 61, and each number x,y, and z are less than 30, the 2 largest numbers could each be 29. 29+29+z=61, so z has to be positive.

If we take 2), x+y=35, it tells us nothing about z, so it could very well be postive or negative.

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## Re: How many of the numbers x, y, and z are positive?

I think the answer is E.
Why are you assuming that 'numbers' means integers?
It could be fractions too.

Am I right?

Lets discuss.

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## Re: How many of the numbers x, y, and z are positive?

A) x+y+z = 61
Since x, y & z are less than 30, the max value of x can be 29.99999... and y can be 29.99999... which implies that z > 1, so x, y & z are all positive.
Sufficient

B) x+y = 35; No info on z. Insufficient

Ans is A.

Thanks,
GMAT-HELP

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## Re: How many of the numbers x, y, and z are positive?

Great! Now I understand.
Thanks

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