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 Post subject: GMAT Algebra
PostPosted: Mon Apr 29, 2013 9:00 am 
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The three integers in the set {x, y, z} are all less than 30. How many of the integers are positive?
(1) x + y + z = 67
(2) x + y = 40

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, meaning that further information would be needed to answer the question.


(A) Statement (1) alone is sufficient. Since all the numbers are less than 30, all three must be positive for their sum to be 67 or greater because there is no way to get a sum greater than or equal to 67 with just two positive numbers less than 30.

Note: If this is confusing, try plugging in numbers and you will find that it is impossible to have a negative number when 3 numbers less than 30 must sum to a number 67 or greater. Since 29 + 29 = 58, then the third number cannot be negative for the sum of all three to be greater than 67. This provides sufficient information to know how many are positive.

Statement (2) alone is insufficient, because it implies that x and y are positive, but gives no information about z.

Since Statement (1) is sufficient alone, and Statement (2) is not, the correct answer is choice (A).
-------------

Statement 2 is also sufficient.
If x + y is 40 and each is less than 30, then max value for either is 29, making the other at least 11. There is no way for either to be negative if they are both less than 30. Also if x and y add up to 40, z must be positive.


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 Post subject: Re: GMAT Algebra
PostPosted: Mon Apr 29, 2013 9:01 am 
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Everything is clear with your reasoning except:
"Also if x and y add up to 40, z must be positive."

My guess is, that in your reasoning, you've also used statement (1).

Note, that we are examining Statement (2) alone. So we only know that:
"The three integers in the set {x, y, z} are all less than 30. x + y = 40".
We clearly know nothing about z, except that it is less than 30. So it can be positive or it can be negative.


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