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GMATprep question

by princessss » Mon Oct 25, 2010 12:40 pm
If k is not equal to 0, 1, or -1, is 1/k>0?

(1) 1/(k-1)>0

(2) 1/(k+1)>0


My question is why B isn't correct.
If k is not 0,1 or -1 it can be 2,3 ... and it can be -2,-3 etc.
If we say that k is 2 than 1/(2+1) > 0 true
But, since it can't be -1 if k is negative the fraction can be >0. Doesn't that make B sufficient? K must be positive?
The correct answer is A.
Please help
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by jeetu_vishnoi » Mon Oct 25, 2010 2:25 pm
In these type of question you can only select a given condition as true iff it is always true. If there is even a single condition in which it can be false then you can not choose this condition as sufficient.

In the given question you can see that in the first condition, required number will always be positive but in second condition there are possibilities of number being -ve hence answer is A.
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by Brian@VeritasPrep » Mon Oct 25, 2010 2:47 pm
Hey Princessss,

Great question - and the big key here is that:

k does not have to be an integer.

So, for statement 2, k could be -1/2 and the statement would still hold: 1/(-.5 + 1) = 1/.5 = 2, which is greater than 0.

For integers, statement 2 guarantees a positive numbers (since 0 is not possible as per the rules in teh question stem), but for a noninteger we can still get the answer "NO" to the overall question, and therefore statement 2 is not sufficient.
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by GMATGuruNY » Mon Oct 25, 2010 5:01 pm
princessss wrote:If k is not equal to 0, 1, or -1, is 1/k>0?

(1) 1/(k-1)>0

(2) 1/(k+1)>0


My question is why B isn't correct.
If k is not 0,1 or -1 it can be 2,3 ... and it can be -2,-3 etc.
If we say that k is 2 than 1/(2+1) > 0 true
But, since it can't be -1 if k is negative the fraction can be >0. Doesn't that make B sufficient? K must be positive?
The correct answer is A.
Please help
In order for 1/k to be positive, k must be positive. Rewritten, the question is asking:

Is k>0?

Statement 1:
In order for 1/(k-1) to be positive, k-1 must be positive. Rewritten, statement 1 tells us:
k-1>0
k>1
Thus, k>0. Sufficient.

Statement 2:
In order for 1/(k+1) to be positive, k+1 must be positive. Rewritten, statement 2 tells us:
k+1>0
k>-1
Thus, k could be negative (k= -1/2, for example), or k could be positive (k=1, for example). Insufficient.

The correct answer is A.
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by goyalsau » Wed Oct 27, 2010 1:23 am
GMATGuruNY wrote:
Statement 1:
In order for 1/(k-1) to be positive, k-1 must be positive. Rewritten, statement 1 tells us:
k-1>0
k>1
Thus, k>0. Sufficient.

Statement 2:
In order for 1/(k+1) to be positive, k+1 must be positive. Rewritten, statement 2 tells us:
k+1>0
k>-1
Thus, k could be negative (k= -1/2, for example), or k could be positive (k=1, for example). Insufficient.

The correct answer is A.
How can you rewrite statements like this,
As per i know we can't do anything with inequalities unless we don't know whether they are positive or negative........
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by GMATGuruNY » Wed Oct 27, 2010 2:29 am
goyalsau wrote:
GMATGuruNY wrote:
Statement 1:
In order for 1/(k-1) to be positive, k-1 must be positive. Rewritten, statement 1 tells us:
k-1>0
k>1
Thus, k>0. Sufficient.

Statement 2:
In order for 1/(k+1) to be positive, k+1 must be positive. Rewritten, statement 2 tells us:
k+1>0
k>-1
Thus, k could be negative (k= -1/2, for example), or k could be positive (k=1, for example). Insufficient.

The correct answer is A.
How can you rewrite statements like this,
As per i know we can't do anything with inequalities unless we don't know whether they are positive or negative........
Statement 1 tells us that 1/(k-1)>0. In other words, 1/(k-1) is positive. Since the numerator of this fraction (1) is positive, the denominator (k-1) must also be positive; otherwise, the fraction will take on a negative value. Thus, rewritten, statement 1 tells us that k-1>0.

Does this clarify how I was able to rewrite the two statements?
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