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DS question: Is 1/k > 0?

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by Geva@EconomistGMAT » Thu Nov 18, 2010 1:39 am
Bnow wrote:If k does not equal 0, 1, or -1, is 1/k > 0?

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


Having trouble reasoning through this one. The answer is A. But could someone explain this to me? Many thanks in advance!
the key is not to let the fractions confuse you. For a fraction to be positive, both the numerator and the denominator need to have the same sign - either both positive, or both negative. For example, 2/3 and -2/-3 will both be positive fractions, but -2/3 will not.

thus, by asking "is 1/k>0, the question is really asking "is k>0?", since 1 is positive, k must be positive as well for the fraction to be positive.

Stat. (1): use the same logic: if 1/k-1>0 and the numerator is positive, then k-1 must be positive as well: k-1>0 means that k>1, which means that k is definitely positive (it's greater than 1!). The answer to the question stem is "yes", and stat. (1) is sufficient.
Stat. (2): the same thing, only now we know that k+1>0 --> k>-1, which allows both positive and negative values of k (k could b -0.5). thus, Stat. (2) allows both a yes and a no answer to the question stem, and is insufficient.
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by Bnow » Thu Nov 18, 2010 2:05 am
Thank you!

In statement 1, I was plugging in 1/2 for k and plugging in -1/2 for k. While both work in statement one, I get mixed results when I plug 1/2 into 1/k > 0. Was it wrong to plug in those fractions?
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by Geva@EconomistGMAT » Thu Nov 18, 2010 2:23 am
Bnow wrote:Thank you!

In statement 1, I was plugging in 1/2 for k and plugging in -1/2 for k. While both work in statement one, I get mixed results when I plug 1/2 into 1/k > 0. Was it wrong to plug in those fractions?
It's the otehr way around - both values are impossible for (1), but work for (2).

Stat. (1) actually says that k needs to be greater than 1 - neither 1/2 nor -1/2 work.

(1) 1/k-1 > 0

Could k equal 1/2? k-1=1/2-1=-1/2.
1/-1/2 is -2: which is not greater than 0, which means that k cannot equal 1/2.
k=-1/2 makes it even worse, as -1/2-1 becomes -3/2 - even more negative.



for stat. (2) 1/k+1>0

could k equal 1/2? k+1=1/2+1=3/2, and 1/3/2 = 2/3, which is positive. so k could equal 1/2.
Could k equal -1/2? k+1=-1/2+1=1/2, and 1/1/2 = 2, which is also positive. so k could also equal -1/2.
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by Geva@EconomistGMAT » Thu Nov 18, 2010 5:34 am
Bnow wrote:Thank you!

In statement 1, I was plugging in 1/2 for k and plugging in -1/2 for k. While both work in statement one, I get mixed results when I plug 1/2 into 1/k > 0. Was it wrong to plug in those fractions?
Just realized a possible point of confusion: if memory serves, the original GMAT question had 1/(k-1) and 1/(k+1) - meaning that the entire expression k-1 and k+1 came in the denominator of the fraction, and not the fraction 1/k, with the addition of subtraction of 1.

Does this make things clearer?

g.
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by Bnow » Thu Nov 18, 2010 1:41 pm
Yes, much clearer! And thank you for explaining about the fractions with neg/pos in the numerator and denominator -- I've been wondering about that.

Since I didn't recognize immediately that the question was asking about whether K was negative or positive, was it wrong to test the fraction approach (plugging in +1/2 and -1/2)? Perhaps it was since I started to confuse myself.
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by Geva@EconomistGMAT » Sun Nov 21, 2010 12:38 am
Bnow wrote:Yes, much clearer! And thank you for explaining about the fractions with neg/pos in the numerator and denominator -- I've been wondering about that.

Since I didn't recognize immediately that the question was asking about whether K was negative or positive, was it wrong to test the fraction approach (plugging in +1/2 and -1/2)? Perhaps it was since I started to confuse myself.
If you don't figure out the issue of the question before diving into the statements, your only recourse is to plug in various numbers in the hope of stumbling on opposing examples. However, I'm sure that it is now painfully obvious that this approach of firing volley after volley blindly is ineffective - the answer may strike you immediately, but you also stand a chance of losing sight of the big picture and confusing yourself.
Therefore, I suggest that you spend some time with the question stem before rushing to the statements. In a yes/no question such as this one, first figure out what constitutes a yes, and what constitutes a no. Ttry to take these definitions one step further:
For example, if a question asks "is x positive", then an answer of "yes" is that x is positive, and an answer of "no" means "x is not positive". From this basic definition, take a step further - does a "no" necessarily mean that x is negative? Not necessarily - no positive also includes zero. Without making the conscious effort to "play around" with the question stem and define to yourself what are the scenarios you're aiming for and what are the end cases that apply, you are left with only the strategy of firing blindly in the hope of finding something.
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by Bnow » Sun Nov 21, 2010 1:59 am
You've just provided the best insight for me. I'll take it to heart and practice that way more instead of jumping into the statements. This approach will save me a lot of time. While I do often try to simplify the question stem info, I will often forget to fully consider what it's asking. I very much appreciate your advice, so many thanks.
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by Night reader » Sun Nov 21, 2010 2:52 am
Bnow wrote:If k does not equal 0, 1, or -1, is 1/k > 0?

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


Having trouble reasoning through this one. The answer is A. But could someone explain this to me? Many thanks in advance!
statement (1)
k<-1, then k=-2 and -1/2-1>0 doesn't satisfy
-1<k<0, then k=-1/2 and -2-1>0 doesn't satisfy
0<k<1, then k=1/2 and 2-1>0 satisfies
k>1, then k=2 and 1/2-1>0 doesn't satisfy

So, statement (1) says k can be in the interval 0<k<1; in other words it can not be less than 0 and greater than 1.

statement (2)
k<-1, then k=-2 and -1/2+1>0 satisfies
-1<k<0, then k=-1/2 and -2+1>0 doesn't satisfy
0<k<1, then k=1/2 and 2+1>0 satisfies
k>1, then k=2 and 1/2+1>0 satisfies

Statement (2) suggests that k can be both less -1 and in the interval 0<k<1 and can be greater than 1. Here 1/k>0 is not true for all terms listed.

I described the rule of four zones, which is very flexible in use with roots, exponents, mods and inequalities on the number line.

Choose Statement (1), k is placed within 0<k<1 and 1/k>0 Answer A.
My knowledge frontiers came to evolve the GMATPill's methods - the credited study means to boost the Verbal competence. I really like their videos, especially for RC, CR and SC. You do check their study methods at https://www.gmatpill.com
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