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GMAT Diagnostic Test Question 15 Field: modules, inequalities Difficulty: 700

Is \(K\) a positive number?

(1) \(|K^3| + 1 > K\) (2) \(K + 1 > |K^3|\)

A. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D. EACH statement ALONE is sufficient E. Statements (1) and (2) TOGETHER are NOT sufficient
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The trick here is that 0 is neither positive nor negative. Both \(K=1\) and \(K=0\) satisfy both statements. So we can't be sure if \(K\) is positive. Does it make sense? Hope it helps.

defoue wrote:

Hi dzyubam would you please explain the case when K=0

In both the cases only 0 & 1 have been considered as values of x. Why not higher values like 2 or 3? Or, fractional values like -1/2? In case K=-1/2, then 2nd equation is true.

-1/2 + 1 = 1/2 |(-1/2)^3| = 1/8, and 1/2>1/8, i.e. K+1>|K^3|.

Am I grossly wrong in assuming that K can be a fractional number?

You're right, \(K\) is not limited to integers only. However, if we can be sure it's E using only two values (0 and 1) to verify that, there's no need to test other values (like the fractional values). I hope this makes sense.

siddhartho wrote:

Hi,

In both the cases only 0 & 1 have been considered as values of x. Why not higher values like 2 or 3? Or, fractional values like -1/2? In case K=-1/2, then 2nd equation is true.

-1/2 + 1 = 1/2 |(-1/2)^3| = 1/8, and 1/2>1/8, i.e. K+1>|K^3|.

Am I grossly wrong in assuming that K can be a fractional number?

You're right, \(K\) is not limited to integers only. However, if we can be sure it's E using only two values (0 and 1) to verify that, there's no need to test other values (like the fractional values). I hope this makes sense.

siddhartho wrote:

Hi,

then 2nd equation is true.

Thanks for the clarification. But why to limit value of K betyween 0 & 1. In my example if K assumes a value of (-)1/2, then B is true. So we can say from B that K is not positive. IMO ans is B.

Siddhartho, I think you're misunderstanding the Data Sufficiency (DS) questions a bit. When you solve DS questions, you have to be 100% sure that say S1 or S2 is sufficient to answer. That means you have to be able to answer the question with a definite YES or NO using additional info given in S1 and/or S2. If the answer to the question can be either YES or NO, the info from S1 and/or S2 is INSUFFICIENT.

Let's see why B can't be the answer for this question. You're right that the equation from S2 holds true when \(K=-\frac{1}{2}\), but it doesn't make B the right answer. We only know that \(K\) can be negative. When you plug \(K=1\) in the same equation, you'll see that it also holds true. Now we know that \(K\) can be either negative (\(-\frac{1}{2}\)) or positive (1) using S2. Therefore S2 is INSUFFICIENT to answer the question. The answer can't be B.

That means you have to be able to answer the question with a definite YES or NO using additional info given in S1 and/or S2. If the answer to the question can be either YES or NO, the info from S1 and/or S2 is INSUFFICIENT.

he he....i have started thinking that i should not have taken this test at first place...till 14 questions there are around 3-4 such questions .....like preying on exception...i hope in real gmat we dont each question like that.... here i thought it was B but 0 is taken as positive number which ruins the things... in another question there was 0! some confusion regarding 13 as well ...

any way good are good but i have started question myself would it be near real gmat...

basically for these type of questions ...you should always check the equations with values -1 , 0 , 1... most of the times you get through your answer using these...

You cannot decide on a particular method for all 'such and such questions'. Your methodology will change according to the question. I anyway do not endorse the positive/negative approach for mod questions. It's very time consuming and there are easier methods available in most cases. What is the first thing you think about when you see a mod? I think that this term is either 0 or positive. K^3 is too cumbersome to be dealt algebraically. So I try to deal with it arithmetically.

Is K a positive number? (Or rephrase - Is it that K cannot be 0 or negative?)

(1) |K^3| + 1 > K 0/Positive + Positive > K K can be positive but of course K can be 0 and negative too here. This relation will still hold. Not sufficient.

(2) K + 1 > |K^3| K + positive > 0/positive Here, my first thought is that if K = 0, this relation still holds (and of course it holds for some positive values of K too) It becomes 0+1 > 0 (Some negative values also satisfy this inequality but I don't need to go there. I need just one value and I got it.) Not sufficient.

Using both statements, there are positive values of K that satisfy both equations and 0 satisfies them both too. So both together are not sufficient.
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The question asks if k is a positive number? The answer is yes, if k is a positive number. The answer is no, if k is a negative number. Why should you take into consideration, a situation in which k is neither positive nor negative?