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# GMAT Diagnostic Test Question 15

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GMAT Diagnostic Test Question 15 [#permalink]

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06 Jun 2009, 22:27
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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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Last edited by Bunuel on 07 Oct 2013, 00:18, edited 3 times in total.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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01 Jul 2009, 08:14
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Explanation:

Statement 1 is insufficient. Consider $$K=1$$ (the answer is YES) and $$K=0$$ (the answer is NO). Both $$K$$ values hold the inequality true.

Statement 2 is insufficient. The logic is the same as in Statement 2. Consider $$K=1$$ (the answer is YES) and $$K=0$$ (the answer is NO).

Combining the two statements doesn't give us new information.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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25 Jul 2009, 03:58
Hi dzyubam would you please explain the case when K=0

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Re: GMAT Diagnostic Test Question 14 [#permalink]

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27 Jul 2009, 01:21
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Hi,

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

Rgds

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Re: GMAT Diagnostic Test Question 14 [#permalink]

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19 Dec 2009, 14:51
it make sense now. I have got to remember 0.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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23 Jan 2010, 22:32
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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?
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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25 Jan 2010, 05:10
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?

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Re: GMAT Diagnostic Test Question 14 [#permalink]

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25 Jan 2010, 06:59
dzyubam wrote:
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.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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26 Jan 2010, 03:17
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.

I hope it helps you. If you're still confused with DS questions, you might want to review the DS section in the Official Guide. There are many very good Math resources on the forums too:
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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26 Jan 2010, 06:41
dzyubam wrote:
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.

I hope it helps you. If you're still confused with DS questions, you might want to review the DS section in the Official Guide. There are many very good Math resources on the forums too:

Thanks very much, I got it now. The 100% concept and the link to resources will both help me.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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01 Mar 2010, 18:47

Why I cannot assume from the statements that k=0? that would answer the question, right?
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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03 Mar 2010, 01:07
Both $$K=1$$ and $$K=0$$ hold for S1 and S2 (even taken together). This is why you can't assume that $$K=0$$. Please see the OE in the second post.

arturocb86 wrote:

Why I cannot assume from the statements that k=0? that would answer the question, right?

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Re: GMAT Diagnostic Test Question 14 [#permalink]

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02 Apr 2010, 11:17
I started by testing -1, 0, +1 for both (1) & (2)- got E
But the solution provides that only 0 and 1 are enough test Nos.
Thanks.
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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03 Sep 2010, 10:46
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...
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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13 May 2011, 07:18
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...
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Re: GMAT Diagnostic Test Question 14 [#permalink]

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07 Oct 2011, 04:02
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Expert's post

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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Re: GMAT Diagnostic Test Question 14 [#permalink]

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14 Oct 2011, 04:23
from stmt 1 & 2 we know that -

k-1<|K^3|<k+1

lets k =-2
then -3<8<-1 not true

lets k=2
1<8<3 not true
lets k=0
-1<0<1 true

E is the answ
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Is K a positive number ? [#permalink]

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09 Feb 2013, 15:06
Statement 1 - |K^3| +1 > k
Statement 2 - k +1 > |K^3|

I disagree with the solution below : Can someone review and let me know if i'm mistaken ?

Statement 1 is insufficient. Consider K=1 (the answer is YES) and K=0 (the answer is NO). Both values hold the inequality true.

Statement 2 is insufficient. The logic is the same as in Statement 2. Consider K=1 (the answer is YES) and K=0 (the answer is NO).

Combining the two statements doesn't give us new information.

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Re: Is K a positive number ? [#permalink]

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09 Feb 2013, 16:46
anartey wrote:
Statement 1 - |K^3| +1 > k
Statement 2 - k +1 > |K^3|

I disagree with the solution below : Can someone review and let me know if i'm mistaken ?

Statement 1 is insufficient. Consider K=1 (the answer is YES) and K=0 (the answer is NO). Both values hold the inequality true.

Statement 2 is insufficient. The logic is the same as in Statement 2. Consider K=1 (the answer is YES) and K=0 (the answer is NO).

Combining the two statements doesn't give us new information.

Statement 1:
If K=0 then $$|k^3|+1 = 1$$ --- Yes
If K=-1 then $$|k^3|+1 = 0$$ --- No
S1 is not sufficient

Statement 2:
If K=1 then $$K+1=2$$ and $$|k^3|=1$$ --- Yes
If K=-1 then$$K+1=0$$ and $$|k^3|=1$$ ---No
S2 is not sufficient

Putting the two together gives no further information
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Re: GMAT Diagnostic Test Question 15 [#permalink]

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06 Apr 2014, 13:28
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?
Re: GMAT Diagnostic Test Question 15   [#permalink] 06 Apr 2014, 13:28

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# GMAT Diagnostic Test Question 15

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