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# D01-15

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:11
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Difficulty:

65% (hard)

Question Stats:

60% (01:09) correct 40% (01:14) wrong based on 178 sessions

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Is $$K$$ a positive number?

(1) $$|K^3| + 1 \gt K$$

(2) $$K + 1 \gt |K^3|$$
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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15 Sep 2014, 23:12
Official Solution:

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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Joined: 03 Feb 2015
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16 Mar 2015, 21:48
hi Bunuel

you wrote-
'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).'

In [highlight]statement 2
if we put value k=0 we will get 1>0. which is true. how is this a No
Math Expert
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17 Mar 2015, 04:33
harDill wrote:
hi Bunuel

you wrote-
'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).'

In [highlight]statement 2
if we put value k=0 we will get 1>0. which is true. how is this a No

The questions asks whether k is a positive number. For (2) if k = 1 (which satisfies second statement) it IS a positive number but if k = 0 (which also satisfies second statement) it is NOT a positive number (0 is not a positive number, it's neither positive nor negative).
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17 Mar 2015, 10:54
harDill wrote:
hi Bunuel

you wrote-
'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).'

In [highlight]statement 2
if we put value k=0 we will get 1>0. which is true. how is this a No

Your target is to find whether K can be negative or Zero or it is only positive. Remember you have to maintain the condition in statement 2

Now if K is positive, say k=1 statement 2 becomes 1+1> 1 which is true. That means by keeping k positive you can satisfy statement 2

Now if K is negative, say k= -0.5, statement 2 becomes -0.5+1> 0.125 or 0.5> 0.125 which is also true. That means by taking K= negative value you can still satisfy statement 2.

So, K can be positive and negative and zero. Therefore The answer of the question (IS K Positive) can be yes and can be no. Sot sufficient
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17 Mar 2015, 22:10
Bunuel wrote:
harDill wrote:
hi Bunuel

you wrote-
'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).'

In [highlight]statement 2
if we put value k=0 we will get 1>0. which is true. how is this a No

The questions asks whether k is a positive number. For (2) if k = 1 (which satisfies second statement) it IS a positive number but if k = 0 (which also satisfies second statement) it is NOT a positive number (0 is not a positive number, it's neither positive nor negative).

ok i got it now. i misunderstood the explanation the first time. thanks guys
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Joined: 03 Dec 2015
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20 Feb 2017, 09:47
Hi all,

I successfully demonstrated that both statements taken singularly weren't sufficient to answer, however, I found myself stuck when it came to consider them together.
Being uncertain between C and E I simply guessed C..

..how can you say that the two statements are not providing any new information? They're not an identity nor equivalent, so I spent valuable seconds trying to figure out the possible scenarios when combining them.
Manager
Joined: 14 Jun 2016
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22 Aug 2017, 09:44
Is there any alternative way rather than just value plugging ?
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Math Expert
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22 Aug 2017, 09:51
buan15 wrote:
Is there any alternative way rather than just value plugging ?

Check here: https://gmatclub.com/forum/gmat-diagnos ... 79342.html
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16 Nov 2017, 05:43
Bunuel,

i could see that both the statements individually are insufficient. But i wasn't sure if combing them would make them sufficient .
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Joined: 31 Dec 2017
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17 Jan 2018, 11:34
Hi everyone,

After demonstrating that each statement alone is not sufficient (by plugging in numbers), I proved that E is the correct answer by adding the two inequalities together:

(1) |K^3|+1>K
(2) K+1>|K^3|
Added together: |K^3|+ K+ 2 > |K^3| + K

After substracting (|K^3| + K) from both sides we get: 2 > 0, which is always true; therefore K can be any number, not only a positive one - the statements taken together are still not sufficent
D01-15   [#permalink] 17 Jan 2018, 11:34
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