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Math Expert V
Joined: 02 Sep 2009
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16 00:00

Difficulty:   65% (hard)

Question Stats: 58% (01:08) correct 42% (01:13) wrong based on 242 sessions

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Is $$K$$ a positive number?

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

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

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Math Expert V
Joined: 02 Sep 2009
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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 1. 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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Intern  Joined: 03 Feb 2015
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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 V
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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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Joined: 11 Sep 2013
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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
Intern  Joined: 03 Feb 2015
Posts: 13
GMAT 1: 680 Q47 V36 GMAT 2: 720 Q49 V39 Show Tags

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
Intern  Joined: 04 Dec 2015
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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  B
Joined: 14 Jun 2016
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GMAT 1: 610 Q49 V21 WE: Engineering (Manufacturing)

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Is there any alternative way rather than just value plugging ?
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Please help me with Kudos dear friends-need few more to reach the next level. Thanks. Math Expert V
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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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Bunuel,

i could see that both the statements individually are insufficient. But i wasn't sure if combing them would make them sufficient .
Intern  B
Joined: 31 Dec 2017
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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 Current Student B
Joined: 28 Dec 2016
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Concentration: Marketing, General Management
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GMAT 1: 700 Q47 V38 Show Tags

1
Bunuel
Excellent question. Not a big deal, but small typo in your explanation:
"Statement 2 is insufficient. The logic is the same as in Statement 2."
It should probably read:
"Statement 2 is insufficient. The logic is the same as in Statement 1."
Math Expert V
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CPGguyMBA2018 wrote:
Bunuel
Excellent question. Not a big deal, but small typo in your explanation:
"Statement 2 is insufficient. The logic is the same as in Statement 2."
It should probably read:
"Statement 2 is insufficient. The logic is the same as in Statement 1."

Thank you. Edited.
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the question is asking for positive number . so why are we checking for k=0
Math Expert V
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StrugglingGmat2910 wrote:
the question is asking for positive number . so why are we checking for k=0

The question is asking "IS k a a positive number". We don't know that and thus are testing different values to check that.
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Wanted to know if my reasoning was correct for statement 2.

Statement 1:
If K=1 then it becomes 1+1>1 This is valid
If K=-1 then it becomes 1+1>-1 This is also valid.

Since we have two options this is not sufficient.

Statement 2:

Since it says K+1>|K^3| that implies K+1>0 = K>-1. This means that K can be negative, 0 or positive. So statement 2 is sufficient.

Combining the statements give us the same information.
Intern  B
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I considered 2 different scenarios for each statements.
a) K>0
b) K<0

lets elaborate each statements in light of these scenarios.
(1) |K^3|+1>K
a) K^3 +1 >K so we have K^3-K>-1 . this statement is true for all K>0
b) -K^3 +1>K so we have K^3+K<1 . this statement is also true for all K<0
According to a&b it seems that we can not understand whether K is positive or negative.

(2) K+1>|K^3|
a) K+1>K^3 so we have K^3-K<1 . this statement can not be true for all K>0. (this statement is only true for 0<K<1)
b) K+1>-K^3 so we have K^3+K>-1 . this statement can not be true for all K<0. (This statement is only true for some -1<K<0)

As you see, neither of statements (1) or (2) are enough. Re: D01-15   [#permalink] 06 Oct 2018, 12:02
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