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Math Expert V
Joined: 02 Sep 2009
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Difficulty:   55% (hard)

Question Stats: 52% (01:04) correct 48% (01:01) wrong based on 182 sessions

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What is the value of nonzero integer $$k$$?

(1) $$|k| + k = 0$$

(2) $$|k^k| = k^0$$

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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

(1) $$|k| + k = 0$$. Re-arrange: $$|k|=-k$$, This implies that $$k\leq{0}$$. Since we are told that $$k$$ is a nonzero integer, then we have that $$k < 0$$. Not sufficient.

(2) $$|k^k| = k^0$$. Any nonzero number to the power of 0 is 1, hence $$k^0=1$$. So, we have that $$|k^k| = 1$$. This implies that $$k=1$$ or $$k=-1$$. Not sufficient.

(1)+(2) Since from (1) $$k < 0$$, then from (2) $$k=-1$$. Sufficient.

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Bunuel wrote:
Official Solution:

(1) $$|k| + k = 0$$. Re-arrange: $$|k|=-k$$, This implies that $$k\leq{0}$$. Since we are told that $$k$$ is a nonzero integer, then we have that $$k < 0$$. Not sufficient.

(2) $$|k^k| = k^0$$. Any nonzero number to the power of 0 is 1, hence $$k^0=1$$. So, we have that $$|k^k| = 1$$. This implies that $$k=1$$ or $$k=-1$$. Not sufficient.

(1)+(2) Since from (1) $$k < 0$$, then from (2) $$k=-1$$. Sufficient.

Hi Bunuel,

Can you please explain how you got $$k\leq{0}$$ from $$|k|=-k$$ in (1) and $$k=1$$ or $$k=-1$$ from in (2).

Math Expert V
Joined: 02 Sep 2009
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MBAinSCM wrote:
Bunuel wrote:
Official Solution:

(1) $$|k| + k = 0$$. Re-arrange: $$|k|=-k$$, This implies that $$k\leq{0}$$. Since we are told that $$k$$ is a nonzero integer, then we have that $$k < 0$$. Not sufficient.

(2) $$|k^k| = k^0$$. Any nonzero number to the power of 0 is 1, hence $$k^0=1$$. So, we have that $$|k^k| = 1$$. This implies that $$k=1$$ or $$k=-1$$. Not sufficient.

(1)+(2) Since from (1) $$k < 0$$, then from (2) $$k=-1$$. Sufficient.

Hi Bunuel,

Can you please explain how you got $$k\leq{0}$$ in 1 and $$k=1$$ or $$k=-1$$. in 2.

For 1:
Absolute value properties:

When $$x \le 0$$ then $$|x|=-x$$, or more generally when $$\text{some expression} \le 0$$ then $$|\text{some expression}| = -(\text{some expression})$$. For example: $$|-5|=5=-(-5)$$;

When $$x \ge 0$$ then $$|x|=x$$, or more generally when $$\text{some expression} \ge 0$$ then $$|\text{some expression}| = \text{some expression}$$. For example: $$|5|=5$$.

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

For 2: can you please tell me what is unclear there?
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Hi Bunuel,

Thanks you for the explanation and the link. I now understand that step clearly. Got the second one too. I think.
|k^k| = 1 can be represented by both -> k > 1 , 1^1 and k <-1 (-1)^-1

Thanks!!!
Intern  Joined: 17 Jan 2016
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Just wondering ---- what is -1^0? I noticed in the solution, it said that any nonzero number raised to zero is 1, but is this true for negative numbers as well? Can't seem to find anything on the web about this...

Thanks.
Math Expert V
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wmichaelxie wrote:
Just wondering ---- what is -1^0? I noticed in the solution, it said that any nonzero number raised to zero is 1, but is this true for negative numbers as well? Can't seem to find anything on the web about this...

Thanks.

__________

(-1)^0 = 0.
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Does the GMAT acknowledge 0^0 as 1 or indeterminate?
Math Expert V
Joined: 02 Sep 2009
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pierce514 wrote:
Does the GMAT acknowledge 0^0 as 1 or indeterminate?

0^0, in some sources equals to 1 (not 0), some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.
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Bunuel wrote:
pierce514 wrote:
Does the GMAT acknowledge 0^0 as 1 or indeterminate?

0^0, in some sources equals to 1 (not 0), some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.

Please see the attached! Bunuel could you please explain this?

Thanks
>> !!!

You do not have the required permissions to view the files attached to this post.

Math Expert V
Joined: 02 Sep 2009
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sunnyattri wrote:
Bunuel wrote:
pierce514 wrote:
Does the GMAT acknowledge 0^0 as 1 or indeterminate?

0^0, in some sources equals to 1 (not 0), some mathematicians say it's undefined. But you won't need this for the GMAT because the case of 0^0 is not tested on the GMAT.

Please see the attached! Bunuel could you please explain this?

Thanks

What is there to explain? Yes, -6^0 = -(6^0)= -1.
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Please see the attached! Bunuel could you please explain this?

Thanks[/quote]

What is there to explain? Yes, -6^0 = -(6^0)= -1.[/quote]

if thats ture then .. shouldn't the ans B .. coz |X^X| has to positive integer, so the only way |X^X| = X^0 if X is 1.... please correct me if i'm wrong.
Math Expert V
Joined: 02 Sep 2009
Posts: 53795

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sunnyattri wrote:
Please see the attached! Bunuel could you please explain this?

Thanks

What is there to explain? Yes, -6^0 = -(6^0)= -1.[/quote]

if thats ture then .. shouldn't the ans B .. coz |X^X| has to positive integer, so the only way |X^X| = X^0 if X is 1.... please correct me if i'm wrong.[/quote]

Ah, I see what you mean. If k = -1, then we'd get (-1)^0 = 1 and not -1^0 = -1.
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sunnyattri wrote:
Please see the attached! Bunuel could you please explain this?

Thanks

What is there to explain? Yes, -6^0 = -(6^0)= -1.[/quote]

if thats ture then .. shouldn't the ans B .. coz |X^X| has to positive integer, so the only way |X^X| = X^0 if X is 1.... please correct me if i'm wrong.[/quote]

Bunuel you quoted in your official solution that "Any nonzero number to the power of 0 is 1" and you agreed that .. "-6^0 is -1"... so, which one is correct?
Math Expert V
Joined: 02 Sep 2009
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sunnyattri wrote:

Bunuel you quoted in your official solution that "Any nonzero number to the power of 0 is 1" and you agreed that .. "-6^0 is -1"... so, which one is correct?

You don't understand the difference.

-6 to the power of 0 is 1: (-6)^0 = 1

If you write -6^0, it's not -6 to the power of 0, it's minus, 6 top the power of 0: -(6^0) = -1.

Hope it's clear now.
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Bunuel wrote:
sunnyattri wrote:
Please see the attached! Bunuel could you please explain this?

Thanks

What is there to explain? Yes, -6^0 = -(6^0)= -1.

if thats ture then .. shouldn't the ans B .. coz |X^X| has to positive integer, so the only way |X^X| = X^0 if X is 1.... please correct me if i'm wrong.[/quote]

Ah, I see what you mean. If k = -1, then we'd get (-1)^0 = 1 and not -1^0 = -1.[/quote]

if K =-1 the we'd get -1^0 = -1 not 1 ( see the attached)
Math Expert V
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sunnyattri wrote:
if K =-1 the we'd get -1^0 = -1 not 1 ( see the attached)

You are wrong.

If k = -1, then k^0 = (-1)^0 = 1.
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Bunuel wrote:
sunnyattri wrote:
if K =-1 the we'd get -1^0 = -1 not 1 ( see the attached)

You are wrong.

If k = -1, then k^0 = (-1)^0 = 1.

Ah, it's clear now, Thanks ..
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GMAT 1: 770 Q49 V47 GPA: 3.95
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Bunuel wrote:
What is the value of nonzero integer $$k$$?

(1) $$|k| + k = 0$$

(2) $$|k^k| = k^0$$

(1)
$$|k|$$ is always positive, so k is any negative integer.
For example $$|-1| + -1 = 0$$ or $$|-2| + -2 = 0$$ etc.
Not sufficient.

(2)
RHS will be 1 (any integer to the power of 0 is 1)
$$|k^k| = 1$$
$$k^k = 1$$ ---> $$k = 1$$
OR
$$k^k = -1$$ ---> $$k = -1$$
Not sufficient.

(+)
From (1) we determined k was negative and from (2) only one answer is negative
k = -1
Sufficient. Re: M30-09   [#permalink] 08 Jan 2019, 08:33
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