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# M30-09

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 01:45
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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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Joined: 02 Sep 2009
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16 Sep 2014, 01:45
4
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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23 Apr 2015, 04:05
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).

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23 Apr 2015, 04:09
1
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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26 Apr 2015, 02:45
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!!!
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Joined: 17 Jan 2016
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25 Aug 2016, 20:46
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.
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26 Aug 2016, 01:27
1
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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05 May 2017, 09:19
Does the GMAT acknowledge 0^0 as 1 or indeterminate?
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05 May 2017, 10:03
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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28 Sep 2018, 02:58
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.

Thanks
>> !!!

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28 Sep 2018, 03:03
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.

Thanks

What is there to explain? Yes, -6^0 = -(6^0)= -1.
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28 Sep 2018, 03:31

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.
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28 Sep 2018, 03:36
sunnyattri wrote:

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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28 Sep 2018, 03:38
sunnyattri wrote:

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?
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28 Sep 2018, 03:42
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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28 Sep 2018, 03:44
Bunuel wrote:
sunnyattri wrote:

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)
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28 Sep 2018, 03:46
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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28 Sep 2018, 03:49
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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08 Jan 2019, 08:33
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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# M30-09

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