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# If w + k = v, what is the value of k ?

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Math Expert
Joined: 02 Sep 2009
Posts: 52152
If w + k = v, what is the value of k ?  [#permalink]

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25 Dec 2017, 23:30
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Difficulty:

25% (medium)

Question Stats:

74% (00:51) correct 26% (01:31) wrong based on 57 sessions

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If w + k = v, what is the value of k ?

(1) v^3 = w^3
(2) v^2 = w^2

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Re: If w + k = v, what is the value of k ?  [#permalink]

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26 Dec 2017, 00:47
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Statement 1 :v^3 = w^3 ; hence v = w
So w + k = v
or, v+k=v , hence k =0, sufficient.
Statement 2 :v^2 = w^2 ; hence v = w, -w
hence k can be 0 or 2v, not sufficient.

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Re: If w + k = v, what is the value of k ?  [#permalink]

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27 Dec 2017, 04:55
Bunuel wrote:
If w + k = v, what is the value of k ?

(1) v^3 = w^3
(2) v^2 = w^2

(1) v^3 = w^3. Then, $$v=w$$ because odd exponents don't change variables sign. So, $$w+k=v$$ then, $$k=v-w; k=w-w=0$$; sufficient.

(2) v^2 = w^2. Then, $$|v|=|w|$$ because even exponents change negative variables to positive. If $$v=1$$, $$w=-1$$ then $$v^2 = w^2$$ is $$(1)^2 = (-1)^2$$ true, but $$1≠-1... v≠w$$; insufficient.

Re: If w + k = v, what is the value of k ? &nbs [#permalink] 27 Dec 2017, 04:55
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