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

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If w + k = v, what is the value of k [#permalink] If w + k = v, what is the value of k   14 Feb 2012, 05:37
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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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A
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Bunuel
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Re: If w + k = v, what is the value of k [#permalink] If w + k = v, what is the value of k   14 Feb 2012, 05:51
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If w + k = v, what is the value of k

(1) v^3 = w^3 --> v=w --> w+k=w --> k=0. Sufficient.

(2) v^2 = w^2 --> |v|=|w| --> if v=w then k=0 (see above) but if v=-w then k=-2w, and k can take multiple values depending on w. Not sufficient.

Answer: A.
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Re: If w + k = v, what is the value of k [#permalink] If w + k = v, what is the value of k   14 Feb 2012, 23:16
Hi could you please elaborate the solution to pt. 1?

I did this :
v^3-w^3=0 --> (v-w)(v^2+w^2+wv)=0--> k(k^2+3vw)=0 ---> therefore k can be 0 or -3vw.. am not sure how A is sufficient



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

(1) v^3 = w^3 --> v=w --> w+k=w --> k=0. Sufficient.

(2) v^2 = w^2 --> |v|=|w| --> if v=w then k=0 (see above) but if v=-w then k=-2w, and k can take multiple values depending on w. Not sufficient.

Answer: A.
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Re: If w + k = v, what is the value of k [#permalink] If w + k = v, what is the value of k   14 Feb 2012, 23:35
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Hi could you please elaborate the solution to pt. 1?

I did this :
v^3-w^3=0 --> (v-w)(v^2+w^2+wv)=0--> k(k^2+3vw)=0 ---> therefore k can be 0 or -3vw.. am not sure how A is sufficient



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

(1) v^3 = w^3 --> v=w --> w+k=w --> k=0. Sufficient.

(2) v^2 = w^2 --> |v|=|w| --> if v=w then k=0 (see above) but if v=-w then k=-2w, and k can take multiple values depending on w. Not sufficient.

Answer: A.

First of all: \(v^2+w^2+wv=0\) only for \(v=w=0\), so the same solution \(v=w\).

Next, \(x^{even}=y^{even}\) --> \(|x|=|y|\), because we should account for the possible negative values of \(x\) and \(y\). For example: if \(x^2=4=2^2=(-2)^2\) then \(|x|=2\) (x is 2 or -2), so the same way if \(x^{even}=y^{even}\) then \(|x|=|y|\);

Now, \(x^{odd}\) will have the same sign as \(x\) and \(y^{odd}\) will have the same sign as \(y\), so from \(x^{odd}=y^{odd}\) --> \(x=y\). For example: if \(x^3=(-3)^3\) then \(x=-3\), so the same way if \(x^{odd}=y^{odd}\) then \(x=y\).

Hope it's clear.
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Re: If w + k = v, what is the value of k ? [#permalink] If w + k = v, what is the value of k   26 Dec 2017, 01:47
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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.

Hence Answer is A
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Re: If w + k = v, what is the value of k ? [#permalink] If w + k = v, what is the value of k   27 Dec 2017, 05:55
Bunuel
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.

(A) is the answer.
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Re: If w + k = v, what is the value of k [#permalink] If w + k = v, what is the value of k   27 Feb 2023, 00:02
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