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

Question

(1) v^3 = w^3

(2) v^2 = w^2

Bunuel · Answer

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.

devinawilliam83 · Answer

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 · Answer

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.

GMATBusters · Answer

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

exc4libur · Answer

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

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

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