OG - 2nd Edition - Question 106

[shanice]

If kmn is not equal to 0, is x/m(m^2 + n^2 + k^2) = xm + yn + zk?

(1) z/k=x/m
(2) x/m=y/n

Answer is C - Both statements together are sufficient.

I need you guys to check out my workings and clear my doubts below:-


Stem - xm^2+xn^2+xk^2=xm^2+ynm+zkm
xm^2-xm^2+xn^2+xk^2=ynm+zkm
xn^2+xk^2=ynm+zkm

Statement 1 - zm=xk
Therefore, xn^2+xk^2=ynm+xk^2
xn^2+xk^2-xk^2=ynm
xn^2=ynm
xn=ym (I arrived at this answer but I don't understand how to use the
answer to decide on the validity of the statement. Does xn=xn is
considered sufficient bcoz it has to be the same or xn=ym is
considered insufficient bcoz the variables are not the same?)


Statement 2 - x/n=y/n

xn^2+xk^2=ynm+zkm
ymn-ymn+xk^2=zkm
xk^2=zkm
xk=zm (same problem as per the 1st statement)

Each statement is insufficient in the OG but both is sufficient.

I don't understand the function of "kmn not equal to 0" in this question and the requirement of this question. So confused.

I really hope someone could help me to clear my doubts. I really want to score good marks in my GMAT. In between, I took a long time to type this. Pleaseeee help!

[Anurag@Gurome]

Statement 1 - zm=xk
Therefore, xn^2+xk^2=ynm+xk^2
xn^2+xk^2-xk^2=ynm
xn^2=ynm
xn=ym (I arrived at this answer but I don't understand how to use the
answer to decide on the validity of the statement. Does xn=xn is
considered sufficient bcoz it has to be the same or xn=ym is
considered insufficient bcoz the variables are not the same?)
You cannot do this because you are assuming x/m(m^2 + n^2 + k^2) = xm + yn + zk
Same for statement 2.

I don't understand the function of "kmn not equal to 0"

This means none of k, m, and n are equal to zero.

If x/m(m^2 + n^2 + k^2) = xm + yn + zk, then as you have derived (xn^2 + xk^2) must be equal to (ynm + zkm)

Now from statement 1, zm = xk --> zkm = xk^2 (as k ≠ 0)
But we don't know whether xn^2 is equal to ynm or not.
Not sufficient

Similarly from statement 2, ym = xn --> ynm = xn^2 (as n ≠ 0)
But we don't know whether xk^2 is equal to zkm or not.
Not sufficient

Combining both the statements, we know that zkm = xk^2 and ynm = xn^2 (as n ≠ 0)
Hence, sufficient

The correct answer is C.

[shanice]

Actually, I understand the meaning of k,m and n are not equal to 0. It's just that I didn't know how to apply it in the question.But thanks to you, Sir, you've cleared my doubts.

Thank you,again, Sir.

[leumas]

There is a typo. Correct answer is 'C'

Statement 1 - zm=xk
Therefore, xn^2+xk^2=ynm+xk^2
xn^2+xk^2-xk^2=ynm
xn^2=ynm
xn=ym (I arrived at this answer but I don't understand how to use the
answer to decide on the validity of the statement. Does xn=xn is
considered sufficient bcoz it has to be the same or xn=ym is
considered insufficient bcoz the variables are not the same?)
You cannot do this because you are assuming x/m(m^2 + n^2 + k^2) = xm + yn + zk
Same for statement 2.

I don't understand the function of "kmn not equal to 0"

This means none of k, m, and n are equal to zero.

If x/m(m^2 + n^2 + k^2) = xm + yn + zk, then as you have derived (xn^2 + xk^2) must be equal to (ynm + zkm)

Now from statement 1, zm = xk --> zkm = xk^2 (as k ≠ 0)
But we don't know whether xn^2 is equal to ynm or not.
Not sufficient

Similarly from statement 2, ym = xn --> ynm = xn^2 (as n ≠ 0)
But we don't know whether xk^2 is equal to zkm or not.
Not sufficient

Combining both the statements, we know that zkm = xk^2 and ynm = xn^2 (as n ≠ 0)
Hence, sufficient

The correct answer is E.