If n + k = m, what is the value of k ?

For Statement 1: N=10

10+K=M, (K&M, are too many #'s, NOT SUFF)

For Statement 2: M+10=N
-10 -10 (subtract -10 on each side)
M = N-10
-N -N (subtract N, to Isolate M & N)
M-N = -10 This is can be solved.

Statement 2: SUFF:

We are given that n + k = m, and we need to determine the value of k. Since we know that n + k = m, we know that k = m – n. Thus, if we determine a value for m – n, we will know the value of k.

Statement One Alone:

n = 10

Although we know that n = 10, without knowing the value of m, we cannot determine the value of k. Statement one alone is not sufficient. We can eliminate answer choices A and D.

Statement Two Alone:

m + 10 = n

Manipulating statement two we get:

m + 10 = n

m – n = -10

Since we know that m – n = -10, we know that k = -10. Statement two alone is sufficient.

The answer is B.

This is an easy question on simple equations. From the question stem, we know that n+k = m. Since we are finding the value of k, we will try to express k in terms of the other variables i.e.

k = m -n

From this, it’s clear that we need the value of m-n, to find the value of k.

From statement I alone, n = 10. Since we do not have the value of m, statement I alone is insufficient.
Answer options A and D can be eliminated, the possible answer options are B, C or E.

From statement II alone, m + 10 = n. Therefore, m = n – 10. Substituting this in the equation for k, we have,
k = n – 10 – n = -10. This is a definite value for k.

Statement II alone is sufficient to find a unique value for k. Answer options C and E can be eliminated since statement II is sufficient when taken individually.
The correct answer option is B.

In a DS question on equations, the variable whose value we are trying to calculate should always be kept on the LHS while everything else can be transferred to the RHS (this is a good practice in general too for all DS questions). This will give you a very clear idea of what data you have to look for, in the statements, to be able to solve the question.

Hope that helps!

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.