What is the value of m + n? (1) jm + kn + nj + km = 36 (2) j + k = 12

Statement 1:

--> jm + kn + nj + km = 36

--> j (m+n) + k(m+n) = 36

--> (j+k) (m+n) = 36

j and k are unknown - Insufficient

Statement 2:

--> j + k = 12

This statement alone does not tell us anything about m + n . Therefore insufficient

Statements 1 and 2 together

--> (j+k) (m+n) = 36

--> 12 * (m+n) = 36

We can determine m+ n. Therefore answer = C

VERITAS PREP OFFICIAL SOLUTION:

If you were given statement (1) alone, it is clearly insufficient, and you would have no idea what to do with it. It is a whole bunch of variables with no clear organization. Statement (2) is also clearly insufficient as the question asks about m + n, and the statement tells you about j + k. For our purposes, though, it serves as a fantastic clue: If you can get the j and k terms together, you can replace them with a number, leaving just m and n.

So that’s your catalyst to do some more algebraic manipulation:

(1) jm + kn + nj + km = 36

Rearrange the order to get like terms together: jm + km + kn + nj = 36

Factor out the m and n: m(j + k) + n (k + j) = 36 and complete the factoring to show that:

(m + n)(j + k) = 36

Using the information from statement (2), replace the (j + k) terms with 12: 12 (m + n) = 36

Divide by 12, and we have an answer: (m + n) = 3

If you don’t use statement (2) as a hint, you could easily miss this and pick answer choice E, as the testmakers want you to do. While it seems like there is not enough information to solve this, there really is, but you will only discover that if you leverage statement (2). Once you do, you will see that answer choice C is correct.

Just have one question. If the values of both m and n is zero, then wouldn't combining the statements be useless? shouldnt question say something like m+n>0 for the solution to be valid?

(1) says that jm + kn + nj + km = 36 ((m + n)(j + k) = 36). Now, if m and n equal 0, then jm + kn + nj + km would equal 0, not 36, so this case is not possible.

ooooh...okay. Thanks!

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