What is the value of j + k?

VERITAS PREP OFFICIAL SOLUTION

Solution: B.

While statement 1 may look sufficient at first, recognize that m could be 0 and the statement would be satisfied regardless of j and k. For example, j could be 9 and k could be 11, but if m is 0 the equation would be: 0(9) + 0(11) = 2(0). If m is not 0, then j + k must equal 2, as you could simply divide both sides by m to get j + k = 2. Because you can get multiple answers to the question, statement 1 is not sufficient.

Statement 2 is sufficient, as you can divide both sides by 5 to get j + k = 2. And remember to ask “Why Are You Here?” for statement 2. The fact that statement 2 is quite clearly sufficient should demonstrate to you that the difficulty in this question lies within statement 1. Statement 2 here is an invitation to go back and spend more time on statement 1 if you inadvertently just divided both sides by m and called it “sufficient”.

What is the value of j + k?

(1) mj + mk = 2m
(2) 5j + 5k = 10


State(1) m(j+k) = 2*m
case 1 - if m is not zero, j+k = 2
case 2 - if m = 0 , j+k may or may not be equal to 2.
So NOT Sufficient.

State(2) 5j+5k = 10
5*(j+k) = 10
j+k = 2
Sufficient.

Answer - B

m in the first statement can be 0 or 1, not sufficient. 2nd is clear, so answer choice B.

I've always loved this one as an example of "if the two statements seem to be essentially the same, it's on you to find out why the small difference matters." Statement 2 is dead easy and Statement 1 is essentially the same, so especially if you think you should be seeing hard questions on test day you'll want to take time to ask "why is it different if I'm using m instead of 5?" And of course with 5 you know 5 isn't 0...but with m there's the possibility that it's 0, which would mean that j + k could be anything.

A big lesson: if the statements seem too similar to be true, try to really dig in on why the difference would matter.

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