If p + q = 2r + 3, what is the value of p?

St (1) p – r = 6, so if we put this back in the original question equation we get r-q+3=6 and that does not tell us the values of p. NS
St (2) r = (q/2) + 2, solving this we get 2r=q+4, so if we put this back in the original question equation we get p=4+3=7 Unique solution. S
Ans B

MAGOOSH OFFICIAL SOLUTION

Whenever the question stem presents you with an equation with multiple variables and asks you to solve for one of them, you should immediately rewrite the equation to find a more useful question. Specifically, you should isolate the variable you’re asked to solve for and then focus on the expression equal to that variable.

Here’s what that would look like for this problem:
p + q = 2r + 3

Subtract q from each side of the equation to isolate p.
p = 2r – q + 3

Because this is Data Sufficiency, ask, “What do I need to know to know the value of 2r – q + 3?” The answer to that question is simply “2r – q.”

Statement (1) includes p (which we don’t want) but not q (which we do want), so it is not sufficient. Eliminate A and D.

Turn to Statement (2) and try to isolate 2r – q.
r = (q/2) + 2

Multiply each side by 2 to clear the fraction.
2r = q + 4

Subtract q from each side to isolate 2r – q.
2r – q = 4

Statement (2) is sufficient.

The correct answer is B.

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