Given that (P + 2Q) is a positive number, what is the value of (P + 2Q

For the first time, i can also post an answer....hope it is right

Stmt 1- Q = 2,
If Q = 2, we can prove that it is not sufficient to answer the target question, we can test some choices
If Q =2, and P = 4, then our answer is 8
If Q = 2, and P = 6, then our answer is 10
Insufficient
Stmt 2 -

Do a reverse FOIL and you get (p+2q) (p+2q) = 28
And the question stem tells us that (p+2q) is a positive number so no need that gives us enough information to prove sufficiency

Statement 1:
P + 2Q can take on multiple positive values
Insufficient

Statement 2:
(p+2q)(p+2q)=28
p+2q=sqrt(28)
Sufficient

Answer: B

MAGOOSH OFFICIAL SOLUTION:

The prompt tells us that (P + 2Q) is a positive number, and we want to know the value of P. Remember number properties! We don’t know that (P + 2Q) is a positive integer, just a positive number of some kind.

Statement #1: Q = 2
Obvious, by itself, this tells us zilch about P. Alone and by itself, this statement is completely insufficient.

Statement #2: P^2 + 4PQ + 4Q^2 = 28

Now, this may be a pattern-recognition stretch for some folks, but this is simply the “Square of a Sum” pattern. It may be clearer if we re-write it like this:
P^2 + 2*P*(2Q) + (2Q)^2 = 28

This is now the “Square of a Sum” pattern, with P in the role of A and 2Q in the role of B. Of course, this should equal the square of the sum:
P^2 + 2*P*(2Q) + (2Q)^2 = (P + 2Q)^2 = 28

All we have to do is take a square root. Normally, we would have to consider both the positive and the negative square root, but since the prompt guarantees that (P + 2Q) is a positive number, we need only consider the positive root:
(P + 2Q) = sqrt{28}

This statement allows us to determine the unique value of (P + 2Q), so this statement, alone and by itself, is sufficient.

Answer = B

A is insufficient , as in the statement it is mentioned P+2Q is +ve number
B. That is in the formula of (a+b)^2 (a2+b2+2ab) = 28^2 , solving this we get a value.

Hence B is suff .

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