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

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

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05 Mar 2015, 09:53
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Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)?

(1) Q = 2
(2) P^2 + 4PQ + 4Q^2 = 28

Kudos for a correct solution.

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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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05 Mar 2015, 14:17
This is may be a C- TRAP question but here the answer is indeed B....

Data 1 ) : is obviously insufficient because there is no value given about P , so we can not determine the value of (p+2q)

Data 2 ) : if we raise the term ( P+2Q ) to power 2 and extend it we can get : p^2 + 4*Q ^2 + 4*P*Q , and data #2 tells us that this equation is equal to 28

So , we have : (P+2Q ) ^2 = 28 or : (p+2Q) = 28 ^(1/2 ) , this is exactly the thing that we are wanted to determine, so this data is sufficient and answer is B...
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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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05 Mar 2015, 14:40
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p^2+4pQ+4Q^2=28
(p+Q)(p+Q)=28
(p+Q)^2=sqrt 28
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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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05 Mar 2015, 16:31
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
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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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05 Mar 2015, 18:54
Bunuel wrote:
Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)?

(1) Q = 2
(2) P^2 + 4PQ + 4Q^2 = 28

Kudos for a correct solution.

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

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

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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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08 Mar 2015, 15:59
Bunuel wrote:
Given that (P + 2Q) is a positive number, what is the value of (P + 2Q)?

(1) Q = 2
(2) P^2 + 4PQ + 4Q^2 = 28

Kudos for a correct solution.

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.

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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q  [#permalink]

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06 Mar 2018, 09:42
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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Re: Given that (P + 2Q) is a positive number, what is the value of (P + 2Q   [#permalink] 06 Mar 2018, 09:42
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