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Suppose 3p + 4q = 11. Then what is the value of q?

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Re: Suppose 3p + 4q = 11. Then what is the value of q? [#permalink]
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Bunuel wrote:
Suppose 3p + 4q = 11. Then what is the value of q?

(1) p is prime.
(2) q = –2p

Target question: What is the value of q?

Given: 3p + 4q = 11

Statement 1: p is prime
Let's test some cases:
Case a: p = 2. Take 3p + 4q = 11 and replace p with 2 to get: 3(2) + 4q = 11. When we solve this, we get q = 1.25
Case b: p = 3. Take 3p + 4q = 11 and replace p with 2 to get: 3(3) + 4q = 11. When we solve this, we get q = 0.5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: q = –2p
Divide both sides by -2 to get: p = -0.5q
Now take 3p + 4q = 11 and replace p with 0.5q to get: 3(-0.5q) + 4q = 11.
Expand: -1.5q + 4q = 11
Simplify: 2.5q = 11
Solve: q = 4.4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Suppose 3p + 4q = 11. Then what is the value of q? [#permalink]
3p+4q=11. What is q?

Statement 1. p is prime. so p can be 2, 3, 5, 7, 11, ...
with every new value of p, there will be a new value of q. Infinite values possible. Insufficient

Statement 2. q=-2p Or p=-q/2
We can substitute this in original equation. 3(-q/2) + 4q = 11
5q/2 = 11 or q=22/5. Sufficient

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Re: Suppose 3p + 4q = 11. Then what is the value of q? [#permalink]
Straight forward,

S1, p can be any prime no. which can give infinite values of q. Insufficient.
S2, q = -2p will give a definite value of p and q. Sufficient.

Option B is correct.
Re: Suppose 3p + 4q = 11. Then what is the value of q? [#permalink]
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