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What is the value of x + 3y + 7?

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vivaslluis
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What is the value of x + 3y + 7? [#permalink] New post   Updated on: 24 Jul 2016, 10:31
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What is the value of x + 3y + 7?

(1) x - 3y = 0
(2) x^2 + 4y^2=0
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B

Originally posted by vivaslluis on 30 Oct 2010, 11:04.
Last edited by Bunuel on 24 Jul 2016, 10:31, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: What is the value of x + 3y + 7? [#permalink] New post   30 Oct 2010, 12:42
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vivaslluis wrote:
Hi,

Question: What is the value of x+3y+7?
(1) X - 3Y = 0
(2) X^2 + 4Y^2=0


Statement 1 is not sufficient, since while we can work out that x = 3y, which means we're trying to work out the value of 6y + 7, we don't have any information about the value of y. It might be that x = y = 0, in which case x + 3y + 7 = 7, or it might be that x = 3 and y = 1, in which case x + 3y + 7 = 13, among many other possibilities.

From Statement 2, since x^2 and y^2 are both squares, they can never be negative; each must be at least zero. The only way for x^2 + 4y^2 = 0 to be true then is if x^2 and y^2 are both zero, in which case x = 0 and y = 0. So Statement 2 is sufficient, and the answer is B.
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Yalephd
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Re: What is the value of x + 3y + 7? [#permalink] New post   30 Oct 2010, 18:10
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vivaslluis wrote:
Hi,

Question: What is the value of x+3y+7?
(1) X - 3Y = 0
(2) X^2 + 4Y^2=0


I think it's B because X^2 + 4Y^2=0 only when X = 0 and Y = 0.
Therefore x+3y+7 = 7
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Re: What is the value of x + 3y + 7? [#permalink] New post   24 Oct 2017, 03:24
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x + 3y + 7 = ?

(1) x - 3y = 0
=> x = 3y

Hence, x + 3y + 7 = 6y + 7

Now, the value of y can be anything.
If y = 1, x + 3y + 7 = 13; if y = -1, x + 3y + 7 = 1. Hence, Insuff.

(2) x^2 + 4y^2=0
x and y can be -ve, 0, or +ve.

Now if any of either x or y is either -ve or +ve, then (x^2 + 4y^2) > 0
The only values that satisfies (x^2 + 4y^2) = 0 is x = 0, and y = 0.
Hence, x and y must be equals to 0. So, x + 3y + 7 = 7. Sufficient.

Ans: B.
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Re: What is the value of x + 3y + 7? [#permalink] New post   30 Oct 2010, 16:37
Thank you Ian.
IMO the right answer was E but I found out OA = B. However I didn't have any explanation why it was B and not E.

Thanks again
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Re: What is the value of x + 3y + 7? [#permalink] New post   09 Jun 2023, 07:38
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vivaslluis wrote:
What is the value of x + 3y + 7?

(1) x - 3y = 0
(2) x^2 + 4y^2=0

Solution:
Pre Analysis:
  • We are asked the value of \(x+3y+7\)

Statement 1: \(x - 3y = 0\)
  • According to this statement, \(x=3y\)
  • So, \(x+3y+7=3y+3y+7=6y+7\)
  • We cannot get the value of \(6y+7\) without the value of \(y\)
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: \(x^2 + 4y^2=0\)
  • As soon as we see \(x^2 + 4y^2=0\), we should be able to make an implicit inference that \(x=y=0\)
    • Because both \(x^2\) and \(4y^2\) has to be non negative and only way their sum is 0 is if \(x=y=0\)

  • Another way to observe this is looking at \(x^2=-4y^2\) which means \(x^2\) is negative which is not possible unless \(x=y=0\)

  • Anyways, if \(x=y=0\), then \(x+3y+7=7\)

Hence the right answer is Option B
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Re: What is the value of x + 3y + 7? [#permalink]
09 Jun 2023, 07:38
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Bunuel
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