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If 3x + 2y = -2z, what is x?

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If 3x + 2y = -2z, what is x? [#permalink]

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New post 30 Sep 2017, 23:13
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (00:23) correct 50% (01:01) wrong based on 14 sessions

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If 3x + 2y = -2z, what is x?

1) x – y – z = 10

2) x + y + z = -2

[Reveal] Spoiler:
This is a question worth giving a try. Could not find it with the search option. So, posting here.Apologies if its already posted.
[Reveal] Spoiler: OA

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Re: If 3x + 2y = -2z, what is x? [#permalink]

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New post 30 Sep 2017, 23:48
I gave one glance at the question and options and marked C - three variables -
three equation required :(

Then realised
You have to find value only of x

Lesson learned don't rush through qstn even if qstn is from your strong topic


3x + 2y = -2z
3x + 2y + 2z = 0
3x + 2(y+z) =0

If you can express y+z in terms of x or constant
You can find x


1) x – y – z = 10

x+10= y+z

If you plug the value of y+z in original eqtn you get value of x

2) x + y + z = -2

y+z = -x-2

plug the value of y+z in original eqtn you get value of x

Hence answer can be derived using both
Option - D

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If 3x + 2y = -2z, what is x? [#permalink]

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New post 01 Oct 2017, 00:32
susheelh wrote:
If 3x + 2y = -2z, what is x?

1) x – y – z = 10

2) x + y + z = -2

[Reveal] Spoiler:
This is a question worth giving a try. Could not find it with the search option. So, posting here.Apologies if its already posted.


Statement 1: Multiply the equation by \(2\) to get \(2x-2y-2z=20\). Now substitute the value of \(-2z\) in this equation to get

\(2x-2y+3x+2y=20\), or \(x=4\). Sufficient

Statement 2: multiply the equation by \(-2\) to get \(-2x-2y-2z=4\). Now substitute the value of \(-2z\) in this equation to get

\(-2x-2y+3x+2y=4\), or \(x=4\). Sufficient

Option D
------------------------------------------
My rationale for multiplying the equation by \(2\) was that in the question stem RHS had -\(2z\). Hence tried by multiplying by \(2\) and it worked off very well. Then statement 2 was just a formality

Last edited by niks18 on 01 Oct 2017, 00:35, edited 2 times in total.

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If 3x + 2y = -2z, what is x? [#permalink]

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New post 01 Oct 2017, 00:32
Exactly akshata19, this is a traditional C trap questions. Seemingly innocent and simple. But vicious if we do not approach with care :-)


Veritas Official Explanation


In the system of equations above, you need to carefully leverage the given information. If you rearrange the given equation to match the statements, you will see that you can eliminate y and z with each statement alone. Remember: the goal in this problem is not to solve for all of the variables, just x.

For statement (1):

Given equation 3x + 2y +2z = 0
Statement (1) x – y – z = 10

Multiply bottom equation by 2 and combine:

3x + 2y +2z = 0
2x – 2y – 2z = 20

5x = 20 and x = 4 so statement (1) is sufficient.

For statement (2):

Given equation 3x + 2y +2z = 0
Statement (1) x + y + z = -2

Multiply bottom equation by -2 and combine:

3x + 2y +2z = 0
-2x – 2y – 2z = 4

x = 4 so statement (2) is also sufficient. The correct answer is (D).


akshata19 wrote:
I gave one glance at the question and options and marked C - three variables -
three equation required :(

Then realised
You have to find value only of x

Lesson learned don't rush through qstn even if qstn is from your strong topic


3x + 2y = -2z
3x + 2y + 2z = 0
3x + 2(y+z) =0

If you can express y+z in terms of x or constant
You can find x


1) x – y – z = 10

x+10= y+z

If you plug the value of y+z in original eqtn you get value of x

2) x + y + z = -2

y+z = -x-2

plug the value of y+z in original eqtn you get value of x

Hence answer can be derived using both
Option - D

Posted from my mobile device

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Re: If 3x + 2y = -2z, what is x? [#permalink]

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New post 01 Oct 2017, 04:23
susheelh wrote:
If 3x + 2y = -2z, what is x?

1) x – y – z = 10

2) x + y + z = -2

[Reveal] Spoiler:
This is a question worth giving a try. Could not find it with the search option. So, posting here.Apologies if its already posted.


Discussed here: https://gmatclub.com/forum/if-3x-2y-2z- ... 43209.html

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Re: If 3x + 2y = -2z, what is x?   [#permalink] 01 Oct 2017, 04:23
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