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If x – y > 6 and 2x + y > 30, then which one represents all possible v

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Carcass
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If x – y > 6 and 2x + y > 30, then which one represents all possible v [#permalink] New post   07 Dec 2021, 08:06
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If x – y > 6 and 2x + y > 30, then which one represents all possible values of x ?

A. x > 6
B. 6 < x < 18
C. x > 12
D. 12 < x < 36
E. x > 36
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C
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GreenlightTestPrep
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible v [#permalink] New post   07 Dec 2021, 08:33
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Carcass wrote:
If x – y > 6 and 2x + y > 30, then which one represents all possible values of x ?

A. x > 6
B. 6 < x < 18
C. x > 12
D. 12 < x < 36
E. x > 36


Key property: If we have two inequalities with the inequality symbols facing the SAME direction, we can ADD the two inequalities.

Given:
x – y > 6
2x + y > 30

Since the inequality symbols are facing the SAME direction, we can ADD the two inequalities to get: 3x > 36
Divide both sides by 3 to get: x > 12

Answer: C
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible v [#permalink] New post   07 Dec 2021, 09:02
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When given two inequalities, you can always rearrange them so that the inequality points the same direction and then add them. In this case, the work has been done for us because they're already the same direction.

That is, we simply need to add the two inequalities:

x – y > 6
2x + y > 30
-------------
3x + 0 > 36

==> x > 12

Simple as that.

Answer C.
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Re: If x y > 6 and 2x + y > 30, then which one represents all possible v [#permalink] New post   23 Apr 2022, 18:49
If x – y > 6 and 2x + y > 30, then which one represents all possible values of x ?

Add both inequalities
x - y > 6
2x + y > 30
3x > 36
x > 12 (Correct Answer: C)
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gmatclubot
Re: If x y > 6 and 2x + y > 30, then which one represents all possible v [#permalink]
23 Apr 2022, 18:49
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