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

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Bunuel
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If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink] New post  20 Nov 2018, 01:07
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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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BrentGMATPrepNow
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If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink] New post  Updated on: 07 Dec 2021, 09:33
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Bunuel 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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Originally posted by BrentGMATPrepNow on 05 Sep 2021, 06:43.
Last edited by BrentGMATPrepNow on 07 Dec 2021, 09:33, edited 1 time in total.
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink] New post  20 Nov 2018, 01:37
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Bunuel 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


add 2 inequalities......

x - y>6
2x + y >30
........................................
3x >36

x>12.

C is our answer.
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink] New post  05 Sep 2021, 07:21
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Bunuel 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


We are allowed to add inequalities in the same direction, adding them together gives \(3x > 36\) and \(x > 12\).

We may also isolate y and chain the inequalities. \(x + 6 > y\) and \(y > 30 - 2x\) gives us \(x + 6 > 30 - 2x\), similarly it gives us \(x > 12\).

Ans: C
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink] New post  06 Sep 2021, 00:32
Adding both equations: 3x > 36 or x > 12

Answer C
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Re: If x – y > 6 and 2x + y > 30, then which one represents all possible [#permalink]
06 Sep 2021, 00:32
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