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# GRE Math Challenge #5-If y - 3x > 12 and x - y > 38

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GRE Math Challenge #5-If y - 3x > 12 and x - y > 38 [#permalink]  02 Sep 2014, 03:17
Expert's post
If $$y - 3x > 12$$ and $$x - y > 38$$, which of the following are possible values of x?

Indicate all such values.

A)-60
B)-30
C)-6
D)4
E)20
F)30

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Re: GRE Math Challenge #5 [#permalink]  03 Sep 2014, 22:43
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A,B
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Re: GRE Math Challenge #5 [#permalink]  01 Nov 2014, 10:59
How to solve this ?
Care to elaborate ple
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Re: GRE Math Challenge #5 [#permalink]  05 Nov 2014, 00:27
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Expert's post
$$y-3x > 12$$
$$x-y > 38$$

Adding them together , the term y cancels out leaving the following equation

$$-2x > 50$$
Now it is just a matter of plugging in the options. So only $$x= -30, -60$$ are the plausible choices.
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Re: GRE Math Challenge #5-If y - 3x > 12 and x - y > 38 [#permalink]  03 Sep 2018, 17:12
y - 3x > 12 ==> y > 3x + 12
x - y > 38 ==> y< x - 38
so we get 3x + 12 < X - 38 ==> x < -25

so the answer is A, B
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Re: GRE Math Challenge #5-If y - 3x > 12 and x - y > 38 [#permalink]  20 Jan 2019, 09:48
Expert's post
soumya1989 wrote:
If $$y - 3x > 12$$ and $$x - y > 38$$, which of the following are possible values of x?

Indicate all such values.

A)-60
B)-30
C)-6
D)4
E)20
F)30

GIVEN:
y - 3x > 12
x - y > 38

To make things easier to follow, let's rewrite the bottom inequality as follows:
y - 3x > 12
-y + x > 38

Since the two inequality symbols are facing the SAME direction, we can ADD the inequalities.
When we do so, we get: -2x > 50
Divide both sides by -2 to get: x < -25 [when we divide both sides of an inequality by a NEGATIVE number, we must REVERSE the direction of the inequality symbol]

So, any value of x that is LESS THAN -25 will be correct.

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Re: GRE Math Challenge #5-If y - 3x > 12 and x - y > 38   [#permalink] 20 Jan 2019, 09:48
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