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2x + 1 > 3x + 2 and 5x + 2 > 4x
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Carcass
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Joined: 18 Apr 2015
Posts: 16944
GRE 1: Q160 V160
2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink] New post  17 Sep 2018, 20:29
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\(2x + 1 > 3x\) + 2 and \(5x + 2 > 4x\)

Quantity A
Quantity B
x
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Re: 2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink] New post  17 Sep 2018, 22:15
1
Carcass wrote:
\(2x + 1 > 3x\) + 2 and \(5x + 2 > 4x\)

Quantity A
Quantity B
x
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.



\(2x + 1 > 3x + 2\)

or \(x < -1\)


\(5x + 2 > 4x\)

or \(x > -2\)

Therefore \(-2 < x < -1\)

So, QTY A < QTY B
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GreenlightTestPrep
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Re: 2x + 1 > 3x + 2 and 5x + 2 > 4x [#permalink] New post  20 Sep 2018, 12:52
1
Expert Reply
Carcass wrote:
\(2x + 1 > 3x\) + 2 and \(5x + 2 > 4x\)

Quantity A
Quantity B
x
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Turns out that we can solve this with only the first inequality: 2x + 1 > 3x + 2

Take: 2x + 1 > 3x + 2
Subtract 2x from both sides: 1 > x + 2
Subtract 2 from both sides: -1 > x

Since x is less than -1, we can be certain that x is less than 1

Answer: B

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