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# x>0 and 2x/3<7

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x>0 and 2x/3<7 [#permalink]  07 Jun 2017, 00:52
Expert's post
00:00

Question Stats:

73% (00:47) correct 26% (00:32) wrong based on 46 sessions

$$x >0$$ and $$\frac{2x}{3} < 7$$

 Quantity A Quantity B $$x^2$$ $$100$$

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.
[Reveal] Spoiler: OA

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Kudos [?]: 1681 [1] , given: 8

Re: x>0 and 2x/3<7 [#permalink]  14 Jun 2017, 06:25
1
KUDOS
Expert's post
Carcass wrote:

$$x>0$$ and $$\frac{2x}{3}<7$$

 Quantity A Quantity B x^2 100

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.

Take: 2x/3 < 7
Multiply both sides by 3 to get: 2x < 21
Divide both sides by 2 to get: x < 10.5

We're also told that x > 0, which is the same as 0 < x

We can COMBINE the inequalities to get: 0 < x < 10.5
In other words, x is BETWEEN 0 and 10.5

We're comparing x² and 100
Let's PLUG IN some values for x

x = 1
We get:
Quantity A: 1² = 1
Quantity B: 100
Quantity B is greater

x = 10
We get:
Quantity A: 10² = 100
Quantity B: 100
The quantities are equal

[Reveal] Spoiler:
D

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Kudos [?]: 8 [0], given: 5

Re: x>0 and 2x/3<7 [#permalink]  11 Feb 2019, 20:26
2x/3 < 7
Solving further 2x < 21, hence x < 10.5

So 10.5<x>0

So we cant really determine the value of x

Re: x>0 and 2x/3<7   [#permalink] 11 Feb 2019, 20:26
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