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x>0 and 2x/3<7

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x>0 and 2x/3<7 [#permalink] New post 07 Jun 2017, 00:52
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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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Re: x>0 and 2x/3<7 [#permalink] New post 14 Jun 2017, 06:25
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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

Answer:
[Reveal] Spoiler:
D


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Re: x>0 and 2x/3<7 [#permalink] New post 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

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