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# 6 < x < 7

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6 < x < 7 [#permalink]  03 May 2015, 00:39
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Question Stats:

75% (00:39) correct 25% (01:23) wrong based on 24 sessions

$$6 < x < 7$$

$$y=8$$

 Quantity A Quantity B $$\frac{x}{y}$$ $$0.85$$

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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Joined: 07 Jun 2014
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Re: 6 < x < 7 [#permalink]  26 Jan 2017, 08:10
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Expert's post
Explanation

Let us assume 2 values of X such that they can cover the whole range $$6 < x < 7$$.

X= 6.001 and X=6.999 and Y=8.

Now evaluating cases individually.

 X 6.001 6.999 Y 8 8 $$\frac{X}{Y}$$ 0.750125 0.874875

Now the first case is clearly Quantity B is greater and in second case Quantity A is Greater.

Hence option D is correct.
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Re: GRE Math Challenge #55- 6 < x < 7 and y = 8 [#permalink]  21 Feb 2018, 03:35
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Explanation

Picking numbers between six and seven such as 6.5 and A is 0.81 which is < b.

But if we consider 6.9 A is 0.86 which is > B.

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Re: GRE Math Challenge #55- 6 < x < 7 and y = 8 [#permalink]  24 Feb 2018, 17:37
D
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Re: GRE Math Challenge #55- 6 < x < 7 and y = 8 [#permalink]  04 Mar 2018, 02:39
picking extreme values, such as 6.1/8 and 6.9/8
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Re: 6 < x < 7 [#permalink]  13 Feb 2019, 13:45
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Carcass wrote:

6 < x < 7 ; y=8

 Quantity A Quantity B $$\frac{x}{y}$$ $$0.85$$

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.

Let's test some possible cases

case i: x = 6.1 and y = 8
We get:
QUANTITY A: 6.5/8 = 0.763
QUANTITY B: 0.85
In this case, Quantity B is greater than Quantity A

case ii: x = 6.9 and y = 8
We get:
QUANTITY A: 6.9/8 = 0.863
QUANTITY B: 0.85
In this case, Quantity A is greater than Quantity B

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Re: 6 < x < 7 [#permalink]  20 Feb 2019, 22:45
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For these kinds of problems, we know that x cannot be 6 or 7, but it can be infinitely close to them. Often, then, you can just use x = 6 and x = 7 in your calculations. Then, when you get your answer, know that the real answer is slightly above or below that value.

For instance, $$\frac{7}{8}$$ = 0.875. Thus, $$\frac{x}{y}$$ can be infinitely close to 0.875. It is slightly less than 0.875, but it could be 0.874999, which is clearly more than 0.85.

Just a trick to do faster calculations, so you don't have to calculate something like $$\frac{6.99}{8}$$. You can round after the calculation instead of before.
Re: 6 < x < 7   [#permalink] 20 Feb 2019, 22:45
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# 6 < x < 7

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