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a = 4 6 < b < 8

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sandy
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a = 4 6 < b < 8 [#permalink] New post   04 Mar 2018, 13:50
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\(a = 4\)
\(6 < b < 8\)

Quantity A
Quantity B
0.6
\(\frac{a}{b}\)


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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D
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sandy
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Re: a = 4 6 < b < 8 [#permalink] New post   04 Mar 2018, 14:19
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Explanation

Start by combining the 2 given equations:
If \(a = 4\) and \(6 < b < 8\), then the acceptable range for \(\frac{a}{b}\) is \(\frac{4}{6}>\frac{a}{b}>\frac{4}{8}\), which can be reduced to or, in decimal form, \(0.5 <\frac{a}{b}< 0.67\).

Select choice (D) because can be either larger or smaller than 0.6.
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Re: a = 4 6 < b < 8 [#permalink] New post   05 Mar 2018, 18:26
1
answer D
we calculate the minimum and maximum of a/b
min : 4/8 = 1/2 with is less than 0.6
max : 4/6 = 2/3 with is more than 0.6

also, we have:
6<b<8
1/8 < 1/b < 1/6
a/8 < a/b < a/6
4/8 < a/b < 4/6
1/2 < a/b < 2/3
so the range of a/b is less than 0.6 from 1/2 to 0.6 and is more than 0.6 from 0.6 to 2/3 and thus D is correct.
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Re: a = 4 6 < b < 8 [#permalink] New post   09 Mar 2018, 07:21
1
Here, you just need to put extremes i.e:

4/8 < a/b < 4/6

As calculator is available in GRE, so you will see clearly, value of a/b will exists between 0.5 and 0.666

Thus choice D correct.
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Re: a = 4 6 < b < 8 [#permalink] New post   15 Apr 2023, 23:03
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Re: a = 4 6 < b < 8 [#permalink]
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