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For which of the following values of y is 2/3^y greatest?

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Bunuel
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For which of the following values of y is 2/3^y greatest? [#permalink] New post   24 Jun 2017, 08:39
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For which of the following values of y is \(\frac{2}{3^y}\) greatest?

A. 0
B. 1/2
C. 1
D. 3/2
E. 2
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A
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For which of the following values of y is 2/3^y greatest? [#permalink] New post   24 Jun 2017, 08:43
Bunuel wrote:
For which of the following values of y is \(\frac{2}{3^y}\) greatest?

A. 0
B. 1/2
C. 1
D. 3/2
E. 2


Lowest the denominator, greatest will be the fraction.

Given , \(\frac{2}{3^y}\) . When \(y = 0\), denominator would become 1.

\(\frac{2}{3^0}\) = \(\frac{2}{1}\) \(= 2\). Answer (A) ...
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Re: For which of the following values of y is 2/3^y greatest? [#permalink] New post   24 Jun 2017, 09:54
The answer option for which the expression \(\frac{2}{3^y}\) is greatest,
is y=0(because the expression is a fraction, which is biggest when the denominator is 1)

Of the answer options, Option A(y = 0) has the highest value of y.
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Re: For which of the following values of y is 2/3^y greatest? [#permalink] New post   24 Jun 2017, 20:54
Bunuel wrote:
For which of the following values of y is \(\frac{2}{3^y}\) greatest?

A. 0
B. 1/2
C. 1
D. 3/2
E. 2


For any value of \(y\), \(\frac{2}{3^{y}}\) will be a fraction with \(denominator > numerator\), except for \(y = 0\), hence Ans - A.
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Re: For which of the following values of y is 2/3^y greatest? [#permalink] New post   25 Jun 2017, 04:46
choice A gives the value of \(\frac{2}{3^y}\) as 2.
Other choices give a value of less than 2 as denominator is greater than numerator, hence A is the answer
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Re: For which of the following values of y is 2/3^y greatest? [#permalink] New post   25 Jun 2017, 06:15
For the value of \(\frac{2}{3^y}\) to be the greatest the denominator has to be the least.

We need to find the value of y for which \(3^y\) is the least. Let us check the options
1. y=0 => \(3^y\)=1
2. y=1/2 => \(3^y\)=\(\sqrt{3}\) = 1.732
3. y=1 => \(3^y\)=3
4. y=3/2 => \(3^y\)=\(\sqrt{3}^3\) > 1.732
5. y=2 => \(3^y\)=9

So for y=0, the value of \(3^y\) is the least and consequently the value of \(\frac{2}{3^y}\) is the greatest.

Answer A
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Re: For which of the following values of y is 2/3^y greatest? [#permalink]
25 Jun 2017, 06:15
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