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# Which of the following has a value less than 1?

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Math Expert
Joined: 02 Sep 2009
Posts: 50000
Which of the following has a value less than 1?  [#permalink]

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17 Sep 2018, 23:57
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Difficulty:

5% (low)

Question Stats:

95% (00:35) correct 5% (00:46) wrong based on 44 sessions

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Which of the following has a value less than 1?

A. $$2(\frac{7}{13})$$

B. $$\frac{\sqrt{10}}{2}$$

C. $$\frac{2}{\sqrt{2}}$$

D. $$\frac{1}{\frac{1}{2}}$$

E. $$(\frac{9}{10})^2$$

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Re: Which of the following has a value less than 1?  [#permalink]

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18 Sep 2018, 00:27
1
Bunuel wrote:
Which of the following has a value less than 1?

A. $$2(\frac{7}{13})$$

B. $$\frac{\sqrt{10}}{2}$$

C. $$\frac{2}{\sqrt{2}}$$

D. $$\frac{1}{\frac{1}{2}}$$

E. $$(\frac{9}{10})^2$$

E
$$(\frac{9}{10})^2$$ = $$\frac{81}{100}$$ < 1
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Re: Which of the following has a value less than 1?  [#permalink]

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18 Sep 2018, 00:47
A. $$2+ \frac{7}{13} > 1$$ --> Out

B. $$\frac{\sqrt{10}}{2} > \frac{\sqrt{4}}{2} = 1$$ --> Out

C. $$\frac{2}{\sqrt{2}} = \sqrt{2} > 1$$ --> Out

D. $$\frac{1}{\frac{1}{2}} = \frac{1*2}{1} = 2 > 1$$ --> Out

E. $$(\frac{9}{10})^2 < 1^2 = 1$$ --> Winner.

Bunuel wrote:
Which of the following has a value less than 1?

A. $$2(\frac{7}{13})$$

B. $$\frac{\sqrt{10}}{2}$$

C. $$\frac{2}{\sqrt{2}}$$

D. $$\frac{1}{\frac{1}{2}}$$

E. $$(\frac{9}{10})^2$$

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Joined: 04 Jan 2015
Posts: 2066
Which of the following has a value less than 1?  [#permalink]

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18 Sep 2018, 03:28

Solution

To find:
• The option which has a value less than 1

Approach and Working:
• If the Numerator < Denominator, then $$\frac{N}{D} < 1$$ (Note D must be > 0)
• Option A: N = 14, D = 13, implies, N > D
• Option B: N = $$\sqrt{10} > 3$$, D = 2, implies, N > D
• Option C: N = 2, D = $$\sqrt{2}$$, implies, N > D
• Option D: $$N = 1, D = \frac{1}{2}$$, implies, N > D
• Option E: $$N = 9^2 = 81$$, $$D = 10^2 = 100$$, implies, N < D

Thus, the value of $$(\frac{9}{10})^2$$ is less than 1

Hence, the correct answer is option E

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Which of the following has a value less than 1? &nbs [#permalink] 18 Sep 2018, 03:28
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