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Quant Chat Moderator
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Concentration: Strategy, Leadership
If the 5 numbers listed above are denoted
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29 Dec 2023, 10:47
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\(-\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}, \quad -\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}, \quad-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}, \quad -\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}},\quad -1\)
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
Screenshot 2023-12-29 230800.png [ 76.08 KiB | Viewed 4178 times ]
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
Attachment:
Screenshot 2023-12-29 230800.png [ 76.08 KiB | Viewed 4178 times ]
Re: If the 5 numbers listed above are denoted
[#permalink]
29 Dec 2023, 11:07
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gmatophobia wrote:
\(-\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}, \quad -\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}, \quad-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}, \quad -\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}},\quad -1\)
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
Attachment:
Screenshot 2023-12-29 230800.png
Let us simplify each
\(-\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}= -\frac{1}{\sqrt{\frac{1}{3}}}=-\sqrt{3}, \quad -\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}= -{\sqrt{\frac{1}{5}}}, \quad-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}= -{\sqrt{\frac{1}{3}}}, \quad -\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}= -\frac{1}{\sqrt{\frac{1}{5}}}=-\sqrt{5},\quad -1\)
Let us compare these negative numbers
\(-\sqrt{5}<-\sqrt{3}<-1<\sqrt{\frac{1}{3}}<-\sqrt{\frac{1}{5}}\)
Thus \(x_4=\sqrt{\frac{1}{3}}\)
The related term is \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
C
General Discussion
Intern
Joined: 27 Dec 2022
Posts: 32
Given Kudos: 230
Location: India
If the 5 numbers listed above are denoted
[#permalink]
Updated on: 15 Jun 2024, 00:39
chetan2u wrote:
gmatophobia wrote:
\(-\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}, \quad -\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}, \quad-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}, \quad -\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}},\quad -1\)
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
If the 5 numbers listed above are denoted \(x_1, x_2, x_3, x_4,\) and \(x_5\), so that \(x_1 < x_2 < x_3 < x_4 < x_5,\) what is the value of \(x_4\) ?
A. \(\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}\)
B. \(-\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}\)
C. \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
D. \(-\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}\)
E. -1
Attachment:
Screenshot 2023-12-29 230800.png
Let us simplify each
\(-\frac{\sqrt{\frac{1}{3}}}{\frac{1}{3}}= -\frac{1}{\sqrt{\frac{1}{3}}}=-\sqrt{3}, \quad -\frac{\frac{1}{5}}{\sqrt{\frac{1}{5}}}= -{\sqrt{\frac{1}{5}}}, \quad-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}= -{\sqrt{\frac{1}{3}}}, \quad -\frac{\sqrt{\frac{1}{5}}}{\frac{1}{5}}= -\frac{1}{\sqrt{\frac{1}{5}}}=-\sqrt{5},\quad -1\)
Let us compare these negative numbers
\(-\sqrt{5}<-\sqrt{3}<-1<\sqrt{\frac{1}{3}}<-\sqrt{\frac{1}{5}}\)
Thus \(x_4=\sqrt{\frac{1}{3}}\)
The related term is \(-\frac{\frac{1}{3}}{\sqrt{\frac{1}{3}}}\)
gmatophobia I think there will be a "-" sign in front of the 1st option A. thanks
Originally posted by ShilpiAgnihotrii on 03 May 2024, 07:02.
Last edited by ShilpiAgnihotrii on 15 Jun 2024, 00:39, edited 4 times in total.
Last edited by ShilpiAgnihotrii on 15 Jun 2024, 00:39, edited 4 times in total.