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In Episode 3 of our GMAT Ninja Critical Reasoning series, we tackle Discrepancy, Paradox, and Explain an Oddity questions. You know the feeling: the passage gives you two facts that seem completely contradictory....- May 08
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![Let W = {-x, -x, -x, x, x, x}[/m] and [m]T = {-y, 0, 0, 0](/forum/styles/gmatclub_light/imageset/icon_post_target_unread.svg "Let W = {-x, -x, -x, x, x, x}[/m] and [m]T = {-y, 0, 0, 0"){kind=icon}
12 Apr 2026, 11:32
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A
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47% (02:53) correct
53%
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Let W = {-x, -x, -x, x, x, x} and T = {-y, 0, 0, 0, 0, 0, y}
If the standard deviation of set \(W\) is 4 times the standard deviation of set \(T\), what is \(x\) in terms of \(y\)?
A) \(\frac{4y\sqrt{14}}{7}\)
B) \(\frac{4y\sqrt{7}}{7}\)
C) \(\frac{2y\sqrt{14}}{7}\)
D) \(\frac{4y}{\sqrt{7}}\)
E) \(\frac{y\sqrt{14}}{7}\)
If the standard deviation of set \(W\) is 4 times the standard deviation of set \(T\), what is \(x\) in terms of \(y\)?
A) \(\frac{4y\sqrt{14}}{7}\)
B) \(\frac{4y\sqrt{7}}{7}\)
C) \(\frac{2y\sqrt{14}}{7}\)
D) \(\frac{4y}{\sqrt{7}}\)
E) \(\frac{y\sqrt{14}}{7}\)
17 Apr 2026, 12:48
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kevincan
SD in a gist:
\(1)\) Find the mean of the elements.
\(2)\) Subtract the mean from each of the elements.
\(3)\) Square the results in step \(2\).
\(4)\) Again find the mean of the squared results in step \(3\). ( this is known as the variance )
\(5)\) Take square root of the mean obtained in step \(4\) ( variance ) this is the SD.
Mean of W \(= 0\)
Subtracting from mean, and then squaring each and then adding them \(= 6x^2\)
Mean of the squares \(= x^2\) ( variance)
SD \(= x\) ( square root of variance )
Mean of T \(= 0\)
Subtracting from mean, and then squaring each and then adding them \(= 2y^2 \)
Mean of the squares =\(\frac{2y^2}{7}\) ( variance)
SD \( = \sqrt\frac{2y^2}{7}\)
Given \( x= 4 \sqrt\frac{2y^2}{7}\)
\(x= 4y \frac{ \sqrt2 \sqrt7}{\sqrt7 \sqrt7}\) (rationalizing)
\(x= \frac{4}{7}y\sqrt{14}\)
Ans A
Hope it helped.
