Which data set has the greater standard deviation, data set K or data set L?
(1) Every element in data set K is a multiple of 3.
(2) Every element in data set L is a multiple of 9.
OA E
Source: Magoosh
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Which data set has the greater standard deviation, data set
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BTGmoderatorDC
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Jay@ManhattanReview
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Certainly, each statement is not sufficient since each statement gives information about only one dataset.BTGmoderatorDC wrote:Which data set has the greater standard deviation, dataset K or dataset L?
(1) Every element in dataset K is a multiple of 3.
(2) Every element in dataset L is a multiple of 9.
OA E
Source: Magoosh
Combining the two statements, we get
Case 1: Say dataset K: {3, 3} and dataset L: {9, 18}
Standard deviation of dataset K = 0 since each element is the same; however, standard deviation of dataset L > 0 since each element is NOT same. The answer is dataset L.
Case 2: Say dataset K: {3, 6} and dataset L: {9, 9}
Standard deviation of dataset L = 0 since each element is the same; however, standard deviation of dataset K > 0 since each element is NOT same. The answer is dataset K.
No unique answer. Insufficient.
The correct answer: E
Hope this helps!
-Jay
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fskilnik@GMATH
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\[?\,\,:\,\,\,{\sigma _{\max }}\,\,\left( {K\,\,{\text{or}}\,\,L} \right)\]BTGmoderatorDC wrote:Which data set has the greater standard deviation, data set K or data set L?
(1) Every element in data set K is a multiple of 3.
(2) Every element in data set L is a multiple of 9.
Source: Magoosh
\[\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,{\text{K}} = \left\{ {0,0} \right\}\,\,\,;\,\,\,L = \left\{ {0,9} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = L \hfill \\
\,{\text{Take}}\,\,{\text{K}} = \left\{ {0,3} \right\}\,\,\,;\,\,\,L = \left\{ {0,0} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = K \hfill \\
\end{gathered} \right.\]
The correct answer is therefore (E).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
POST-MORTEM: in this very special situation, a careful reader may correctly mention that K=L={0} is enough to guarantee the correct answer is (E).
(We don´t want to explain this delicate issue here. We have just mentioned it because our own students will correctly think about that option at once!)
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Every element in data set K is a multiple of 3.BTGmoderatorDC wrote:Which data set has the greater standard deviation, data set K or data set L?
(1) Every element in data set K is a multiple of 3.
(2) Every element in data set L is a multiple of 9.
Since we don't know anything about set L, statement one alone is not sufficient.
Statement Two Alone:
Every element in data set L is a multiple of 9.
Since we don't know anything about set K, statement two alone is not sufficient.
Statements One and Two Together:
Even with both statements, it's still not sufficient to answer the question. For example, if set K is {3, 6} and set L is {9, 18}, then set L has a larger standard deviation (recall that numbers are further apart from one another produce a larger standard deviation). However, if set K is {3, 3} and set L is {9, 9}, then the standard deviation of set K and set L is equal, and it's 0 (recall that a set with all numbers the same has standard deviation of 0).
Answer: E
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