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earnit
Joined: 06 Mar 2014
Last visit: 21 Dec 2016
Posts: 161
Given Kudos: 84
Location: India
Schools: INSEAD Jan '16 Tepper '16 ISB '16 Simon '18 (A)
GMAT Date: 04-30-2015
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06 May 2015, 14:10
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:32) correct
24%
(01:32)
wrong
based on 33
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Is the standard deviation of the set (10-4x, 10-2x, 10, 10+2x, 10+4x) greater than the greatest element of the set?
1) x>0
2) x<0
1) x>0
2) x<0
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06 May 2015, 20:02
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See the attached table.
The given set is set of evenly spaced numbers. Its very easy to find the SD of evenly spaced numbers by drawing a table.
You will see that SD of this set is 2\(\sqrt{2}\) x
Statement 1 : When X > 0 10+4x is the greatest element of set S and you are comparing it with 2\(\sqrt{2}\) x . Obviously 10+4x is greater. Suff
Statement 2 : When X < 0 10 - 4x is the greatest element of set S and you are comparing it with 2\(\sqrt{2}\) x . Obviously 10- 4x is greater. Suff
Answer is D
Ambarish
The given set is set of evenly spaced numbers. Its very easy to find the SD of evenly spaced numbers by drawing a table.
You will see that SD of this set is 2\(\sqrt{2}\) x
Statement 1 : When X > 0 10+4x is the greatest element of set S and you are comparing it with 2\(\sqrt{2}\) x . Obviously 10+4x is greater. Suff
Statement 2 : When X < 0 10 - 4x is the greatest element of set S and you are comparing it with 2\(\sqrt{2}\) x . Obviously 10- 4x is greater. Suff
Answer is D
Ambarish
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sd.jpg [ 26.31 KiB | Viewed 7341 times ]
06 May 2015, 21:33
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earnit
First of all, note that this question is incorrect. You cannot have contradictory statements. Both statements should hold simultaneously. x cannot be less than 0 and greater than 0 at the same time.
That said, what is SD? It quantifies the amount of deviation from the mean. The deviations are 4x, 2x, 0, 2x and 4x. The standard deviation will certainly be less than the highest deviation which is 4x. So in any case, 10 + 4x will be greater than 4x (assuming x is positive).
