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Standard deviation of the number of oranges in 7 crates

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by gmattesttaker2 » Mon Jun 02, 2014 10:07 pm
Hello,

Can you please help with this:

A store received 7 crates of oranges. What was the standard deviation of the numbers of oranges in the 7 crates?

(1) For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
(2) For the 7 crates of oranges, the range of the numbers of oranges was 0.

OA: B

Thanks a lot,
Sri
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by moumi2013 » Mon Jun 02, 2014 11:56 pm
Lets arrange the crates in order (no. of oranges in each crate, crate1 having the smallest number and crate7 having the largest number of oranges)

Crate1,Crate2,Crate3,Crate4,Crate5,Crate6,Crate7

From Statement -I
number in crate4=median
any number less than what is present in crate4=number in crate1,crate2,crate3 respectively
number in crate5,crate6,crate7=same as number in crate4 (the median of the numbers of oranges was equal to the greatest of the numbers of oranges)

We don't have enough information about the numbers in crate1,crate2,crate3
INSUFFICIENT

From Statement -II
Range=0 , So all the crates have same number of oranges.
So Standard Deviation=0
SUFFICIENT

Answer: B
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by Brent@GMATPrepNow » Tue Jun 03, 2014 2:43 am
gmattesttaker2 wrote:
A store received 7 crates of oranges. What was the standard deviation of the numbers of oranges in the 7 crates?

(1) For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
(2) For the 7 crates of oranges, the range of the numbers of oranges was 0.
Aside: When solving questions involving standard deviation, always be on the lookout for scenarios where the standard deviation is zero. These are scenarios where all the values in a set are equal.


Target question: What was the standard deviation of the numbers of oranges in the 7 crates?

Statement 1: For the 7 crates of oranges, the median of the numbers of oranges was equal to the greatest of the numbers of oranges.
There are several sets of numbers that satisfy this condition. Here are two:
Case a: the 7 values are {2, 2, 2, 2, 2, 2, 2} in which case the standard deviation equals 0
Case b: the 7 values are {1, 1, 2, 2, 2, 2, 2} in which case the standard deviation does not equal 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: For the 7 crates of oranges, the range of the numbers of oranges was 0.
If the range = 0, then all 7 values are equal, which means the standard deviation equals 0
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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