A store received 7 crates of oranges. What was the standard

That's not true. Consider: {1, 1, 1, 2, 2, 2, 2} --> median=2=greatest.

Hope it helps.
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Its a very tricky concept , Even I commited mistake assuming its works similar to mean . If it was for Mean = greatest no then , the answer would have been D .
GMAT tricks with these very fine line of difference in concept.

Thanks Bunuel .

but in statement 1 it is given that median is equal to the greatest no so definitely all will be equal hence SD should be 0 so this statement is also sufficient kindly clear my doubt?

My reasoning is as follows

set ={a,b,c,5,5,5,5}where 5 is the median as well as the highest number of oranges in crate.
Hence it can't be determined. Nothing about about lowest value in set i.e a
I is insufficient.

But from II it is known 5-a=0, so all the crates had same number of oranges, sufficient to see SD =0

Statement 1 - Insufficient
There are 2 possibilities
- Set {a, b, c, n, n, n, n}. We cannot know the SD
- Set {n, n, n, n, n, n, n}. SD = 0

Statement 2 - Sufficient
- Set {n, n, n, n, n, n, n}. SD = 0

Hence, option B

I was tricked into thinking (1) is sufficient with SD = 0.

thats why you'd take some notes and then you'll see it


1, 1, 1, 4, 4, 4, 4

1, 2, 5, 50, 50 50, 50
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A great question indeed. Had the statement 1 mentioned "mean" instead of "median" the answer would have been D

AjiteshArun chetan2u Maxximus

In St:1 --- What if it were given that " the MEAN of the numbers of oranges was equal to the greatest of the numbers of oranges."

Had it been correct?? If yes, how???
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warrior1991 I figured it out by putting some numbers eg. 1+2+3/3 average 2 , but 3+3+3/3 average 3
1+4+4/3 average 3 , but 4+4+4/3 average 4
so I guess in order for the mean to be equal with the greatest of the numbers then all the numbers have to be the same , thus statement 1 would be enough.

The above seems right but i guess we need an expert to give his opinion on the matter.

HI Bunuel,

Please add the tag as GMATPrep EP1
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Done. Thank you!
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Hi,
If it was for Mean = greatest no in a) then the answer would have been D?

Key concept: The standard deviation of a set of values is zero if and only if all of the values in the set are equal

Given: A store received 7 crates of oranges.

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 many different scenarios that satisfy statement 1. Here are two:
Case a: The number of oranges in each of the seven crates is {9,9,9,9,9,9,9}. In this case, the answer to the target question is the standard deviation of the numbers of oranges in the 7 crates is 0
Case b: The number of oranges in each of the seven crates is {2,2,2,9,9,9,9}. In this case, the answer to the target question is the standard deviation of the numbers of oranges in the 7 crates is NOT 0
Since we can’t 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 equals 0, then (biggest number in the set) - (smallest number in the set) = 0, which means all of the numbers in the set must be equal.
If all of the numbers in the set are the same, then the standard deviation of the set must be zero
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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