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Manager  Status: One last try =,=
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A store received 7 crates of oranges. What was the standard  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 66% (00:56) correct 34% (00:50) wrong based on 572 sessions

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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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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Posts: 61549
Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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18
6
vibhutijain wrote:
windofchange 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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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?

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

Hope it helps.
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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2
Bunuel wrote:
vibhutijain wrote:
windofchange 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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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?

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

Hope it helps.

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 .
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Intern  Joined: 18 Jul 2013
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Concentration: Entrepreneurship, Finance
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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1
windofchange 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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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?
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Joined: 24 Jun 2014
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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windofchange 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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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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
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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I was tricked into thinking (1) is sufficient with SD = 0.
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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anon12 wrote:
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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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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1
A great question indeed. Had the statement 1 mentioned "mean" instead of "median" the answer would have been D
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Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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Bunuel wrote:
vibhutijain wrote:
windofchange 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.

My approach:
Statement 1: The numbers of oranges in the 7 crates are n1, n2, n3, n4, n4, n4, n4, so we can't determine the SD. Hence insufficient.
Statement 2: We are given that the range of the numbers of oranges was 0, so can I say that all the numbers of oranges are of the same value? If it is the case, then the SD = 0. Sufficient.

Please confirm if my reasoning is correct.
Thank you.

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?

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

Hope it helps.

Bunuel I aggresively concluded in statement A that considering if median = greatest element of the set, then Set must be containing all equal elements. Can you please tell me how to think widely like you in such questions?
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Posts: 369
Re: A store received 7 crates of oranges. What was the standard  [#permalink]

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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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A store received 7 crates of oranges. What was the standard  [#permalink]

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warrior1991 wrote:
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???

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. A store received 7 crates of oranges. What was the standard   [#permalink] 10 Aug 2019, 09:32
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