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# If the average (arithmetic mean) of 6 numbers is 75, how

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If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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26 Sep 2010, 06:10
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If the average (arithmetic mean) of 6 numbers is 75, how many of the numbers are greater than 75?

(1) Four of the numbers are equal to 75.
(2) One of the numbers is less than 75.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 13 Nov 2012, 08:13, edited 2 times in total.
Renamed the topic and edited the question.

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26 Sep 2010, 06:24
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rxs0005 wrote:
if the average of 6 numbers is 75 , how many of these numbers are > 75

four of the numbers are equal to 75

One of the numbers is less than 75

If the average (arithmetic mean) of 6 numbers is 75, how many of the numbers are greater than 75?

(1) Four of the numbers are equal to 75 --> either other two are also equal to 75, so we would have the following set {75, 75, 75, 75, 75, 75}, in this case zero numbers are more than 75 OR one of the numbers is more than 75 and another is less than 75 for example: {70, 75, 75, 75, 75, 80}, in this case one number is more than 75. Not sufficient.

(2) One of the numbers is less than 75. Clearly insufficient.

(1)+(2) Statement (2) leaves us with only second option from statement (1), so there is one number more than 75. Sufficient.

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26 Sep 2010, 06:36
If S1 stated 'only' 4 numbers are = 75 then would A be correct ?

As i made the mistake of assuming S1 as only 4 while its necessarily not the case
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26 Sep 2010, 06:38
rxs0005 wrote:
If S1 stated 'only' 4 numbers are = 75 then would A be correct ?

As i made the mistake of assuming S1 as only 4 while its necessarily not the case

Yes, if we were told that exactly 4 out of 6 numbers equal to 75 then statement (1) would be sufficient.
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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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22 Feb 2014, 06:43
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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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31 Jul 2015, 22:12
Hello from the GMAT Club BumpBot!

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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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01 Aug 2015, 20:46
Hi All,

This question is remarkably similar to a question found in the last few Official Guides:

In the OG13 and GMAT2015: page 288 #146
In the GMAT2016: page 292 #157

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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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03 Aug 2017, 07:50
rxs0005 wrote:
If the average (arithmetic mean) of 6 numbers is 75, how many of the numbers are greater than 75?

(1) Four of the numbers are equal to 75.
(2) One of the numbers is less than 75.

The question is really good, but the statement 1 creates confusion as to if 4 numbers are equal to 75 or exactly 4 numbers are equal to 75.... I don't think any such ambiguous question is asked in the exam as GMAT is renowned for clean questions. They are required to test QA skill and not ambiguity skill here. Many people have done mistake in this question just because of the language of statement 1 which justifies the ambiguity of the statement 1. If someone can give reference to similar question from OG it would be highly helpful (Do provide the GMAT Club link of the same). Bunuel can you throw some light in this regard.

Anyway we can write the solution as per the original answer as below :

AM of 6 numbers 75.
DS : How many numbers are greater than 75.

Statement 1 : 4 numbers are equal to 75.
We don't know about the other 2 numbers
2 possibilities : (a) one number is smaller than 75 and the other number is greater than 75 (b) Both numbers are equal to 75.
NOT SUFFICIENT

Statement 2 : One number is less than 75
We don't know about the other 5 numbers.
NOT SUFFICIENT

Combined :
one number is smaller than 75 and the other number is greater than 75
SUFFICIENT

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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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24 Aug 2017, 10:31
Hi - why is S2 not sufficient ...

is it because it doesnt confirm if "only" one number is below 75 ?

is that the reason...

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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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24 Aug 2017, 10:36
jabhatta@umail.iu.edu wrote:
Hi - why is S2 not sufficient ...

is it because it doesnt confirm if "only" one number is below 75 ?

is that the reason...

Yes but we also don't know know how many numbers are equal to 75.
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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink]

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25 Aug 2017, 10:40
This question is brilliant at testing DS.
It just took me around 4 minutes to solve this question.

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Re: If the average (arithmetic mean) of 6 numbers is 75, how   [#permalink] 25 Aug 2017, 10:40
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