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

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13 Nov 2012, 08:08
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.

I chose A as the answer as I thought since they mentioned only 4 of the numbers are equal to 75 so among the other 2, one must be less than 75 and another more than 75.

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

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13 Nov 2012, 08:18
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joylive 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.

I chose A as the answer as I thought since they mentioned only 4 of the numbers are equal to 75 so among the other 2, one must be less than 75 and another more than 75.

Merging similar topics. Please refer to the solution above.
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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
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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31 Jul 2015, 22:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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Rich
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Re: If the average (arithmetic mean) of 6 numbers is 75, how   [#permalink] 01 Aug 2015, 20:46
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