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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] New post 26 Sep 2010, 05:10
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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, 07:13, edited 2 times in total.
Renamed the topic and edited the question.
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Re: Average [#permalink] New post 26 Sep 2010, 05:24
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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.

Answer: C.
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Re: Average [#permalink] New post 26 Sep 2010, 05:36
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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Re: Average [#permalink] New post 26 Sep 2010, 05:38
Expert's post
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] New post 13 Nov 2012, 07:08
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.

Why is the answer C?
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Re: If the average (arithmetic mean) of 6 numbers is 75 [#permalink] New post 13 Nov 2012, 07:18
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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.

Why is the answer C?


Merging similar topics. Please refer to the solution above.
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COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If the average (arithmetic mean) of 6 numbers is 75, how [#permalink] New post 22 Feb 2014, 05:43
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Re: If the average (arithmetic mean) of 6 numbers is 75, how   [#permalink] 22 Feb 2014, 05:43
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