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

Question

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.

Bunuel · Accepted Answer

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.

rxs0005 · Answer

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

Bunuel · Answer

Yes, if we were told that exactly 4 out of 6 numbers equal to 75 then statement (1) would be sufficient.

EMPOWERgmatRichC · Answer

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

GMAT assassins aren't born, they're made,
Rich

shashankism · Answer

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

Answer C

jabhatta2 · Answer

Hi - why is S2 not sufficient ...

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

is that the reason...

Bunuel · Answer

Yes but we also don't know know how many numbers are equal to 75.

amitpandey25 · Answer

This question is brilliant at testing DS.
It just took me around 4 minutes to solve this question.

ravigupta2912 · Answer

I got confused with statement 2 -- if it means -- exactly one number is less than 75 or that one of the six numbers is less than 75.

jabhatta2 · Answer

Hi bunuel

Have you seen any gmatprep or OG questions actually testing this concept ?

this doesn't seem like a logic or reasoning question but more of a discrepancy like question

Could you perhaps give an example of a gmat prep or OG question testing something like this

Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi jabhatta@umail.iu.edu, This question is remarkably similar to a question found in the last few Official Guides (going all the way back to the OG13). In the two most recent versions, the question can be found here: GMAT2019 pg. 286 DS #396 GMAT2020 pg. 293 DS #452 GMAT assassins aren't born, they're made, Rich

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

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