GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Oct 2018, 15:52

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 10 Nov 2010
Posts: 196
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE: Information Technology (Computer Software)
If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

### Show Tags

21 Feb 2011, 09:40
5
21
00:00

Difficulty:

5% (low)

Question Stats:

79% (00:53) correct 21% (01:10) wrong based on 1311 sessions

### HideShow timer Statistics

If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

_________________

The proof of understanding is the ability to explain it.

Math Expert
Joined: 02 Sep 2009
Posts: 50000
Re: Average of 6 numbers  [#permalink]

### Show Tags

21 Feb 2011, 09:46
9
8
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

Given: sum of six numbers = 6*75

(1) None of the six numbers is less than 75 --> all 6 numbers must be 75, because if even one of them is more than 75 then the sum will be more than 6*75. Sufficient.

(2) None of the six numbers is greater than 75 --> the same here: all 6 numbers must be 75, because if even one of them is less than 75 then the sum will be less then than 6*75. Sufficient.

_________________
##### General Discussion
Director
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 514
Re: Average of 6 numbers  [#permalink]

### Show Tags

21 Feb 2011, 09:50
1
GMATD11 wrote:
104) If the average of six numbers is 75, how many of the numbers are equal to 75?

a) None of the six numbers is less than 75
b) None of the six numbers is greater than 75

a)none is less than 75 so all numbers are 75 as averagege is 75
b) Noe is greater than 75 so all numbers are 75 as average is 75. If any number become less than 75 then average will not 75 it will less than 75.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Senior Manager
Joined: 29 Jun 2017
Posts: 473
GPA: 4
WE: Engineering (Transportation)
Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

### Show Tags

17 Aug 2017, 05:10
sum of all numbers is 6*75 = 450

a1+a2+a3+a4+a5+a6 = 450

1) none is less than 75 , if any one will go more than 75 then other have to go less than 75 which is not possible, hence all must be 75, so A or D
2) none is more than 75, again if anyone is less than 75 then other have to more than 75 which is again not possible. so again all are 75 so D
Note this is because 75*6=450
_________________

Give Kudos for correct answer and/or if you like the solution.

Retired Moderator
Joined: 19 Mar 2014
Posts: 948
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

### Show Tags

18 Aug 2017, 14:48
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75?

$$Sum = 75 * 6$$

(1) None of the six numbers is less than 75.

If none of the six numbers is less than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (1) ===== is SUFFICIENT

(2) None of the six numbers is greater than 75.

If none of the six numbers is greater than 75, then we can have only one possibility that all the 6 numbers are 75

Hence, (2) ===== is SUFFICIENT

_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Director
Joined: 12 Nov 2016
Posts: 749
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

### Show Tags

10 Sep 2017, 21:51
GMATD11 wrote:
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

I actually found this to be a bit harder than a 500 level question but anyways 1 must be true on the same basis as 2 and vice versa. Logically, one of the numbers must be greater than 75 if any of the numbers are less than 75. If none of the six numbers are greater than 75 then all six numbers must be 75. The same holds true if none of the numbers are less than 75.

D
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3864
Location: United States (CA)
Re: If the average (arithmetic mean) of six numbers is 75, how  [#permalink]

### Show Tags

04 Apr 2018, 17:51
2
GMATD11 wrote:
If the average (arithmetic mean) of six numbers is 75, how many of the numbers are equal to 75 ?

(1) None of the six numbers is less than 75.
(2) None of the six numbers is greater than 75.

We are given that the average of 6 numbers in a list is 75. Using this information we see that the sum of the 6 numbers is 6 x 75 = 450. We need to determine how many numbers in the list are equal to 75.

Statement One Alone:

None of the six numbers is less than 75.

Recall that the sum of the 6 numbers is 6 x 75 = 450.

Using the information in statement one we know that all the numbers in the list must be greater than or equal to 75.

However, if any of the numbers in our list are greater than 75, we would need another number to be less than 75 in order for the 6 numbers to sum to 450.

For example, let’s say we had the following 6 numbers:

75, 75, 75, 75, 75, 76

The sum of these numbers is 451, which is greater than the required sum of 450.

The only way to get our list to sum to 450 is if one of the 75s were reduced to 74. However, this is not possible, according to the information provided in statement one. Thus, all the numbers in the list must equal 75. Statement one is sufficient to answer the question.

Statement Two Alone:

None of the six numbers is greater than 75.

We can apply similar logic to the information provided in statement two as we did with the information in statement one.

Once again, we know that the sum of the 6 numbers is 6 x 75 = 450.

Using the information in statement two we know that all the numbers in the list must be less than or equal to 75.

Thus, if any of the numbers in our list are less than 75, we would need another number to be greater than 75 in order for the 6 numbers to sum to 450.

For instance, let’s say we had the following 6 numbers:

75, 75, 75, 75, 75, 74

The sum of these numbers is 449, which is less than the required sum of 450.

The only way to get our list to sum to 450 is if one of the 75s were increased to 76. However, this is not possible, according to the information provided in statement two. Thus, all the numbers in the list must equal 75. Statement two is sufficient to answer the question.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Re: If the average (arithmetic mean) of six numbers is 75, how &nbs [#permalink] 04 Apr 2018, 17:51
Display posts from previous: Sort by