Last visit was: 13 Jun 2024, 23:48 It is currently 13 Jun 2024, 23:48
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: Sub 505 Level,    Statistics and Sets Problems,                                        
Show Tags
Hide Tags
User avatar
Manager
Manager
Joined: 10 Nov 2010
Posts: 129
Own Kudos [?]: 2642 [111]
Given Kudos: 22
Location: India
Concentration: Strategy, Operations
GMAT 1: 520 Q42 V19
GMAT 2: 540 Q44 V21
WE:Information Technology (Computer Software)
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93696
Own Kudos [?]: 631599 [45]
Given Kudos: 82279
Send PM
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19013
Own Kudos [?]: 22400 [16]
Given Kudos: 286
Location: United States (CA)
Send PM
General Discussion
Director
Director
Joined: 14 Jul 2010
Status:No dream is too large, no dreamer is too small
Posts: 966
Own Kudos [?]: 4987 [3]
Given Kudos: 690
Concentration: Accounting
Send PM
Re: Average of 6 numbers [#permalink]
2
Kudos
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.
User avatar
Manager
Manager
Joined: 24 Mar 2011
Posts: 228
Own Kudos [?]: 730 [3]
Given Kudos: 20
Location: Texas
Send PM
Re: If the average of six numbers is 75, how many of the numbers are equal [#permalink]
3
Kudos
The easiest way to answer this is just by looking at statements, you dont need to actually solve the statement -

there are 6 numbers and average of them is 75. Meaning you will immediately think that some are lower than 75 and some are higher... to get the average of 75. 75 CANNOT be the 1st of 6 numbers OR last of 6 numbers.

but if you now see st-1 ==> None of 6 numbers is less than 75 meaning 75 is 1st in the list of 6 numbers... to get the average now ALL numbers have to be 75.

St - 2 ==> same explanation.

So answer is D.
User avatar
Senior Manager
Senior Manager
Joined: 03 Mar 2010
Posts: 257
Own Kudos [?]: 1388 [5]
Given Kudos: 22
Send PM
Re: If the average of six numbers is 75, how many of the numbers are equal [#permalink]
3
Kudos
2
Bookmarks
1) None of the six number is less than 75
1) 5(75) + (75+x) = 6(75) + x, which is greater than (6)(75), contrary to the fact that sum is equal to 6*75.
it is using indirect proof method.

See it this way, let 5 numbers be all 75 and 6th number be x.
75+75+75+75+75+x =375+x----(1)
and Sum of 6 numbers all 75 is 6*75=450-----(2)
Equating
375+x=450
x=75
Now suppose 5 numbers are all 76 and 6th number is x
5*76+x=380+x
Again equating
380+x=450
x=70 which contradicts statement 1 i.e None of the six number is less than 75


2) None of the six numbers is greater than 75
2) 5(75) + (75-x) = 6(75) -x, which is less than 6*75, contrary to the fact that sum is equal to 6*75

Again, let 5 numbers be all 75 and 6th number be x.
75+75+75+75+75+x =375+x----(1)
and Sum of 6 numbers all 75 is 6*75=450-----(2)
Equating
375+x=450
x=75
Now suppose 5 numbers are all 74 and 6th number is x
5*74+x=370+x
Again equating
370+x=450
x=80 which contradicts statement 2 i.e None of the six numbers is greater than 75

OA. D.
Retired Moderator
Joined: 19 Mar 2014
Posts: 817
Own Kudos [?]: 974 [1]
Given Kudos: 199
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Send PM
Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]
1
Kudos
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

Hence, Answer is D
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6814
Own Kudos [?]: 30534 [2]
Given Kudos: 799
Location: Canada
Send PM
If the average (arithmetic mean) of six numbers is 75, how [#permalink]
2
Bookmarks
Expert Reply
Top Contributor
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.


Target question: How many of the numbers are equal to 75 ?

Given: The average (arithmetic mean) of six numbers is 75

Statement 1: None of the six numbers is less than 75
One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is less than 75, AND the average is 75
Notice that if we increase ANY of the 6 values, the resulting average will be greater than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is all 6 numbers are equal to 75
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: None of the six numbers is greater than 75.
One possible scenario is that the 6 number are {75, 75, 75, 75, 75, 75}. This satisfies the conditions that none of the six numbers is greater than 75, AND the average is 75
Notice that if we decrease ANY of the 6 values, the resulting average will be less than 75
So, it must be the case that the 6 number are {75, 75, 75, 75, 75, 75}.
The answer to the target question is all 6 numbers are equal to 75
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

RELATED VIDEO FROM OUR COURSE
Tutor
Joined: 17 Jul 2019
Posts: 1304
Own Kudos [?]: 2137 [6]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Send PM
Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]
6
Kudos
Expert Reply
Video solution from Quant Reasoning:
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5230
Own Kudos [?]: 4066 [0]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]
GMATD11

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.
All numbers are 75.
SUFFICIENT

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

IMO D
GMAT Club Bot
Re: If the average (arithmetic mean) of six numbers is 75, how [#permalink]
Moderator:
Math Expert
93696 posts