Last visit was: 13 Jul 2024, 12:15 It is currently 13 Jul 2024, 12:15
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

The average (arithmetic mean) length per film for a group of 21 films

SORT BY:
Tags:
Show Tags
Hide Tags
Tutor
Joined: 10 Jul 2015
Status:Expert GMAT, GRE, and LSAT Tutor / Coach
Affiliations: Harvard University, A.B. with honors in Government, 2002
Posts: 1181
Own Kudos [?]: 2438 [147]
Given Kudos: 273
Location: United States (CO)
Age: 44
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169

GRE 2: Q170 V170
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11468
Own Kudos [?]: 34279 [59]
Given Kudos: 322
Alum
Joined: 12 Aug 2015
Posts: 2272
Own Kudos [?]: 3195 [28]
Given Kudos: 893
GRE 1: Q169 V154
General Discussion
Tutor
Joined: 10 Jul 2015
Status:Expert GMAT, GRE, and LSAT Tutor / Coach
Affiliations: Harvard University, A.B. with honors in Government, 2002
Posts: 1181
Own Kudos [?]: 2438 [5]
Given Kudos: 273
Location: United States (CO)
Age: 44
GMAT 1: 770 Q47 V48
GMAT 2: 730 Q44 V47
GMAT 3: 750 Q50 V42
GMAT 4: 730 Q48 V42 (Online)
GRE 1: Q168 V169

GRE 2: Q170 V170
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
4
Kudos
1
Bookmarks
Logic tells us that the average length per film will go down, so we can eliminate all answers that add to the original average of t. That leaves either B or E. When executing the algebra, the key step is being able to quickly and easily turn one fraction with two numerators $$(\frac{21t-14}{21})$$ into two fractions with one numerator each $$(\frac{21t}{21}-\frac{14}{21})$$.

Above is a visual that should help.

Originally posted by mcelroytutoring on 05 May 2016, 19:28.
Last edited by mcelroytutoring on 06 May 2016, 12:30, edited 6 times in total.
Wharton Moderator
Joined: 30 May 2015
Posts: 32
Own Kudos [?]: 33 [5]
Given Kudos: 103
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
4
Kudos
1
Bookmarks
average = sum of numbers/total number
t = s/21
s = 21t
Now as per question
s =21t -66 +52
s = 21t - 14
New average
t1 = (21t - 14) / 21
=> t - 2/3
VP
Joined: 09 Mar 2016
Posts: 1143
Own Kudos [?]: 1024 [1]
Given Kudos: 3851
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
1
Kudos
stonecold wrote:
Great Solutions above.
Here is my solution =>
Average length = t minutes
Sum(21) = 21t
New sum = 21t-66+52 = 21t-14
Hence new mean = 21t-14 / 21 = t-2/3

Hence B

stonecold how from this 21t-14 / 21 you got t-2/3 , I understand you divided by 7 , but there are two 21 could you write in detail
CEO
Joined: 26 Feb 2016
Posts: 2865
Own Kudos [?]: 5307 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
1
Kudos
dave13 wrote:
stonecold wrote:
Great Solutions above.
Here is my solution =>
Average length = t minutes
Sum(21) = 21t
New sum = 21t-66+52 = 21t-14
Hence new mean = 21t-14 / 21 = t-2/3

Hence B

stonecold how from this 21t-14 / 21 you got t-2/3 , I understand you divided by 7 , but there are two 21 could you write in detail

Hey dave13

$$\frac{21t-14}{21} = \frac{21t}{21} - \frac{14}{21} = t - \frac{2}{3}$$

Hope that helps
Manager
Joined: 10 Apr 2018
Posts: 185
Own Kudos [?]: 456 [0]
Given Kudos: 115
Location: United States (NC)
The average (arithmetic mean) length per film for a group of 21 films [#permalink]
Hi,
Understanding averages conceptually requires some imagination.

Say we have group A and their combined strength is x
we have two persons B and C with different strength Let the strength of B> C,

Now if strength of person B is same as strength of Group A , and the person B is added to group A then then the overall strength of group A along with B does not change

However if we added Person C to the group A in place of B, then the overall strength of group would not increase for sure .

So u see how we can reject choices A, C, D ,and the two choices we are having at hand are B and E.

So in situation of time crunch, where we guess the answer choices, we need to increase our odds of getting it right. Choices A,C,D if marked show conceptual gap in understanding averages.

We can use deviation technique to solve such type of questions. The answer would be in less than 30 Secs

refer: https://gmatclub.com/forum/a-student-s- ... l#p2113194

So new average would be
t-(14/21)
t-2/3
Hence B.

Originally posted by Probus on 15 Aug 2018, 16:09.
Last edited by Probus on 15 Oct 2019, 13:12, edited 1 time in total.
Intern
Joined: 28 Sep 2020
Posts: 15
Own Kudos [?]: 3 [0]
Given Kudos: 49
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
let's consider the fraction before the number we want to switch a constant X. Because this fraction is intact when changing the 66 by the 51, we will have the following formula:

X+66/21-66/21+52/21=T+52/21-66/21

this will be X+ 52/21=T-2/3

so it is the answer B
VP
Joined: 11 Aug 2020
Posts: 1247
Own Kudos [?]: 207 [0]
Given Kudos: 332
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
Just want to understand this further, what happens if we do the opposite and add a film that is 14 minutes longer?

The answer then would be t + 14/21 = t + 2/3 correct?

So basically the main idea for these types of questions is

We either add or subtract | x - y | / average to the original average (x is the original term, y is the new term).
Intern
Joined: 01 Sep 2020
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 17
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
For me personally, this seems really tricky for a sub-600 question. Any experts want to comment if this is something to expect in the 500-600 range?
Director
Joined: 29 Apr 2019
Status:Learning
Posts: 729
Own Kudos [?]: 588 [0]
Given Kudos: 49
The average (arithmetic mean) length per film for a group of 21 films [#permalink]
The average (arithmetic mean) length per film for a group of 21 films is t minutes = ($$21*t$$)

If a film that runs for 66 minutes is removed from the group and replaced by one that runs for 52 minutes = (66-52)

what is the average length per film, in minutes, for the new group of films, in terms of t?

New Film =$$\frac{ [21t - (66-52)] }{ 21}$$ = $$\frac{21t}{21}$$ - $$\frac{14}{21}$$ = $$t$$ - $$\frac{2}{3}$$ = Option B
Non-Human User
Joined: 09 Sep 2013
Posts: 33963
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: The average (arithmetic mean) length per film for a group of 21 films [#permalink]
Moderator:
Math Expert
94339 posts