Which n would raise average to 55?

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LulaBrazilia: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue Mar 31, 2009 10:50 amFollowed by: 1 member

by LulaBrazilia » Tue Mar 11, 2014 7:01 pm

For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 unites raises the average to 55 units per day, what is the value of n?

A) 30
B) 18
C) 10
D) 9
E) 7

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Mar 11, 2014 7:11 pm

To bump the average up by 5 units, these 90 units will have to increase the total by 5n (5 extra unit for each previous day) + 55 (units for the new day). So we can write 90=5n+55, making n=7.

We could also solve by working backwards, testing answer choices to see which value of n fits the problem. The answer is E. I go through the question in detail in the full solution below (taken from the GMATFix App).

-Patrick

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Mar 11, 2014 9:24 pm

P/n = 50

P = 50n

(P+90)/(n+1) = 55

P + 90 = 55n + 55

50n = 55n - 35

5n = 35

n = 7
[spoiler]
{E}[/spoiler]

R A H U L

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Mar 11, 2014 10:21 pm

For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 units raises the average to 55 units per day, what is the value of n ?

(A) 30
(B) 18
(C) 10
(D) 9
(E) 7

This is a weighted average/mixture question.

Average for the first n days = 50.
Average for today = 90.
Average for the MIXTURE of all the days = 55.

To determine the value of n, use ALLIGATION.

Step 1: Plot the 3 averages on a number line, with the average for the first n days and that for today on the ends and the average for the mixture in the middle.
50----------------55----------------90

Step 2: Calculate the distances between the averages.
50--------5-------55--------35------90

Step 3: Determine the ratio in the mixture.
The required ratio of 50-unit days to 90-unit days is equal to the RECIPROCAL of the distances in red.
(50-unit days) : (90-unit days) = 35:5 = 7:1.

Thus, for every 1 day with 90 units, there must be 7 days with 50 units.
Thus, today's production of 90 units requires n=7 days with 50 units.

The correct answer is E.

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https://www.beatthegmat.com/ratios-fract ... 15365.html

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by [email protected] » Wed Mar 12, 2014 12:22 am

Hi LulaBrazilia,

While I'm a fan of the algebraic approach for this type of question (because it's just about using the "average formula" and doing a bit of algebra), you have other ways to get to the correct answer. You could TEST THE ANSWERS. Here's how:

One of the 5 answers must be the number of days that will "fit" the given information in the question stem and lead to the end result that's written.

Let's start with answer D...
If N = 9 then....
9(50) + 90 = 540 over 10 days
540/10 = average = 54

The prompt says that the average IS 55 though, so we're really close, but D is incorrect. It's got to be C or E.

Most people would say that Answer C looks easier to deal with, so we can test that one next....

If N=10 then...

10(50) + 90 = 590 over 11 days
590/11 = average = a little over 53....
This isn't the answer EITHER. The average appears to be getting smaller, so E is probably the correct answer.

If N=7 then....

7(50) + 90 = 440 over 8 days
440/8 = average = 55
THAT is the MATCH.

Final Answer:E

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

Contact Rich at [email protected]

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Wed Mar 12, 2014 9:54 am

LulaBrazilia wrote:For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 unites raises the average to 55 units per day, what is the value of n?

A) 30
B) 18
C) 10
D) 9
E) 7

55 ( n + 1) - 50 n = 90

55n + 55 - 50n = 90

5n + 55 = 90

5n = 35

Hence N = 7

Abhishek

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Tue Jul 28, 2015 2:09 pm

LulaBrazilia wrote:For the past n days, the average (arithmetic mean) daily production at a company was 50 units. If today's production of 90 unites raises the average to 55 units per day, what is the value of n?

A) 30
B) 18
C) 10
D) 9
E) 7

Solution:

We start with the formula for calculating the average.

average = sum/quantity

This is equivalent to saying:

sum = average x quantity

We are given that the initial quantity is n days and that the average for those n days is 50 units. We can use this to determine a sum for the n days:

sum = (50)(n) = 50n

We are next given that: today the production was 90 units. Thus, we can add "1" to the current quantity and "90" to the current sum. We are also given that this new average is 55 units per day. Substituting this information into the average formula we get:

55 = (50n + 90)/(n + 1)

55(n + 1) = 50n + 90

55n + 55 = 50n + 90

5n = 35

n = 7 days

The answer is E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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nikhilgmat31: Legendary Member; Posts: 518; Joined: Tue May 12, 2015 8:25 pm; Thanked: 10 times

by nikhilgmat31 » Tue Jul 28, 2015 11:55 pm

E
50n + 90 = 55(n+1)
5n = 35
n=7

Hope all the questions in real GMAT are like this

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