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Which n would raise average to 55?

This topic has 4 expert replies and 3 member replies
LulaBrazilia Master | Next Rank: 500 Posts Default Avatar
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Which n would raise average to 55?

Post Tue Mar 11, 2014 7:01 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post 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).



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    theCodeToGMAT Legendary Member
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    Post 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

    {E}

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    R A H U L

    Post Tue Mar 11, 2014 10:21 pm
    Quote:
    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.

    For two similar problems, check here:

    http://www.beatthegmat.com/ratios-fraction-problem-t115365.html

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    Post 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

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    Abhishek009 Master | Next Rank: 500 Posts
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    Post 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

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    Post 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

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    nikhilgmat31 Legendary Member Default Avatar
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    Post 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 Smile

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