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The mean of twenty-five consecutive positive integers. . .

This topic has 3 expert replies and 0 member replies

The mean of twenty-five consecutive positive integers. . .

Post Mon Nov 06, 2017 6:29 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The mean of twenty-five consecutive positive integers numbers is what percent of the total?

    (A) 4%

    (B) 5%

    (C) 20%

    (D) 25%

    (E) Cannot be determined by the information provided.

    The OA is A.

    I can't understand why the correct answer is A. It shouldn't be D? Experts, can you clarify this for me?

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    Post Mon Nov 06, 2017 7:49 am
    Hello M7MBA.

    The mean of 25 consecutive positive integers is: $$M=\frac{a_1+a_2+.\ .\ .\ +\ a_{25}}{25}.$$

    The total is: $$T=a_1+a_2+.\ .\ .\ +\ a_{25}.$$

    So, the mean can be write as follows:

    $$M=\frac{1}{25}\cdot T=\frac{4}{100}\cdot T=4\%\cdot T.$$

    So, the mean is the 4% of the total.

    So, the correct answer is A.

    I hope this can help you.

    Feel free to ask me again if you have any doubt.

    Regards.

    _________________
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    Post Fri Nov 10, 2017 4:05 pm
    M7MBA wrote:
    The mean of twenty-five consecutive positive integers numbers is what percent of the total?

    (A) 4%

    (B) 5%

    (C) 20%

    (D) 25%

    (E) Cannot be determined by the information provided.
    ----------ASIDE----------------------
    There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
    For example, in each of the following sets, the mean and median are equal:
    {7, 9, 11, 13, 15}
    {-1, 4, 9, 14}
    {3, 4, 5, 6}
    ------------------
    For this question, let x = first value
    So, x+1 = second value
    x+2 = third value
    .
    .
    .
    x+24 = last value

    This means x+12 is the median AND the mode

    Since x+12 = the mean of the 25 numbers, we can conclude that (25)(x+12 ) = the SUM of the 25 numbers

    The mean of twenty-five consecutive positive integers numbers is what percent of the total?
    We must convert (x+12)/(25)(x+12) to a PERCENT
    (x+12)/(25)(x+12) = 1/25
    = 4/100
    = 4%
    Answer: A

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    Post Sat Nov 11, 2017 4:14 am
    M7MBA wrote:
    The mean of twenty-five consecutive positive integers numbers is what percent of the total?

    (A) 4%

    (B) 5%

    (C) 20%

    (D) 25%

    (E) Cannot be determined by the information provided.
    The question stem asks for the following value:
    (mean)/(sum) * 100.

    For any evenly spaced set:
    Sum = (count)(mean).

    Here, there are 25 consecutive integers, implying a count of 25.

    Case 1: mean = 20
    In this case:
    sum = (count)(mean) = (25)(20) = 500.
    (mean/sum) * 100 = (20/500) * 100 = 4%.

    Case 2: mean = 40
    In this case:
    sum = (count)(mean) = (25)(40) = 1000.
    (mean/sum) * 100 = (40/1000) * 100 = 4%.

    In each case, the mean is 4% of the sum.

    The correct answer is A.

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