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A set X={a_1, a_2, a_3, a_4, a_5} . . .

This topic has 1 expert reply and 0 member replies

A set X={a_1, a_2, a_3, a_4, a_5} . . .

Post Wed Nov 08, 2017 7:36 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A set $$X=\left\{a_1,\ a_2,\ a_3,\ a_4,\ a_5\right\}$$ with non-zero elements have mean M. What is the mean of the set $$Y=\left\{a_1-1,\ a_2-2,\ \ a_3-3,\ a_4+5,\ a_5+1\right\}?$$

    A. M-3
    B. M-2
    C. M-1
    D. M
    E. M+1

    The OA is D.

    Why the mean of Y is equal to the mean of X? How can I prove it? Experts, I need your help.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Nov 08, 2017 10:51 am
    Quote:
    A set $$X=\left\{a_1,\ a_2,\ a_3,\ a_4,\ a_5\right\}$$ with non-zero elements have mean M. What is the mean of the set $$Y=\left\{a_1-1,\ a_2-2,\ \ a_3-3,\ a_4+5,\ a_5+1\right\}?$$

    A. M-3
    B. M-2
    C. M-1
    D. M
    E. M+1

    The OA is D.

    Why the mean of Y is equal to the mean of X? How can I prove it? Experts, I need your help.
    Hi VJesus12,
    Let's take a look at your question.

    The mean of the set $$X=\left\{a_1,\ a_2,\ a_3,\ a_4,\ a_5\right\}$$ is M.
    We know that mean is equal to the sum of the values divided by the number of the values, therefore,
    $$M\ =\ \frac{a_1+a_2+a_3+a_4+a_5}{5}$$

    Now , lets find the mean of the set $$Y=\left\{a_1-1,\ a_2-2,\ \ a_3-3,\ a_4+5,\ a_5+1\right\}.$$
    $$Mean\ =\ \frac{\left(a_1-1\right)+\left(a_2-2\right)+\left(a_3-3\right)+\left(a_4+5\right)+\left(a_5+1\right)}{5}$$
    $$Mean\ =\ \frac{a_1-1+a_2-2+a_3-3+a_4+5+a_5+1}{5}$$
    $$Mean\ =\ \frac{a_1+a_2+a_3+a_4+a_5-1-2-3+5+1}{5}$$
    $$Mean\ =\ \frac{a_1+a_2+a_3+a_4+a_5-6+6}{5}$$
    $$Mean\ =\ \frac{a_1+a_2+a_3+a_4+a_5+0}{5}$$
    $$Mean\ =\ \frac{a_1+a_2+a_3+a_4+a_5}{5}$$
    Which is equal to the mean of the set $$X=\left\{a_1,\ a_2,\ a_3,\ a_4,\ a_5\right\}$$, i.e. M, therefore,
    $$Mean\ =\ M$$

    Therefore, Option D is correct.

    Hope it helps.
    I am available if you'd like any follow up.

    _________________
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