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Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above,

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sandy

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Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above, [#permalink]

Updated on: 10 Jun 2021, 08:36

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Question Stats:

25% (01:33) correct

75% (01:19) wrong

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Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21}
In Set A above, if positive integer x is subtracted from the 3 largest numbers in the list and x is added to the 3 smallest even numbers in the list, which of the following will be true ?

A. The average of the set will increase by x.
B. The average of the set will decrease by x.
C. The average of the set will stay the same.
D. There will be no mode in the new set.
E. The standard deviation of the set will stay the same.
F. The median of the set will stay the same.
G. The median of the set will increase by x.

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Originally posted by sandy on 08 Dec 2017, 20:47.
Last edited by Carcass on 10 Jun 2021, 08:36, edited 1 time in total.

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sandy

Retired Moderator

Joined: 07 Jun 2014

Posts: 4805

GRE 1: Q167 V156

WE:Business Development (Energy and Utilities)

Re: Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above, [#permalink]

29 Dec 2017, 15:18

Expert Reply

Explanation

There are variables in the answer choices, so Plug In.

Try x = 3. Now write out your new set of numbers. Since you are subtracting 3 and adding 3 the same number of times, the sum and average stay the same, so eliminate choices (A) and (B). The median decreases by 0.5, so eliminate choices (F) and (G). There are now two modes in the set, so eliminate choice (D).

The distance of the numbers from the mean changes in the new set, so the standard deviation is not the same. Eliminate choice (E). The correct answer is choice C.
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san9090

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Joined: 10 Aug 2019

Posts: 16

Re: Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above, [#permalink]

24 Sep 2019, 04:35

How does the median decrease by 0.5?

pranab223

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Joined: 20 Apr 2016

Posts: 1307

WE:Engineering (Energy and Utilities)

Re: Set A: {−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} In Set A above, [#permalink]

01 Oct 2019, 05:57

san9090 wrote:

How does the median decrease by 0.5?

Here, SET A ={−7, −4, −1, 0, 5, 8, 10, 10, 13, 21} , and median = \(\frac{{5+8}}{2} = 6.5\)

As we are assuming \(x = 3\)

the new SET A =\((-7, -1 ,-1, 3, 5, 11, 5, 5, 8, 16) = ( -7, -1, -1, 3, 5, 5, 5, 8, 11, 16)\) ( Subtracting X from 3 largest numbers in the list and x is added to the 3 smallest even numbers )

median = \(\frac{{5+5}}{2} = 5\)

Therefore the median decreased by \(0.5\)

You can pick any value for X and the median will decrease
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