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# Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.

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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.  [#permalink]

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13 Aug 2017, 01:38
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00:00

Difficulty:

55% (hard)

Question Stats:

45% (01:08) correct 55% (00:43) wrong based on 22 sessions

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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?

I. Mean would not change.

II. Median would not change.

III. Standard deviation would not change

A. I only

B. II only

C. III only

D. Both I and II

E. Both II and III

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Chasing the dragon
Senior Manager
Joined: 17 Oct 2016
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WE: Pharmaceuticals (Health Care)
Re: Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.  [#permalink]

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13 Aug 2017, 01:54
1
arjittak wrote:
It's C

Sent from my ONEPLUS A5000 using GMAT Club Forum mobile app

Hi arjittak

The question states that ONE element a, not all elements,is replaced by b, where b<a. \
So the new set is {b, 2a, 3a, 4a, 5a}

So Mean and SD will change, Median would not!

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Chasing the dragon
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Re: Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.  [#permalink]

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13 Aug 2017, 03:15
We can answer by looking the options.
If suppose mean changes, then definitely standard deviation would change and vice versa. But in options I & III together are not given. So definitely D & E are not the answer. Similar to that A & C can't be the answer also. So only option remaining is B
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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.  [#permalink]

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13 Aug 2017, 09:22
2
fitzpratik wrote:
Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. If element ‘a’ in Set X is replaced by ‘b’ and b < a, then which of the following must be true?

I. Mean would not change.

II. Median would not change.

III. Standard deviation would not change

A. I only

B. II only

C. III only

D. Both I and II

E. Both II and III

With values this small, try numbers if not sure. It's very quick.

Only first term, a, changes, not the multiples of a. Otherwise prompt would say "If [EACH] element ‘a’ in Set X is replaced by . . ."

a = 2
Set 1: (2, 4, 6, 8, 10)

b = 1
Set 2: (1, 4, 6, 8, 10)

MUST be true?

I. Mean would not change.
Set 1 mean = 6
Set 2 mean = 29/5 = 5.8
FALSE

II. Median would not change.
Set 1 median = 6
Set 2 median = 6
TRUE

III. Standard deviation would not change

Either remember: If you add or subtract the same number to every number in original set, SD does not change. If you change just one number, SD changes. OR

SD, roughly: how tightly are all the values clustered around the mean? Look at values on the right side of the mean that don't change (here, numbers 8 and 10).

In Set 1, mean is 6. Value 8 is exactly 2 away from mean, 10 is exactly 4 away from mean

In Set 2, mean is 5.8. Values 8 and 10 are farther from 5.8 than they are from 6. The numbers now are "clustered" differently around (in test cases farther from) the mean. FALSE

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Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.   [#permalink] 13 Aug 2017, 09:22
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# Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer.

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