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

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Manager
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S
Joined: 17 Oct 2016
Posts: 74

Kudos [?]: 25 [0], given: 15

Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GPA: 3.05
WE: Pharmaceuticals (Health Care)
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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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New post 13 Aug 2017, 01:38
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

48% (01:08) correct 52% (00:45) wrong based on 21 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
[Reveal] Spoiler: OA

_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Kudos [?]: 25 [0], given: 15

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Manager
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User avatar
S
Joined: 17 Oct 2016
Posts: 74

Kudos [?]: 25 [1], given: 15

Location: India
Concentration: General Management, Healthcare
GMAT 1: 640 Q40 V38
GPA: 3.05
WE: Pharmaceuticals (Health Care)
Premium Member Reviews Badge CAT Tests
Re: Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. [#permalink]

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New post 13 Aug 2017, 01:54
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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!

So the answer is B
_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

Dr. Pratik



Kudos [?]: 25 [1], given: 15

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B
Joined: 08 Jun 2015
Posts: 20

Kudos [?]: 2 [0], given: 35

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Concentration: Finance, Economics
WE: Engineering (Other)
Re: Set X is given by {a, 2a, 3a, 4a, 5a} where ‘a’ is a positive integer. [#permalink]

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New post 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

Kudos [?]: 2 [0], given: 35

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Kudos [?]: 184 [2], given: 497

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

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New post 13 Aug 2017, 09:22
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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

Answer B

Kudos [?]: 184 [2], given: 497

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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