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# In the sets above, which of the numbers in set Y, if added to set X, w

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Senior DS Moderator
Joined: 27 Oct 2017
Posts: 1141
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WE: Business Development (Energy and Utilities)
In the sets above, which of the numbers in set Y, if added to set X, w  [#permalink]

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04 Jul 2018, 06:37
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:39) correct 38% (01:44) wrong based on 42 sessions

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x = {10, 3, 6, 5}
Y = {5, 6, 10}
In the sets above, which of the numbers in set Y, if added to set X, will
be equal to both the average (arithmetic mean) and the median of the
changed set X?
I. 5
II. 6
III 10

A. Only I
B. only II
C. only III
D. Only II and III
E. None of the numbers

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Joined: 06 Jun 2018
Posts: 61
Location: India
Concentration: Finance, Marketing
GPA: 4
Re: In the sets above, which of the numbers in set Y, if added to set X, w  [#permalink]

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04 Jul 2018, 08:06
Given
X -(10,3,6,5)
Y- (5,6,10)

If we add 5 to X
X- (3,5,5,6,10)
median - 5
mean 3+5+5+6+10 /5 =29/5 not equal to 5
5 doesnt satisfy the conditions

If we add 6 to X
X - (3,5,6,6,10)
median - 6
mean - 3+5+6+6+10 /5 = 30/5 =6
clearly 6 satisfies.

We dont need to solve for 10 as it cannot be the median of X.

B

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Math Expert
Joined: 02 Aug 2009
Posts: 7111
Re: In the sets above, which of the numbers in set Y, if added to set X, w  [#permalink]

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04 Jul 2018, 08:14
gmatbusters wrote:
x = {10, 3, 6, 5}
Y = {5, 6, 10}
In the sets above, which of the numbers in set Y, if added to set X, will
be equal to both the average (arithmetic mean) and the median of the
changed set X?
I. 5
II. 6
III 10

A. Only I
B. only II
C. only III
D. Only II and III
E. None of the numbers

set X = {3,5,6,10}
by adding any number the median can never be the extremes, so discard 10 in y..

MEDIAN : addition of either of 5 and 6 will make it the median of set X.
so lets check on MEAN..
Mean of X is $$\frac{3+5+6+10}{4}=\frac{24}{4}=6$$......
so if you add 5, the mean cannot be 5 of the set
But when we add 6, the mean will remain 6

B
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Re: In the sets above, which of the numbers in set Y, if added to set X, w &nbs [#permalink] 04 Jul 2018, 08:14
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