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# If sequence Q has four terms: x, 12, y, and 20, is it true that the me

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Joined: 02 Sep 2009
Posts: 60481
If sequence Q has four terms: x, 12, y, and 20, is it true that the me  [#permalink]

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06 Nov 2019, 02:33
00:00

Difficulty:

75% (hard)

Question Stats:

36% (02:10) correct 64% (01:44) wrong based on 46 sessions

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If sequence Q has four terms: x, 12, y, and 20, is it true that the median of sequence Q is 16?

(1) The average of sequence Q is 16
(2) x = 16

Are You Up For the Challenge: 700 Level Questions

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Joined: 20 Jul 2017
Posts: 1233
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
If sequence Q has four terms: x, 12, y, and 20, is it true that the me  [#permalink]

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Updated on: 06 Nov 2019, 08:12
Bunuel wrote:
If sequence Q has four terms: x, 12, y, and 20, is it true that the median of sequence Q is 16?

(1) The average of sequence Q is 16
(2) x = 16

Are You Up For the Challenge: 700 Level Questions

Edited.

(1) The average of sequence Q is 16
—> (x + 12 + y + 20)/4 = 16
—> x + y = 32

Since the sum of lowest and highest term is 32, irrespective of any value of x and y, median = 16 always
Many values of median are possible—> Sufficient

(2) x = 16
Many values of median are possible since we do not know the value of y —> Insufficient

IMO Option A

Posted from my mobile device

Originally posted by Dillesh4096 on 06 Nov 2019, 02:46.
Last edited by Dillesh4096 on 06 Nov 2019, 08:12, edited 1 time in total.
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If sequence Q has four terms: x, 12, y, and 20, is it true that the me  [#permalink]

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Updated on: 06 Nov 2019, 06:22
2
Statement tells us that average of x, 12, y, and 20.

Since average of 12 and 20 is 16, average of x and y must be 16. There are 2 cases possible.

Case 1-
If one of x or y is less than 12, then other must be greater than 20. hence median of Q=$$\frac{12+20}{2}$$=16

Case 2

If one of x or y lies in the range 12-20(both inclusive), other will lie in the range 12-20 (both inclusive) too. Median would be $$\frac{x+y}{2}$$=16

Sufficient

Statement 2-

if y=16, median is 16
if y has value other than 16, median would be different from 16

Insufficient

A

Bunuel wrote:
If sequence Q has four terms: x, 12, y, and 20, is it true that the median of sequence Q is 16?

(1) The average of sequence Q is 16
(2) x = 16

Are You Up For the Challenge: 700 Level Questions

Originally posted by nick1816 on 06 Nov 2019, 05:18.
Last edited by nick1816 on 06 Nov 2019, 06:22, edited 1 time in total.
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Re: If sequence Q has four terms: x, 12, y, and 20, is it true that the me  [#permalink]

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06 Nov 2019, 06:29
1
Bunuel wrote:
If sequence Q has four terms: x, 12, y, and 20, is it true that the median of sequence Q is 16?

(1) The average of sequence Q is 16
(2) x = 16

Are You Up For the Challenge: 700 Level Questions

Pure DS trap
From 1)
X+Y=32
(X,Y)=(16,16), (15,17),(14,18),(13,19),(12,20),(11,21)
In all case median will be 16
Sufficient
A:)
From 2)
No information about Y
Not sufficient
A:)
Manager
Status: So far only Dreams i have!!
Joined: 05 Jan 2015
Posts: 213
WE: Consulting (Consulting)
Re: If sequence Q has four terms: x, 12, y, and 20, is it true that the me  [#permalink]

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06 Nov 2019, 07:13
True, A trap. I got it wrong.
Lesson learned - should not do in haste!

satya2029 wrote:
Bunuel wrote:
If sequence Q has four terms: x, 12, y, and 20, is it true that the median of sequence Q is 16?

(1) The average of sequence Q is 16
(2) x = 16

Are You Up For the Challenge: 700 Level Questions

Pure DS trap
From 1)
X+Y=32
(X,Y)=(16,16), (15,17),(14,18),(13,19),(12,20),(11,21)
In all case median will be 16
Sufficient
A:)
From 2)
No information about Y
Not sufficient
A:)
Re: If sequence Q has four terms: x, 12, y, and 20, is it true that the me   [#permalink] 06 Nov 2019, 07:13
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# If sequence Q has four terms: x, 12, y, and 20, is it true that the me

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