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# M70-38

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Math Expert
Joined: 02 Sep 2009
Posts: 60561

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04 Sep 2018, 02:40
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Difficulty:

25% (medium)

Question Stats:

83% (01:41) correct 17% (01:07) wrong based on 12 sessions

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The integer $$x$$ was added to the sequence 4, 4, 9, 11, 14, 15. Is $$x$$ the median?

(1) $$9 \leq x \leq 11$$

(2) After the addition, the average of the sequence is 10.

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Math Expert
Joined: 02 Sep 2009
Posts: 60561

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04 Sep 2018, 02:40
Official Solution:

We’ll go for LOGICAL because that is our first choice in Data Sufficiency.

We’ll begin by looking at the sequence and checking which integers, when added, can be medians: 9, 10 and 11 all work. (1) tells us $$x$$ is definitely one of these numbers, and thus it must be the median. (B), (C) and (E) are eliminated. (2) Using the average, we’d be able to find $$x$$ ($$\frac{previous \ sum + x}{7}$$), and thus we’d be able to tell whether $$x$$ is the median. (A) is eliminated.

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Intern
Joined: 28 Oct 2018
Posts: 1

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30 Oct 2018, 08:45
Can some one explain to me how 1 and 2 are both sufficient?

I under stand 1. the options would be 9-10-11 and all three work and would be the median if added to the sequence.

but with 2, x=13 ((57+x)/7=10) which is greater than 11 from the prior answer and would not be the median?

How can x be equal to both: 9-10-11 and 13?
Director
Joined: 09 Aug 2017
Posts: 678

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01 Nov 2018, 09:33
Statement 2,
(X +57)/7= 10
X= 13
but after inserting 13 in given series, median will change.
It is not D.
A is correct.
Intern
Joined: 20 May 2018
Posts: 1
GMAT 1: 600 Q38 V34

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27 Nov 2018, 18:23
I think this is a poor-quality question and I don't agree with the explanation.
Manager
Joined: 12 Mar 2019
Posts: 157

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10 Aug 2019, 10:36
gvij2017 wrote:
Statement 2,
(X +57)/7= 10
X= 13
but after inserting 13 in given series, median will change.
It is not D.
A is correct.

We don't need to find median, we just need to tell if X will be a median, Answer is NO, As NO is also an answer, so St 2 is sufficient.
Manager
Joined: 12 Mar 2019
Posts: 157

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10 Aug 2019, 10:37
ReevT wrote:
I think this is a poor-quality question and I don't agree with the explanation.

Can you please tell what makes it poor quality, so that your doubts can be cleared.
Re: M70-38   [#permalink] 10 Aug 2019, 10:37
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# M70-38

Moderators: chetan2u, Bunuel