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Harry, Davis and John had only $1 coins in their pockets when they wen

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Harry, Davis and John had only $1 coins in their pockets when they wen  [#permalink]

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New post 21 Dec 2018, 04:31
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Difficulty:

  65% (hard)

Question Stats:

42% (01:57) correct 58% (01:08) wrong based on 12 sessions

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Harry, Davis and John had only $1 coins in their pockets when they went to the market. The total number of coins they had was 30. What is the median number of coins they had?

(1) Harry had 9 coins.

(2) John had 10 coins.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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Joined: 04 Dec 2015
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GRE 1: Q170 V170
Re: Harry, Davis and John had only $1 coins in their pockets when they wen  [#permalink]

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New post 21 Dec 2018, 16:03
chand567 wrote:
Harry, Davis and John had only $1 coins in their pockets when they went to the market. The total number of coins they had was 30. What is the median number of coins they had?

(1) Harry had 9 coins.

(2) John had 10 coins.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
EACH statement ALONE is sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.


There are a few reasons to be very suspicious of this problem! First, the two statements look very similar - which sometimes means that they're either both sufficient or both sufficient. But, sometimes it's a trick, and they're actually testing whether you can find a very subtle difference between the two statements to show that the answer is either A or B.

Second, notice that they're asking for the median of a set. It's easy to think that you need to know every member of a set to find its median. But technically, you only need to know the number in the middle! There are a lot of different ways you could find the median of a set without knowing every single number in it.

Anyways, here's an analysis:

Question: H + D + J = 30. What's the median of H, D, and J?

Statement 1: H = 9. So, D + J = 21. Could we get two different medians?

If D = 10 and J = 11, then the median is D, at 10. Now, try to get a median that's different from 10. I'd try making the median equal 9 if possible.

If D = 8 and J = 13, then the median is 9. Two different medians, so the statement is insufficient.

Statement 2: D = 10. So, H + J = 20. Try some possibilities...

H = 10, J = 10. Median is still 10.
H = 8, J = 12. Median is still 10.

No matter what we try, we can't get the median to be anything other than 10! (The math reason for this is that if a 3-element set includes its mean, which is 10, that number will also always be the median.)

This statement is sufficient, and the answer is B.
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Re: Harry, Davis and John had only $1 coins in their pockets when they wen &nbs [#permalink] 21 Dec 2018, 16:03
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