What is the median of 15 integers?

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Tue Jul 03, 2018 7:01 am

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What is the median of 15 integers?

(1) Exactly seven of the numbers are greater than 7.
(2) Exactly seven of the numbers are less than 7.

OA is C

Please give examples of a set of numbers.

Thanks

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Source: Beat The GMAT — Data Sufficiency | Tue Jul 03, 2018 7:01 am

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by [email protected] » Tue Jul 03, 2018 9:46 am

Hi vinni.k,

We're asked for the MEDIAN of 15 integers. To find the median of a group of numbers, we must put them in 'order' from least to greatest. With 15 integers, the median would be the '8th' number in that row.

1) Exactly seven of the numbers are greater than 7.

With the information in Fact 1, we know a little bit about the 7 biggest values, but we don't know about the smallest 8 values (nor the 8th value exactly).
Fact 1 is INSUFFICIENT

2) Exactly seven of the numbers are less than 7.

With the information in Fact 2, we know a little bit about the 7 smallest values, but we don't know about the biggest 8 values (nor the 8th value exactly).
Fact 2 is INSUFFICIENT

Combined, we know:
-Exactly seven of the numbers are greater than 7.
-Exactly seven of the numbers are less than 7.

Since the seven largest numbers are GREATER than 7 and the seven smallest numbers are LESS than 7, the remaining number (re: the 8th number) MUST be exactly 7.
Combined, SUFFICIENT.

Final Answer: C

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Rich

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vinni.k: Master | Next Rank: 500 Posts; Posts: 421; Joined: Sun Apr 17, 2011 4:27 amFollowed by: 2 members; Location: India; Thanked: 6 times; GMAT Score:620

by vinni.k » Tue Jul 03, 2018 10:38 am

I am a bit confused now. Let me show you my work.

With 15 integers, the median would be 8th number in that row.

S(1): Exactly seven of the numbers are greater than 7
Case 1: 7,7,7,7,7,7,7,7,9,10,11,12,13,14,15 --> Median is 7
Case 2: 1,2,3,4,5,6,7,7,9,10,11,12,13,14,15 --> Median is 7

S(2): Exactly seven of the numbers are less than 7.
Case 1: -1,0,1,2,3,4,5,7,7,7,7,7,7,7,7 --> median is 7
Case 2: -1,0,1,2,3,4,5,7,9,10,11,12,13,14,15 --> median is 7

Both statements seem sufficient to me. What is wrong here then ?

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