Find the Median of the set of integers A? 1) Mean of the se

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GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members; Location: New Delhi, India; Thanked: 205 times

by GMATinsight » Mon May 22, 2017 7:27 am

Find the Median of the set of integers A?

1) Mean of the set A is 10
2) Range of the set A is 2

Source: www.GMATinsight.com

Answer: option C

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Source: Beat The GMAT — Data Sufficiency | Mon May 22, 2017 7:27 am

DavidG@VeritasPrep: Legendary Member; Posts: 2663; Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members; Location: Boston, MA; Thanked: 1153 times; GMAT Score:770

by DavidG@VeritasPrep » Mon May 22, 2017 8:08 am

GMATinsight wrote:Find the Median of the set of integers A?

1) Mean of the set A is 10
2) Range of the set A is 2

Source: www.GMATinsight.com

Answer: option C

1) Set 1: {10,10} Median = 10
Set 2: {0,0,30} Median = 0
Not sufficient

2)Set 1: {1,3} Median = 2
Set 2: {2, 4} Median = 3
Not sufficient

Together: Notice how important it is that we're dealing with integers - If the range is 2, this dictates that our high and low will have to be 9 and 11, otherwise the mean won't be 10.

Set 1: {9,11} Median = 10
Set 2: {9, 10, 11} Median = 10
Set 3: {9, 9, 9, 11, 11, 11} Median = 10

No matter set we assemble, the median will always be 10. Sufficient. The answer is C

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Mon May 29, 2017 10:24 pm

GMATinsight wrote:Find the Median of the set of integers A?

1) Mean of the set A is 10
2) Range of the set A is 2

Source: www.GMATinsight.com

Answer: option C

Statement 1: Mean of Set A is 10.

Clearly insufficient.

Say, for example, Set A: {10, 10, 10}; Mean = 10 and Median = 10; however, if Set A: {0, 0, 30}; Mean = 10 and Median = 0. No unique value. Insufficient.

Statement 2: Range of Set A is 2.

Clearly insufficient.

Say, for example, Set A: {10, 10, 12}; Median = 10; however, if Set A: {20, 20, 22}; Median = 20. No unique value. Insufficient.

Statement 1 and 2:

Since the mean of the set is 10, the maximum value of an element of the set must be at least 10, thus the minimum value of an element of the set must be at least 10 - 2 = 8.

We cannot have a set such that the minimum value of an element equals 8, and have mean = 10. Thus, the minimum value of an element must be 9; this follows that the maximum value of an element of the set must be 11.

If there are Odd numbers of elements in the set, the middlemost element must 10, or Median = 10; however, if there are Even numbers of elements in the set, there is no middlemost element, thus Median = Average of 9 and 11 = 10. In each case Median = 10. Sufficient.

The correct answer: C

-Jay
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