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M05-37

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M05-37 [#permalink]

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Is the average of a set of 5 distinct positive integers {\(a\), \(b\), 4, 6, 2} greater than the median?



(1) The highest number in the set is 6

(2) The lowest number in the set is 2
[Reveal] Spoiler: OA

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Statement (1) by itself is insufficient. It helps us limit the highest value and since we know that the values of \(a\) and \(b\) cannot be negative or 0, we can try a scenario such as \(a = 1\) and \(b = 3\) and find out that median is 3 and average is 3.2. However, if we try \(a = 3\) and \(b = 5\), the average will be equal to the median, 4.

Statement (2) by itself is insufficient. If \(a\) and \(b\) are very large numbers, the average will be greater than the median, which will be no higher than 6. But if \(a = 3\) and \(b = 5\), then the average is equal to the median.

Statements (1) and (2) combined are sufficient. We know that \(a = 3\) and \(b = 5\).


Answer: C
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Re: M05-37 [#permalink]

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New post 16 Nov 2016, 07:48
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?

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New post 17 Nov 2016, 23:24
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?


{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.
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New post 18 Nov 2016, 07:49
Aww. I see where I went wrong. Thank you!

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Re: M05-37 [#permalink]

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New post 05 Aug 2017, 13:26
Bunuel wrote:
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?


{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.


Hello Bunnel,

I got the answer as D

Case 1 {2 3 4 4 6} Median =4 Avg = 3.8 Avg is not greater than median
Case 2 {2 4 4 6 6} Median 4, Avg =4.4 Avg is greater than median
so i got the statement that both are insufficient.

Am i doing something wrong here?

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Re: M05-37 [#permalink]

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New post 06 Aug 2017, 00:46
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piyushasthita wrote:
Bunuel wrote:
banner03 wrote:
The question asks if the average is greater than the median. Statement one proves that the average is either equal to or less than the median, so couldn't we get a definitive NO answer for this question?


{a, b, 2, 4, 6}
{1, 3, 2, 4, 6} --> average = 3.2 and median = 3 --> the average IS greater than the median.
{3, 5, 2, 4, 6} --> average = 4 and median = 4 --> the average is NOT greater than the median.


Hello Bunnel,

I got the answer as D

Case 1 {2 3 4 4 6} Median =4 Avg = 3.8 Avg is not greater than median
Case 2 {2 4 4 6 6} Median 4, Avg =4.4 Avg is greater than median
so i got the statement that both are insufficient.

Am i doing something wrong here?


You should read more carefully: Is the average of a set of 5 distinct positive integers...
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 128524 [1], given: 12180

Re: M05-37   [#permalink] 06 Aug 2017, 00:46
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