Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

Question

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

is my understanding correct ? 1) possibilities of sets with 6 highest number are  1 ,2, 3 ,4,6],  1 ,2,4, 5 ,6],  3 ,4, 5 ,6] ... Thus sufficient.... 2) 2 being the lowest element in set, the possibility of the sets are numerous but Avg will be always greater than Mean. e.g  3 ,4,6, 100 ] or  5 ,6, 1000 ] in all cases Avg will greater than Mean, thus sufficient. So answer is D.....

M05-37

Aj85 · Answer

statement 1 -the highest number in the set is 6

1 possible set can be (1,2,3,4,6) Then avg =3.2 and median 3 , so avg > median .
Another set can be (2,3,4,5,6) then avg =4 and median 4, so avg =median 
so statement 1 insufficient.

statement 2 -the lowest number in the set is 2 
1possible set can be (2,3,4,5,6) then avg =4 and median 4, so avg =median 
Another possible set can be (2,3,4,6,10) avg =6 and median 4 , so avg > median
so statement 2 insufficient.

combining 2 statements, only set possible is (2,3,4,5,6). avg = median. we get a definite answer 'No' average is not greater than median. Answer C.

Ned · Answer

Hey, here's how I would answer this question. I'm going to try and write it out as clearly as I can. Minus the explanation this can be solved well within 2 minutes.

1. Highest number in the set is 6

Since they're all integers and distinct, the mean will be highest when a and b equal 3 & 5 (or vice versa, doesn't matter).

=> {2,3,4,5,6} 
 Mean = 4
 Median = 4

Mean will be at its lowest when a & b equal 1 & 3.

=> {1,2,3,4,6}
 Mean = 3.2
 Median = 3

This is all we need to know to conclude that the first statement is INSUFFICIENT. In the first case the mean is not greater than the median, but in the second case it is.

2. The lowest number in the set is 2

Since the numbers are positive and there is now no upper limit on the integers, it is important to first find the lowest possible value of the mean since adding 300 or any huge number will ensure that the mean is greater than the median.

a & b equal 3 & 5

=> {2,3,4,5,6}
 Mean = 4, Median = 4.

Again we have a case where the mean is not greater and one where it is (i.e. adding a huge number to the set). INSUFFICIENT.

Combining the two we know that 2 is the lowest number and 6 is the highest, and from our calculations it is clear that while the mean can equal the median, it CAN NOT be greater.

Answer: C

Hope this was helpful.

shrive555 · Answer

Thanks Guys, i know what i was missing ...

keats · Answer

I have a question w.r.t Statement 2. Can we get a 'Yes' case. The cases that I can see in the official solution and the ones that are posted here produce a 'No' in case of Statement 2 (precisely Mean is not greater than Median, and Mean=Median) I cannot locate a case where Mean > Median and I believe that probably can make Statement 2 sufficient.

Bunuel - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

Thank You in advance

Bunuel  - I would like to understand where am I going wrong or may be there is an altered version of this question that's present in the database?

Thank You in advance

Bunuel · Answer

The average of {2, 4, 6, 100, 200}, which is ~62, is greater than the median of {2, 4, 6, 100, 200}, which is 6.

keats · Answer

Thanks  Bunuel

Bunuel · Answer

Is the average of a set of 5 distinct positive integers { a ,  b , 4, 6, 2} greater than the median? 
 
First of all, we must remember that the set contains  distinct   positive   integers .
 
(1) The largest number in the set is 6.
 
Since 6 is the largest number in the set, both  a  and  b  must be less than 6. Therefore,  a  and  b  can be any two from 1, 3, and 5. If  a = 1  and  b = 3 , the median is 3 and the average is 3.2. However, if  a = 3  and  b = 5 , the average and the median are equal, at 4. Not sufficient.
 
(2) The smallest number in the set is 2.
 
Since 2 is the smallest number in the set, both  a  and  b  must be greater than 2. If  a  and  b  are very large numbers, say 10 and 20, the average will be greater than the median, which will be 6. However, if  a = 3  and  b = 5 , the average and the median are equal, at 4. Not sufficient.
 
(1)+(2) From the information given, we know that both  a  and  b  must be greater than 2, and less than 6. Thus,  a=3  and  b=5 , or vice-versa. In either case, the average and the median are equal, at 4. Sufficient.

Answer: C

Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is the average of a set of 5 distinct positive integers {a, b, 4, 6, 2

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards