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If 5 different positive integers have 3 as its median, is the average 01 Dec 2016, 02:03
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If 5 different positive integers have 3 as its median, is the average (arithmetic mean) of them greater than 5?

1) The greatest integer of them is 16
2) The smallest integer of them is 1
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A
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If 5 different positive integers have 3 as its median, is the average Updated on: 01 Dec 2016, 05:37
Originally posted by atturhari on 01 Dec 2016, 02:15.
Last edited by atturhari on 01 Dec 2016, 05:37, edited 1 time in total.
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A.

Total of 5 integers = 5 Avg * 5 = 25.

Given,
Median (3rd digit) = 3
5th digit = 16

Min value for all unique digits would be.
1+2+3+4+16 >25
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If 5 different positive integers have 3 as its median, is the average 01 Dec 2016, 03:51
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Answer A : The crux is 5 different positive integers therefore . 1st and 2nd int must be 1 and 2 and 3rd int is 3( given) therefore 4th int can be more than 3. Min value of 4th int is 4
Therefore total
1+2+3+4+16=26, sufficient.
St 2: insufficient.


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If 5 different positive integers have 3 as its median, is the average 05 Dec 2016, 01:33
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==> If you modify the original condition and the question, the sum of 5 integers>585=25?, and so there are 5 variables and 1 equation. Therefore, E is most likely to be the answer. However, if the question is “greater than”, you need to find the least value. By solving con 1) and con 2),
The least value of the sum becomes 1+2+3+4+16=26>25 yes, hence it is sufficient. The answer is C. However, this question is a key question, so you need to apply CMT 4 (A).
For con 1), the least value of the sum=1+2+3+4+16=26>25, hence yes, it is sufficient.
For con 2), 1+2+3+4+5=15<25 is no, 1+2+3+10+30=46>25 is yes, hence it is not sufficient. Therefore, the answer is A.
This question, related to CMT 4 (A), is 5051-level question in current GMAT.

Answer: A
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If 5 different positive integers have 3 as its median, is the average 22 Nov 2021, 12:13
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MathRevolution
If 5 different positive integers have 3 as its median, is the average (arithmetic mean) of them greater than 5?

1) The greatest integer of them is 16
2) The smallest integer of them is 1
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Breaking Down the Info:

The first three integers have to be 1, 2, 3 since we have unique positive integers.

Rephrase the question:

Is the total of the five integers greater than \(5*5 = 25\)? Is the total of the 2 biggest integers greater than \(25 - 1 - 2 - 3 = 19\)?

Statement 1 Alone:

The 2nd greatest integer must be at least 4. Then the greatest 2 integers must be at least 20. Therefore statement 1 is sufficient.

Statement 2 Alone:

This is already known. Then statement 2 is insufficient.

Answer: A
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If 5 different positive integers have 3 as its median, is the average 22 Nov 2025, 07:12
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