Bunuel wrote:
12 Days of Christmas GMAT Competition with Lots of FunSet X = {a, b, c, d, 9}, where a, b, c, d and 9 are five distinct positive integers. If 9 is the only odd integer in the set, what is the average (arithmetic mean) of set X?
(1) The standard deviation of set X is 2.
(2) The range of {a, b, c} is 4 and the average (arithmetic mean) of {a, b, c} is 10.
The question is not GMAT-like because you need to calculate the SD of 5 numbers. GMAT expects you to understand the SD concept and use it effectively but not use the formula of calculating SD.
The answer of course is (A) and this is how I got it.
Set X = {a, b, c, d, 9}
a, b, c and d are distinct even integers so something like 6, 8, 10, 12 or 2, 6, 10, 12 etc.
To get the mean, we need to know all the 4 unknown numbers or at least mean of some of them and the other numbers.
(1) The standard deviation of set X is 2.
Normally, I would ignore and move on. There are many ways in which one can get a particular SD and I don't expect GMAT to make me calculate the SD. But the odd thing is that the SD is very small. Considering that all numbers must be distinct and not consecutive, they must be tightly packed so they would be able to take very few values.
The closest packed set can be 6, 8, 9, 10, 12 which gives an SD on 2 upon calculation. This means the moment I change any one number, the SD will increase. So the numbers must be these and their avg would be 9.
Sufficient.
(2) The range of {a, b, c} is 4 and the average (arithmetic mean) of {a, b, c} is 10.
This tells us that a, b, c are 8, 10, 12 (range 4 and avg 10 with 3 distinct even integers) but tells us nothing about d.
Not sufficient
Answer (A)
_________________
Karishma
Owner of Angles and Arguments at https://anglesandarguments.com/
NOW PUBLISHED - READING COMPREHENSION MODULE
For Individual GMAT Study Modules, check Study Modules >
For Private Tutoring, check Private Tutoring >