Question: Adding k to a Set

Comment on Adding k to a Set

I got confused and assumed that K is a value that is added to the for number and the new average of the 4 numbers is 10. hence got the new equation as
(sum of 4 numbers + 4K = 40).
What wordings should I be looking for on the test day to be sure.
gmat-admin's picture

You make a good point. A better way to phrase the question would have been "When k is added to the 4 numbers, the average of the 5 numbers is 10."

Having said that, if we wanted to convey that we add k to each of the 4 values, we'd write "When k is added to EACH OF the 4 numbers, the new average is 10."

Hey Brent,

Cant we take 8 as an individual value ( since all 4 numbers on averaging out = 8) and then add k to it and divide by 2 . ie. (8+k)/2 = 10 .and k = 10*2 - 8 = 12 ?
gmat-admin's picture

Unfortunately, your solution does not take into account that we originally have FOUR numbers in the set. Instead, you reduced the question to having only ONE value (8) in the set before adding k.

Consider this illustrative example:
The average age of 1000 university students is 20 years old.
If a 100 year-old person is added to the population, what is the NEW average age of the population?

If we were to use your strategy, we'd take 20 as an individual value and then add 100
So, the new average age = (20 + 100)/2 = 120/2 = 60
This is incorrect.
Adding 1 old person to a group of 1000 young people would not increase the average age to 60.

You COULD, however, say that all FOUR original numbers are 8s.

Then, when we add k to the set, we get: {8, 8, 8, 8, k}

Since the resulting average is 10, we can write: (8 + 8 + 8 + 8 + k)/5 = 10
When we solve this equation, we get: k = 18

Does that help?

Cheers,
Brent

Hi Brent

I think you meant =10 at the end here?
"Since the resulting average is 10, we can write: (8 + 8 + 8 + 8 + k)/5 = 12"
gmat-admin's picture

Good catch! I've edited my response above.
Thanks!

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