In a certain year, the difference between Mary's and Jim's annual salaries was twice the difference between Mary's and Kate's annual salaries. If Mary's annual salary was the highest of the 3 people, what was the average (arithmetic mean) annual salary of the 3 people that year?
(1) Jim's annual salary was $30,000 that year.
(2) Kate's annual salary was $40,000 that year.
All I could figure out was the following:
a) M-J = 2(M-K); and
b) M>K>J
The actual answer was "Statement (2) ALONE..." can someone please explain this? I'm sure it's much easier than I'm making for myself.
- Thank you
GMAT Forum
4 postsPage 1 of 1
- dr_o
Hi Gus!
I think the key here is is to notice the data talks about difference --> absolute value --> use distance chart
the data:
1) abs(m-j) = 2x
2) abs(m-k)= x
3) m>k and m>j ---> you can rewrite 1 & 2 but this time remove the "abs"
you can draw something like this:
x x
----j-----k------m----
from you can clearly see that k is avg salary of the 3.
on the other hand, knowing J will not be sufficient to know the avg (or k) since you lack the value of x.
hope that helps
I think the key here is is to notice the data talks about difference --> absolute value --> use distance chart
the data:
1) abs(m-j) = 2x
2) abs(m-k)= x
3) m>k and m>j ---> you can rewrite 1 & 2 but this time remove the "abs"
you can draw something like this:
x x
----j-----k------m----
from you can clearly see that k is avg salary of the 3.
on the other hand, knowing J will not be sufficient to know the avg (or k) since you lack the value of x.
hope that helps
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
dr_o Wrote:Hi Gus!
I think the key here is is to notice the data talks about difference --> absolute value --> use distance chart
the data:
1) abs(m-j) = 2x
2) abs(m-k)= x
3) m>k and m>j ---> you can rewrite 1 & 2 but this time remove the "abs"
you can draw something like this:
x x
----j-----k------m----
from you can clearly see that k is avg salary of the 3.
on the other hand, knowing J will not be sufficient to know the avg (or k) since you lack the value of x.
hope that helps
helpful hints:
(1) the 'x's in the post above are meant as length labels: one 'x' is supposed to label the length from j to k, and the other is supposed to label the length from k to m. because of the way in which the forum auto-formats text, these things didn't turn out the way they were supposed to.
(2) here in the general principle at work here - a principle that's usually considered somewhat obscure in textbooks, but that turns up in a surprisingly large number of questions: if 3 (or 5, or 7, ...) numbers are equally spaced, then the middle number must be the arithmetic mean of all the numbers. therefore, if you have the middle value (which, as you've determined, is K), you have the average.
4 posts Page 1 of 1