from Gmat prep

In a certain year,the difference between Mary's and Jim's salaries was twice the difference between Mary's and Kate's annual salaries.If Mary's annual Salary was highest of the 3 people what is the arithmetic mean of the annual salary of the 3 people last year

I)Jim's annual salary was $ 30,000
II)Kate's annual salary was $ 40,000


IMO:b

Tks
Ram

I think the answer is C. Here's how:

Since M has the greatest annual salary, the differences can be setup so that:
(M-J) = 2*(M-K)
Simplifying, you will get: (2K - M) = J

Stmt I alone, or Stmt II alone will not give you all 3 annual salaries so you can compute mean. But both together, give you K and J's salaries and allow you to find M's salary from which you can find the mean.

hey party people, we have a folder dedicated to GMATPREP problems. do not post GMATPREP problems anywhere but in that folder. i'll move this one; thanks.

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you should be EXTREMELY wary of choosing (c) on questions like this one.

(c) is a "SUCKER ANSWER": they hand you so much information that you can figure out EVERY QUANTITY IN THE PROBLEM with NOTHING BUT SIMPLE ARITHMETIC.
i.e., if you have both of the statements together, then it's a simple matter to figure out that mary's salary is 50,000, giving you ALL of the salaries in the problem.

this is not the way DS problems usually work on the official test. if the two choices together just HAND you all the information in the problem - with little to no work, apart from simple arithmetic - then the answer is most likely NOT (c).
we've dealt with this elsewhere in this forum; do a search for the term "c trap" to find that treatment.

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in this case, the key is to figure out that the salaries are EVENLY SPACED. i.e., the distance between jim's and kate's salaries is the same as the distance between kate's and mary's.
i.e., on a number line:
<----------jim----------kate----------mary---------->
(where the blue distances are the same)

remember that, in equally spaced sets, the MEAN is equal to the MEDIAN.
therefore, the middle value is sufficient to answer the problem.

(1) doesn't give the middle value, so (1) is insufficient.

(2) gives the middle value, so (2) is sufficient.

ans = (b)

Gr8 explanation Ron!!
I had one doubt: You said that salaries are evenly placed, but what if ---K(200)---M(400)---J(800)---

in your example, you are giving specific values; that's not what a data sufficiency problem looks like. in fact, if a data sufficiency problem looked like that, it would be impossible to solve -- you would already have the values!

what you may be trying to ask is something more like, "what if they generally told us that, rather than mary/kate/jim being equally spaced, that the distance between mary and jim was three times the distance between mary and kate?"

if that were true -- with the same two numbered statements that are provided here -- then the answer to the question would indeed be (c). the basic reason is that, if the three salaries are not equally spaced, then none of them is a “fixed point” -- if you kept the same average but spread them farther apart, then all three of them would change.
by contrast, if you have a set of three equally spaced numbers, then, if you spread them farther apart but keep the average the same, then the median number won't change.

illustrations:
say your three numbers are 3, 7, and 8. these are not equally spaced; the average is 6.
if you spread these to twice the standard deviation (twice as far away from the mean), you get 0, 8, and 10. the average is still 6, but all three numbers have changed: the smallest number went from 3 to 0, the middle number went from 7 to 8, and the largest number went from 8 to 10.

now, say your three numbers are 4, 6, and 8. these are equally spaced, and the average is the same number (= 6).
if you spread these to twice the standard deviation (twice as far away from the mean), you get 2, 6, and 10. the average is still 6. this time, the two extreme numbers have changed -- the smallest number went from 4 to 2, and the largest number went from 8 to 10 -- but the median does not change.