10, 6, p, q, 11 Given the above series of positive integers arranged

Question

10, 6, p, q, 11
Given the above series of positive integers arranged in a random order, what is the value of p/q

(1) The average (arithmetic mean) of given numbers is 7 
(2) p is the median of the given series

Source-> E-gmat

mikemcgarry · Answer

Dear stonecold , I'm happy to respond.

I really like this question: it's clever! Statement #1 : We know the average is 7, so the sum must be 35. 10 + 6 + p + q + 11 = 35 p + q = 8 We know the sum of p & q, but there are several pairs of positive integers that work, so we cannot determine a ratio. This statement, alone and by itself, is insufficient . Statement #2 : We know 11 is the biggest number, then 10, then p 6 and p > q. This establishes a range for p, but we still cannot determine a ratio. This statement, alone and by itself, is also insufficient . Combined statements : The variable p and q have a sum of 8, and p must be a median in a set in which 6 is a member. It could be q = 1, p = 7, set = {1, 6, 7, 10, 11} That set has a mean of 7 and median of p. It could also be q = 2, p = 6, set = {2, 6, 6, 10, 11} That set also has a mean of 7 and a median of p. The median doesn't have to be distinct or unique in the set: the middle number, the third number in a set of five, is always the median, regardless of how many other numbers have that same value. Two different possible values of the ratio are consistent with the information of the combined statements. We cannot determine a unique answer. Even with everything together, it's still insufficient . OA = (E) Does all this make sense? Mike

10, 6, p, q, 11 Given the above series of positive integers arranged

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