Set B has three positive integers with a median of 9. If the largest

Question

Set B has three positive integers with a median of 9. If the largest possible range of the three numbers is 19, given a certain mean, what is that mean?

(A) 22
(B) 10
(C) 9.6
(D) 9
(E) It cannot be determined from the information given

thkkrpratik · Answer

Set B has 3 positive integers, and the median is 9. So the integers would be x, 9, y.
The largest possible range is 19, aka y - x = 19.

It is given that the integers are positive so the least integer that x could be is 1 and the maximum it could be is 9. (As 0 is a non-negative and a non-positive integer).

Therefore, y could be between 20 (x being 1) and 28 (x being 9).

The mean could range from 10 to 15.33.

One of the answer choices given is 10.

Option B

satishov · Answer

I guess E is the answer.

Given: median is 9, there are 3 numbers in set, and range is 19.

Clearly median cannot be part of range unless range is zero (0).

That leaves us with two extreme terms. Difference of these extreme terms will be range.

Let's assume numbers as 2, 9, and 21 satisfying positive intergers criterion and range being 19

Mean is (2+9+21)/3=~ 10.06
If numbers chosen are 1, 9 and 20

We will get mean as 10

So, mean is dependent on how First term of set is chosen.

So E is the answer.Am I missing something here? OA says B

Posted from my mobile device

thkkrpratik · Answer

I selected answer as B because it is the ONLY option among the given numbers as answer choices that do satisfy the condition.

satishov · Answer

Makes sense,clearly I misunderstood the question.

IanStewart · Answer

What is the source? The question makes no sense as written. If a GMAT PS question tells you "x is an integer", then x is some fixed integer that we don't know. The question can't then talk about "the largest possible value of x", because x is a fixed number. It's not something that can vary, so it can't have a maximum or minimum value. The same is true here: if B is a set of three integers, B is some fixed set that has some fixed range. It makes no sense to talk about its "largest possible range", because set B is not a variable. Its range has one value and one value only.

The question is trying to ask something a bit convoluted, something the wording doesn't correctly convey. It is trying to ask: suppose you were told to make a set of three positive integers, and you were told the set needs to have a mean equal to some number M and a median of 9. If you then discovered that 19 was the largest possible range this set could have, what is M?

To answer that question: if we know the mean of the set, then we know the sum of the three values in the set (the sum is the mean multiplied by 3). Since we know the middle value is 9, we could then find the sum L + S of the largest (L) and smallest (S) values. So we could find the value of L+S, and if we want to maximize the range L-S, we want to make S and L as far apart as possible, so we want to make S as small as we can and L as large as we can. But S is a positive integer, so S = 1 is its minimum value. So if we figured out that the maximum possible range of our set is 19, then since we'd always make S = 1 to maximize that range, we'd then know L = S + 19 = 20, so the set needs to be 1, 9, 20, and the mean is 10.

Set B has three positive integers with a median of 9. If the largest

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards