New GRE quant problem

GRE Quant Problem Solving
1

In this problem :
How many unique lists of 3 numbers exist, where each number is

  1. 1 to 10, inclusive
  2. Median of the list is 5
  3. There is a unique mode in the list

My doubt is : In greg’s solution the pairs (5,1,5), (5,2,5) etc; are included. However, In order to calculate median, we need to arrange the no’s in ascending order. Hence. in the solution (5,1,5), (5,2,5) etc; cannot be included right? Because, if, in this case we arrange them in ascending order, we get 1,5,5, 2,5,5 which are already included in the list.

Hence the possible pairs should be :

1,5,5

2,5,5

3,5,5

4,5,5

5,5,5

5,5,6

5,5,7

5,5,8

5,5,9

5,5,10

It would be great if someone could clear this up :slight_smile:

2

Hint: the order matters in the list. So [1,5,5] and [5,1,5] are not the same list.

3

Hi! thank you for the hint, it means that the possible lists are now 20=10*2. However, still don’t get where to find 8 more cases. I see that it possible 4 lists that then doubled, but still don’t get it. Like, I tried 1,5,1 list, hovewer it would result in median equals 1, right (because to find median we first arrange the list in ascending order)? would you mind helping with this please? Thank you!

4

Correct, that would not work.

No - think about how many ways you can rearrange.

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