Let’s look at statement 1 :

which says median is 3: thus, list can be : {2,3,5} or {1,3,6} . A point to be noted that if median is 3 then min+max = 7 (which is statement 3) \rightarrow Thus, if you notice this fact too then you can eliminate statement 3 too… (In both cases we can’t narrow it down between both the list thus, not sufficient!)

As for statement 2 : Max - Min = 5 which implies that the minimum value = 1 , why ? Because if we take min. value = 2 then Max = 5+2 = 7 thus, the remaining integer has to be 1 (because they should add to 10 and are distinct )which contradicts our max -min =5 {info given} as the min. will be` 1`

→ thus, the only possible solution is {1,3,6}.

Here are all the list:

{1,2,7}

{1,3,6}

{1,4,5}

{2,3,5}

Also, can you list the **source** of the question ?

I think that’s PPP1? Looks like a screenshot from the official practice test.

I agree that these are the possible values for sum to be 10 but as per my understanding the correct should be applicable to all possible sets and any of the options does not apply to all sets.

Is there anything wrong in my understanding?

This is power prep plus 1 difficult quant section question number 18

I think they’re asking for just one list due the choice of word :`A list `

which I think implies singular list out of all the combinations we can make which along with the individual statement provided can satisfy our criteria . But maybe , My thought process was not exactly correct… In that case maybe @Leaderboard can ponder some of this thought on how to approach it!

Here’s how I would do it. Let the numbers be a, b and c. We know that a + b + c = 10. Without loss of generality, assume that a \leq b \leq c. Our goal is to find c, the largest number in the list.

- If we know that the median of the three integers is 3, that means that b = 3. But then we can come up with at least two different values for c - consider the lists (1, 3, 6) and (2, 3, 5). Since c is not unique, that isn’t an option.
- If the range of the integers is 5, that means that c - a = 5. Let a = 1. Then c = 6, and the list is (1, 3, 6). Can a = 2? In that case, c = 7. However, b = 1 in that case, which does not work as the range becomes 6 instead. Hence option B does work, as there is only one list that satisfies this condition, namely (1, 3, 6), with the largest integer being 6.
- Option C cannot work because (1, 3, 6) and (2, 3, 5) are both valid options.

Hence the correct option is option B.

No, and you want each option to apply to only *one* set (unless the option is such that *c* does not change), as otherwise uniqueness cannot be guaranteed.

@HoldMyBeer @Leaderboard thank you for thorough explanations but this question goes above my head. I will skip this if i encounter it in real

Now i understood.

The answer should be the one whose condition should be satisfied by only one set among different set whose sum is 10. Range can be 5 for only one set i.e {1,3,6} so option B is correct.

I completely understood it now. Thank you!