Problem Solving

Set X has a range of 20000. Set Y has a range of 50000. IF there is a set which contains both X and Y, What is the maximum and minimum range of the set comprising of both Set X and Set Y.

IMO max range will be 70000 and min range will be 50000

can you please explain as to how to calculate it

maximum: 1 set is from -20000 to 0, 2nd set is from 0 to 50000, so total range of set is -20000 to 50000, or a range of 70000.

minimum: 1 set is from 0 to 20000, 2nd set is from 0 to 50000, so total range of this combined set is 0 to 50000, for a range of 50000.

Thanks for the explaination! But, how did you conclude -20,000 to be the Lower range in Set A.. As the range is 20,000, it can be written as

20,000 = H ( A) - L (A). In this case higher value can be 20,000 and Lower value in set A can be 0.

I am sort of confused in deducing it. Your help is really appreciated.

It's asking you for maximum and minimum, so its up to you to figure out different scenarios while making sure it satisfies what is given.

You are given that the range is 20,000. It can be from 0 to 20,000, or it could be from -20,000 to 0, or it could be 100,000 to 120,000 (all of these satisfy H(A) -L(A) = 20,000).

However, you are trying to find what the maximum will be in the combined sets.

If 1st set is from 0 to 20,000, and second set is from 0 to 50,000, then your range is 0 to 50,000. But ask yourself - could you find an even bigger range?? What if 1st set was 0 to 20,000, and second set had a range from 20,000 to 70,000 (again, it satisfies the other set where H(A) - L(A) = 50,000), then in this case your range is from 0 to 70,000. You have just made the combined set have an even bigger range than before!

Now for minimum, if one set is contained within another set, you are minimizing the range. What I mean by that is say 1st set is 0 to 20,000, and 2nd set is 0 to 50,000, then your range is 0 to 50,000. Can you make it even smaller? Try it, I don't think you can.

@mp2437: Nice explanation.

Don't you think we can maximise the range if we the min value of X is 0 and max is 20000 and the min in Y is
150000 and max is 200000. In this case the combined range will be 200000.

What say?
What am I missing here?
Thanks.

cheeseburst,

your point is valid. There is no limit for the maximum value of range, though on GMAT, the question is targeted more on the minimum range of the group. IF it is targeted at maximum range, then you have to choose the maximum value provided in the answer choice.

~Nik