Question: Truth About Sets A & B

Comment on Truth About Sets A & B

thanks for these helpful videos
why the first set is {5,5}
we know that we have 2 numbers which is an even set so the median is the average 5=s/2 mean that we have 2 numbers equal 10 it could be 3,7 ,4,6 or 5,5
gmat-admin's picture

I believe you're referring to my counter-example at 1:10 in the video.

Please note that I'm not saying that set A is definitely {5, 5}. I'm just saying that {5, 5} is a POSSIBLE set of numbers that satisfies the information we have about set A. I chose these values because they're easy to work with.

Note: The question asks, "Which of the following MUST be true?" So, my goal here is to find a counter-example for statement I in which the statement is NOT TRUE, since this will allow my to eliminate statement I from the answer choices.

I got it..
Thanks

On the module page, what do the colors next to the play button mean? Is that level of difficulty? Green-Easy, Yellow-Medium, Red-Hard? Thanks!
gmat-admin's picture

That's correct.

Hi, I have a small doubt, is zero in the set of positive integers or non-negative integers?
gmat-admin's picture

Zero is neither positive nor negative.
So, we can say that n is a non-negative integer.
We can ALSO say that n is a non-positive integer.

Cheers,
Brent

Is zero and even number or odd?
gmat-admin's picture

Zero is even.

Even integers: {. . . -6, -4, -2, 0, 2, 4, 6, . . . }
Odd integers: {. . .-7, -5, -3, -1, 1, 3, 5, 7, . . . }

Cheers,
Brent

Hi Brent,
The set B can be considered as {1,2,6}, {2,3,4} ,{3,3,3}. So when we consider this the Median of Set and B can't have a fixed answer, which is why we are eliminating I. However, I'd like to clarify whether III must be the eliminated too since even that will have contradicting answers i.e. the numbers considered for Set B( as mentioned above)
Thank you
gmat-admin's picture

Even though there are different possible configurations of set B, that doesn't mean we can't make any conclusions about set B.
If the mean of set B is 3, then there are seven possible sets for set B:
{1,1,7}
{1,2,6}
{1,3,5}
{1,4,4}
{2,2,5}
{2,3,4}
{3,3,3}

However, in all seven cases, the median of set B is less than 5, which means statement III must be true.

Does that help?

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