Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} If a, b

BTGmoderatorDC wrote:Set P {a, b, c, d, e, f, g}
Set Q {a, b, c, d, e, f}
If a, b, c, d, e, f, and g are distinct integers, which of the following MUST be true?

A)Range P ≥ Range Q
B)Mean P = Mean Q
C)Range P ≠ Range Q
D)Median P ≠ Median Q
E)Range P > Range Q

The key here is MUST be true.
So, if we can find an example in which a statement is NOT true, then we can ELIMINATE it.
We have:
Set P {a, b, c, d, e, f, g}
Set Q {a, b, c, d, e, f}
I'll make the extra value red so it's easier to compare the two sets

So, the sets COULD be:
Set P {1, 2, 3, 4, 5, 6, 7}
Set Q {1, 2, 3, 5, 6, 7}
Notice that the range of set P = the range of set Q (the range for each is 6)
So, we can ELIMINATE answer choices C and E

Also, the median of set P = 4, and the median of set Q = (3 + 5)/2 = 4.
Since the two sets have the SAME median, we can ELIMINATE answer choice D

Only answer choices A and B remain.
Let's examine another possible scenario.
The sets COULD be:
Set P {1, 2, 3, 5, 6, 7, 1,000,000,000}
Set Q {1, 2, 3, 5, 6, 7}
Here, it's obvious that the two sets do NOT have the same mean
So, we can ELIMINATE answer choice B

By the process of elimination, the correct answer is A

Cheers,
Brent