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

[BTGmoderatorDC]

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

OA A

Source: Princeton Review

[GMATGuruNY]

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

One approach:
Show that four of the five answers do NOT have to be true.

P--> a=1, b=2, c=3, d=5, e=6, f=7, g=4
Range = 7-1 = 6, median = 4, mean = (1+2+3+5+6+7+4)/7 = 28/7
Q --> a=1, b=2, c=3, d=5, e=6, f=7
Range = 7-1 = 6, median = (3+5)/2 = 4, mean = (1+2+3+5+6+7)/6 = 24/6 = 4

Since P and Q do not have the same mean, eliminate B.
Since P and Q have the same range, eliminate C and E.
Since P and Q have the same median, eliminate D.

The correct answer is A.

[Scott@TargetTestPrep]

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

OA A

Source: Princeton Review

We see that set P has one more element that set Q, namely, g. If g is the largest or smallest element of set P, then the range of P would be greater than the range of Q. If g is neither the largest nor smallest element of set P, then the range of P would be equal to the range of Q. In either case, we see that the range of P ≥ the range of Q.

Answer: A