BTGmoderatorDC wrote: ↑Fri May 22, 2020 1:12 am
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:
A
Source: Princeton Review
Say a > b > c > d > e > f. Thus, range of Set Q = a – f.
So far we have not decided about g.
Case1: Say a > g > f
Range of Set P = a – f.
So, Range of Set P = Range of Set Q.
Case2: Say g > a
Range of Set P = g – f.
Since g – f > a – f, we have
Range of Set P ≥ Range of Set Q.
The correct answer is A.
Let's discuss other options for the sake of discussion.
B) Mean P = Mean Q
If a > b > c > d > e > f > g. Mean P > Mean Q. This is incorrect.
C) Range P ≠ Range Q
If a > g > f
Range of Set P = Range of Set Q = a – f. This is incorrect.
D) Median P ≠ Median Q
Say the integers are a, b, c, d, e, and f are 2, 4, 6, 8, 10 and 12, respectively and g = 7.
Median P = 7
Median Q = (6 + 8)/2 = 7
This is incorrect.
E) Range P > Range Q
If g > a
Range of Set P = g – f. And Range of Set Q = a – f.
Since g – f > a – f, we have
Range of Set P > Range of Set Q. This is incorrect.
The correct answer:
A
Hope this helps!
-Jay
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