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

[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: A

Source: Princeton Review

[Jay@ManhattanReview]

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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