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

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by BTGmoderatorDC » Sun Nov 25, 2018 7:07 am

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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
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by Brent@GMATPrepNow » Sun Nov 25, 2018 7:33 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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If a, b, c, d, e, f, and g are distinct integers, which of t

by fskilnik@GMATH » Sun Nov 25, 2018 10:50 am
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
Source: Princeton Review
Set Q is contained in set P , therefore all the differences between any two elements of Q belong to the set of the differences between any two elements of P.

That understood, it is immediate that Range P ≥ Range Q . The fact that Range P and Range Q may be equal (see below), guarantees that the correct answer is (A).

Example to refute (E) : Q= {0,1,2,3,4,6} and P = {0,1,2,3,4,5,6} -- In this case, Range Q = Range P


(There is only one correct alternative choice among the 5 alternative choices. The time it takes to refute all other 3 may be spared!)


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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by Scott@TargetTestPrep » Wed Mar 27, 2019 6:09 pm
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

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

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