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
Set P {a, b, c, d, e, f, g} Set Q {a, b, c, d, e, f} If a, b
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The key here is MUST be true.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
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
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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.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
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)
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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.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
Answer: A
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