If a, b, c, d, e, f, and g are distinct integers, which of the

Question

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

chetan2u · Answer

Hi..

There is an extra integer in P as compared to Q, while rest all are SAME..
So Range of P can never be less than range of Q or A)Range P ≥ Range Q..
A

mcmoorthy · Answer

Hi Chetan

Won't the median of P and Q be different? Can you pls clarify?

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chetan2u · Answer

Hi,

Not always..

Two cases..
P is 1,2,3,4,5,6,7 and Q is 1,2,3,4,5,6... Median is different 
P is 1,2,3,4,5,6,7 and Q is 1,2,3,5,6,7... Median is 4 in each case so Same
So it can be same or different in the given scenario

Krystallized · Answer

Hi Chetan

Won't the median of P and Q be different? Can you pls clarify?

Sent from my iPad using  GMAT Club Forum mobile app

Hi,

Not always..

Two cases..
P is 1,2,3,4,5,6,7 and Q is 1,2,3,4,5,6... Median is different 
P is 1,2,3,4,5,6,7 and Q is 1,2,3,5,6,7... Median is 4 in each case so Same
So it can be same or different in the given scenario

Hi  chetan2u 
Set P {a, b, c, d, e, f, g} is P {1,2,3,4,5,6,7}
Set Q {a, b, c, d, e, f } is Q {1,2,3,5,6,7 }

This means that a=1, b=2, c=3 and so on.
But in set P d=4, whereas d=5 in set Q.
I think the two values of d in set P & Q must be same..
Plz correct me if i am wrong.

Because if not so, than Set P {a, b, c, d, e, f, g} = {2,3,4,5,6,7,8} Range= 6
Set Q {a, b, c, d, e, f } = Q {1,4,5,6,7,8 } range = 7
where Range(P) < Range(Q)

chetan2u · Answer

Hi..
It is not necessary that the elements are in ascending order...
(a, b, c, d,e, f) is (1,2,3,5,6,7)
(a, b, c, d, e, f, g) is (1,2,3,5,6,7,4)..
So both cases median is 4...

ravjai81 · Answer

I couldn't think of a case where Range of P = Range of Q, I considered the following sets:
P: 0 to 6 so Q: 0 to 5
P: 1 to 7 so Q: 1 to 6
P: -3 to 3 so Q -3 to 2
P: -6 to 0 so Q -6 to -1
In all the above Range of P is 6 and Range of Q is 5, so I picked answer as E i.e. Range P > Range of Q.

chetan2u · Answer

hi..

you are taking a,b,c,d.. in increasing and consecutive integers..
these are variables and a,b do not mean a<b.
variables can take any value and hence g can be any value ..
if Q is 1,2,3,5,6,7.. range = 7-1=6
P is 1,2,3,4,5,6,7.. range is again 7-1=6

GMATinsight · Answer

For any ordered and non-ordered sets,

Let, P {a, b, c, d, e, f, g} = {1, 2, 3, 4, 5, 7, 6}

Then, Q {a, b, c, d, e, f} = {1, 2, 3, 4, 5, 7}

i.e. Range is 6 for both sets

For any ordered set,

Let, P {a, b, c, d, e, f, g} = {1, 2, 3, 4, 5, 6, 7}

Then, Q {a, b, c, d, e, f} = {1, 2, 3, 4, 5, 6}

i.e. Range for P = 6 and Range for Q = 5
i.e. range of P > raneg of Q

Hence, Range of P ≥ Raneg of Q

Answer: Option A

BrentGMATPrepNow · Answer

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

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=Y9f_0QJU1ug

ScottTargetTestPrep · Answer

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

bumpbot · Answer

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If a, b, c, d, e, f, and g are distinct integers, which of the

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If a, b, c, d, e, f, and g are distinct integers, which of the

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