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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  [#permalink]

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New post 15 Jul 2017, 08:31
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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
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 15 Jul 2017, 09:29
srikanth9502 wrote:
3. 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



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
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 15 Jul 2017, 09:43
chetan2u wrote:
srikanth9502 wrote:
3. 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



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

Hi Chetan

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


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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 15 Jul 2017, 09:52
mcmoorthy wrote:
chetan2u wrote:
srikanth9502 wrote:
3. 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



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

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
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 15 Jul 2017, 10:03
chetan2u wrote:
mcmoorthy wrote:
chetan2u wrote:
[quote="srikanth9502"]3. 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



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

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[/quote]
Thanks Chetan!


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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 20 Aug 2017, 23:16
1
chetan2u wrote:
srikanth9502 wrote:
3. 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



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

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[/quote]


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[/quote]


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)
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 21 Aug 2017, 04:49
Kevinjoshi wrote:
chetan2u wrote:
srikanth9502 wrote:
3. 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



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

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..
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...
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 21 Aug 2017, 09:39
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.
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 21 Aug 2017, 09:44
1
ravjai81 wrote:
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.



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
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 03 Oct 2018, 02:15
srikanth9502 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


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
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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 25 Nov 2018, 08:41
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srikanth9502 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

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Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

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New post 19 Mar 2019, 19:22
srikanth9502 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


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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Re: If a, b, c, d, e, f, and g are distinct integers, which of the   [#permalink] 19 Mar 2019, 19:22
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