GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 May 2019, 03:08 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # If a, b, c, d, e, f, and g are distinct integers, which of the

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Manager  G
Joined: 27 Jan 2016
Posts: 130
Schools: ISB '18
GMAT 1: 700 Q50 V34 If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

4
14 00:00

Difficulty:

(N/A)

Question Stats: 37% (01:24) correct 63% (01:28) wrong based on 163 sessions

### HideShow timer Statistics

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
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
_________________
Intern  B
Joined: 12 Dec 2010
Posts: 42
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
_________________
Intern  B
Joined: 12 Dec 2010
Posts: 42
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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!

Sent from my iPad using GMAT Club Forum mobile app
Current Student B
Joined: 05 Nov 2016
Posts: 28
Location: India
Concentration: Operations
GMAT 1: 610 Q48 V26 GMAT 2: 660 Q49 V31 GPA: 3.9
WE: Engineering (Consulting)
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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)
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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...
_________________
Intern  B
Joined: 29 Jul 2012
Posts: 15
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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.
Math Expert V
Joined: 02 Aug 2009
Posts: 7686
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
_________________
CEO  D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
CEO  V
Joined: 12 Sep 2015
Posts: 3726
Location: Canada
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

Top Contributor
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

RELATED VIDEO FROM OUR COURSE

_________________
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6228
Location: United States (CA)
Re: If a, b, c, d, e, f, and g are distinct integers, which of the  [#permalink]

### Show Tags

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
_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If a, b, c, d, e, f, and g are distinct integers, which of the   [#permalink] 19 Mar 2019, 19:22
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.

#### MBA Resources  