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

It is currently 22 Apr 2019, 23:22

Close

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.

Close

Request Expert Reply

Confirm Cancel

Which of the following CANNOT be the median of the four positive integ

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

Hide Tags

 
Intern
Intern
avatar
B
Joined: 08 Jul 2017
Posts: 19
Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 03 Aug 2017, 15:13
4
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (01:02) correct 17% (01:32) wrong based on 81 sessions

HideShow timer Statistics

Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?

(A) c
(B) d
(C) (a+d)/2
(D) (a+b+c)/2
(E) a + b + d

I understand why A, B, and C are not the correct answers. But, could someone explain D & E?
Senior Manager
Senior Manager
avatar
G
Joined: 24 Apr 2016
Posts: 331
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 03 Aug 2017, 16:22
2
(A) c

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = C

(B) d

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = D

(C) (a+d)/2

If the 4 number are : 2, 4, 6, 8
Then median = (a+d)/2 = (b+c)/2

(D) (a+b+c)/2

If the 4 numbers are : 0, 4, 6, 8
Then median = (b+c)/2 = (a+b+c)/2

(E) a + b + d

If the four numbers are a,b,c,d and d > c > b > a
So median = (b+c)/2
Let's assume the median = a+b+d
then, a+b+d = (b+c)/2
==> 2a+2b+2d = b+c
==> 2a+b+2d - c = 0

As we know d > c, therefore 2d > c, hence 2d-c>0. So 2a+b+2d-c will result in a positive number.
Given per question, a,b,c,d are all positive numbers. Hence if the a+b+d is the median, then 2a+b+2d - c comes out to be 0, which is not possible. Hence Option E cannot be the median.

Answer is E
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54440
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 03 Aug 2017, 23:46
daftypatty wrote:
Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?

(A) c
(B) d
(C) (a+d)/2
(D) (a+b+c)/2
(E) a + b + d

I understand why A, B, and C are not the correct answers. But, could someone explain D & E?


Similar questions to practice:
https://gmatclub.com/forum/which-of-the ... 10864.html
https://gmatclub.com/forum/which-of-the ... -2436.html
https://gmatclub.com/forum/which-of-the ... 84440.html
_________________
Current Student
User avatar
P
Joined: 18 Aug 2016
Posts: 619
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38
GMAT ToolKit User Reviews Badge
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 04 Aug 2017, 00:36
quantumliner wrote:
(A) c

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = C

(B) d

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = D

(C) (a+d)/2

If the 4 number are : 2, 4, 6, 8
Then median = (a+d)/2 = (b+c)/2

(D) (a+b+c)/2

If the 4 numbers are : 0, 4, 6, 8
Then median = (b+c)/2 = (a+b+c)/2

(E) a + b + d

If the four numbers are a,b,c,d and d > c > b > a
So median = (b+c)/2
Let's assume the median = a+b+d
then, a+b+d = (b+c)/2
==> 2a+2b+2d = b+c
==> 2a+b+2d - c = 0

As we know d > c, therefore 2d > c, hence 2d-c>0. So 2a+b+2d-c will result in a positive number.
Given per question, a,b,c,d are all positive numbers. Hence if the a+b+d is the median, then 2a+b+2d - c comes out to be 0, which is not possible. Hence Option E cannot be the median.

Answer is E

Hi quantumliner
Correct choice of numbers would be 4,6,8,10 (0 is not positive - a,b,c,d are all positive numbers). Although it does not change the methodology. Just wanted to highlight. Thanks for the solution
_________________
We must try to achieve the best within us


Thanks
Luckisnoexcuse
Intern
Intern
User avatar
B
Joined: 09 Dec 2014
Posts: 37
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 04 Aug 2017, 00:38
quantumliner wrote:
(A) c

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = C

(B) d

If all 4 numbers are same. Ex. 1,1,1,1. Then Median = D

(C) (a+d)/2

If the 4 number are : 2, 4, 6, 8
Then median = (a+d)/2 = (b+c)/2

(D) (a+b+c)/2

If the 4 numbers are : 0, 4, 6, 8
Then median = (b+c)/2 = (a+b+c)/2

(E) a + b + d

If the four numbers are a,b,c,d and d > c > b > a
So median = (b+c)/2
Let's assume the median = a+b+d
then, a+b+d = (b+c)/2
==> 2a+2b+2d = b+c
==> 2a+b+2d - c = 0

As we know d > c, therefore 2d > c, hence 2d-c>0. So 2a+b+2d-c will result in a positive number.
Given per question, a,b,c,d are all positive numbers. Hence if the a+b+d is the median, then 2a+b+2d - c comes out to be 0, which is not possible. Hence Option E cannot be the median.

Answer is E


The question says:

Quote:
Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?


While evaluating option D you have taken 0 as one of the numbers. But zero is neither positive nor negative integer. Can you explain?
Let me know if I am making some mistake here :)
_________________
Thanks,
Ramya
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9132
Location: Pune, India
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 04 Aug 2017, 02:34
daftypatty wrote:
Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?

(A) c
(B) d
(C) (a+d)/2
(D) (a+b+c)/2
(E) a + b + d

I understand why A, B, and C are not the correct answers. But, could someone explain D & E?


Note that a, b, c and d are positive integers.

The median will be the average of the second and third terms. If the second and third terms are equal, median will be equal to each.

But the median cannot be greater than 3 terms. a + b + d will be greater than all 3 because they are all positive integers. So (E) is definitely not possible.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Intern
User avatar
B
Joined: 09 Dec 2014
Posts: 37
Re: Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 04 Aug 2017, 03:04
VeritasPrepKarishma wrote:
daftypatty wrote:
Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?

(A) c
(B) d
(C) (a+d)/2
(D) (a+b+c)/2
(E) a + b + d

I understand why A, B, and C are not the correct answers. But, could someone explain D & E?


Note that a, b, c and d are positive integers.

The median will be the average of the second and third terms. If the second and third terms are equal, median will be equal to each.

But the median cannot be greater than 3 terms. a + b + d will be greater than all 3 because they are all positive integers. So (E) is definitely not possible.


Hi VeritasPrepKarishma :)

Is there a way we can eliminate option D without picking numbers?
_________________
Thanks,
Ramya
GMAT Tutor
avatar
S
Joined: 24 Jun 2008
Posts: 1422
Which of the following CANNOT be the median of the four positive integ  [#permalink]

Show Tags

New post 04 Aug 2017, 08:01
1
daftypatty wrote:
Which of the following CANNOT be the median of the four positive integers a, b, c, and d ?

(A) c
(B) d
(C) (a+d)/2
(D) (a+b+c)/2
(E) a + b + d


Where is this question from? It has two correct answers. a+b+d cannot be the median, as Karishma explains above, but (a+b+c)/2 cannot be the median either, if our numbers are all positive.

I won't go through a complete proof, since it's not the kind of thing you need to do on the GMAT, but if you wanted to prove it you'd consider two cases:

- first assume that two out of the three letters a, b and c are the two "middle numbers". Set the median equal to (a+b+c)/2. You'll find one letter must equal zero, which we know is impossible, so answer D cannot be the median in this case;

- only one possibility remains: assume that the fourth letter, d, is one of the two "middle numbers", and assume some other letter, say c, is the other "middle number" (it won't matter which one - you could repeat the proof identically using any letter). Again set the median equal to (a + b + c)/2. You'll find that d = a + b. But that means, if a and b are positive, that d is larger than both a and b, and if that's true, d and c cannot be the two "middle numbers" in the set. So we can't make answer choice D the median in this case either.

That second case gets a bit technical to explain fully, so I've just outlined it in enough detail to hopefully help anyone attempting it on their own. I feel like there's probably an easier way to prove this that I might not be seeing so early in the morning, but the question is flawed unless there's a typo among the answer choices.
_________________
GMAT Tutor in Toronto

If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com
GMAT Club Bot
Which of the following CANNOT be the median of the four positive integ   [#permalink] 04 Aug 2017, 08:01
Display posts from previous: Sort by

Which of the following CANNOT be the median of the four positive integ

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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®.