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

 It is currently 20 Nov 2018, 22:30

### 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

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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# A list of numbers has six positive integers. Three of those integers

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50711
A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

07 Mar 2016, 10:20
3
21
00:00

Difficulty:

95% (hard)

Question Stats:

25% (03:12) correct 75% (02:58) wrong based on 352 sessions

### HideShow timer Statistics

A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2702
Location: India
GMAT: INSIGHT
WE: Education (Education)
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

10 Apr 2017, 18:14
3
3
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Terms are {4, 5, 24, x, y, z}
Mean = 10 i.e. Sum = 10*6 = 60
i.e.4+5+24+x+y+z = 60
i.e. x+y+z = 27

Media = between 7 and 8
But since number of terms in the set is even so median is the average of two middle terms which can only be 7.5
Hence, Median = 7.5
Media 7.5 is possible when two of the terms in the sets are {7,8} or {6,9} or {5,10} or {4,11} or {3,12} or {2,13} or {1,14}

Lets check options
(A) 13 {x, y, z} may be {2, 13, 12} hence Possible

(B) 12 {x, y, z} may be {5, 10, 12} hence Possible

(C) 11 {x, y, z}hence NOT Possible as the pair needed is {4, 11} but 4 can't be third term ever as sum of other two of x, y, z is 16 which can't be each smaller than 4. CORRECT ANSWER

(D) 10

(E) 5

_________________

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

##### General Discussion
SC Moderator
Joined: 13 Apr 2015
Posts: 1688
Location: India
Concentration: Strategy, General Management
GMAT 1: 200 Q1 V1
GPA: 4
WE: Analyst (Retail)
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

07 Mar 2016, 11:55
The 6 positive integers can be 4, 5, x, y, z, 24.
Mean = 10 --> 4 + 5 + x + y + z + 24 = 60 --> x + y + z = 27
Median lies between 7 and 8. Since all the numbers are integers, median = (x + y)/2 --> x + y = 2 * Median

x + y = integer value between 14 and 16 --> x + y = 15. So value of z = 12

We now have 4, 5, x, y, 12, 24. We can now substitute for the options for x and y and check for the median value.

If one of the unknowns is 13 then the values take 2, 4, 5, 12, 13, 24 and Median = 17/2 > 8.

Manager
Joined: 21 Apr 2016
Posts: 176
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

04 Feb 2017, 08:34
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

How can this be solved in 2 mins?
Director
Joined: 14 Nov 2014
Posts: 637
Location: India
GMAT 1: 700 Q50 V34
GPA: 3.76
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

04 Feb 2017, 21:24
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

it took me more than 5 min to try each n every possible combination ...how to tackle it within 2 min.. In actual exam ,i would have skipped it :p
Math Expert
Joined: 02 Aug 2009
Posts: 7041
A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

04 Feb 2017, 23:13
1
4
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Hi all those looking for a short method..

points to NOTE..
1) the median of 6 integers will be the centre value of two MIDDLE integers, here it will be 3rd and 4th in ascending/descending order.
2) when you are looking for centre of two integers, the centre value will be either an integer or a number with .5 in decimals. Here it is given between 7 and 8, the value is 7.5
3) sum of two of the three unknowns is 7.5*2=15

Let's work further..
Total of unknowns=10*6-(24+5+4)=27..
The third unknown =27-15=12..

for other two totalling 15, the lower one cannot be less than 5, as the two lowest are 4 and 5..
So values can be 5 and 10,... or 6 and 9... or 7 and 8...
So A and C are not possible...
Bunuel , we may have to change the median from ' between 7 and 8(exclusive) to from 7 to 8(exclusive)..

So now the Q says that the median could be 7 also,
total of two is 2*7=14 and third unknown becomes 27-14=13....
And other two values can be 5 and 9...... Or 6 and 8.....

Now only 11 is not possible..
Ans C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Intern
Joined: 08 Jul 2016
Posts: 18
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

10 Apr 2017, 14:23
chetan2u wrote:
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Hi all those looking for a short method..

points to NOTE..
1) the median of 6 integers will be the centre value of two MIDDLE integers, here it will be 3rd and 4th in ascending/descending order.
2) when you are looking for centre of two integers, the centre value will be either an integer or a number with .5 in decimals. Here it is given between 7 and 8, the value is 7.5
3) sum of two of the three unknowns is 7.5*2=15

Let's work further..
Total of unknowns=10*6-(24+5+4)=27..
The third unknown =27-15=12..

for other two totalling 15, the lower one cannot be less than 5, as the two lowest are 4 and 5..
So values can be 5 and 10,... or 6 and 9... or 7 and 8...
So A and C are not possible...
Bunuel , we may have to change the median from ' between 7 and 8(exclusive) to from 7 to 8(exclusive)..

So now the Q says that the median could be 7 also,
total of two is 2*7=14 and third unknown becomes 27-14=13....
And other two values can be 5 and 9...... Or 6 and 8.....

Now only 11 is not possible..
Ans C

How did you know that two lowest are 4 and 5 ? ...one of the possibility can be 3,4,5,10,14,24
VP
Joined: 05 Mar 2015
Posts: 1000
A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

10 Apr 2017, 17:48
manishcmu wrote:
chetan2u wrote:
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Hi all those looking for a short method..

points to NOTE..
1) the median of 6 integers will be the centre value of two MIDDLE integers, here it will be 3rd and 4th in ascending/descending order.
2) when you are looking for centre of two integers, the centre value will be either an integer or a number with .5 in decimals. Here it is given between 7 and 8, the value is 7.5
3) sum of two of the three unknowns is 7.5*2=15

Let's work further..
Total of unknowns=10*6-(24+5+4)=27..
The third unknown =27-15=12..

for other two totalling 15, the lower one cannot be less than 5, as the two lowest are 4 and 5..
So values can be 5 and 10,... or 6 and 9... or 7 and 8...
So A and C are not possible...
Bunuel , we may have to change the median from ' between 7 and 8(exclusive) to from 7 to 8(exclusive)..

So now the Q says that the median could be 7 also,
total of two is 2*7=14 and third unknown becomes 27-14=13....
And other two values can be 5 and 9...... Or 6 and 8.....

Now only 11 is not possible..
Ans C

How did you know that two lowest are 4 and 5 ? ...one of the possibility can be 3,4,5,10,14,24

Yes , you r correct

only we must look for defined median , mean and the three unknown to be distinct
SVP
Joined: 12 Dec 2016
Posts: 1674
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

13 Jun 2017, 16:54
chetan2u wrote:
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Hi all those looking for a short method..

points to NOTE..
1) the median of 6 integers will be the centre value of two MIDDLE integers, here it will be 3rd and 4th in ascending/descending order.
2) when you are looking for centre of two integers, the centre value will be either an integer or a number with .5 in decimals. Here it is given between 7 and 8, the value is 7.5
3) sum of two of the three unknowns is 7.5*2=15

Let's work further..
Total of unknowns=10*6-(24+5+4)=27..
The third unknown =27-15=12..

for other two totalling 15, the lower one cannot be less than 5, as the two lowest are 4 and 5..
So values can be 5 and 10,... or 6 and 9... or 7 and 8...
So A and C are not possible...
Bunuel , we may have to change the median from ' between 7 and 8(exclusive) to from 7 to 8(exclusive)..

So now the Q says that the median could be 7 also,
total of two is 2*7=14 and third unknown becomes 27-14=13....
And other two values can be 5 and 9...... Or 6 and 8.....

Now only 11 is not possible..
Ans C

this is not fair, from 7 to 8 (exclusive), 8 is not counted while 7 is included.
Intern
Joined: 02 Nov 2017
Posts: 27
Location: India
Concentration: General Management, Finance
GMAT 1: 660 Q49 V29
GPA: 3.31
WE: General Management (Energy and Utilities)
A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

23 Jul 2018, 02:08
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

. if u take 10 the order is (3,4,5,10,14,24)
median will stay between 7 and 8.
If u take 13...median won't stay in range
if u take 11 median won't stay in range.
the question needs to introspect and evaluate itself ..... because its wrong in the first place and has no right to challenge us
Intern
Joined: 12 Jun 2018
Posts: 1
Re: A list of numbers has six positive integers. Three of those integers  [#permalink]

### Show Tags

27 Jul 2018, 20:23
GMATinsight wrote:
Bunuel wrote:
A list of numbers has six positive integers. Three of those integers are known: 4, 5 and 24 and three of those are unknown: x, y and z. The three unknowns are known to be distinct. It is also known that the mean of the list is 10 and the median lies between 7 and 8 (exclusive).

Which of the following CANNOT be the value of any one of the unknowns?

(A) 13

(B) 12

(C) 11

(D) 10

(E) 5

Terms are {4, 5, 24, x, y, z}
Mean = 10 i.e. Sum = 10*6 = 60
i.e.4+5+24+x+y+z = 60
i.e. x+y+z = 27

Media = between 7 and 8
But since number of terms in the set is even so median is the average of two middle terms which can only be 7.5
Hence, Median = 7.5
Media 7.5 is possible when two of the terms in the sets are {7,8} or {6,9} or {5,10} or {4,11} or {3,12} or {2,13} or {1,14}

Lets check options
(A) 13 {x, y, z} may be {2, 13, 12} hence Possible

(B) 12 {x, y, z} may be {5, 10, 12} hence Possible

(C) 11 {x, y, z}hence NOT Possible as the pair needed is {4, 11} but 4 can't be third term ever as sum of other two of x, y, z is 16 which can't be each smaller than 4. CORRECT ANSWER

(D) 10

(E) 5

If we consider option A, including 13 would make the sequence {4,5,12,13,24} with space to accomodate another integer which is 12. but all numbers are supposed to be distinct. How is it possible?
Re: A list of numbers has six positive integers. Three of those integers &nbs [#permalink] 27 Jul 2018, 20:23
Display posts from previous: Sort by