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

 It is currently 18 Oct 2019, 14:20 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  S is a set of positive integers. The average of the terms in

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

Hide Tags

Intern  Joined: 07 Jul 2012
Posts: 22
GMAT Date: 10-12-2012
S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

7
17 00:00

Difficulty:   95% (hard)

Question Stats: 49% (02:23) correct 51% (02:34) wrong based on 452 sessions

HideShow timer Statistics

S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is the sum of all the integers in S?

(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

Originally posted by rohitgarg on 23 Sep 2012, 20:27.
Last edited by Bunuel on 07 Nov 2013, 11:43, edited 2 times in total.
Renamed the topic.
GMAT Tutor G
Joined: 24 Jun 2008
Posts: 1806
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

7
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is the sum of all the integers in S?

(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

Neither statement is sufficient alone.

From Statement 1, the range (and thus the average) is either 3 or 7. From Statement 2, we know that the range cannot be 3, since no set with a range of 3 could contain five different integers. So the mean is 7, and we have 5 things in our set, so the sum is 5*7=35 which is what the question asked for. The answer is C.

If the OA in the original source is 'E' here because the OA claims that S could contain repeated elements, the OA is wrong. The ambiguous wording of Statement 2 aside, the word 'set' has a precise definition in mathematics, and sets cannot contain repeated elements. You don't need to know that for the GMAT, but there's a reason GMAT questions always talk about 'lists of values' or 'data sets' or use some similar term in questions where repeated elements might be relevant.
_________________
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
General Discussion
Senior Manager  B
Joined: 11 May 2011
Posts: 295
Re: Real Challenge  [#permalink]

Show Tags

rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is
the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

My answer is E.
Based on option A - prime numbers less than 11 are 2, 3, 5, 7. 2 & 5 is rejected because they are factors of 10. we get two numbers - 3 & 7.- Insuff.
Based on option B - multiple combination possible - Insuff.

Together - 3 & 7 both doesn't fall under creteria. Answer E.

Cheers!
_________________
-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: Real Challenge  [#permalink]

Show Tags

4
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is
the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

A - average
(1) Primes less than 11 are 2, 3, 5, and 7. Not factor of 10, we are left with 3 and 7.
If A = 3, we can have {2, 2, 3, 5} or {1, 2, 3, 4, 4, 4}.
Not sufficient.

(2) For 5 evenly spaced numbers, k - 2d, k - d, k, k + d, k + 2d the range is 4d and the average is k.
We can simply take k = 4d, and we have infinitely many sets fulfilling the condition of the form {2d, 3d, 4d, 5d, 6d}.
For example {2, 3, 4, 5, 6}, {20, 30, 40, 50, 60}...
Not sufficient.

(1) and (2) together:
We have seen above that the range can be either 3 or 7.
If the range is 3, we cannot have 5 distinct integers in the set, so only 7 is left.

We know that the sum of the 5 integers is 5 * 7 = 35, the smallest number is k and the largest number is k + 7, where k is some positive integer.
Necessarily 35 - 7 = 28 > 5k, so k must be not greater than 5.
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

CORRECTION:

What a miss! We have to find the sum of the numbers and not the set of numbers. Although there is more than one possibility, the total sum is clearly 7*5 = 35.

And IanStewart is right about (1), in a set of numbers, each element is different.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.

Originally posted by EvaJager on 24 Sep 2012, 00:18.
Last edited by EvaJager on 24 Sep 2012, 22:55, edited 2 times in total.
Senior Manager  B
Joined: 11 May 2011
Posts: 295
Re: Real Challenge  [#permalink]

Show Tags

1
EvaJager wrote:
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is
the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

A - average
(1) Primes less than 11 are 2, 3, 5, and 7. Not factor of 10, we are left with 3 and 7.
If A = 3, we can have {2, 2, 3, 5} or {1, 2, 3, 4, 4, 4}.
Not sufficient.

(2) For 5 evenly spaced numbers, k - 2d, k - d, k, k + d, k + 2d the range is 4d and the average is k.
We can simply take k = 4d, and we have infinitely many sets fulfilling the condition of the form {2d, 3d, 4d, 5d, 6d}.
For example {2, 3, 4, 5, 6}, {20, 30, 40, 50, 60}...
Not sufficient.

(1) and (2) together:
We have seen above that the range can be either 3 or 7.
If the range is 3, we cannot have 5 distinct integers in the set, so only 7 is left.

We know that the sum of the 5 integers is 5 * 7 = 35, the smallest number is k and the largest number is k + 7, where k is some positive integer.
Necessarily 35 - 7 = 28 > 5k, so k must be not greater than 5.
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfills the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

@EvaJager - in (2) why are you considering "5 evenly spaced numbers"? This is not mentioned anywhere in the question.
_________________
-----------------------------------------------------------------------------------------
What you do TODAY is important because you're exchanging a day of your life for it!
-----------------------------------------------------------------------------------------
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: Real Challenge  [#permalink]

Show Tags

1
Capricorn369 wrote:
EvaJager wrote:
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is
the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

A - average
(1) Primes less than 11 are 2, 3, 5, and 7. Not factor of 10, we are left with 3 and 7.
If A = 3, we can have {2, 2, 3, 5} or {1, 2, 3, 4, 4, 4}.
Not sufficient.

(2) For 5 evenly spaced numbers, k - 2d, k - d, k, k + d, k + 2d the range is 4d and the average is k.
We can simply take k = 4d, and we have infinitely many sets fulfilling the condition of the form {2d, 3d, 4d, 5d, 6d}.
For example {2, 3, 4, 5, 6}, {20, 30, 40, 50, 60}...
Not sufficient.

(1) and (2) together:
We have seen above that the range can be either 3 or 7.
If the range is 3, we cannot have 5 distinct integers in the set, so only 7 is left.

We know that the sum of the 5 integers is 5 * 7 = 35, the smallest number is k and the largest number is k + 7, where k is some positive integer.
Necessarily 35 - 7 = 28 > 5k, so k must be not greater than 5.
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

@EvaJager - in (2) why are you considering "5 evenly spaced numbers"? This is not mentioned anywhere in the question.

It is the easiest to express the average when the numbers are evenly spaced. The goal is to find as easily as possible one/more examples which fulfill the condition.
And it is nowhere stated that the numbers cannot be evenly spaced. Also, in (1) it was not mentioned that some of the numbers cannot be equal.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern  Joined: 29 Aug 2012
Posts: 25
Schools: Babson '14
GMAT Date: 02-28-2013
Re: Real Challenge  [#permalink]

Show Tags

EvaJager wrote:
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

^^^ what's this that you have done , can you please explain thinking why did you calculate the above, I would like to mention that I understand the problem sufficiently clear.

Thanks..
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: Real Challenge  [#permalink]

Show Tags

himanshuhpr wrote:
EvaJager wrote:
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

^^^ what's this that you have done , can you please explain thinking why did you calculate the above, I would like to mention that I understand the problem sufficiently clear.

Thanks..

I edited my first post, see the CORRECTION attached :

What a miss! We have to find the sum of the numbers and not the set of numbers. Although there is more than one possibility, the total sum is clearly 7*5 = 35.

And IanStewart is right about (1), in a set of numbers, each element is different.

I was trying to find sets which fulfill the given conditions, which was in fact unnecessary. We were only asked what is the sum of the numbers.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern  B
Joined: 11 Jul 2012
Posts: 47
GMAT 1: 650 Q49 V29 Re: Real Challenge  [#permalink]

Show Tags

EvaJager wrote:
himanshuhpr wrote:
EvaJager wrote:
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfill the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

^^^ what's this that you have done , can you please explain thinking why did you calculate the above, I would like to mention that I understand the problem sufficiently clear.

Thanks..

I edited my first post, see the CORRECTION attached :

What a miss! We have to find the sum of the numbers and not the set of numbers. Although there is more than one possibility, the total sum is clearly 7*5 = 35.

And IanStewart is right about (1), in a set of numbers, each element is different.

I was trying to find sets which fulfill the given conditions, which was in fact unnecessary. We were only asked what is the sum of the numbers.

EvaJager.... could you please explain the entire solution.....please do it independently and not as an extension of some other post...
Director  Joined: 22 Mar 2011
Posts: 588
WE: Science (Education)
Re: Real Challenge  [#permalink]

Show Tags

1
EvaJager.... could you please explain the entire solution.....please do it independently and not as an extension of some other post...[/quote]

This is my original post:

s-is-a-set-of-positive-integers-the-average-of-the-terms-in-139444.html#p1124575

Which part didn't you understand?

As I mentioned before, I misunderstood the question and I was trying to find concrete sets of numbers which fulfill the conditions.

Please, refer to IanStewart's post for a correct solution:

s-is-a-set-of-positive-integers-the-average-of-the-terms-in-139444.html#p1124943
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Intern  Joined: 20 Nov 2012
Posts: 13
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

(A+B+C+D+E)/5=E-A
A+B+C+D+E= 5(E-A)

Range can only by a 3 or a 7: 5*3=15

Therefore, the sum of A+B+C+D+E =15
this can only happen if A+B+C+D+E = 1+2+3+4+5

n(n+1)/2=(5*6)/2=15

but it cannot be 15 because 5-1 is 4 which is not a prime number. Therefore, the range must be 7 and the sum equal to 35.
Retired Moderator S
Joined: 14 Dec 2013
Posts: 2861
Location: Germany
Schools: German MBA
GMAT 1: 780 Q50 V47 WE: Corporate Finance (Pharmaceuticals and Biotech)
Re: Real Challenge  [#permalink]

Show Tags

Capricorn369 wrote:
EvaJager wrote:
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is
the sum of all the integers in S?
(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

A - average
(1) Primes less than 11 are 2, 3, 5, and 7. Not factor of 10, we are left with 3 and 7.
If A = 3, we can have {2, 2, 3, 5} or {1, 2, 3, 4, 4, 4}.
Not sufficient.

(2) For 5 evenly spaced numbers, k - 2d, k - d, k, k + d, k + 2d the range is 4d and the average is k.
We can simply take k = 4d, and we have infinitely many sets fulfilling the condition of the form {2d, 3d, 4d, 5d, 6d}.
For example {2, 3, 4, 5, 6}, {20, 30, 40, 50, 60}...
Not sufficient.

(1) and (2) together:
We have seen above that the range can be either 3 or 7.
If the range is 3, we cannot have 5 distinct integers in the set, so only 7 is left.

We know that the sum of the 5 integers is 5 * 7 = 35, the smallest number is k and the largest number is k + 7, where k is some positive integer.
Necessarily 35 - 7 = 28 > 5k, so k must be not greater than 5.
If k = 5, the first and the last number are 5 and 12. The smallest 3 remaining integers are 6, 7, and 8 together with 5 and 12 will give a sum of 37.
If k = 4, we find sets which fulfills the condition: {4, 5, 7, 8, 11} and also (4, 5, 6, 9, 11}.
Obviously, not sufficient.

@EvaJager - in (2) why are you considering "5 evenly spaced numbers"? This is not mentioned anywhere in the question.

From statement 1 and statement 2, we have range = 7 ( cannot be 2,5 or 3), hence average is also 7, hence sum = 5*7 = 35
Intern  Status: Never give up
Joined: 09 Aug 2013
Posts: 1
Location: India
Concentration: Finance, Entrepreneurship
WE: Analyst (Investment Banking)
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

I think the answer should still be E.

Statement two says that set S is composed of 5 different integers- this IMO doesn't mean that S is composed of exactly 5 integers.

Two contrasting examples:

S= {3,6,7,9,10) - range = 7 and mean = 7. The Sum is 35
S= {3,6,7,7,9,10)- range = 7 and mean = 7. The Sum is 42

Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

1
vivin0292 wrote:
I think the answer should still be E.

Statement two says that set S is composed of 5 different integers- this IMO doesn't mean that S is composed of exactly 5 integers.

Two contrasting examples:

S= {3,6,7,9,10) - range = 7 and mean = 7. The Sum is 35
S= {3,6,7,7,9,10)- range = 7 and mean = 7. The Sum is 42

(2) says that S is composed of 5 different integers.
_________________
Intern  B
Joined: 30 Nov 2016
Posts: 15
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

Quote:
It is the easiest to express the average when the numbers are evenly spaced. The goal is to find as easily as possible one/more examples which fulfill the condition.
And it is nowhere stated that the numbers cannot be evenly spaced. Also, in (1) it was not mentioned that some of the numbers cannot be equal.

Nowhere stated that the numbers cannot be evenly spaced DOESN'T MEAN that the numbers are evenly spaced. Do you have another explanation?
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8104
Location: United States (CA)
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

2
1
rohitgarg wrote:
S is a set of positive integers. The average of the terms in S is equal to the range of the terms in S. What is the sum of all the integers in S?

(1) The range of S is a prime number that is less than 11 and is not a factor of 10.
(2) S is composed of 5 different integers.

We are given that S is a set of positive integers and the average of the terms in S is equal to the range of the terms in S. We need to determine the sum of all the integers in S.

Statement One Alone:

The range of S is a prime number that is less than 11 and is not a factor of 10.

Using information in statement one, we know that the range of S is 3 or 7. Thus, the average of S is also 3 or 7. However, since we don’t know whether it is 3 or 7, nor do we know the number of integers in S, statement one alone is not sufficient to answer the question.

Statement Two Alone:

S is composed of 5 different integers.

Since we don’t know any of the 5 integers, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

From statement one, we know that the range and average are either both 3 or both 7. From statement two, we know S is composed of 5 different positive integers. Thus, the sum of these 5 integers is either 15 (if the average is 3) or 35 (if the average is 7). Therefore, we have two cases to consider: range = average = 3 (case 1) and range = average = 7 (case 2).

Case 1: range = average = 3

We can let x = the smallest number, so the largest number = x + 3. We can “squeeze” 2 more integers between x and x + 3, namely x + 1 and x + 2. So, there could be only 4 different total integers. However, remember that there should be 5 different integers in S; thus, case 1 is not possible.

So, it must be case 2: range = average = 7. If that is the case, the sum of the 5 integers is 35.

For example, the 5 integers could be 4, 5, 7, 8, and 11. We see that the range is 11 - 4 = 7 and the sum is 4 + 5 + 7 + 8 + 11 = 35 with an average of 7.

_________________

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.

Intern  B
Joined: 02 Sep 2017
Posts: 22
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

Bunuel wrote:
vivin0292 wrote:
I think the answer should still be E.

Statement two says that set S is composed of 5 different integers- this IMO doesn't mean that S is composed of exactly 5 integers.

Two contrasting examples:

S= {3,6,7,9,10) - range = 7 and mean = 7. The Sum is 35
S= {3,6,7,7,9,10)- range = 7 and mean = 7. The Sum is 42

(2) says that S is composed of 5 different integers.

Hi Bunuel - Can you pls help me in this, its really confusing.

IMO,
From Statements (1) and (2) together, we know that the range of the terms in S must be 7. This means that the average of the terms in S is also 7. It may be concluded form this that the sum of the terms in S is equal to the average (7) multiplied by the number of terms (5) = 7 × 5 = 35. However, while Statement (2) says that S is composed of 5 different integers, this does not mean that S is composed of exactly 5 integers since each integer may occur in S more than once. So I think the correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient.
Can you pls elaborate a bit by taking the above mentioned example
Intern  Joined: 02 Oct 2013
Posts: 11
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

shringi87 wrote:
Bunuel wrote:
vivin0292 wrote:
I think the answer should still be E.

Statement two says that set S is composed of 5 different integers- this IMO doesn't mean that S is composed of exactly 5 integers.

Two contrasting examples:

S= {3,6,7,9,10) - range = 7 and mean = 7. The Sum is 35
S= {3,6,7,7,9,10)- range = 7 and mean = 7. The Sum is 42

(2) says that S is composed of 5 different integers.

Hi Bunuel - Can you pls help me in this, its really confusing.

IMO,
From Statements (1) and (2) together, we know that the range of the terms in S must be 7. This means that the average of the terms in S is also 7. It may be concluded form this that the sum of the terms in S is equal to the average (7) multiplied by the number of terms (5) = 7 × 5 = 35. However, while Statement (2) says that S is composed of 5 different integers, this does not mean that S is composed of exactly 5 integers since each integer may occur in S more than once. So I think the correct answer is E: Statements (1) and (2) TOGETHER are NOT sufficient.
Can you pls elaborate a bit by taking the above mentioned example

Hi Bunel / Experts

Can you please explain this in a new thread maybe.

Thanks
Intern  B
Joined: 21 Sep 2018
Posts: 12
Location: India
Concentration: Marketing, Other
GPA: 3.6
Re: S is a set of positive integers. The average of the terms in  [#permalink]

Show Tags

Why no set with range 3 cannot have 5 distinct integers?

Posted from my mobile device Re: S is a set of positive integers. The average of the terms in   [#permalink] 13 Oct 2018, 07:43
Display posts from previous: Sort by

S is a set of positive integers. The average of the terms in

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

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  