Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 17 Jul 2019, 01:42

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

n is the product of least and greatest 6 consecutive integers. What is

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

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 03 Jun 2010
Posts: 4
n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post Updated on: 05 Jan 2015, 04:15
4
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

77% (01:21) correct 23% (01:30) wrong based on 240 sessions

HideShow timer Statistics


n is the product of least and greatest 6 consecutive integers. What is n?

(1) The greatest integer is 20
(2) The average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.

Originally posted by anuragsingal on 11 Sep 2010, 04:53.
Last edited by Bunuel on 05 Jan 2015, 04:15, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Intern
Intern
avatar
Joined: 21 Aug 2009
Posts: 39
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 11 Sep 2010, 04:55
1
Hi anurag,

Could you please change the colour of the font. For some reason the top part shows yellow....Maybe its only in my system.

Thanks. :)
Intern
Intern
avatar
Joined: 03 Jun 2010
Posts: 4
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 11 Sep 2010, 04:57
2
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.
Senior Manager
Senior Manager
User avatar
Status: Time to step up the tempo
Joined: 24 Jun 2010
Posts: 346
Location: Milky way
Schools: ISB, Tepper - CMU, Chicago Booth, LSB
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 11 Sep 2010, 21:28
@Moderators -- Please move this post to the DS forum.
_________________
:good Support GMAT Club by putting a GMAT Club badge on your blog :thanks
CEO
CEO
User avatar
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2553
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Reviews Badge
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 24 Sep 2010, 01:18
anuragsingal wrote:
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.


First of all, do post the questions in the relevant forums.
Secondly the question is badly written it should say :

n is the product of least and greatest integers of the 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5
_________________
Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned :)

Jo Bole So Nihaal , Sat Shri Akaal

:thanks Support GMAT Club by putting a GMAT Club badge on your blog/Facebook :thanks

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html
Manager
Manager
avatar
Joined: 30 Aug 2010
Posts: 85
Location: Bangalore, India
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 24 Sep 2010, 03:18
anuragsingal wrote:
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.



Anurag:

You do not have to sum up all the 6 #s (t1,t2....) to find iut the #s for a given average.
As it is given that the 6#s are cosecutive intergers, the average of those 6 #s shud be th average of the middle 2 numbers ==> sum of middle 2 #s = 35 i.e 17.5*2 ==> middle #s, which are consecutive are 17 and 18 hence the first 2 are 15 and 16 and last two #s are 19 and 20.

Hope it helps
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 31 Jan 2016, 22:11
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

n is the product of least and greatest 6 consecutive integers. What is n?

(1) The greatest integer is 20
(2) The average arithmetic mean of 6 consecutive integers is 17.5


In the original condition, you need to figure out the number of consecutive integers and the first integer. So, there are 2 variables. In this question, it’s given that there are 6 consecutive integers and you only need to figure out the first integer. Thus, there is 1 variable, which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), 15,16,17,18,19,20, which is unique and sufficient.
For 2), also 15,16,17,18,19,20, which is unique and sufficient.
Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Intern
Intern
avatar
Joined: 08 Sep 2016
Posts: 1
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 21 Dec 2016, 21:59
anuragsingal wrote:
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.



When they say 'Consecutive numbers' do we assume that they are normal consecutive numbers (2,3,4,5,etc) rather than even / odd consecutive numbers?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56266
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 22 Dec 2016, 01:58
nischaynshah wrote:
anuragsingal wrote:
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.



When they say 'Consecutive numbers' do we assume that they are normal consecutive numbers (2,3,4,5,etc) rather than even / odd consecutive numbers?


"Consecutive integers" ALWAYS mean integers that follow each other in order with common difference of 1: ... x-3, x-2, x-1, x, x+1, x+2, ....

For example:

-7, -6, -5 are consecutive integers.

2, 4, 6 ARE NOT consecutive integers, they are consecutive even integers.

3, 5, 7 ARE NOT consecutive integers, they are consecutive odd integers.
_________________
Intern
Intern
avatar
Joined: 18 Dec 2016
Posts: 18
Location: United Kingdom
GMAT 1: 690 Q47 V38
GPA: 4
WE: Investment Banking (Investment Banking)
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 22 Dec 2016, 02:30
Did someone actually come across cosecutive even/odd integers in the GMAT? I know the GMAT OG introduces the theory shortly but I never saw a question where we think about them. Only (normal) consecutive integers ?!?!?!?
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42
GPA: 3.82
n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 10 Jan 2017, 23:16
nischaynshah wrote:
anuragsingal wrote:
106. n is the product of least and greatest 6 consecutive integers. What is n?
1) the greatest integer is 20
2) the average arithmetic mean of 6 consecutive integers is 17.5

Solution:
If n is the product of the least and the greatest of 6 consecutive integers, what is the value of n?
What do we know? We have a list of 6 consecutive integers. So, if we can determine which integers make up our list, we can certainly answer the question.

(1) the greatest integer in the list is 20
Well, if we know the biggest number on the list we can certainly count backwards to determine the other 5: sufficient.
(2) the average (arithmetic mean) of the integers is 17.5
Since our numbers are consecutive, we can certainly use this information to figure out exactly what the list is: sufficient.

If we needed to actually do so, we could:
1) know that for a set of consecutive numbers, mean = median. Since we have an even number of terms, the median is the average of the two middle terms, so the two middle terms in our set must be 17 and 18, which we can then expand to {15, 16, 17, 18, 19, 20}; or
2) use the average formula.
Average = (sum of terms)/(# of terms)
17.5 = (t1 + t2 + t3 + t4 + t5 + t6)/6
105 = t1 + t2 + t3 + t4 + t5 + t6
And, since our terms are consecutive, we know that:
t1 + t2 + t3 + t4 + t5 + t6 = t1 + (t1 + 1) + (t1 + 2) + (t1 + 3) + (t1 + 4) + (t1 + 5)
so
105 = 6(t1) + 15
90 = 6(t1)
15 = t1
so our set must be {15, 16, 17, 18, 19, 20}
Lots of other tricks we could use to also figure out the exact set.
Each of (1) and (2) is sufficient alone: choose D.



When they say 'Consecutive numbers' do we assume that they are normal consecutive numbers (2,3,4,5,etc) rather than even / odd consecutive numbers?



Hi,

In the original condition, from n,n+1,n+2,n+3,n+4,n+5, there is 1 variable(n).
Hence, D is likely to be an answer.

Happy Studying!
Math Revolution
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 11667
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

Show Tags

New post 09 Aug 2018, 17:25
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Bot
Re: n is the product of least and greatest 6 consecutive integers. What is   [#permalink] 09 Aug 2018, 17:25
Display posts from previous: Sort by

n is the product of least and greatest 6 consecutive integers. What is

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





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