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

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4 00:00

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  Joined: 21 Aug 2009
Posts: 39
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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

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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.
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Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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@Moderators -- Please move this post to the DS forum.
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GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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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
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Manager  Joined: 30 Aug 2010
Posts: 85
Location: Bangalore, India
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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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
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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]

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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.

 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.
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Intern  Joined: 08 Sep 2016
Posts: 1
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 56266
Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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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.
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Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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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 ?!?!?!?
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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]

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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
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Re: n is the product of least and greatest 6 consecutive integers. What is  [#permalink]

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_________________ Re: n is the product of least and greatest 6 consecutive integers. What is   [#permalink] 09 Aug 2018, 17:25
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