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# In a set of consecutive integers the least number is – 23. If the aver

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Math Expert
Joined: 02 Sep 2009
Posts: 52230
In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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02 Jan 2018, 22:41
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Difficulty:

35% (medium)

Question Stats:

69% (01:34) correct 31% (01:22) wrong based on 74 sessions

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In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

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Joined: 25 Feb 2013
Posts: 1220
Location: India
GPA: 3.82
In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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03 Jan 2018, 03:22
1
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

Sum of $$n$$ consecutive integers $$= \frac{n(-23+last term)}{2}$$ (here last term of the series will have the greatest value)

Therefore average of $$n$$ terms $$= \frac{n(-23+last term)}{2n}=1$$

$$=> -23+Last term=2 => last Term=25$$

Option C
Manager
Joined: 02 Jan 2016
Posts: 124
Re: In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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23 Feb 2018, 21:27
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

Using logic

-23 + -22 ...0 + 1 + 2 ...+23, uptill this the sum = 0,

now we n = 24 (including "0") + 23 = 47; so n = 47 now we need avg as 1 i.e 1 distributed to 47 different no.'s, thus it we need 24 + 25 = 49 and then 47+ 2 = new N
thus 49/49 = 1
BSchool Forum Moderator
Joined: 07 Jan 2016
Posts: 872
Location: India
GMAT 1: 710 Q49 V36
Re: In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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23 Feb 2018, 22:03
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

-23 to 23 sum is 0 and we have 47 terms now 24+25 = 49 and we will have 49 terms

avg = 0 + 24 +25/49 = 1

thus largest 25
(C) imo
Manager
Joined: 27 Jul 2017
Posts: 50
Re: In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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24 Feb 2018, 07:31
2
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

A basic rule of number properties, we know that average of consecutive integers = (First term + Last term)/2. Now relating to the question first term is -23 and average of the set is 1. Putting above values in the formula will give us the answer 25. Therefore the answer is (C).
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Manager
Joined: 23 Sep 2016
Posts: 214
In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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26 Feb 2018, 23:37
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the average (arithmetic mean) of the set is 1, what is the greatest value in the set?

A. 27
B. 26
C. 25
D. 24
E. 23

answer is C i use the approach of plug in back i used c 1st as rest smaller or larger number will be eliminated as options are in descending order then total number of variables are 25-(-23)+1 because both terms are included. so total terms are 49 now total sum will be till 23 every thing is eliminated left with only 24+25 whose sum is also 49 and then average will be 1.
If you like my explanation please provide me kudos
Intern
Joined: 20 Dec 2017
Posts: 36
Location: Singapore
Re: In a set of consecutive integers the least number is – 23. If the aver  [#permalink]

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27 Feb 2018, 00:10
Would be easy by just using the mean formula: $$\frac{Xmin + Xmax}{2}= 1$$

Hence $$\frac{-23 + x}{2} = 1$$

$$x = 25$$

Re: In a set of consecutive integers the least number is – 23. If the aver &nbs [#permalink] 27 Feb 2018, 00:10
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