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

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

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10 Dec 2016, 05:20
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76% (01:02) correct 24% (01:54) wrong based on 88 sessions

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In a set of consecutive integers the least number is –23. If the sum of the set is 49 what is the greatest value in the set?

A. 49
B. 26
C. 25
D. 24
E. 0

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Posts: 367
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Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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10 Dec 2016, 05:55
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Sum of positive elements - Sum of negative elements = 49

Zero does not add any value so for a sum we can ignore it.

$$\frac{n(n+1)}{2} – \frac{23*24}{2} = 49$$

$$\frac{n(n+1)}{2} – 276 = 49$$

$$\frac{n(n+1)}{2} = 325$$

$$n(n+1) = 650 = 25*26$$

$$n=25$$

We have sum of $$25$$ consecutive positive integers (natural numbers) so the greatest value should be $$25$$.

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In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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10 Dec 2016, 06:54
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Bunuel wrote:
In a set of consecutive integers the least number is –23. If the sum of the set is 49 what is the greatest value in the set?

A. 49
B. 26
C. 25
D. 24
E. 0

The set is: $$-23, -22,-21,...,n$$

We could use formula to calculate the sum of the set.

Here is another solution for this question.

Note that the least number is $$-23$$, next is $$-22, -21,..., -1,0$$.

The sum of all these numbers is negative, so in order to make the sum positive, first we need to make it equal to 0.

Hence, the list of the next numbers are: $$1,2,3,...,22,23$$

Now, the sum of the set $$-23,-22,...,0,...,22,23$$ is $$0$$.

The next numbers are 24 and 25. Now the sum of the set $$-23,-22,...,0,...,22,23,24,25$$ is $$0+24+25=49$$. This means the final number in the set is $$25$$.

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In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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10 Dec 2016, 10:39
1
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the sum of the set is 49 what is the greatest value in the set?

A. 49
B. 26
C. 25
D. 24
E. 0

-23 + ( - 22) + ( - 21)............... 21 + 22 + 23 = 0

Now, after 23 there will be 2 numbers which will add upto 49 , ie 24 + 25 = 49

The greatest number is thus (C) 25
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Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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10 Dec 2016, 12:27
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the sum of the set is 49 what is the greatest value in the set?

A. 49
B. 26
C. 25
D. 24
E. 0

let n=number of integers in set
sum of n-1 integers=49+23=72
24=72/3
let n-1=3
23+24+25=72
25
C
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Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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10 Dec 2016, 16:46
For Consecutive Integers Sum = ( last-first ) + 1
49 = L - (-23) + 1
49 = L + 23
L = 25
C
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Posts: 13
Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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21 Dec 2017, 21:59
kanusha wrote:
For Consecutive Integers Sum = ( last-first ) + 1
49 = L - (-23) + 1
49 = L + 23
L = 25
C

sum=N/2*(first term+ last term)

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Posts: 13
Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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21 Dec 2017, 22:00
Just curious to know if there is any other way to solve above question by using equations of Arithmetic progression

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Re: In a set of consecutive integers the least number is –23. If the sum  [#permalink]

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11 Feb 2019, 10:11
Bunuel wrote:
In a set of consecutive integers the least number is –23. If the sum of the set is 49 what is the greatest value in the set?

A. 49
B. 26
C. 25
D. 24
E. 0

This question is all about set that contains both positive and negative integers.

Problem i faced while solving this question is clueless set. amorphous set. Don't know anything about the set except sum and the least value.

Important thing is that if the set contains all the negative integers sum sum can't be positive. ****

It indicates that the set includes positive and negative integers.

now what about the no. of items.

set starts with -23. Thus , at least we have to have + 23 to overcome negative impact.

-23 +.......................................+ 23 =0

Given sum is 49.

we conclude that we have more elements in the set.

24 + 25 = 49.

Thus , 25 is the correct answer.
Re: In a set of consecutive integers the least number is –23. If the sum   [#permalink] 11 Feb 2019, 10:11
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