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

Question

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

broall · Accepted Answer

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 $25$.

The correct answer is C

vitaliyGMAT · Answer

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 .

Answer C.

Abhishek009 · Answer

-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

gracie · Answer

let n=number of integers in set
sum of n-1 integers=49+23=72
looking at answer choices,
24=72/3
let n-1=3
23+24+25=72
25
C

kanusha · Answer

For Consecutive Integers Sum = ( last-first ) + 1
49 = L - (-23) + 1
49 = L + 23
L = 25
C

anamika4 · Answer

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

Sent from my Pixel 2 using  GMAT Club Forum mobile app

anamika4 · Answer

Just curious to know if there is any other way to solve above question by using equations of Arithmetic progression

Sent from my Pixel 2 using  GMAT Club Forum mobile app

KSBGC · Answer

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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards