What is the sum of the integers from 1 to 999 , inclusive?

Question

What is the sum of the integers from 1 to 999, inclusive?

A. 499000
B. 499500
C. 499999
D. 500500
E. 500999

Vinayak Shenoy · Answer

B
number of integers = (999-1)+1=999
if you observe 1st term and last term gives you a sum of 1000
there are 999/2= 499.5 499 such pairs
so 499*1000+500= 499500

ashishahujasham · Answer

Summation of n numbers = n*(n+1)/2

If n= 1000 summation of first 1000 numbers

So 1000*1001/2 = 500500

500500-1000 as we don't need the last term.... 499500

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Abhishek009 · Answer

Sum of the integers from 1 to 999, inclusive =  \frac{999 ( 999 + 1 )}{2} = 499500

Answer will be (B) 499500

naorba · Answer

simplest way i noticed would be:

quantity of numbers: (999-1)+1 =  999  --->  (Last number - First number) + 1

Average: (999+1)/2 =  500  ---->  (Last number + First number)/2

now:
  Average * quantity   
999* 500

for fast calc we notice that 999 i very close to 1,000, So:
500*1000 = 500,000 
500,000 - 500 =  499,500

B

EMPOWERgmatRichC · Answer

Hi All,

These types of 'bunching' questions often come down to how you choose to 'organize' the math involved.

Here, we're asked for the sum of all of the integers from 1 to 999, inclusive. We're talking about the first 999 positive integers, but I'm going to make the math a little easier by adding one extra integer that won't affect the sum at all: the number 0.

By including 0, we now have 1,000 total integers and we can 'bunch' them into groups of 2:

0 and 999 = 999
1 and 998 = 999
2 and 997 = 999
Etc.

Since we have 1,000 total numbers, there will be 500 'pairs' that add up to 999. Thus, the sum of those terms is...

(500)(999)

While that calculation might seem a little tough, you can avoid it if you think about the math in a different way...

(500)(1000) = 500,000

999 is "one less" than 1,000 so we just have to subtract "one" of those 500s from 500,000. That gives us:

500,000 - 500 = 499,500

Final Answer:  B

GMAT assassins aren't born, they're made,
Rich

dumbodingo · Answer

Sum = number of terms * mean

- # of terms = (999-1), but we need to add '1' to the resultant as this is an inclusive set, bringing us back to '999'.
- mean of the set = first term+last term divided by 2 which gives us 500 (1+999 = 1000/2 = 500)

Putting it into the original equation:
- sum = 999 (number of terms) * 500 (mean) = 499500

Hope that helps!

ladyrenee95 · Answer

Number of Integers (Inclusive) = N = (Last # - First #)+1

Sum of Integers = (First # + Last #)*N))/2

1 . N= (999-1) + 1 = 999

2 . (1+999)*999))/2 = 499,500  B

ScottTargetTestPrep · Answer

The sum of the integers from 1 to 999, inclusive, is:

sum = quantity x average = 999 x (1 + 999)/2 = 999 x 1000/2 = 999 x 500 = 499,500

Answer: B

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What is the sum of the integers from 1 to 999 , inclusive?

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What is the sum of the integers from 1 to 999 , inclusive?

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