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# What is the difference between the sum of the even integers from 1–100

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the difference between the sum of the even integers from 1–100  [#permalink]

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23 Jan 2019, 01:12
00:00

Difficulty:

45% (medium)

Question Stats:

67% (01:14) correct 33% (01:15) wrong based on 38 sessions

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What is the difference between the sum of the even integers from 1–100 and the sum of the odd integers from 1–100?

A 0
B 25
C 26
D 50
E 52

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Joined: 15 Feb 2018
Posts: 246
Re: What is the difference between the sum of the even integers from 1–100  [#permalink]

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23 Jan 2019, 05:11
They are in pairs
1 with 2
3 with 4
...
99 with 100

Each pair has a difference of 1. There are 50 such pairings. D
Manager
Joined: 13 Feb 2018
Posts: 156
GMAT 1: 640 Q48 V28
Re: What is the difference between the sum of the even integers from 1–100  [#permalink]

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24 Jan 2019, 08:12
First even integer 2, last one 100
$$\frac{100-2}{2}$$+1=50 even integers
Average of these 50 even integers $$\frac{100+2}{2}$$=51
Sum of even integers=average*number of even int=51*50

First odd integer 1, last one 99
$$\frac{99-1}{2}$$+1=50 odd integers
average of these odd integers $$\frac{99+1}{2}$$=50
Sum of odd integers=average*number of odd int=50*50

difference between the sum of even and odd integers
51*50-50*50=50(51-50)=50

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Re: What is the difference between the sum of the even integers from 1–100  [#permalink]

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27 Jan 2019, 19:13
Bunuel wrote:
What is the difference between the sum of the even integers from 1–100 and the sum of the odd integers from 1–100?

A 0
B 25
C 26
D 50
E 52

If we compare the first few even and odd integers starting from 1, we have:

1 and 2

3 and 4

5 and 6

7 and 8

Notice that each even integer is “one more” than its odd counterpart. Since there are 50 even integers and 50 odd integers between 1 and 100, the sum of the even integers will be 50 more than the sum of the odd integers.

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Re: What is the difference between the sum of the even integers from 1–100  [#permalink]

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27 Jan 2019, 19:45
Bunuel wrote:
What is the difference between the sum of the even integers from 1–100 and the sum of the odd integers from 1–100?

A 0
B 25
C 26
D 50
E 52

1 to 100, 50 even & 50 odd

Apart from that 1st even number 2 to 100

1st odd number 1 to last odd number 99

Sn = n/2 (1st term + last term), since the series will be an AP

Sn(even) = 50/2 * 102
= 50 * 51

Sn(odd) = 50/2 * 100
= 50 * 50

Difference = 50 * (51 - 50)
=50

D
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Re: What is the difference between the sum of the even integers from 1–100   [#permalink] 27 Jan 2019, 19:45
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