AEMCE

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Meek_21: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sun Sep 24, 2017 8:46 pm

by Meek_21 » Sun Sep 24, 2017 9:14 pm

Find the sum of all even integers from 12 to 650

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Source: Beat The GMAT — Problem Solving | Sun Sep 24, 2017 9:14 pm

pannalal: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Wed Sep 20, 2017 5:42 pm; Thanked: 2 times

AEMCE

by pannalal » Sun Sep 24, 2017 11:49 pm

Find the sum of all even integers from 12 to 650

We can solve question in different ways. Below, I give two methods:

(1) Let us divide the number 12 and 650 by 2 as we want sum of even numbers. We get 6 to 325. We add these numbers and multiply by 2. Total numbers = 325-6+1 = 320. So,
Sum = 320*(6+325)/2*2 = 320*331 = 105920.

(2) Using Arithmetic Progression Sum.
Sum = n/2*{2a+(n-1)d} where n = 320, a = 12, d = 2.
= 320/2*(24 + 319x2) = 160*(24 + 638) = 160*662 = 105920.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Sep 25, 2017 2:49 am

Meek_21 wrote:Find the sum of all even integers from 12 to 650

For any EVENLY SPACED SET:
Number of terms = (biggest-smallest)/interval + 1, where the interval is the distance between successive terms.
Average = median = (biggest + smallest)/2.
Sum = (number of terms)(average).

Here, the interval between successive terms is 2.
Thus:
Number of terms = (650-12)/2 + 1 = 325 - 6 + 1 = 320.
Average = (650+12)/2 = 325 + 6 = 331.
Sum = 320*331 = 105920.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8151; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: AEMCE

by Scott@TargetTestPrep » Sun Feb 02, 2020 12:42 pm

Meek_21 wrote: ↑
Sun Sep 24, 2017 9:14 pm
Find the sum of all even integers from 12 to 650

We can use the formula sum = average x quantity

sum = (12 + 650)/2 x [(650 - 12)/2 + 1]

sum = 331 x 320 = 105,920

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