AEMCE
This topic has expert replies
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.
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.
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
For any EVENLY SPACED SET:Meek_21 wrote:Find the sum of all even integers from 12 to 650
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7247
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can use the formula sum = average x quantity
sum = (12 + 650)/2 x [(650 - 12)/2 + 1]
sum = 331 x 320 = 105,920
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews