BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

OG#157

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 116
Joined: Wed Oct 03, 2012 10:44 pm
Thanked: 5 times
Followed by:1 members

OG#157

by theachiever » Mon Nov 19, 2012 11:47 pm
For positive integer n,the sum of the first n positive integers equals n(n+1)/2.What is the sum of all the even integers between 99 and 301?

A.10,100
B.20,200
C.22,650
D.40,200
E.45,150
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1248
Joined: Thu Mar 29, 2012 2:57 pm
Location: Everywhere
Thanked: 503 times
Followed by:192 members
GMAT Score:780

by Bill@VeritasPrep » Mon Nov 19, 2012 11:53 pm
We have a set of even numbers from 100 to 300 (since 99 and 301 are odd), so the range is 200. This means that we have (200/2) + 1 = 101 even numbers. (We add one because it is inclusive).

We also know that the median in an evenly distributed set can be found by finding the mean of the minimum and maximum values. 100 + 300 = 400; 400/2 = 200.

The final step is to multiply 101 and 200. 200 * 101 = 20,200.
Join Veritas Prep's 2010 Instructor of the Year, Matt Douglas for GMATT Mondays

Visit the Veritas Prep Blog

Try the FREE Veritas Prep Practice Test
Top
User avatar
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

by GMATGuruNY » Tue Nov 20, 2012 3:51 am
I posted a solution here:

https://www.beatthegmat.com/for-any-posi ... tml#361604
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
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 20, 2012 8:49 am
theachiever wrote:For positive integer n,the sum of the first n positive integers equals n(n+1)/2.What is the sum of all the even integers between 99 and 301?

A.10,100
B.20,200
C.22,650
D.40,200
E.45,150
Here's another approach:

We want 100+102+104+....298+300
This equals 2(50+51+52+...+149+150)
From here, a quick way is to evaluate this is to first recognize that there are 101 integers from 50 to 150 inclusive (150-50+1=101)

To evaluate 2(50+51+52+...+149+150) I'll add values in pairs:

....50 + 51 + 52 +...+ 149 + 150
+150+ 149+ 148+...+ 51 + 50
...200+ 200+ 200+...+ 200 + 200

How many 200's do we have in the new sum? There are 101 altogether.
101x200 = 20,200 = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pm
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1268 members
GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 20, 2012 8:51 am
theachiever wrote:For positive integer n,the sum of the first n positive integers equals n(n+1)/2.What is the sum of all the even integers between 99 and 301?

A.10,100
B.20,200
C.22,650
D.40,200
E.45,150
Alternatively, if we want to evaluate 2(50+51+52+...+149+150), we can evaluate the sum 50+51+52+...+149+150, and then double it.

Important: notice that 50+51+.....149+150 = (sum of 1 to 150) - (sum of 1 to 49)

Now we use the formula:
sum of 1 to 150 = 150(151)/2 = 11,325
sum of 1 to 49 = 49(50)/2 = 1,225

So, sum of 50 to 150 = 11,325 - 1,225 = 10,100

So, 2(50+51+52+...+149+150) = 2(10,100) = 20,200 = B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Post new topic Post Reply
• Page 1 of 1