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

Redeem

Arithmetic

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Junior | Next Rank: 30 Posts
Posts: 26
Joined: Tue Feb 02, 2016 10:25 am
Thanked: 1 times

Arithmetic

by John fran kennedi » Fri Apr 01, 2016 9:39 am
100. M is the sum of the reciprocals of the consecutive integers from 201 to 300, inclusive. Which of the following is true?
(A) 1/3 < M < 1/2
B) 1/5 < M < 1/3
(C) 1/7 < M < 1/5
(D)1/9 < M < 1/7
(E) 1/12 < M < 1/9

The correct answer : A

What's the best strategy to solve this ?
Top
Source: — Problem Solving |

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 » Fri Apr 01, 2016 9:45 am
M is the sum of the reciprocals of the consecutive integers from 201 to 300 inclusive. Which of the following is true?
A) 1/3 <M 1/2
B)1/5<M<1/3
C)1/7 <M< 1/5
D) 1/9 < M < 1/7
E) 1/12 <M< 1/9
We want to find 1/201 + 1/202 + 1/203 + . . . + 1/299 + 1/300

NOTE: there are 100 fractions in this sum.

Let's examine the extreme values (1/201 and 1/300)

First consider a case where all of the values are equal to the smallest fraction (1/300)
We get: 1/300 + 1/300 + 1/300 + ... + 1/300 = 100/300 = 1/3
So, the original sum must be greater than 1/3

Now consider a case where all of the values are equal to the biggest fraction (1/201)
In fact, let's go a little bigger and use 1/200
We get: 1/200 + 1/200 + 1/200 + ... + 1/200 = 100/200 = 1/2
So, the original sum must be less than 1/2

Combine both cases to get 1/3 < M < 1/2 = A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 am
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by DavidG@VeritasPrep » Fri Apr 01, 2016 9:53 am
The GMAT likes these types of problems. See here for another one: https://www.beatthegmat.com/sum-of-recip ... 27092.html
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pm
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:511 members
GMAT Score:800

by [email protected] » Fri Apr 01, 2016 2:32 pm
Hi John fran kennedi,

In this prompt, the answer choices are "ranges"; this usually means that there's a way to avoid doing lots of math and instead use patterns and logic to save you time.

Brent's already pointed out the easiest way to figure out the minimum and maximum values of the sum of the reciprocals. You can actually stop working once you figure out the minimum though:

Since 1/300 < 1/201 and the sum of those 100 terms would be 1/3 AT THE MINIMUM, the only answer that's possible would be A. The extra work that Mitch did just confirms the maximum value of the sum, but it's unnecessary.

As you continue to study, be mindful of how the answer choices are written - they can sometimes provide a huge hint into the fastest way to answer the question.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pm
Thanked: 1443 times
Followed by:247 members

by ceilidh.erickson » Sat Apr 02, 2016 12:34 pm
To add to what Rich said... make sure that you always scan the answer choices on PS questions before you dive in and start solving. They can often give you clues about how to approach the problem.

I've written an entire article about that here:
https://www.manhattanprep.com/gmat/blog ... -pen-down/
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top
Post new topic Post Reply
• Page 1 of 1