Skip to Main Content

Source: Official Guide for the GMAT 13th Ed. Problem Solving; #80 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #80

▲

7

M is the sum of the reciprocals

M is the sum of the reciprocals of the consecutive integers from 201 to 300 inclusive. Which of the following is true?

3 Explanations

▲

2

Tobias Meyerding

wouldn't it be faster to simply take the middle value of this list (1/250) and multiply by 100 (number of different values) which yields 100/250 = 2/5; a value clearly between 1/2 and 1/3?

Nov 14, 2016 • Comment

Sam Kinsman

Hi Tobias,

That's a clever way of looking at it! However, it doesn't quite work. If we take that approach, we happen to get a similar value to M. But that's actually a bit of a coincidence. Let me explain why this doesn't work using a simpler example!

Let's say we have the following sum:

1/1 + 1/2 + 1/3 + 1/4 + 1/5.

If we solve this with a calculator, we get 2.283

If we use the approach you suggested for this one, we would have the middle value (1/3) multiplied by 5.

(1/3) * 5 = 5/3 = 1.66

This is not the same as 2.283. So the method doesn't really work when we have fractions.

If we have a sum that doesn't involve fractions, the method does work. For example:

1+2+3+4+5 = 15

3 * 5 = 15

However, this doesn't work with fractions.

Nov 15, 2016 • Reply

▲

4

Number of fractions in the secuence:

last - first + 1 = 300 - 201 + 1 = 301 - 201 = 100

So, we have 50 couples of fractions (The sum of the first term and the last one is equal to the sum of the second term and the term #99, and so on)

sum of the first and the last term:

(1/201) + (1/300)

Let´s simplify (we will obtain a result slightly greater than the "real" one, since 1/200 is greater than 1/201.

(1/200) + (1/300) = 5 / 600

The sum of the sequence will be this term multiply by the # of couples (every couple sum 5/600 aprox).

(5/600) * # couples = (5/600) * 50 = (250/600) = 5/12

Since our term is slightly greater than the real one, the result will be slightly less than 0,4.

Option A links to our prediction.

0.3333 < M < 0.5

pdta: thanks for pointing out 5/600 :)

Jan 25, 2015 • Comment

How does (1/200) + (1/300) = 6 / 600? Is it not 5/600 instead?

Mar 24, 2015 • Reply

▲

3

Mike McGarry, Magoosh Tutor

Dec 27, 2013 • Comment

Add Your Explanation

You must have a Magoosh account in order to leave an explanation.

Learn More About Magoosh

Official GMAT Material

Official Guide for GMAT Review 2016

Official Guide for the GMAT 2015 14th Ed.

Official Guide for the GMAT 13th Ed.

Nova's GRE Prep

Official Guide for the GMAT 12th Ed.

Revised GRE PDF 2nd Ed.

Section 5.3 Problem Solving

Section 5.3 Problem Solving

Improve Your Score

Magoosh GMAT is an affordable online course for studying the GMAT.

Learn More About Magoosh

Share Post

Return to Forum