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## Official Guide Explanation:Problem Solving #89

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 89
Page: 164
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Fractions >
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: To keep things simple, call the product of the integers from 100 to 200, inclusive, p. Thus, s = p. Since t is the same, only it also multiplies the total by 201, t = 201p.

To find (1/(s)) + (1/(t)), start in terms of p:

(1/(p)) + (1/(201p))

= (201/(201p)) + (1/(201p))

= (202/(201p))

We're looking for the same answer, but in terms of t. Since t = 201p, we can directly substitute t for the denominator:

= (202/(t)), choice (D).

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