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## Official Guide Explanation:Problem Solving #68

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 68
Page: 70
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Remainder

Explanation: The question tells us two things about n. It is one greater than a multiple of 5, which means the units digit is either 1 or 6. Also it is 3 greater than a multiple of 7. To find at least one possible value of n, go through the numbers that are 3 greater than a multiple of 7, looking for one with a units digit of 1 or 6:

3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73

The two possibilities are 31 and 66, each of which are 4 less than a multiple of 35 (35 or 70). Thus, if k + n is a multiple of 35, if n = 31, k = 4. The same applies if n = 66. Since a pattern seems to be developing, we don't need to worry about the possibility of a smaller value of k. Choice (B) is correct.

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