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## Official Guide Explanation:Problem Solving #109

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: 109
Page: 75
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Factors and Multiples
Category 2: Arithmetic > Properties of Integers > Primes
Category 3: Arithmetic > Properties of Integers > Evens and Odds

Explanation: Another way of phrasing this question is, "Which of the following CANNOT be a multiple of 10?" Look at each answer choice, checking to see if there is a way for it to be a multiple of 10:

(A) 3 and 7 are two odd integers, and the sum of 3 and 7 is a multiple of 10.

(B) Any negative multiple of 10 yields an integer when divided by 10. For instance, ((-20)/10)= - 2.

(C) 2 and 5 are primes, and their product is a multiple of 10.

(D) 9, 10, and 11 are consecutive integers, and their sum is a multiple of 10.

(E) is correct: all multiples of 10 are even, so an odd integer cannot yield an integer when divided by 10.

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