Official Guide Explanation:
Problem Solving #109




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Solution and Metadata

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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