Official Guide Explanation:
Problem Solving #50

Background

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Solution and Metadata

Question: 50
Page: 159
Difficulty: 5 (Moderate)
Category 1: Algebra > Absolute Value >

Explanation: An expression inside absolute value signs can never be negative, so we're looking for the value of 23 - 5y that is closest to zero. Given that we're working with small numbers, the best way to find this is some simple trial and error. Since 5(5) = 25, that will get us close to zero--if y = 5, 23 - 5y= - 2, so the absolute value is 2. If y is larger, the value of 23 - 5y gets smaller, so the absolute value gets larger. y could also be smaller; if y = 4, 23 - 5y = 3. That's not as close to zero; the absolute value is greater than the absolute value when y = 5. Thus, the least possible value of |23 - 5y| is 2, choice (B).

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