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A quality inspector accepts a steel rod only if the difference between its length L, in centimeters, and the target length of 50 centimeters has an absolute value of exactly 3; that is, only if |L − 50| = 3. Of the following rod lengths, how many would the inspector accept: 44, 47, 50, 53, and 56?
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Correct answer
C
Method 1 (split into two cases): |L − 50| = 3 means L − 50 = 3 or L − 50 = −3. The first gives L = 53 and the second gives L = 47. Checking the list 44, 47, 50, 53, 56, exactly two values qualify: 47 and 53. So the answer is 2.
Method 2 (distance on a number line): |L − 50| = 3 says L sits exactly 3 units from 50, which is 50 + 3 = 53 or 50 − 3 = 47. Both appear in the list, giving 2 acceptable rods.
The wrong choices each come from a specific slip. Choice 0 puts the 50 on the wrong side, solving L + 50 = 3, so it finds no listed length. Choice 1 keeps only the positive case and counts 53 alone, dropping the negative case that produces 47. Choice 3 reads the equals sign as at most, sweeping in 47 through 53 and counting 47, 50, and 53. Choice 4 reads it as at least, counting the lengths 3 or more units away: 44, 47, 53, and 56. Only choice 2 handles both sign cases and matches the exact-distance condition.
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