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Mathematics > Standard Multiple Choice

Read the following SAT test question and then click on a button to select your answer. 

If (absolute value of a) minus (absolute value of b) equals 5, which of the following could be true?

Answer Choices

Yep! That's right.

Explanation

If b equals 0 and a equals 5, then (absolute value of a) minus (absolute value of b) equals (absolute value of 5) minus (absolute value of 0) equals 5. Hence if (absolute value of a) minus (absolute value of b) equals 5, it could be true that b equals 0.

If (absolute value of a) minus (absolute value of b) equals 5, none of the other four statements could be true:

  •   If a equals 0, then (absolute value of a) minus (absolute value of b) equals 0 minus (absolute value of b) equals negative (absolute value of b). However, since (absolute value of b) is greater than or equal to 0, there is no value of b for which negative (absolute value of b) equals 5.
  •   If a equals b, then (absolute value of a) minus (absolute value of b) equals (absolute value of a) minus (absolute value of a) equals 0 does not equal 5.
  •   If a equals negative b, then (absolute value of a) minus (absolute value of b) equals (negative absolute value of b) minus (absolute value of b) equals (absolute value of b) minus (absolute value of b) equals 0 does not equal 5.
  •   If a equals 1, then (absolute value of a) minus (absolute value of b) equals (absolute value of 1) minus (absolute value of b) equals 1 minus (absolute value of b). However, since (absolute value of b) is greater than or equal to 0, there is no value of b for which 1 minus (absolute value of b) equals 5.

 

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