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18 Jun 2024, 23:52
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X is the set of all integers n that satisfy the inequality 2≤|n|≤5.
Quantity A
The absolute value of the greatest integer in X
Quantity B
The absolute value of the least integer in X
Quantity A
The absolute value of the greatest integer in X
Quantity B
The absolute value of the least integer in X
13 Jul 2024, 11:28
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Official Explanation
When comparing these quantities, it is important to remember that a nonzero number and its negative have the same absolute value. For example, |-2|=|2|=2. Keeping this in mind, you can see that the positive integers 2, 3, 4, and 5 and the negative integers -2, -3, -4, and -5 all satisfy the inequalities 2≤|n|≤5, and that these are the only such integers. Thus, the set X consists of the integers -5, -4, -3, -2, 2, 3, 4, and 5. The greatest of these integers is 5, and its absolute value is 5. The least of these integers is -5, and its absolute value is also 5. Therefore, Quantity A is equal to Quantity B. The correct answer is Choice C.
When comparing these quantities, it is important to remember that a nonzero number and its negative have the same absolute value. For example, |-2|=|2|=2. Keeping this in mind, you can see that the positive integers 2, 3, 4, and 5 and the negative integers -2, -3, -4, and -5 all satisfy the inequalities 2≤|n|≤5, and that these are the only such integers. Thus, the set X consists of the integers -5, -4, -3, -2, 2, 3, 4, and 5. The greatest of these integers is 5, and its absolute value is 5. The least of these integers is -5, and its absolute value is also 5. Therefore, Quantity A is equal to Quantity B. The correct answer is Choice C.
