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Directions: Select one of the following answer choices.
Q. 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
- a)Quantity A is greater.
- b)Quantity B is greater.
- c)The two quantities are equal.
- d)The relationship cannot be determined from the information given.
Correct answer is option 'C'. Can you explain this answer?
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Directions: Select one of the following answer choices.Q. X is the se...
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.
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Directions: Select one of the following answer choices.Q. X is the se...
To determine the relationship between the two quantities, let's first find the set X of integers that satisfy the given inequality.
We are given the inequality 2 ≤ |n| ≤ 5, which means that the absolute value of n must be greater than or equal to 2 and less than or equal to 5.
To find the set X, we consider the two cases: n is positive and n is negative.
Case 1: n is positive
If n is positive, then the inequality becomes 2 ≤ n ≤ 5. In this case, the set X consists of the integers 2, 3, 4, and 5.
Case 2: n is negative
If n is negative, then the inequality becomes 2 ≤ -n ≤ 5. To solve this inequality, we can multiply both sides by -1 and reverse the inequality signs, giving us -5 ≤ n ≤ -2. In this case, the set X consists of the integers -5, -4, -3, and -2.
Now that we have found the set X, let's determine Quantity A and Quantity B.
Quantity A: The absolute value of the greatest integer in X
The greatest integer in X is 5 (from case 1), so Quantity A is |5| = 5.
Quantity B: The absolute value of the least integer in X
The least integer in X is -5 (from case 2), so Quantity B is |-5| = 5.
Since both Quantity A and Quantity B are equal to 5, the answer is (c) The two quantities are equal.
We are given the inequality 2 ≤ |n| ≤ 5, which means that the absolute value of n must be greater than or equal to 2 and less than or equal to 5.
To find the set X, we consider the two cases: n is positive and n is negative.
Case 1: n is positive
If n is positive, then the inequality becomes 2 ≤ n ≤ 5. In this case, the set X consists of the integers 2, 3, 4, and 5.
Case 2: n is negative
If n is negative, then the inequality becomes 2 ≤ -n ≤ 5. To solve this inequality, we can multiply both sides by -1 and reverse the inequality signs, giving us -5 ≤ n ≤ -2. In this case, the set X consists of the integers -5, -4, -3, and -2.
Now that we have found the set X, let's determine Quantity A and Quantity B.
Quantity A: The absolute value of the greatest integer in X
The greatest integer in X is 5 (from case 1), so Quantity A is |5| = 5.
Quantity B: The absolute value of the least integer in X
The least integer in X is -5 (from case 2), so Quantity B is |-5| = 5.
Since both Quantity A and Quantity B are equal to 5, the answer is (c) The two quantities are equal.
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Directions: Select one of the following answer choices.Q. X is the set of all integers n that satisfy the inequality 2 ≤ | n | ≤ 5Quantity A: The absolute value of the greatest integer in XQuantity B: The absolute value of the least integer in Xa)Quantity A is greater.b)Quantity B is greater.c)The two quantities are equal.d)The relationship cannot be determined from the information given.Correct answer is option 'C'. Can you explain this answer?
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