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27 May 2022, 03:17
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E
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If r and s are integers such that |r – s| > 4, which of the following cannot be possible values of (r, s)?
A. (-1, -6)
B. (-6, -1)
C. (1, 6)
D. (6, 1)
E. (-1, 1)
A. (-1, -6)
B. (-6, -1)
C. (1, 6)
D. (6, 1)
E. (-1, 1)
27 May 2022, 08:30
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Bunuel
Two properties involving absolute value inequalities:
Property #1: If |something| < k, then –k < something < k
Property #2: If |something| > k, then EITHER something > k OR something < -k
Note: these rules assume that k is positive
The given inequality, |r – s| > 4, matches the format of property #2.
So we can conclude that: EITHER r – s > 4 OR r – s < -4
So, for each answer choice in the form (r, s), we'll find the value of r - s and check whether it falls in one of the two ranges above.
A. (-1, -6). r - s = (-1) - (-6) = 5. These coordinates satisfy the inequality r – s > 4. Eliminate A.
B. (-6, -1). r - s = (-6) - (-1) = -5. These coordinates satisfy the inequality r – s < -4. Eliminate B.
C. (1, 6). r - s = 1 - 6 = -5. These coordinates satisfy the inequality r – s < -4. Eliminate C.
D. (6, 1). r - s = 6 - 1 = 5. These coordinates satisfy the inequality r – s > 4. Eliminate D.
E. (-1, 1). r - s = (-1) - 1 = -2. These coordinates satisfy neither inequality.
Answer: E
General Discussion
Updated on: 18 Jul 2025, 04:35
Originally posted by BrushMyQuant on 27 Aug 2022, 23:58.
Last edited by BrushMyQuant on 18 Jul 2025, 04:35, edited 2 times in total.
Last edited by BrushMyQuant on 18 Jul 2025, 04:35, edited 2 times in total.
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Given that |r – s| > 4 and we need to find which of the following cannot be possible values of (r, s)
Let's solve the problem using two methods
Method 1: Graphing Absolute Values
| r -s| = Distance between r and s on the number line
=> |r -s| > 4 means that distance between r and s on the number line is > 4
Out of all the option choices only option E has distance between r and s not greater than 4
So, Answer will be E!
Method 2: Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
A. (-1, -6)
We will put r = -1 and s = -6 in |r – s| > 4 and see if it satisfies or not
=> |(-1) – (-6)| > 4
=> |-1 + 6| > 4
=> | 5| > 4
=> 5 > 4 which is TRUE
B. (-6, -1)
We will put r = -6 and s = -1 in |r – s| > 4 and see if it satisfies or not
=> |(-6) – (-1)| > 4
=> |-6 + 1| > 4
=> |-5| > 4
=> 5 > 4 which is TRUE
C. (1, 6)
We will put r = 1 and s = 6 in |r – s| > 4 and see if it satisfies or not
=> |1 – 6| > 4
=> |-5| > 4
=> 5 > 4 which is TRUE
D. (6, 1)
We will put r = 6 and s = 1 in |r – s| > 4 and see if it satisfies or not
=> |6 – 1| > 4
=> |5| > 4
=> 5 > 4 which is TRUE
E. (-1, 1)
We will put r = -1 and s = 1 in |r – s| > 4 and see if it satisfies or not
=> |-1 – 1| > 4
=> |-2| > 4
=> 2 > 4 which is FALSE
So, Answer will be E
Hope it helps!
Playlist on Solved Problems on Absolute Values here
Watch the following video to learn How to Solve Absolute Value Problems
Let's solve the problem using two methods
Method 1: Graphing Absolute Values
| r -s| = Distance between r and s on the number line
=> |r -s| > 4 means that distance between r and s on the number line is > 4
Out of all the option choices only option E has distance between r and s not greater than 4
So, Answer will be E!
Method 2: Substitution
We will values in each option choice and plug in the question and check if it satisfies the question or not.
A. (-1, -6)
We will put r = -1 and s = -6 in |r – s| > 4 and see if it satisfies or not
=> |(-1) – (-6)| > 4
=> |-1 + 6| > 4
=> | 5| > 4
=> 5 > 4 which is TRUE
B. (-6, -1)
We will put r = -6 and s = -1 in |r – s| > 4 and see if it satisfies or not
=> |(-6) – (-1)| > 4
=> |-6 + 1| > 4
=> |-5| > 4
=> 5 > 4 which is TRUE
C. (1, 6)
We will put r = 1 and s = 6 in |r – s| > 4 and see if it satisfies or not
=> |1 – 6| > 4
=> |-5| > 4
=> 5 > 4 which is TRUE
D. (6, 1)
We will put r = 6 and s = 1 in |r – s| > 4 and see if it satisfies or not
=> |6 – 1| > 4
=> |5| > 4
=> 5 > 4 which is TRUE
E. (-1, 1)
We will put r = -1 and s = 1 in |r – s| > 4 and see if it satisfies or not
=> |-1 – 1| > 4
=> |-2| > 4
=> 2 > 4 which is FALSE
So, Answer will be E
Hope it helps!
Playlist on Solved Problems on Absolute Values here
Watch the following video to learn How to Solve Absolute Value Problems
