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27 Sep 2021, 11:41
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
37% (00:59) correct
63%
(01:08)
wrong
based on 141
sessions
History
Date
Time
Result
Not Attempted Yet
If x is an integer, what is the value of |x-5|?
(1) (x-1)(x-9)=0
(2) (x-1)(2x-9)=0
(1) (x-1)(x-9)=0
(2) (x-1)(2x-9)=0
27 Sep 2021, 11:46
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chetan2u
|x-5| = ?
1)x = 1, x = 9
Case1(x = 1):
|x-5| = 4
Case2(x = 9):
|x-5| = 4 - Sufficient!
2)x = 1, x = 4.5
Case1(x = 1):
|x-5| = 4
Case2(x = 4.5):
This is not possible as x is an integer
As x = integer(x = 4)- Sufficient
IMO D
27 Sep 2021, 12:22
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chetan2u
Nice question, chetan2u!
Given: x is an integer
Target question: What is the value of |x-5|?
Statement 1: (x - 1)(x - 9) = 0
From this, we can conclude that EITHER x = 1 OR x = 9
Aside: Many students will conclude that, since there are two possible values of x, statement 1 must be insufficient. These students, however, are answering the wrong target question. The target question isn't asking us to determine the value of x; it's asking us to determine the value of |x - 5|
If x = 1, then |x - 5| = |1 - 5| = |-4| = 4
If x = 9, then |x - 5| = |9 - 5| = |4| = 4
Since the only two possible values of x yield the SAME answer to the target question, we can be certain that |x - 5| = 4
Statement 1 is SUFFICIENT
Statement 2: (x-1)(2x-9)=0
From this, we can conclude that EITHER x = 1 OR x = 4.5
Since we are told that x is an integer, x can't equal 4.5.
Since we can be certain that x = 1, the answer to the target question is |x - 5| = |1 - 5| = |-4| = 4
Statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
