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10 Jul 2019, 22:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:29) correct
35%
(01:44)
wrong
based on 176
sessions
History
Date
Time
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Not Attempted Yet
11 Jul 2019, 01:10
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In questions on Modulus/absolute values, remember that the output of the modulus function is positive regardless of the input being positive or negative.
To find the value of |x-5| will mean that we need to find a unique value of x.
From statement I, \((x-7)^2\) = 16. This means, (x-7) = ± 4.
If (x-7) = 4, x = 11 and |x-5| = 6.
When (x-7) = -4, x = 3 and |x-5| = 2.
Since we have two values of x, we don’t have a unique value for |x-5|. Statement I alone is insufficient.
Answer options A and D can be eliminated. Possible answers are B, C or E.
From statement II, |x+3| = 14. This means that x = 11 or x = -17. Since we have two values of x, we will again have two values for |x-5| i.e. 6 or 22.
Statement II alone is insufficient. Answer option B can be eliminated.
From statements I and II, the only common value that satisfies both the equations is x = 11. Therefore, we will get a unique value of |x-5|. The combination of statements is sufficient.
The correct answer option is C.
Hope this helps!
To find the value of |x-5| will mean that we need to find a unique value of x.
From statement I, \((x-7)^2\) = 16. This means, (x-7) = ± 4.
If (x-7) = 4, x = 11 and |x-5| = 6.
When (x-7) = -4, x = 3 and |x-5| = 2.
Since we have two values of x, we don’t have a unique value for |x-5|. Statement I alone is insufficient.
Answer options A and D can be eliminated. Possible answers are B, C or E.
From statement II, |x+3| = 14. This means that x = 11 or x = -17. Since we have two values of x, we will again have two values for |x-5| i.e. 6 or 22.
Statement II alone is insufficient. Answer option B can be eliminated.
From statements I and II, the only common value that satisfies both the equations is x = 11. Therefore, we will get a unique value of |x-5|. The combination of statements is sufficient.
The correct answer option is C.
Hope this helps!
08 Nov 2022, 18:42
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Kinshook
Question Stem Analysis:
We need to determine the value of |x - 5|. If we can determine the value of x, we can determine the value of |x - 5|.
Statement One Alone:
\(\Rightarrow\) (x-7)^2=16
It follows that x - 7 is either equal to 4, or equal to -4.
If x - 7 = 4, then x = 11. In this case, |x - 5| = |11 - 5| = |6| = 6.
If x - 7 = -4, then x = 3. In this case, |x - 5| = |3 - 5| = |-2| = 2.
Since there are more than one possible values for |x - 5|, statement one alone is not sufficient.
Eliminate answer choices A and D.
Statement Two Alone:
\(\Rightarrow\) |x + 3| = 14.
It follows that x + 3 is either equal to 14, or equal to -14.
If x + 3 = 14, then x = 11. In this case, |x - 5| = |11 - 5| = |6| = 6.
If x + 3 = -14, then x = -17. In this case, |x - 5| = |-17 - 5| = |-22| = 22.
Since there are more than one possible values for |x - 5|, statement two alone is not sufficient.
Eliminate answer choice B.
Statements One and Two Together:
From statement one, we know that x is either equal to 11 or 3. From statement two, we know that x is either equal to 11 or -17. Assuming both statements, it follows that x = 11. Thus, |x - 5| = |11 - 5| = 6.
Statements one and two together are sufficient.
Answer: C
