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16 Jan 2012, 22:50
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Difficulty:
25%
(medium)
Question Stats:
72% (01:26) correct
28%
(01:33)
wrong
based on 596
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Is |x − 6| > 5 ?
(1) x is an integer
(2) x^2 < 1
M25-01
(1) x is an integer
(2) x^2 < 1
M25-01
[Reveal] Spoiler:
When (x-6) is positive
x-6 > 5 => x > 11
When (x-6) is negative
6 - x > 5 => x < 1
So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1
1)x is an integer - doesn't help much.
2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.
Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
When (x-6) is positive
x-6 > 5 => x > 11
When (x-6) is negative
6 - x > 5 => x < 1
So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1
1)x is an integer - doesn't help much.
2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.
Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
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17 Jan 2012, 00:45
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|x-6| > 5 if x>11 OR x<1
Using statement (1), we know that x is an integer. However, it may lie between 1 and 11 or not. Insufficient.
Using statement (2), x^2<1 => x lies between -1 and 1 (both not inclusive). This satisfies the condition that x<1. Sufficient.
The answer is therefore (B).
Using statement (1), we know that x is an integer. However, it may lie between 1 and 11 or not. Insufficient.
Using statement (2), x^2<1 => x lies between -1 and 1 (both not inclusive). This satisfies the condition that x<1. Sufficient.
The answer is therefore (B).
17 Jan 2012, 00:57
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Apex231
Is |x-6| > 5?
1)x is an integer
2)x^2 < 1
When (x-6) is positive
x-6 > 5 => x > 11
When (x-6) is negative
6 - x > 5 => x < 1
So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1
1)x is an integer - doesn't help much.
2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.
Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
1)x is an integer
2)x^2 < 1
When (x-6) is positive
x-6 > 5 => x > 11
When (x-6) is negative
6 - x > 5 => x < 1
So the question is (is this re-phrasing of question correct?) -
Is x > 11
or
Is x < 1
1)x is an integer - doesn't help much.
2)x^2 < 1 => x lies between -1 and 1 exclusive; means x is less than 1. answers the question.
Does this solution look okay? though it's not the most elegant. Considering |x-6| as distance is quite lucid.
Yes, all of your work looks perfect. I personally prefer the 'distance approach' (|x - 6| is just the distance between x and 6 on the number line, so the question is just asking if that distance is greater than 5, from which we see right away that the question is asking if we can be sure that either x > 11 or x < 1), but the algebraic cases approach also works, of course.
