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Is x < 2?

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Is x < 2?  [#permalink]

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New post 24 Jan 2016, 05:35
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

70% (01:35) correct 30% (01:35) wrong based on 77 sessions

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Re: Is x < 2?  [#permalink]

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New post 25 Jan 2016, 18:14
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is x < 2?

(1) x > x^2
(2) 1⁄x > 3


When it comes to inequality questions, if range of que includes range of con, the con is sufficient.
In the original condition, there is 1 variable(x), which should match with the number of equations. So you need 1 equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), in x^2-x<0, x(x-1)<0, 0<x<1, the range of que includes the range of con, which is sufficient.
For 1), multiply x^2 to both equations, which becomes x>3x^2, x(3x-1)<0 -> 0<x<1/3. In 0<x<1/3, the range of que includes the range of con, which is sufficient.
Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: Is x < 2?  [#permalink]

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New post 30 Jan 2016, 00:20
1
Hi All,

Certain DS questions can be dealt with using a bit of logic and Number Property knowledge. Sometimes eliminating 'possibilities' is all you really need to do to get to the correct answer.

We're asked is X < 2? This is a YES/NO question.

1) X > X^2

With this Fact, we can make several quick deductions:
1) Since X > X^2, X CANNOT be 0 or 1.
2) X^2 MUST be positive (since X cannot be 0 in this situation); by extension, X itself MUST be positive (since it's greater than X^2)
3) As X increases beyond the number 1, X^2 becomes greater than X. (e.g.. 1.5 vs 1.5^2, 2 vs 2^2, etc.), so X CANNOT be greater than 1.

With these three deductions, we know that X is POSITIVE and that X is less than 1. The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT.

2) 1⁄X > 3

With this Fact, we can also make several quick deductions:
1) Since 1/X is greater than 3, the fraction MUST be positive - thus, X CANNOT be 0 or negative. Thus, X MUST be positive.
2) X CANNOT be 1 (since 1/1 is NOT greater than 3). As X increases beyond the number 1, the fraction 1/x DECREASES. Those fractions are NOT greater than 3, so X CANNOT be greater than 1.

With these two deductions, we know that X is POSITIVE and that X is less than 1. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.

Final Answer:

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Re: Is x < 2?  [#permalink]

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New post 18 Sep 2018, 05:03
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Re: Is x < 2? &nbs [#permalink] 18 Sep 2018, 05:03
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