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Inequalities

by vinay1983 » Thu Sep 05, 2013 1:47 am
lf x is an integer, is x IxI < 2^x ?
IxI means modulus x



(1) x<0
(2) x = -10
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by ganeshrkamath » Thu Sep 05, 2013 2:51 am
vinay1983 wrote:lf x is an integer, is x IxI < 2^x ?
IxI means modulus x



(1) x<0
(2) x = -10
Statement 1: x<0
2^x is always positive
x |x| is always negative
Sufficient.

Statement 2: x = -10
Sufficient.

Choose D

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by [email protected] » Thu Sep 05, 2013 11:42 pm
Hi vinay1983,

ganeshrkamath has provided the correct answer, but he didn't provide many details. Here's WHY the correct answer is D.

We're told that X is an integer. We're asked IF X(|X|) < 2^X? This is a YES/NO question.

Fact 1: X < 0

So, X is NEGATIVE. You can use Number Properties to deal with this Fact.

Negative(|Negative|) = Neg(Pos) = Neg.

The left "side" of the question is ALWAYS NEGATIVE.

2^(Negative) = Positive fraction.

Under these conditions, the question asks if a NEGATIVE is < POSITIVE FRACTION
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

Fact 2: X = -10

With 1 value of X, it doesn't matter what the answer to the question is because there's ONLY ONE ANSWER.
In this case, the answer is YES.
Fact 2 is SUFFICIENT.

So, Final Answer = D

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by Java_85 » Sun Sep 08, 2013 9:46 am
IMO also it is D.
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by lunarpower » Fri Sep 13, 2013 11:32 pm
i received a private message about this thread.

the other moderators seem to have this covered already, but, one more thing:
[email protected] wrote:Fact 1: X < 0

So, X is NEGATIVE. You can use Number Properties to deal with this Fact.

Negative(|Negative|) = Neg(Pos) = Neg.

The left "side" of the question is ALWAYS NEGATIVE.

2^(Negative) = Positive fraction.

Under these conditions, the question asks if a NEGATIVE is < POSITIVE FRACTION
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
If you don't realize these things right away, then you should start testing specific cases. Just throw in some negative integers, -1, -2, -3, etc., and see what's going on.
If you try -1, the left side is (-1)(1) = -1. The right side is 2^-1 = 1/2.
If you try -2, the left side is (-2)(2) = -4. The right side is 2^-2 = 1/4.
Etc.
Even by trying just two or three numbers, you'll find out exactly what is going on -- the left side is always negative, and the right side is always positive.

Keep this in mind: If you don't know what's happening in a DS problem, TESTING CASES is the best way to DISCOVER what's happening.
Ron has been teaching various standardized tests for 20 years.

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