lf x is an integer, is x IxI < 2^x ?
IxI means modulus x
(1) x<0
(2) x = -10
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- ganeshrkamath
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Statement 1: x<0vinay1983 wrote:lf x is an integer, is x IxI < 2^x ?
IxI means modulus x
(1) x<0
(2) x = -10
2^x is always positive
x |x| is always negative
Sufficient.
Statement 2: x = -10
Sufficient.
Choose D
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
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- lunarpower
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i received a private message about this thread.
the other moderators seem to have this covered already, but, one more thing:
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.
the other moderators seem to have this covered already, but, one more thing:
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.[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 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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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron