If x is an integer, is x|x|<2^x ?
(1) x < 0
(2) x = -10
D
OG Is x|x| < 2^x?
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Hi AbeNeedsAnswers,
We're told that X is an integer. We're asked if X|X| < 2^X. This is a YES/NO question. We can answer it with a bit of Number Property knowledge.
1) X < 0
With Fact 1, we know that X is NEGATIVE. By definition, that means...
X|X| = (Neg)|Neg| = Negative
2^(Negative) = Positive
Thus, X|X| will ALWAYS be less than 2^X and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) X = -10
With the value of X, we can absolutely answer the question (we would just need to plug in that value:
Is (-10)|-10| < 2^(-10)?
The answer to the question IS yes, but we don't have to actually do that work. There would be just one answer to the question, so it doesn't really matter what that one answer is.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
We're told that X is an integer. We're asked if X|X| < 2^X. This is a YES/NO question. We can answer it with a bit of Number Property knowledge.
1) X < 0
With Fact 1, we know that X is NEGATIVE. By definition, that means...
X|X| = (Neg)|Neg| = Negative
2^(Negative) = Positive
Thus, X|X| will ALWAYS be less than 2^X and the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT
2) X = -10
With the value of X, we can absolutely answer the question (we would just need to plug in that value:
Is (-10)|-10| < 2^(-10)?
The answer to the question IS yes, but we don't have to actually do that work. There would be just one answer to the question, so it doesn't really matter what that one answer is.
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Target question: Is x|x|< 2^x ?AbeNeedsAnswers wrote:If x is an integer, is x|x|<2^x ?
(1) x < 0
(2) x = -10
D
Given: x is an integer
Statement 1: x < 0
In other words, x is NEGATIVE
So, x|x| = (NEGATIVE)(|NEGATIVE|) = (NEGATIVE)(POSITIVE) = NEGATIVE
IMPORTANT: 2^x will be POSITIVE for all values of x.
Since x|x| must be NEGATIVE, and since 2^x must be POSITIVE, we can be certain that x|x|< 2^x
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = -10
So, x|x| = (-10)(|-10|) = (-10)(10) = -100 = a NEGATIVE
On the other hand, 2^x = 2^(-10) = 1/(2^10) = some POSITIVE number
Since x|x| is NEGATIVE, and since 2^x must be POSITIVE, we can be certain that x|x|< 2^x
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent