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Notice that the RHS (right hand side) of the expression is always positive (\(2^x>0\)), but the LHS is positive when \(x>0\) (\(x>0\) --> \(x*|x|=x^2\)), negative when \(x<0\) (\(x<0\) --> \(x*|x|=-x^2\)) and equals to zero when \(x={0}\).

(1) x < 0. According to the above \(x*|x|<0<2^x\). Sufficient.

(2) x = -10. The same here \(x*|x|=-100<0<\frac{1}{2^{10}}\). Sufficient.

OA is D for the following reasons: When you first see a DS question, see if there is anyway to simplify the question stem In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient S2: x = -10 and -10 < 2 = sufficient

OA is D for the following reasons: When you first see a DS question, see if there is anyway to simplify the question stem In this case, since |x| is positive, we can divide both sides by |x| giving us a new question stem --> is x < 2?

S1: x<0, therefore x must be <2 = sufficient S2: x = -10 and -10 < 2 = sufficient

Let me know if this helps!

The OA is wrong here because of the following reasons:

(1) if x=-10 then -100<-20, on the other hand if x= -1, x<0 then the inequality changes from < to >, namely, -1 > -2 ; This statement is absolutely insufficient!

For x to be Negative LHS i.e. x|x| will always be NEGATIVE and 2^x will be positive for any value of x i.e. x|x|<2^x will always be true SUFFICIENT

Statement 1: x = -10 For x =-10 LHS i.e. x|x| will always be NEGATIVE (-100) and 2^x will be positive for given x (1/2^10) i.e. x|x|<2^x will always be true SUFFICIENT

Answer: option D
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Hi, we have an equation and the RHS 2^x will be positive irrespective of value of x and LHS xlxl will depend on the value of x.. 1) x is -ive .. so LHS is -ive and RHS is +ive.. suff 2) x=-10... again LHS is -ive and RHS is +ive.. suff ans D
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Re: If x is an integer, is x|x|<2^x ? [#permalink]

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24 Apr 2016, 15:22

1

This post was BOOKMARKED

This question can be solved as follows.

stmt1) it says that x /x/ < 2^x. and also we are told that x< 0. So if x is zero and the abs of x is always positive then we know that x/x/ will be negative. In addition to that, we know that 2^negative number will be positive because it will be in the form of 1/2^x, it will be less than 1 but it will be greater than a negative number. So stmt1 is SUFF.

stmt2) this is a repetition of stmt1 because the left side is negative and the right side is positive. SUFF.

Re: If x is an integer, is x|x|<2^x ? [#permalink]

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17 Apr 2017, 02:20

Bunuel wrote:

Walkabout wrote:

If x is an integer, is x|x|<2^x ?

(1) x < 0 (2) x= -10

If x is an integer, is x|x|<2^x ?

Notice that the RHS (right hand side) of the expression is always positive (\(2^x>0\)), but the LHS is positive when \(x>0\) (\(x>0\) --> \(x*|x|=x^2\)), negative when \(x<0\) (\(x<0\) --> \(x*|x|=-x^2\)) and equals to zero when \(x={0}\).

(1) x < 0. According to the above \(x*|x|<0<2^x\). Sufficient.

(2) x = -10. The same here \(x*|x|=-100<0<\frac{1}{2^{10}}\). Sufficient.

Answer: D.

just for the sake of time saving:

(2) x = -10 --> we could test it! done.... next question
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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

I know this is an OG Q, but is it not strange that st 2 is an integral part of st 1. During actual exam I do not think to need to evaluate S2 separately since x=-10 is always going to be x<0. Let me know if my understanding is correct
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Re: If x is an integer, is x|x|<2^x ? [#permalink]

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22 Oct 2017, 16:14

Hi,

For statement 1 I tested values i.e. x = -1 or x = -2.This is more so a question regarding reciprocals and inequalities. If x = -2, then -2 (|-2|) = 2^-2. Then, this is equal to -2 (2) = 1/2^2. In the second step where I converted 2^-2 to 1/2^2 -- would I have to also flip the other side to become 1 / -2 (2) or is that wrong?

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