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vikkimba17
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can anyone please explain attached problem
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Hi vikkimba17,vikkimba17 wrote:can anyone please explain attached problem
We have to see whether x|x| < 2^x, given that x is an integer.
We see that RHS (2^x) is always positive whether x is negative, positive, or 0, while LHS (x|x|) is not so.
At x = 0
x|x| < 2^x => 0*0 < 2^0 => 0 < 1. Answer is Yes.
At x = 1
x|x| < 2^x => 1*1 < 2^1 => 1 < 2. Answer is yes.
At x = 2
x|x| < 2^x => 2*2 < 2^2 => 4 = 4. Answer is No.
Let's take each statement one by one.
S1: x < 0
We see that when x is negative, LHS (x|x|) is negative, while RHS (2^x) is positive, thus RHS > LHS. Sufficient.
Try at x = -1.
-1*|-1| < 2^(-1) => -1 < 1/(2^1) => -1 < 1/2. Sufficient.
S2: x = -10.
x = -10 is one of the cases of 'x is negative,' which we have seen in statement 1.
-10*|-10| < 2^(-10) => -100 < 1/(2^10) => -1 < a positive number. Sufficient.
The correct answer: D
Hope this helps!
Relevant book: Manhattan Review GMAT Data Sufficiency Guide
-Jay
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