vikkimba17 wrote:can anyone please explain attached problem

Hi vikkimba17,

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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Hi vikkimba17,

This DS question is built around a couple of Number Properties, so you can actually solve it without doing much math.

We're told that X is an INTEGER. We're asked if X|X| is less than 2^X. This is a YES/NO question.

1) X < 0

This Fact tells us that X is NEGATIVE, which means....

X|X| = (negative)|negative| = (-)(+) = ALWAYS negative
2^X = 2^(negative) = 1/[2^(positive)] = ALWAYS positive

Thus, the answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) X = -10

Since this tells us the only value of X, there will be only one answer to the given question (the answer happens to be YES).
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich