X / |X| < X

IMO A

uptowngirl92 wrote:X / |X| < X . Which of the following must be true about integer X ? X is not equal to 0.

A X > 1
B X > -1
C |X| < 1
D |X| = 1
E |X|^2 > 1

LOST!! :roll:

We know that x doesn't equal 0. So let's break it down into the two other possible cases:

x>0 and x<0

If x is positive, then |x| = x and we can simplify:

x/x < x

1 < x

So, if x is positive, x must be greater than 1.

If x is negative, then |x| = -x (since a negative times a negative gives us a positive) and we can simplify:

x/-x < x

-1 < x

However, we know that x must be an integer (because that's what the question tells us). Since there are no negative integers greater than -1, there are no possible negative values for x.

Accordingly, we can ignore the x < 0 case. Since x must be postive, x must be greater than 1: choose A.

Stuart,

I didnt understand this bit,
"Since there are no negative integers greater than -1, there are no possible negative values for x. "

sanjana wrote:Stuart,

I didnt understand this bit,
"Since there are no negative integers greater than -1, there are no possible negative values for x. "

We were looking at the case in which x is negative.

Based on our math, we know that:

x > -1

Well, if x is negative and x > -1, then:

-1 < x < 0,

i.e. x is a negative fraction.

So, in order for x to be negative we have to meet two conditions: x must be an integer and x must be a fraction; since no numbers meet both of those conditions, there are no possible negative values of x.

X / |X| < X . Which of the following must be true about integer X ? X is not equal to 0.

A X > 1
B X > -1
C |X| < 1
D |X| = 1
E |X|^2 > 1

I still don't understand. X = |X| * |X| therefore, X/|X| = |X|

Equation says, |X| < X , So we can consider 3 cases, X = 0, -1 and 1

When X = 0 , LHS = RHS , therefore, not true
When X = 1 or X >0 , LHS = RHS , not true
When X=-1 or x <0, LHS >RHS, which is contrary to whats given in the question, therefore, not true.

I don't think the relation given in the question can hold true. If We go by the answer provided by Stuart, X>1, consider X = 2

LHS = 2 , RHS = 2 , not true...