Problem Solving

gary391 wrote: A) x>1

(B) x>−1

(C) |x|<1

(D) |x|=1

(E) |x|^2>1

B

Please post questions in the correct format. The prompt is missing in your post.

You should do this way:

gary391 wrote:
If X/|X| < X which of the following must be true about X?

(A) x>1

(B) x>−1

(C) |x|<1

(D) |x|=1

(E) |x|^2>1

B

We are given that X/|X| < X.

This question is a good case for testing smart values.

We can pick values: -2, -1, -1/2, 0, 1/2, 1, and 2.

1. If X = -2, X/|X| = -2/|-2| = -1; -1 is NOT less than X =-2. Thus, -2 does not fit.

2. If X = -1, X/|X| = -1/|-1| = -1; -1 is NOT less than X =-1. Thus, -1 does not fit.

3. If X = -1/2, X/|X| = -1/2/(|-1/2|) = -1; -1 < X =-1/2. Thus, X=-1/2 fits. Or we can conclude that X > -1.

4. If X = 0, X/|X| = 0/|0| = Indeterminable. So far, we can conclude that 0 > X > -1.

5. If X = 1/2, X/|X| = 1/2/(|1/2|) = 1; 1 is NOT less than X =1/2. Thus, X=1/2 does not fit. However, we can still conclude that 0 > X > -1.

6. If X = 1, X/|X| = 1/|1| = 1; 1 is NOT less than X =1. Thus, 1 does not fit. We can still conclude that 0 > X > -1.

7. If X = 2, X/|X| = 2/(|2|) = 1; 1 < X =2. Thus, X=2 fits. Or we can conclude that X > 1.

So either it is: 0 > X > -1 or X > 1. The best way to satisfy both the ranges is x > -1. It does not mean that all the values lying in x > -1 must satisfy the inequality.

Answer: B

Let us analyze each option.

A. X > 1; It is partly correct. This option is a contender for 'Could be True' type of question, but this one is a 'Must be True' type. If X lies between 0 and -1, this option fails.

C. |X|<1: This means that -1 < X < 1. Like option A, it is partly correct for -1 < X.

D. |X|=1: This means that X is either -1 or 1. It is outrightly incorrect.

E. |X|^2>1: |X|^2>1 => |X| > 1 => X < -1 or X > 1. Again this option is partly correct for X > 1.

Hope this helps!

-Jay
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Hi gary391,

This question is based around a couple of simple Number Property rules that will likely come in handy on Test Day (and it has some design patterns that we can take advantage of...). To start, here are the two rules...

1) Any number divided by itself = 1
2) Any number divided by the OPPOSITE of itself = -1

eg. 2/2 = 1, 2/-2 = -1

Based on the answer choices, we're meant to think about numbers that are relatively close to 1 and/or -1, so considering fractional values for X would probably be the most efficient way to approach this question. We can TEST VALUES to get to the solution....

IF....
X = +1/2, then we'd have (1/2)/|1/2| < 1/2..... 1 < 1/2.... but that is NOT mathematically correct, so X CANNOT be +1/2

IF....
X = -1/2, then we'd have (-1/2)/|-1/2| < -1/2.... -1 < -1/2... which IS mathematically correct, so X CAN be -1/2. Eliminate Answers A, D and E.

From here, it's actually really easy to find the correct answer between the two remaining choices (and we can use the very first example from above:

IF....
X = +2, then we'd have (2)/|2| < 2.... 1 < 2... which IS mathematically correct, so X CAN be 2. Eliminate Answer C.

Final Answer: B

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