Is the Answer wrong? [Inequalities]

[JoyceC784]

Hope you are well. I come across the below article and think that the answer for one the question was wrong (or I just couldn’t get my head around it) : https://www.manhattanprep.com/gmat/blog ... a-minutes/

Can you help?

Is x > 0?

x² < 1
x³ > x

The answer in the article was E. But In my view I think it should be C, I will explain:

x² < 1
This indicates that :
- X is less than 1
- X can be both negative and positive

x³ > x
This indicates that:
- If X is positive, X is larger than 1
- If X is negative, X has to be less than 1

So using two statements we know that X has to be negative - the answer should be C - Am I right.?

Thanks all.

[Sage Pearce-Higgins]

Well done for trying to "decode" the statements and see what they're really saying. However, what's going to help with this is our favorite strategy of testing cases. Think of numbers that agree with statement (1). X could be a number less than 1, say, 1/2, but try some negative numbers too. X could also be -1/2. Statement 1 really says that -1 < x < 1. So statement (1) isn't sufficient.

As for statement (2), x could be a simple integer such as 2. If we think of x=1/2, then that doesn't work with our statement, as x^3 is 1/8, and that's not bigger than x. But think about some negative numbers: if x=-1/2, then x^3=-1/8, which is bigger than x. Statement 2 is really saying that -1 < x < 0 or x > 1. So statement (2) is insufficient.

As for taking the statements together, the only cases that satisfy both statements are numbers between -1 and 0, so x must be negative (i.e. a sufficient "no") and the answer is C. Unless I've missed something here, I agree with you, that the given answer is incorrect. I'll confer with Ryan.

[NikhilN487]

Correct me if im wrong here, but following up on what you said about combining the 2 statements, if x= 0, -1, it still remains insufficient right?
Considering that the 2 statements say
1. x^2 < 1
2. x^3 > x

2. If 0, -1 were subbed in Eq 2, (x^3 > x) would either be = since 0^3 = 0, or (-)1^3 = (-)1

Hope to get some clarity from your end in case I'm missing the trick somewhere here.
Thanks

[esledge]

Correct me if im wrong here, but following up on what you said about combining the 2 statements, if x= 0, -1, it still remains insufficient right?
Considering that the 2 statements say
1. x^2 < 1
2. x^3 > x

2. If 0, -1 were subbed in Eq 2, (x^3 > x) would either be = since 0^3 = 0, or (-)1^3 = (-)1

Hope to get some clarity from your end in case I'm missing the trick somewhere here.
Thanks

x cannot be either 0 or -1 for either statement ... alone or together. When you plug these values in, the inequality sign in each statement would be invalid (the sides of each equation would be equal). So, you are not allowed to consider these values at all.

But I think you might be asking more of a logic question about the Yes/No aspect of this DS question. Let's pretend for a second that there's a statement (3) that says -1 <= x <= 0 . If the question were still "Is x>0?" the answer would still be a definite No, because none of the values in the given range are greater than 0. So, hypothetical statement (3) would still have a definite answer (No) and would still be sufficient.

Let me know if I missed your point!