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avohden
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Is x^3 less than x ? 10 Oct 2013, 17:31
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

63% (01:43) correct 37% (01:26) wrong based on 170 sessions

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Is x^3 less than x ?

(1) x^3 is less than 1.

(2) x is greater than -1.


GH-03.20.13
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Official Answer
E
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Qoofi
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Is x^3 less than x ? 11 Oct 2013, 01:17
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avohden
Is x^3 less than x ?

(1) x^3 is less than 1.

(2) x is greater than -1.


GH-03.20.13
Show more

Q : x^3 < x ? yes or no

Solution

Statement 1 : x^3 <1, which implies x = 0 or or -1 or any of the negative integers

if x = 0, then x^3 = x. If x = -1 integer, then x^3 = x. If it is any other integer, then x^3<x. Not sufficient

Statement 2 : x > -1, which implies x = 0, 1 or positive integers

If x = 0, then x^3 = x. If x = 1, then x^3 = x. If x = any positive integer, then x^3 is not less than x. Not sufficient.

Combining both.

x^3 < 1 & x > -1,which x = 0

When x = 0, x^3 = x. Hence it is sufficient to say x^3 is not less than x.
Hence Option C

But Option E is OA.

Can you find out my mistake ?
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Is x^3 less than x ? 11 Oct 2013, 01:55
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Qoofi basically you're making the assumption that the question deals with integers. As that is never stated when you combine the two statements you can use both a positive and negative number such as 0.75 and -0.75 which gives us different results.

Hope that made it clear. Otherwise just ask and I'll gladly explain further.
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Is x^3 less than x ? Updated on: 13 Oct 2013, 10:07
Originally posted by shameekv on 11 Oct 2013, 02:37.
Last edited by shameekv on 13 Oct 2013, 10:07, edited 1 time in total.
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avohden
Is x^3 less than x ?

(1) x^3 is less than 1.

(2) x is greater than -1.


GH-03.20.13
Show more

is \(x^3 - x < 0\)?

is \(x(x^2 - 1) < 0\)

is \((x-1) * (x) * (x+1) < 0\)??

which will be true for following ranges of x :-
    a) x< -1
    b) 0<x<1

You can use alternate -ve +ve system to determine the ranges of x. Similar to the attached snapshot.

Statement 1 :-
\(X^3 < 1\);
Simply means \(x < 1\)
(Since x has an odd power x can also take negative numbers.. Remember if x had even powers then the range for x would have been 0<=x<1)

So \(x\) can be between \(-1<x<0\) where the result will be positive. Hence insufficient.

Statement 2 :-
\(x > -1\)

Again x can be greater than 1 and x can also be between 0 & 1 where the results will be positive and negative respectively. Hence insufficient.

Combining 2 statements :-
we get -\(1<x<1\)

For -1 to 0 the result will be positive and for 0 to 1 the result will be negative.

Hence insufficient.

Therefore Answer will be E

Kudo if the post helps!!! :-D
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Is x^3 less than x ? 11 Oct 2013, 02:39
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GGarland
Qoofi basically you're making the assumption that the question deals with integers. As that is never stated when you combine the two statements you can use both a positive and negative number such as 0.75 and -0.75 which gives us different results.

Hope that made it clear. Otherwise just ask and I'll gladly explain further.
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So we should consider Fractions when it is not mentioned ?
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Is x^3 less than x ? 11 Oct 2013, 02:48
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I do. I mean this is the GMAT, it's designed to try and trick you. Either with hard equations or specific wording.
I try to make as few assumptions as possible and since the question does not state specifically that it is integers one can not assume that x is one.
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Is x^3 less than x ? 11 Oct 2013, 05:51
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Is x^3 less than x ?

Is \(x^3<x\)? --> is \(x(1-x^2)>0\)? --> is \((1+x)x(1-x)>0\) --> the "roots" are -1, 0, and 1 (equate each multiple to zero to get the roots and list them in ascending order), this gives us 4 ranges:
\(x<-1\);
\(-1<x<0\);
\(0<x<1\);
\(1<x\).

Now, test some extreme value: for example if \(x\) is very large number then all multiples but 1-x are positive, which gives a negative product, so when \(x>1\) the expression is negative.

Now the trick: as in the 4th range expression is negative, then in 3rd it'll be positive, in 2nd negative, and finally in 1st it'll be positive again: + - + - . So, the ranges when the expression is positive are: \(x<-1\) (1st range) and \(0<x<1\) (3rd range).

So, the question asks whether \(x<-1\) or \(0<x<1\)

(1) x^3 is less than 1. This implies that \(x<1\). Not sufficient.

(2) x is greater than -1 --> \(x>-1\). Not sufficient.

(1)+(2) \(-1<x<1\). Not sufficient.

Answer: E.

Theory on Inequalities:
x2-4x-94661.html#p731476
inequalities-trick-91482.html
data-suff-inequalities-109078.html
range-for-variable-x-in-a-given-inequality-109468.html
everything-is-less-than-zero-108884.html
graphic-approach-to-problems-with-inequalities-68037.html

All DS Inequalities Problems to practice: search.php?search_id=tag&tag_id=184
All PS Inequalities Problems to practice: search.php?search_id=tag&tag_id=189

700+ Inequalities problems: inequality-and-absolute-value-questions-from-my-collection-86939.html
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Is x^3 less than x ? 22 Oct 2013, 09:00
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Official Explanation

Answer: E Statement (1) is insufficient. If x^3 is less than 1, there are multiple possibilities to consider. Either x is positive and less than 1, or x is negative. Consider those possibilities in light of the question:

If x is positive and less than 1, the relationship between x, x^2, and x^3 will always be the same, so use x = 1/2 as an example. If x = 1/2, x^3 = 1/8, so x^3 is less than x. If x is negative and greater than -1, again, the relationship between x, x^2, and x^3 will always be the same. Use x = -1/2. If x = -1/2, then x^3 = -1/8. In this case, x^3 is greater than x, so there are multiple answers to the question. Statement (2) is insufficient as well. In fact, the work we've already done shows this. If x is greater than -1, it could be either -1/2 or 1/2. As we've seen, if x = -1/2, x is less than x^3. If x = 1/2, x is greater than x^3. Taken together, the statements are still insufficient. They tell us that x and x^3 are between -1 and 1, but we've seen that the relationship between x and x^3 changes depending on whether the value of x is positive or negative. Choice (E) is correct.
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Is x^3 less than x ? 05 Feb 2017, 04:40
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avohden
Is x^3 less than x ?

(1) x^3 is less than 1.

(2) x is greater than -1.


GH-03.20.13
Show more

This can be easily answered by picking numbers. Point to remember : x here can be ANYTHING

1) \(x^3\) is less than 1. Insuff

If \(x = 0 ------>\) Is\(0 < 0\)? No
If \(x = 1/2 ------>\) Is \(1/8 < 1/2\)? Yes

2) x is greater than -1. Insuff

If \(x = 0 ------>\) Is\(0 < 0\)? No
If \(x = 1/2 ------>\) Is \(1/8 < 1/2\)? Yes

We need not calculate further coz we have used same test cases. Both together insuff.

Hence E :lol:
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Is x^3 less than x ? 17 Jan 2024, 03:49
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