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605-655 Level|   Algebra|   Inequalities|                           
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KarishmaB
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What is the value of x if x^3 < x^2? Updated on: 28 Nov 2023, 00:17
Originally posted by KarishmaB on 29 Jul 2019, 22:27.
Last edited by KarishmaB on 28 Nov 2023, 00:17, edited 1 time in total.
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578vishnu
gmatbusters
Wavy Curve method for inequality is a very important tool
Wavy curve method

See this question approach using this method.


Hi,

Can somebody please explain to me why gmatbusters has considered -infinity <x < 1 as the range?
During wavy line method, shouldn't the signs be alternate? Why has he considered two subsequent signs as negatives?

Please help!

chetan2u VeritasKarishma Bunuel egmat
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There are various ways of handling an even exponent term.

Don't plot it on the number line to avoid confusion. It may come into play while writing out the range only if the inequality has an equal to sign too.
e.g. if the given inequality is this (discussed in the post)

\((x – 4)(x – 2)(x + 8)^4 \leq 0\)

the required range is \(2 \leq x \leq 4\) or x = -8
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What is the value of x if x^3 < x^2? Updated on: 24 Aug 2021, 14:18
Originally posted by faat99 on 18 Jul 2021, 05:49.
Last edited by faat99 on 24 Aug 2021, 14:18, edited 1 time in total.
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There is no way I know to use x ≠ 0 the first time I do this question, probably one of the hardest questions in gmat.
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What is the value of x if x^3 < x^2? 24 Aug 2021, 06:34
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To Bunuel, chetan2u VeritasKarishma

Can we solve this question like this:

Given X^3 < x^2
since, the minimum value any square can have is X^2<=0
therefore, X^3<0 and it follows that x<0
Now, we have to find a specific NEGATIVE value of x from the given statements, which can ONLY be proved from the statement 2. Please let me know if this is the correct approach?
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What is the value of x if x^3 < x^2? 24 Aug 2021, 07:48
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bv8562
To Bunuel, chetan2u VeritasKarishma

Can we solve this question like this:

Given X^3 < x^2
since, the minimum value any square can have is X^2<=0
therefore, X^3<0 and it follows that x<0
Now, we have to find a specific NEGATIVE value of x from the given statements, which can ONLY be proved from the statement 2. Please let me know if this is the correct approach?
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No, that will not be correct.
\(x^2>x^3………x^2(1-x)>0\)
x^2>0, so 1-x>0….x<1

Thus x can be any negative number, but x can be only between 0 and 1 when positive.

If someone says x is an integer, then surely x is negative
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What is the value of x if x^3 < x^2? 24 Aug 2021, 17:45
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bv8562
To Bunuel, chetan2u VeritasKarishma

Can we solve this question like this:

Given X^3 < x^2
since, the minimum value any square can have is X^2<=0
therefore, X^3<0 and it follows that x<0
Now, we have to find a specific NEGATIVE value of x from the given statements, which can ONLY be proved from the statement 2. Please let me know if this is the correct approach?
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Hi bv8562,

While many GMATers would look at the inequality X^3 < X^2 and immediately think about negative values; since (negative)^3 = a negative and (negative)^2 = a postive - you have to be careful about assuming that these are the only possibilities. Some interesting Number Property patterns occur with positive fractions and negative fractions (re: numbers in the range of 0 < X < 1 and -1 < X < 0).

In this case of this inequality, positive fractions ALSO fit the range of acceptable values.

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KarishmaB
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What is the value of x if x^3 < x^2? 24 Aug 2021, 23:33
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bv8562
To Bunuel, chetan2u VeritasKarishma

Can we solve this question like this:

Given X^3 < x^2
since, the minimum value any square can have is X^2<=0
therefore, X^3<0 and it follows that x<0
Now, we have to find a specific NEGATIVE value of x from the given statements, which can ONLY be proved from the statement 2. Please let me know if this is the correct approach?
Show more


bv8562

Note that:

When x > 1
\(...x<x^2< x^3… \)

When 0 < x < 1
\(…x^3<x^2<x… \)

When –1 < x < 0
\(x<x^3<0<x^2… \)

When x < –1
\(x^3<x<0<x^2 \)
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What is the value of x if x^3 < x^2? 26 Aug 2021, 00:32
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Understanding that (X)^3 < (X)^2 is really “code” for saying ———-> the value of X must be a negative value or

X < 0

What’s is the value of X?

Notice that no constraint is given for X’s value.

X could be a fraction, integer, or irrational number


(1) -2 < X < 2

With the given inequality this becomes:

-2 < X < 0

X can equal any value on the number line between -2 and 0.

Not sufficient.

(2) X is a negative integer greater than -2

The only negative integer greater than -2 is ——> (-)1

Since we already know that X must be less than 0, statement 2 tells us that the only value that X can take is (-)1

S2 sufficient

B

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What is the value of x if x^3 < x^2? 19 Oct 2021, 22:39
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What is the value of x if x^3 < x^2?

(1) –2< x < 2
(2) x is an integer greater than –2.
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What is the value of x if x^3 < x^2? 01 Oct 2023, 00:23
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AbdurRakib
What is the value of x if x^3 < x^2?

(1) –2< x < 2
(2) x is an integer greater than –2.
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When we are told x^3<x^2
we know that x cannot be 0
x can be either -1 or a fraction say 1/2
x cannot be negative
We need to figure the exact value of x

St 1: –2< x < 2
Here x can be neg (-1) or x can be a fraction (example 1/2)

St 2: x is an integer greater than -2
The word to focus here is x is an integer. so x cannot be 1/2 1/3 etc
so the only option that leaves us with is x=-1
Hence sufficient B
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What is the value of x if x^3 < x^2? 06 Oct 2025, 07:18
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Hey, just a quick doubt - why can't x be 0?

Thanks
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What is the value of x if x^3 < x^2? 06 Oct 2025, 07:50
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Hey, just a quick doubt - why can't x be 0?

Thanks
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If x is 0, then x^3<x^2 is not valid as it will become 0^3<0^2
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