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Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is

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Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]

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New post 24 Feb 2017, 06:16
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jscott319 wrote:
Is x between 0 and 1 ?

(1) x² is less than x
(2) x³ is positive



Target question: Is x between 0 and 1 ?

Statement 1:x² is less than x
In other words, x² < x
We can apply some inequality rules here.
Since x² must be POSITIVE here, we can take x² < x and divide both sides by x²
We get: 1 < 1/x
Since 1/x is greater than 1, we can conclude that 1/x is positive, which means x is POSITIVE (i.e., x > 0)
Since x is POSITIVE, we can take 1 < 1/x and multiply both sides by x to get: x < 1
When we combine our two inequalities, we get 0 < x < 1
In other words, x IS between 0 and 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x³ is positive
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 1/2 (so, x³ = (1/2)³ = 1/8). In this case, x IS between 0 and 1
Case b: x = 2 (so, x³ = 2³ = 8). In this case, x is NOT between 0 and 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

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Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]

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New post 28 Oct 2017, 22:33
Sir, i am having one query . In this question condition is not given , that X is negative. How can we say that multiples must have opposite signs to find 0<X<1.

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Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]

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New post 30 Oct 2017, 20:29
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Raj94* wrote:
Sir, i am having one query . In this question condition is not given , that X is negative. How can we say that multiples must have opposite signs to find 0<X<1.


Using statement 1,
If X were negative, X^2 would be positive and certainly greater than X. Hence X cannot be negative.
So X must be positive.
If X is 0 or 1, X^2 = 0 or 1 too.
If X is greater than 1, X^2 would be greater than X.
If X is less than 1, X^2 will be less than X.

So 0 < X < 1
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Kudos [?]: 18128 [1], given: 236

Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is   [#permalink] 30 Oct 2017, 20:29

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