Hi,
From(1): x^2 < x
So, x^2 - x <0
So, x(x-1)<0
So, 0<x<1
Sufficient
From(2): x^3 is positive.
So, x is positive. Not sure whether x is less than 1 or not
Not sufficient
Hence, A
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Source: Beat The GMAT — Data Sufficiency |
Yes A is clearly the answer.
Square of no which is between 0 and 1 is always less than the no itself.
Statement 2 is insufficient.
Square of no which is between 0 and 1 is always less than the no itself.
Statement 2 is insufficient.
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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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