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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 < 1When we combine our two inequalities, we get
0 < x < 1In 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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