# If x1/5 > x1/3, then how many of the following statements are definitely true about x?

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If x1/5  > x1/3 , then how many of the following statements are definitely true about x?

x> x3

x1/3 > x4

1 > x1/3 > x-3

x-1/3 > x3

1. 1
2. 2
3. 3
4. 4

x1/5  > x1/3

Dividing by x1/3 on both sides we get

x1/5 - 1/3 > 1

x-2/15 > 1

x2/15 < 1

So, x is less than 1. Here, x can be either < -1 or between 0 and 1.

1. x> x3
Is always true
2. x1/3 > x4
Is true only for positive x. If x is < -1, this becomes false as (-1)4 turns out to be even.
3. 1 > x1/3 > x-3
Is not true for positive x as x-3 > x1/3
4. x-1/3 > x3
Is always true

So, 1, and 4 are true. 2, 3 are false.

3.7k points 1 4 28
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