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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
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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.

So, answer is 2. 2

 

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