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Abstract number problem

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by Anindya Madhudor » Wed Nov 14, 2012 8:25 pm
I am wondering whether there is any systematic approach to the following problem. I am afraid if i start with numbers for similar problems, i am going to miss something out.

If x>y^2>z^4, which of the following statement could be true?
I. x>y>y
II. z>y>x
III. x>z>y

a) I only
b) I and II only
c) I and III only
d) II and III only
e) I, II, and III

OA: E
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by Anurag@Gurome » Thu Nov 15, 2012 4:55 am
Anindya Madhudor wrote:I am wondering whether there is any systematic approach to the following problem. I am afraid if i start with numbers for similar problems, i am going to miss something out.

If x>y^2>z^4, which of the following statement could be true?
I. x>y>y
II. z>y>x
III. x>z>y

a) I only
b) I and II only
c) I and III only
d) II and III only
e) I, II, and III

OA: E
(I) x > y^2
  • Certainly for integer values of x and y, x is always greater than y. But what about fractional values> f y is a fraction then y^2 is < y. Now always there is a fraction x, such that y > x > y^2. Thus for fractional values x may be less than y. Therefore regarding the relation between x and y all of the options could be true.
(II) x > z^4
  • Same logic as above.
(II) y^2 > z^4
  • This directly implies y > z^2. Now again apply same logic as above.
The correct answer is E.
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