Let z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z? 

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. -1
  2. 0
  3. 1
  4. 2

Answer (Detailed Solution Below)

Option 1 : -1
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Detailed Solution

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Explanation:

Since, {x}+[x] = x

⇒x – [x] = {x}

⇒ 0≤ x – [x] < 1 (0 ≤ {x} < 1)

⇒ –1 ≤ [x] –x ≤ 0

But x is positive and non-integer; then

⇒ –1 < [x]–x < 0

⇒ –1 < y < 0

⇒ [y] = –1 

∴ Option (a) is correct.

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