Quantitative Aptitude – Equation – Find z, if it is known that


XAT 2021 Exam Paper – Quantitative Aptitude – Equation – Find z, if it is known that

Q. Find z, if it is known that:
a. -y^2 + x^2 = 20,
b. y^3 – 2x^2 – 4z ≥ -12 and
c. x,y and z are all positive integers
  1. we need one more equation to find z
  2. 1
  3. 6
  4. 24
  5. any integer greater then 0 and less then 24

Answer: 1

Solutions:
As x, y, z all are positive integers .
x^2- y^2=20
(x-y)(x+y)= 20 =2×10=4×5
So the only possibility is x-y = 2 and x+y = 10
Or x= 6 and y =4
Now y^3-2x^2-4z≥-12
64-72-4z≥-12
-4z≥ -4
z≤1
Thus option b ) z= 1 is correct.

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