Quantitative Aptitude – Algebra – Quadratic Equation


Slot – 2 – Quantitative Aptitude – Algebra – Quadratic Equation – Let a, b, x, y, be real numbers

Q. Let a, b, x, y, be real numbers such that a^2 + b^2 = 25, x^2 + y^2 = 169, and ax+by = 65. if k = ay-bx, then?
  1. k>5/13
  2. k=0
  3. k=5/13
  4. 0
Answer: k=0

Solution: As a,b, x , y are real and as we know 3^2 + 4^2 = 25 or 5^2 + 0= 25 also 13^2 + 0= 169 and 5^2 + 12^2 = 169
ax+ by = 65 is possible only when (a,b) = (0,5) and (x,y)= (0,13)
Thus k = 0*13 – 0*5 =0

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