Civil Services Prep

Prelims 2026 · CSAT / Quantitative Aptitude · Question 30

Suppose x, y and z are variables taking positive real numbers as their possible values. It is given that y is directly proportional to x^2 and x is inversely proportional to z. For z = (7/25), the values of x and y are 5 and 50, respectively. If y = 98, what is z equal to?<br/>

  1. (1/7)
  2. (1/5)
  3. (5/7)
  4. 1

Answer

(1/5)

Since y ∝ x², let y = kx². From x = 5, y = 50, we get 50 = 25k, so k = 2. Thus y = 2x². If y = 98, then 2x² = 98 ⇒ x² = 49 ⇒ x = 7. Also x ∝ 1/z, so xz is constant. Initially, xz = 5 × 7/25 = 7/5. Hence for x = 7, z = (7/5)/7 = 1/5.

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