JAMB 2010 Mathematics · Question 2

If y varies directly as the square root of x and y = 3 when x = 16. Calculate y when x = 64

Options

A.12
B.6
C.3
D.5

Answer: B. 6

Explanation written with AI and checked against the answer key

Analyze the question "y varies directly as the square root of x" means y ∝ √x. We're given one pair of values, which lets us find the constant, then use it to find y at the new x. Concept Direct variation: y = k√x, where k is the constant of proportionality. Solution Step 1: Find k using y = 3 when x = 16. 3 = k√16 3 = 4k k = 3/4 Step 2: Write the equation. y = (3/4)√x Step 3: Find y when x = 64. y = (3/4) × √64 y = (3/4) × 8 y = 6 Check using a ratio (faster method): y₁/√x₁ = y₂/√x₂ 3/4 = y₂/8 y₂ = (3 × 8)/4 = 6 ✓ Answer: B (6) Exam tip: When x goes from 16 to 64, it multiplies by 4, so √x multiplies by 2 (since √4 = 2). Since y varies directly as √x, y also doubles: 3 × 2 = 6. This is a quick shortcut you can do in your head in seconds. Watch out for the trap of doubling y when x is quadrupled (which would be wrong for a square-root relationship, but here it happens to work because √4 = 2).

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