If x3y : xy :: xy : a, then which expression gives the value of a?
2026
If x3y : xy :: xy : a, then which expression gives the value of a?
Answer: A. y/x — ConceptFor a proportion A : B :: C : D, the two ratios are equal: A/B = C/D. Equivalently, the product of the extremes equals the product of the means, A × D…
- A.
y/x
- B.
y2/x2
- C.
y/x2
- D.
y2/x
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Correct answer: A
Concept
For a proportion A : B :: C : D, the two ratios are equal: A/B = C/D. Equivalently, the product of the extremes equals the product of the means, A × D = B × C, provided the denominators are non-zero.
Application
Interpret the given proportion as (x³y)/(xy) = (xy)/a.
For non-zero x and y, simplify (x³y)/(xy) to x².
Therefore x² = xy/a, so multiplying by a gives ax² = xy.
Divide by x² to obtain a = y/x.
Cross-check
Substitute a = y/x. Then (xy)/(y/x) = x², while (x³y)/(xy) = x², so the two ratios are equal.