Given (9\ inches)1/2=(0.25\ yards)1/2, which statement is TRUE?

GATE 2016 EC (EC2) – Question 4

General Aptitude · Quantitative Aptitude: Data Interpretation, Arithmetic and Number Computation · 1 mark · Multiple choice

Given $(9\ \mathrm{inches})^{1/2}=(0.25\ \mathrm{yards})^{1/2}$, which statement is TRUE?

3 inches = 0.5 yards
9 inches = 1.5 yards
9 inches = 0.25 yards
81 inches = 0.0625 yards

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Show answer and explanation

Correct answer: (C) 9 inches = 0.25 yards

Explanation

Square both sides of the given equality to recover $9\ \mathrm{inches}=0.25\ \mathrm{yards}$. This also agrees with 1 yard=36 inches, so a quarter yard is 9 inches.

Taking square roots does not allow the unit symbols to be left unchanged while rooting only the numbers. The true equality is **C**.

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