If Log(P) = (1/2)Log(Q) = (1/3) Log(R), then which of the following options is TRUE? A) P2 = Q3 R2 B) Q2 = PR C) Q2 = R3 P D) R = P2 Q2

Official answer: B) Q2 = PR. Explanation: Let: log(P) = (1)/(2)log(Q) = (1)/(3)log(R) = k Expressing P, Q, and R in terms of the base of the logarithm b and constant k: log(P) = k P = bk log(Q) = 2k Q = b2k log(R) = 3k R = b3k Now, test the relation Q2: Q2 = (b2k)2 = b4k P R = (bk)(b3k) = bk+3k = b4k Thus, Q2 = PR, which corresponds to option (B).

Quantitative Aptitude

GATE CSE 2011 · Q57

MCQ1 markEasy

Time00:00

If $\text{Log}(P) = (1/2)\text{Log}(Q) = (1/3) \text{Log}(R)$ , then which of the following options is TRUE?

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Solution

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Official answer: B) Q2 = PR

Quantitative Aptitude

Let:

\log(P) = \frac{1}{2}\log(Q) = \frac{1}{3}\log(R) = k

Expressing $P$ , $Q$ , and $R$ in terms of the base of the logarithm $b$ and constant $k$ :

\log(P) = k \implies P = b^k

\log(Q) = 2k \implies Q = b^{2k}

\log(R) = 3k \implies R = b^{3k}

Now, test the relation $Q^2$ :

Q^2 = (b^{2k})^2 = b^{4k}

P R = (b^k)(b^{3k}) = b^{k+3k} = b^{4k}

Thus, $Q^2 = PR$ , which corresponds to option (B).

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This Quantitative Aptitude previous year question is Q57 of the GATE CSE 2011 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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