ABC26GN1983 · Surds and Indices

Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2003 · Marks: · Difficulty:

If $3^{(x-y)}=27$ and $3^{(x+y)}=243$, then $x$ is equal to

(a)0

(b)2

(c)4

(d)6

Answer

Answer (as printed): C

Explanation

$3^{x-y}=27=3^{3}$ $$\begin{aligned} & \Leftrightarrow \quad x-y=3 \\ & 3^{x+y}=243=3^{5} \\ & \Leftrightarrow \quad x+y=5 \end{aligned}$$ On solving (i) and (ii), we get $x=4$.

Explanation as extracted from the printed page; notation may be imperfect.

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