Subject: General Aptitude · Chapter: Surds and Indices · Exam: · Marks: · Difficulty:
If $4^{x+y}=1$ and $4^{x-y}=4$, then the values of $x$ and $y$ respectively are
(a)$-\frac{1}{2}$ and $\frac{1}{2}$
(b)$-\frac{1}{2}$ and $-\frac{1}{2}$
(c)$\frac{1}{2}$ and $-\frac{1}{2}$
(d)$\frac{1}{2}$ and $\frac{1}{2}$
Answer
Answer (as printed): C
Explanation
$4^{x+y}=1=4^{0} \Leftrightarrow x+y=0$ $4^{x-y}=4=4^{1} \Rightarrow x-y=1$ Adding (i) and (ii), we get : $2 x=1$ or $x=\frac{1}{2}$. Putting $x=\frac{1}{2}$ in (i), we get : $y=-\frac{1}{2}$.
Explanation as extracted from the printed page; notation may be imperfect.