Let r be the result of doubling both thebase and the exponent of ab, b 0. If r equals the product of ab by xb, then x equals

ABC26GN1991 · Surds and Indices

Subject: General Aptitude · Chapter: Surds and Indices · Exam: 2010 · Marks: · Difficulty:

Let $r$ be the result of doubling both thebase and the exponent of $a^{b}, b \neq 0$. If $r$ equals the product of $a^{b}$ by $x^{b}$, then $x$ equals

(a)2

(b)4

(c)$2 a$

(d)$4 a$

Answer

Answer (as printed): D

Explanation

$r=(2 a)^{2 b}=2^{2 b} \times a^{2 b}=\left(2^{2}\right)^{b} \times\left(a^{b}\right)^{2}=4^{b} \times\left(a^{b}\right)^{2}$. Also, $r=a^{b} \times x^{b}$. $$\therefore \quad a^{b} \times x^{b}=4^{b} \times\left(a^{b}\right)^{2} \Leftrightarrow x^{b}=4^{b} \times a^{b}=(4 a)^{b} \Leftrightarrow x=4 a .$$

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

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