GMAT related question: If the standard deviation of $a,b$ and $c$ is $d$. What is the standard deviation of $105\%$ of $a$ ,$105b/100$ and $1.05c$?

GMAT-related question: If the standard deviation of $a,b$ and $c$ is $d$. What is the standard deviation of $105\%$ of $a$ ,$105b/100$ and $1.05c$?

A)$d$

b)$5d$

c)None of these

d)$125\% d$

e)$1.05d$

From the above, we know that the mean equals $(a+b+c)/3$ and that $105\%$ of $a$ can be expressed as $1.05a; 105b/100$ as $1.05b$, so the answer should be option e). More than the solution, I would like to know the intuition/strategy in order to solve this problem efficiently. It is a GMAT advance problem.

If a random variable $X$ has standard deviation $\sigma$ = $d$, then its variance $\sigma^2=d^2$. Also note that $Var(aX)=a^2Var(X)=a^2\sigma^2$. To find the standard deviation, you simply have to again find the square root. Thus the answer will be $(e)$. Hope this helps.