CAT 1997 — QA Question 33

$A=\frac{2.000004}{[{(2.000004)}^2+2(2.000004\left)\right]}$

$=\frac{2.000004}{2.000004\left[\right(2.000004)+2]}$

= $\frac{1}{\left[\right(2.000004)+2]}$

$=\frac{1}{4.000004}$

= $\frac{1}{4}=0.25$ (Approximately)

$B=\frac{3.000003}{[{(3.000003)}^3+3(3.000003\left)\right]}$

$=\frac{3.000003}{3.000003\left[\right(3.000003)+3]}$

$=\frac{1}{\left[\right(3.000003)+3]}=\frac{1}{6.000003}$

$C=\frac{4.000002}{[{(4.000002)}^2+2(4.000002\left)\right]}$

$=\frac{4.000002}{4.000002\left[\right(4.000002)+2]}$

$=\frac{1}{\left[\right(4.000002)+2]}=\frac{1}{6.000002}$

Looking at the answer choices, we can see that the only (d) satisfies the relationship, viz. B is the smallest.