CAT 2003 Slot 2 — QA Question 39

y − x = z − y

2y = x + z                                                  ... (i)

xyz = 4                                                      ... (ii)

It is known that Arithmetic Mean (A.M.) is greater than or equal to Geometric Mean (G.M.)

i.e. A.M. ≥ G.M.

Hence, $\frac{x+y+z}{3}$ ≥ (xyz)^1/3 .....(iii)

From (i), (ii) and (iii), we get $\frac{3y}{3}$ ≥ 4^1/3

∴ y ≥ 2^2/3

∴ The minimum value of y is 2^2/3

Hence, option (b).