in Quantitative Aptitude edited by
0 votes
0 votes

If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$

  1. $2^{\frac{1}{3}}$
  2. $2^{\frac{2}{3}}$
  3. $2^{\frac{1}{4}}$
  4. $2^{\frac{3}{4}}$
in Quantitative Aptitude edited by
13.4k points

1 Answer

1 vote
1 vote
Best answer
y - x = z - y

x + z = 2y$\dots(1)$

xyz =4 $\dots(2)$

We know that, AM  >= GM

Hence, $\frac{x+y+z}{3}$  >= $(xyz)^{\frac{1}{3}}$

From (1) and (2)

$\frac{3y}{3}$ >= $4^{\frac{1}{3}}$

y  >= $2^{\frac{2}{3}}$


Hence,Option(B)$2^{\frac{2}{3}}$ is the correct choice.
selected by
11.1k points

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true