in Quantitative Aptitude retagged by
137 views
1 vote
1 vote

Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x > 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals

  1. $12$
  2. $8$
  3. $14$
  4. $10$
in Quantitative Aptitude retagged by
2.7k points
137 views

1 Answer

1 vote
1 vote
Given that, $x,y, \text{and}\; z$ are in A.P.

So, $y-x = z-y$

$\Rightarrow \boxed{2y = x+z}$

And, $y-x > 2\;{\color{Blue}{\text{(Increasing A.P.)}}}$

Also, $x \times y \times z = 5(x+y+z)$

$\Rightarrow x \times y \times z = 5(3y) \quad [\because x+z=2y]$

$\Rightarrow \boxed{x \times z = 15}$

$ \qquad \begin{array} {cc} \underline{x} & \underline{z} \\ 1 & 15 \\ 3 & 5 \end{array}$

Now, we can calculate the value of $y.$

$\qquad \begin{array}{} \underline{x} & \underline{y} & \underline{z} \\  1 & 8  & 15\quad {\color{Green}{\text{in A.P.}}} \\ 3 & 4 & 5 \quad {\color{Red}{\text{in A.P.}}} \end{array}$

$\therefore$ The value of $z-x = 15-1 = 14.$

Correct Answer $:\text{C}$
edited by
10.3k points
Answer:

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