If r = 0.345, s = (0.345)^2, and t = sqrt(0.345) , which

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Sun Apr 14, 2019 9:50 am

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If $$r=0.345,\ \ \ \ \ s=\left(0.345\right)^2\ \ \ \ and\ \ \ \ \ \ t=\sqrt{0.345},$$ which of the following is the correct ordering of r, s, and t ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

[spoiler]OA=D[/spoiler]

Source: Official Guide

Source: Beat The GMAT — Problem Solving | Sun Apr 14, 2019 9:50 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Sat Apr 20, 2019 4:08 am

If $$r=0.345,\ \ \ \ \ s=\left(0.345\right)^2\ \ \ \ and\ \ \ \ \ \ t=\sqrt{0.345},$$ which of the following is the correct ordering of r, s, and t ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

[spoiler]OA=D [/spoiler]

Source: Official Guide

Hi Vjesus12.

Here, we need to use the following fact:

if $ x $ is a positive number less than 1, $(0 < x < 1)$ then $0 < x^2 < x < \sqrt{x}<1.$

Using this we can easily conclude that the correct order for the given 3 number is $ s < r < t. $

This is why the correct answer is the option _D_.

I hope it helps you. <i class="em em---1"></i>

GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Apr 26, 2019 2:33 pm

VJesus12 wrote:If $$r=0.345,\ \ \ \ \ s=\left(0.345\right)^2\ \ \ \ and\ \ \ \ \ \ t=\sqrt{0.345},$$ which of the following is the correct ordering of r, s, and t ?

A. r < s < t
B. r < t < s
C. s < t < r
D. s < r < t
E. t < r < s

[spoiler]OA=D[/spoiler]

Source: Official Guide

Since 0.345 is between 0 and 1, we know that when it is squared, the value decreases and when it is square rooted, the value increases. Thus:

s < r < t

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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