Last visit was: 01 May 2026, 10:04 It is currently 01 May 2026, 10:04
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
Sub 505 (Easy)|   Exponents|   Roots|      
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 109,996
Own Kudos:
812,313
 [1]
Given Kudos: 105,974
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,996
Kudos: 812,313
 [1]
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 04 Mar 2019, 00:58
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

5% (low)

Question Stats:

78% (01:11) correct 22% (01:25) wrong based on 260 sessions

History

Date
Time
Result
Not Attempted Yet
If \(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\) then

A. w < x < y
B. x < w < y
C. y < x < w
D. y < w < x
E. x < y < w
ShowHide Answer
Official Answer
B
User avatar
Archit3110
User avatar
Major Poster
Joined: 18 Aug 2017
Last visit: 01 May 2026
Posts: 8,636
Own Kudos:
5,193
 [1]
Given Kudos: 243
Status:You learn more from failure than from success.
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1: 545 Q79 V79 DI73
GMAT Focus 2: 645 Q83 V82 DI81
GPA: 4
WE:Marketing (Energy)
Products:
GMAT Club Tests Forum Quiz
GMAT Focus 2: 645 Q83 V82 DI81
Posts: 8,636
Kudos: 5,193
 [1]
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 04 Mar 2019, 01:01
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\) then

A. w < x < y
B. x < w < y
C. y < x < w
D. y < w < x
E. x < y < w
Show more

solving expression we get
\(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\)
w= 1/4 = .25
x=1/10= 0.1
y= 16
so y>w>x
IMO B
User avatar
KSBGC
User avatar
Joined: 31 Oct 2013
Last visit: 10 Mar 2022
Posts: 1,240
Own Kudos:
1,510
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Posts: 1,240
Kudos: 1,510
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 04 Mar 2019, 01:08
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\) then

A. w < x < y
B. x < w < y
C. y < x < w
D. y < w < x
E. x < y < w
Show more


w = 1/4

x = 1/10

y = 16..

y>w>x.

B is the correct answer.
User avatar
NandishSS
User avatar
Joined: 06 Jan 2015
Last visit: 28 Jan 2021
Posts: 700
Own Kudos:
1,790
Given Kudos: 579
Location: India
Concentration: Operations, Finance
GPA: 3.35
WE:Information Technology (Computer Software)
Posts: 700
Kudos: 1,790
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 04 Mar 2019, 02:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\) then

A. w < x < y
B. x < w < y
C. y < x < w
D. y < w < x
E. x < y < w
Show more

\(w = \sqrt{\frac{1}{16}}\)= \(\frac{1}{4}\)

\(x = \sqrt[3]{\frac{1}{1000}}\) = \(\frac{1}{10}\)

\(y = (\frac{1}{4})^{(-2)}\) = 16

Hence B
avatar
basabidas
avatar
Joined: 19 Mar 2018
Last visit: 24 Oct 2019
Posts: 4
Own Kudos:
2
Given Kudos: 21
Posts: 4
Kudos: 2
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 05 Mar 2019, 00:20
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hi Bunuel,

Why didn't we have the negative root of w?
In that case w will be +1/4 and -1/4.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 01 May 2026
Posts: 109,996
Own Kudos:
812,313
Given Kudos: 105,974
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,996
Kudos: 812,313
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 05 Mar 2019, 00:26
Kudos
Add Kudos
Bookmarks
Bookmark this Post
basabidas
Hi Bunuel,

Why didn't we have the negative root of w?
In that case w will be +1/4 and -1/4.
Show more

\(\sqrt{...}\) is the square root sign, a function (called the principal square root function), which cannot give negative result. So, this sign (\(\sqrt{...}\)) always means non-negative square root.


The graph of the function f(x) = √x

Notice that it's defined for non-negative numbers and is producing non-negative results.

TO SUMMARIZE:
When the GMAT provides the square root sign for an even root, such as a square root, fourth root, etc. then the only accepted answer is the non-negative root. That is:

\(\sqrt{9} = 3\), NOT +3 or -3;
\(\sqrt[4]{16} = 2\), NOT +2 or -2;
Similarly \(\sqrt{\frac{1}{16}} = \frac{1}{4}\), NOT +1/4 or -1/4.


Notice that in contrast, the equation \(x^2 = 9\) has TWO solutions, +3 and -3. Because \(x^2 = 9\) means that \(x =-\sqrt{9}=-3\) or \(x=\sqrt{9}=3\).
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 01 May 2026
Posts: 22,309
Own Kudos:
26,562
Given Kudos: 302
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 22,309
Kudos: 26,562
If w = 1/16^(1/2), x = 1/1000^(1/3) and y = (1/4)^(-2) then 06 Mar 2019, 19:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(w = \sqrt{\frac{1}{16}}\), \(x = \sqrt[3]{\frac{1}{1000}}\) and \(y = (\frac{1}{4})^{(-2)}\) then

A. w < x < y
B. x < w < y
C. y < x < w
D. y < w < x
E. x < y < w
Show more

Simplifying, we have:

w = 1/4

x = 1/10

y = 4^2 = 16

Thus, x < w < y.

Answer: B
Moderators:
Bunuel
Math Expert
109996 posts
Krunaal
Tuck School Moderator
852 posts