Last visit was: 10 Jul 2025, 04:05 It is currently 10 Jul 2025, 04:05
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.
Close
Request Expert Reply
Confirm Cancel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 10 Jul 2025
Posts: 102,612
Own Kudos:
Given Kudos: 98,069
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,612
Kudos: 740,014
 [22]
1
Kudos
Add Kudos
21
Bookmarks
Bookmark this Post
User avatar
PKN
Joined: 01 Oct 2017
Last visit: 22 Jan 2025
Posts: 816
Own Kudos:
1,541
 [3]
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 816
Kudos: 1,541
 [3]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
User avatar
VaCeFe
Joined: 15 Oct 2018
Last visit: 03 Jun 2021
Posts: 13
Own Kudos:
Given Kudos: 27
Posts: 13
Kudos: 6
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
fskilnik
Joined: 12 Oct 2010
Last visit: 03 Jan 2025
Posts: 885
Own Kudos:
Given Kudos: 57
Status:GMATH founder
Expert
Expert reply
Posts: 885
Kudos: 1,692
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In which of the following choices must a be less than b?


(A) \(4^{(-2b)} = 4^{(-a)}\)

(B) \(-4^b < 4^a\)

(C) \(4^{(-b)} < 4^{(-a)}\)

(D) \(4^{(-b)} > 4^{(-a)}\)

(E) \(4^{(-b)} = 4^{(-2a)}\)
\(?\,\,\,\,:\,\,\,\,a\,\, < \,\,\,b\)

\(\left( {a,b} \right) = \left( {0,0} \right)\,\,{\text{satisfies}}\,\,\left( A \right),\left( B \right)\,\,{\text{and}}\,\,\left( E \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{they}}\,\,{\text{are}}\,\,{\text{out}}!\)

\(\left( {a,b} \right) = \left( {1,0} \right)\,\,{\text{satisfies}}\,\,\left( D \right)\,\,\,\,\, \Rightarrow \,\,\,{\text{out}}!\)


Alternative choice (C) is the only survivor, therefore it must be the right answer.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
User avatar
PKN
Joined: 01 Oct 2017
Last visit: 22 Jan 2025
Posts: 816
Own Kudos:
Given Kudos: 41
Status:Learning stage
WE:Supply Chain Management (Energy)
Posts: 816
Kudos: 1,541
Kudos
Add Kudos
Bookmarks
Bookmark this Post
VaCeFe
Bunuel
In which of the following choices must a be less than b?


(A) \(4^{(-2b)} = 4^{(-a)}\)

(B) \(-4^b < 4^a\)

(C) \(4^{(-b)} < 4^{(-a)}\)

(D) \(4^{(-b)} > 4^{(-a)}\)

(E) \(4^{(-b)} = 4^{(-2a)}\)


Why E is wrong? From E : b = 2a; b always gonna be greater than a

Hi VaCeFe,

1) Say a=1 then b=2a=2*1=2; b>a-------Your reasoning is CORRECT
2) Say a=-1 then b=2a=2*(-1)=-2; b<a-------Your reasoning is NOT CORRECT. (Since -2<-1)

This is the reason we have to DISCARD option(E).

Hope it helps.
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 10 Jul 2025
Posts: 21,066
Own Kudos:
26,121
 [2]
Given Kudos: 296
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: 21,066
Kudos: 26,121
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
In which of the following choices must a be less than b?


(A) \(4^{(-2b)} = 4^{(-a)}\)

(B) \(-4^b < 4^a\)

(C) \(4^{(-b)} < 4^{(-a)}\)

(D) \(4^{(-b)} > 4^{(-a)}\)

(E) \(4^{(-b)} = 4^{(-2a)}\)
Solution:

Recall that if x > 1, then x^m > x ^n implies that m > n. Similarly, if x^m < x^n, then m < n. Therefore, let’s look at choice C first:

4^(-b) < 4^(-a)

-b < -a

b > a

We see that b > a or a < b.

Answer: C
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,373
Own Kudos:
Posts: 37,373
Kudos: 1,010
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Math Expert
102612 posts
PS Forum Moderator
683 posts