Last visit was: 14 Jul 2024, 07:56 It is currently 14 Jul 2024, 07:56
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Intern
Intern
Joined: 17 Aug 2010
Posts: 46
Own Kudos [?]: 298 [3]
Given Kudos: 18
 Q41  V19
Send PM
User avatar
Retired Moderator
Joined: 02 Sep 2010
Posts: 613
Own Kudos [?]: 2963 [2]
Given Kudos: 25
Location: London
 Q51  V41
Send PM
User avatar
Manager
Manager
Joined: 03 Sep 2010
Posts: 53
Own Kudos [?]: 78 [1]
Given Kudos: 2
Location: Israel
GMAT 1: 660 Q47 V34
GMAT 2: 670 Q48 V34
GPA: 3.2
WE:Operations (Non-Profit and Government)
Send PM
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11778 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]
Expert Reply
Hi All,

This question can be solved with a combination of Exponent Rules and TESTing VALUES.

We're told that B is an INTEGER. We're asked if 2^44 < B^11. This is a YES/NO question.

Fact 1: B is EVEN

IF....
B = 0
Then 2^44 is NOT < 0^11 and the answer to the question is NO

IF....
B = 10,000,0000
Then 2^44 is < 10,000,000^11 and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: B is greater than 16

This Fact is more about knowing how to 'rewrite' exponents than anything else.

16^11 can be rewritten as (2^4)^11, which is equal to 2^44.

Since we now know that B is GREATER than 16, B^11 will be GREATER than 2^44. The answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
Senior Manager
Senior Manager
Joined: 14 Oct 2019
Status:Today a Reader; Tomorrow a Leader.
Posts: 344
Own Kudos [?]: 374 [0]
Given Kudos: 127
Location: India
GPA: 4
WE:Engineering (Energy and Utilities)
Send PM
Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]
Is a^44 < b^11, given that a =2 and b is an integer ?

(1) b is even
b can be any large even integer. Is a^44 < b^11? answer will be yes.
but if b=2 . answer will be no. insufficient
(2) b is greater than 16
so, B=17,18,19..... 17^11>(2^44=16^11). sufficient

correct answer B
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33968
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]
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.
GMAT Club Bot
Re: Is a^44 < b^11, given that a =2 and b is an integer ? [#permalink]
Moderator:
Math Expert
94342 posts