Last visit was: 23 Sep 2026, 14:28 It is currently 23 Sep 2026, 14:28
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
505-555 (Easy)|   Algebra|   Exponents|      
User avatar
Simplify (16^3-15^3)(16^2-15^2) 05 Sep 2014, 21:50
2
Kudos
Add Kudos
26
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:

15% (low)

Question Stats:

82% (01:45) correct 18% (02:12) wrong based on 305 sessions

History

Date
Time
Result
Not Attempted Yet
Simplify \((16^3-15^3)(16^2-15^2)\) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Sep 2026
Posts: 113,831
Own Kudos:
843,224
 [11]
Given Kudos: 111,781
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,831
Kudos: 843,224
 [11]
Simplify (16^3-15^3)(16^2-15^2) 05 Sep 2014, 21:57
8
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
ankitaprsd
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon
Show more

(16^3 - 15^3)(16^2 - 15^2) =

= ({number with units digit of 6} - {smaller number with units digit of 5})*({number with units digit of 6} - {smaller number with units digit of 5}) =

= {number with units digit of 1}*{number with units digit of 1} = {number with units digit of 1}.

Answer: B.

P.S. You must provide the OA if you have it.

User avatar
JeffTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,973
Own Kudos:
8,985
 [7]
Given Kudos: 1,646
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert
Expert reply
Posts: 2,973
Kudos: 8,985
 [7]
Simplify (16^3-15^3)(16^2-15^2) 15 Sep 2017, 10:08
4
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
ankitaprsd
Simplify \((16^3-15^3)(16^2-15^2)\) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106
Show more

We can focus on units digits to solve the question.

Since 6 raised to an exponent always produces a units digit of 6, and 5 raised to an exponent always produces a units digit of 5, we have the units digit of the expression as:

(6 - 5)(6 - 5) = 1 x 1 = 1

Thus, the correct answer must have a units digit of 1. Thus, the answer is 22,351.

Answer: B
General Discussion
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Own Kudos:
8,449
 [3]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Kudos: 8,449
 [3]
Simplify (16^3-15^3)(16^2-15^2) 08 Sep 2014, 00:23
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
ankitaprsd
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon
Show more

\((16^3 - 15^3)(16^2 - 15^2)\)

\(= (16-15)(16^2 + 16*15 + 15^2)(16+15)(16-15)\)

= (256+225+16*15) * 31

(256+225+16*15) >> This expression would give 1 at the units place

Multiplying it by 31 also gives 1 at the units place

Out of the 5 options, only 22351 qualifies

Answer = B
avatar
PareshGmat
avatar
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Own Kudos:
8,449
 [4]
Given Kudos: 193
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Kudos: 8,449
 [4]
Simplify (16^3-15^3)(16^2-15^2) 08 Sep 2014, 01:05
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
ankitaprsd
Simplify (16^3-15^3)(16^2-15^2) =

A. 22468
B. 22351
C. 22216
D. 22192
E. 22106

Looking for a shortcut to solve this
OA soon
Show more

One More method

\((16^3-15^3)(16^2-15^2)\)

\(= 16^5 - 16^3 * 15^2 - 15^3 * 16^2 + 15^5\)

Writing down the last digits (Units digits) of the above 4 terms

= 6 - 0 - 0 + 5

= 1

Last digit comes to 1, only 22351 fits in

Answer = B
User avatar
DangerPenguin
User avatar
Joined: 10 Sep 2014
Last visit: 22 Dec 2014
Posts: 90
Own Kudos:
123
Given Kudos: 25
Posts: 90
Kudos: 123
Simplify (16^3-15^3)(16^2-15^2) 01 Oct 2014, 08:42
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Is there an alternate way to solve this problem? Or can someone explain how to know what the units digits will be please? :)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 23 Sep 2026
Posts: 113,831
Own Kudos:
843,224
 [1]
Given Kudos: 111,781
Products:
GMAT Club Tests
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 113,831
Kudos: 843,224
 [1]
Simplify (16^3-15^3)(16^2-15^2) 01 Oct 2014, 09:23
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
DangerPenguin
Is there an alternate way to solve this problem? Or can someone explain how to know what the units digits will be please? :)
Show more

This might help: math-number-theory-88376.html
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 39,274
Own Kudos:
1,162
Posts: 39,274
Kudos: 1,162
Simplify (16^3-15^3)(16^2-15^2) 25 Aug 2025, 06:58
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.
Moderator:
Bunuel
Math Expert
113831 posts