BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If a and b are positive integers and x = 4^a and y = 9^b,

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members
by BTGmoderatorDC » Mon Aug 20, 2018 3:08 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?

a. 1
b. 4
c. 5
d. 7
e. 8

OA B

Source: Manhattan Prep
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members
Location: Grand Central / New York
Thanked: 470 times

by Jay@ManhattanReview » Tue Aug 21, 2018 12:33 am
BTGmoderatorDC wrote:If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?

a. 1
b. 4
c. 5
d. 7
e. 8

OA B

Source: Manhattan Prep
We have to get the unit digit of xy = 4^a*9^b; where a and b are positive integers

We know that the power cycle of 4 is 2, i.e., 4^a has the unit digits 4/6/4/6/4/6 ...
Also, note that the power cycle of 9 is 2, i.e., 9^b has the unit digits 9/1/9/1/9/1 ...

Unit digits of the product 4 with 9/1 are 6 and 4 -- thus, option B is the correct answer.

For the sake of understanding better, let's find out the unit digits of the product 6 with 9/1

Unit digits of the product 6 with 9/1 are 4 and 6

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Hyderabad | Mexico City | Toronto | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Tue Aug 21, 2018 3:21 am
BTGmoderatorDC wrote:If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?

a. 1
b. 4
c. 5
d. 7
e. 8
x is equal to a POWER OF 4:
4, 16, 64...
y is equal to a POWER OF 9:
9, 81...
If x=4 and y=81, then xy = 324, which has a units digit of 4.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8136
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Thu Aug 23, 2018 3:44 pm
BTGmoderatorDC wrote:If a and b are positive integers and x = 4^a and y = 9^b, which of the following is a possible units digit of xy?

a. 1
b. 4
c. 5
d. 7
e. 8
Since x is even (notice that x is a power of 4) and y is odd (notice that y is a power of 9), then xy must be even and thus it has an even units digit. We can rule out choices A, C and D.

Furthermore, the units digits of powers of 4 are 4 and 6, and the units digits of powers of 9 are 9 and 1. Therefore, a possible units digit of xy is 4 * 1 = 4.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1