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 →

Ones digit Challenge

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
MBA Admissions Consultant
Posts: 2279
Joined: Fri Nov 11, 2011 7:51 amFollowed by: 266 members
Location: New York
Thanked: 660 times
GMAT Score:770
by Jim@StratusPrep » Sun Jul 08, 2012 4:58 pm
For the positive integers W, X, Y, and Z, Z = 2x + 1, and W=Y^Z. What is the remainder of W when it is divided by 10?

1) Y = 9
2) X = 3
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Legendary Member
Posts: 520
Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members
Thanked: 339 times
GMAT Score:770

by eagleeye » Sun Jul 08, 2012 5:16 pm
Jim@StratusPrep wrote:For the positive integers W, X, Y, and Z, Z = 2x + 1, and W=Y^Z. What is the remainder of W when it is divided by 10?

1) Y = 9
2) X = 3
The key to solving this lies in recognizing that Z=2X+1 means that Z is odd.
Also, when a positive integer is divided by 10, the remainder is the units digit itself.
After that the problem is a breeze. We are told that W=Y^2 and we need to find whether we can determine the units digit of W.

1) Y=9
W=9^Z, but recall that Z is odd.
Now 9 is a cool number because 9^1=9 , 9^2 =9*9 = 81, 9^3= 81*9 =729, 9^4=729*9 = something ending in 1. We see that for even
powers of 9, last digit is 1, for odd powers it is always 9. (The pattern practically shouts itself).
Since the units digit of W for odd Z is always 9, this is Sufficient.

2) X=3, this means that Z=7.
For Y=1, W=1^7 = 1, units digit is 1
For Y=2, W=2^7 = 128, units digit is 8
(I wrote these counter examples for reference only, in reality if we have an expression W^7, it is obvious that the units digit is going to depend on W, and hence we can't determine what it is!)
Indeterminable units digit, Hence Insufficient.

A is the final answer.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1