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 →

What is the remainder when 1+n+n^2 +…+ n^8 is divided by

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times
by Max@Math Revolution » Thu Aug 15, 2019 5:28 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[GMAT math practice question]

What is the remainder when 1+n+n^2 +...+ n^8 is divided by 5?

1) The remainder when n is divided by 5 is 3
2) n is less than 5
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members
Location: Las Vegas, USA
Thanked: 19 times

by Max@Math Revolution » Sun Aug 18, 2019 5:13 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

The easiest way to solve remainder questions is to plug in numbers.
The units digits of 3^n for n = 1, 2, 3, 4, ... are 3, 9, 7, 1, 3, 9, 7, 1, ...
So, the units digits of 3^n have period 4:
They form the cycle 3 -> 9 -> 7 -> 1.
Thus, if n has remainder 3 when it is divided by 5, 1+n+n^2 +...+ n^8 has the same remainder as 1 + 3 + 9 + 7 + 1 + 3 + 9 + 7 + 1 = 21 when it is divided by 5. It has a remainder of 1 when it is divided by 5.
Condition 1) is sufficient.

Condition 2)
If n = 1, then 1+n+n^2 +...+ n^8 = 9, which has remainder 4 when it is divided by 5.
If n = 3, then 1+n+n^2 +...+ n^8 has remainder 1 when it is divided by 5.
Since condition 2) doesn't yield a unique solution, it is not sufficient.

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