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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

An “Armstrong number” is an n-digit number that is equal to

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 1223
Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member
by BTGModeratorVI » Sun Jul 26, 2020 6:42 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6
Answer: B
Source: Official guide
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

Re: An “Armstrong number” is an n-digit number that is equal to

by Jay@ManhattanReview » Sun Jul 26, 2020 10:47 pm
BTGModeratorVI wrote: ↑
Sun Jul 26, 2020 6:42 am
 An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6
Answer: B
Source: Official guide
So, as per the given information, we have 1,6k4 = 1^4 + 6^4 + k^4 + 4^4

1,6k4 = 1 + 1,296 + k^4 + 256

1,6k4 = 1,553 + k^4

1,000 + 600 + 10k + 4 = 1,553 + k^4

1,604 – 1,553 + 10k = k^4

51 + 10k = k^4

Now solving this higher-order equation is a tedious task. Let's make things easier by analyzing options.

Note that irrespective of the value of k, the units digits of 10k would be 0. Thus, the units digits of 51 = 10k would be 1. This means that the units digits of k^4 is also 1.

Only option B (= 3) qualifies as 3^4 = 81, the units digits = 1.

Correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: GMAT Prep Atlanta | SAT Prep San Francisco | GMAT Prep USA | TOEFL Prep Minneapolis | 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
Legendary Member
Posts: 2579
Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: An “Armstrong number” is an n-digit number that is equal to

by swerve » Mon Jul 27, 2020 4:31 am
BTGModeratorVI wrote: ↑
Sun Jul 26, 2020 6:42 am
 An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6
Answer: B
Source: Official guide
\(1^4+6^4+k^4+4^4=1604+10k\)
\(1+1296+k^4+256=1604+10k\)
\(k^4-10k=1604-1553=51\)

By replacing the options with \(k\), 3 would be the answer.

\(3^4-30=51\quad \Longrightarrow\quad\) B
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: An “Armstrong number” is an n-digit number that is equal to

by Brent@GMATPrepNow » Mon Jul 27, 2020 5:46 am
BTGModeratorVI wrote: ↑
Sun Jul 26, 2020 6:42 am
 An “Armstrong number” is an n-digit number that is equal to the sum of the nth powers of its individual digits. For example, 153 is an Armstrong number because it has 3 digits and 1^3 + 5^3 + 3^3 = 153. What is the digit k in the Armstrong number 1,6k4 ?

A. 2
B. 3
C. 4
D. 5
E. 6
Answer: B
Source: Official guide
1,6k4 is a 4-digit number.
So, 1⁴ + 6⁴ + k⁴ + 4⁴ = 16k4
Evaluate: 1 + 1296 + k⁴ + 256 = 16k4
Simplify: 1553 + k⁴ = 16k4

Whatever k is, it must be the case that the UNITS digit of k⁴ is 1, so that 1553 + k⁴ = 16k4
Test some values..
k = 1: 1⁴ = 1, so we get: 1553 + 1 = 1554 NO GOOD
k = 3: 3⁴ = 81, so we get: 1553 + 81 = 1634 WORKS!!

Answer: k = 3

Cheers,
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1