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
GMATBootcamp Starts Sep 21
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE BOOTCAMP

Live Online Bootcamp Class with Top GMAT Expert Chris Peckover

Sep 21 to Oct 9, 2026

Schedule
Mon to Fri · 7:00 to 10:00 PM ET
Included
Live classes + 6 months of TTP OnDemand
  • Boost your GMAT score in less than one month in a live online class
  • 6 months access to TTP OnDemand video courses included
View bootcamp & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

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
Limited cohort · enrollment openTarget 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.

A positive 5-digit integer is called "friendly" if

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times
by fskilnik@GMATH » Tue Feb 12, 2019 7:05 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

GMATH practice exercise (Quant Class 18)

A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is:

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1

Answer: [spoiler]____(B)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
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 Feb 12, 2019 7:41 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18)

A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is:

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1


Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120.
There are 5 options for the first digit: 1, 2, 3, 4, or 5.
120/5 = 24.
Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows:
The integers beginning with 1 constitute friendly numbers 1-24.
The integers beginning with 2 constitute friendly numbers 25-48.
The integers beginning with 3 constitute friendly numbers 49-72.
The integers beginning with 4 constitute friendly numbers 73-96.
The integers beginning with 5 constitute friendly numbers 97-120.

The 32nd friendly number is contained within the blue range above.

Friendly numbers in the blue range, from least to greatest:
21345 --> 25th friendly number
21354 --> 26th friendly number
21435 --> 27th friendly number
21453 --> 28th friendly number
21534 --> 29th friendly number
21543 --> 30th friendly number
23145 --> 31st friendly number
23154 --> 32nd friendly number

The units digit for the 32nd friendly number = 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
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

by fskilnik@GMATH » Tue Feb 12, 2019 5:49 pm
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 18)

A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is:

(A) 5
(B) 4
(C) 3
(D) 2
(E) 1


FOCUS: the units digit of the 32nd friendly number

1. The first P4 = 4! = 24 friendly numbers "start with 1" (i.e., 1 _ _ _ _ ) , the (few) next ones "start with 2".

2. "Starting with 2" (i.e., 2 _ _ _ _ ), there are P3 = 3! = 6 friendly numbers "beginning with 21" (i.e., 2 1 _ _ _ ), hence:
All friendly numbers, from the 25th until the 30th (both included) are of the form 21 _ _ _ .

3. The 31st friendly number is the smallest friendly number that starts with "23", that is, 23145.

4. Finally, the 32nd friendly number is the next one (23154), hence ? = 4.


The correct answer is (B).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1