• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

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

This topic has 2 expert replies and 0 member replies

GMAT/MBA Expert

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

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



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: ____(B)__

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Post
fskilnik@GMATH wrote:
[size=17]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.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

  • +1 Upvote Post
  • Quote
  • Flag
Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Post
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

  • +1 Upvote Post
  • Quote
  • Flag
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review

Top First Responders*

1 Ian Stewart 57 first replies
2 Brent@GMATPrepNow 31 first replies
3 Jay@ManhattanReview 29 first replies
4 GMATGuruNY 21 first replies
5 ceilidh.erickson 15 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

199 posts
2 image description Max@Math Revolution

Math Revolution

84 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

69 posts
4 image description Ian Stewart

GMATiX Teacher

65 posts
5 image description GMATGuruNY

The Princeton Review Teacher

40 posts
See More Top Beat The GMAT Experts