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 units digit of a positive integer n?

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 Nov 08, 2018 12:34 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[Math Revolution GMAT math practice question]

What is the units digit of a positive integer n?

1) n is a common multiple of 13 and 14.
2) n is a common multiple of 13 and 15.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members
Thanked: 59 times

What is the units digit of a positive integer n?

by fskilnik@GMATH » Thu Nov 08, 2018 9:33 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the units digit of a positive integer n?

1) n is a common multiple of 13 and 14.
2) n is a common multiple of 13 and 15.
$$n \ge 1\,\,{\mathop{\rm int}} $$
$$?\,\,\,:\,\,n\,\,{\rm{units}}\,\,{\rm{digit}}$$
$$\left( 1 \right)\,\,n\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,LCM\left( {13,14} \right) = 13 \cdot 14\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 13 \cdot 14\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,{\rm{ 2}}\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 13 \cdot 14 \cdot 2\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,{\rm{ 4}} \hfill \cr} \right.$$
$$\left( 2 \right)\,\,n\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,LCM\left( {13,15} \right) = 13 \cdot 15\,\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,n = 13 \cdot 15\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,{\rm{ 5}}\,\, \hfill \cr
\,{\rm{Take}}\,\,n = 13 \cdot 15 \cdot 2\,\,\,\,\, \Rightarrow \,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,{\rm{ 0}} \hfill \cr} \right.$$
$$\left( {1 + 2} \right)\,\,n\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,13 \cdot 14 \cdot 15 = 13 \cdot 7 \cdot \underline {2 \cdot 5} \cdot 3\,\,\,\,\,\, \Rightarrow \,\,\,\,\,n\,\,{\rm{is}}\,\,{\rm{a}}\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,10\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{?}}\,\,{\rm{ = }}\,{\rm{ 0}}\,\,\,\,\,$$

This solution follows 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
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

edited

by deloitte247 » Sat Nov 10, 2018 3:20 pm
n is a positive integer, hence $$n\ >0$$

Statement 1
n is a common multiple of 13 and 14
multiple of 13 = 1 and 13
multiple of 14 = 1, 2,7, and 14
common multiple =1
n = 1

Statement 2
n is a common multiple of 13 and 15
multiple of 13 = 1, 13
multiple of 15 = 1, 3, 5 and 15
common multiple = 1
n=1

Statement 1 and 2 are SUFFICIENT.
$$answer\ is\ option\ D$$
Last edited by deloitte247 on Sat Nov 10, 2018 3:30 pm, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

repetition

by deloitte247 » Sat Nov 10, 2018 3:25 pm
n is a positive integer, hence $$n\ >0$$

Statement 1
n is a common multiple of 13 and 14
multiple of 13 = 1 and 13
multiple of 14 = 1, 2,7, and 14
common multiple =1
n = 1

Statement 2
n is a common multiple of 13 and 15
multiple of 13 = 1, 13
multiple of 15 = 1, 3, 5 and 15
common multiple = 1
n=1

Statement 1 and 2 are SUFFICIENT
$$answer\ is\ option\ D$$
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
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 Nov 11, 2018 9:45 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.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since n is a common multiple of 13 and 14, n is a multiple of lcm(13,14) = 182. Thus units digits of multiples of n are 0, 2, 4, 6, 8 since the units digit of 182 is 2.
Condition 1) is not sufficient.

Condition 2)
Since n is a common multiple of 13 and 15, n is a multiple of lcm(13,15) = 195. Thus units digits of multiples of n are 0, 5 since the units digit of 182 is 2.
Condition 2) is not sufficient.

Conditions 1) & 2)
The common units digit of multiples of 182 and 195 is 0 only.
Both conditions together are sufficient.

Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1