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 →

When n is a positive integer, is n / 4 an integer?

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 Dec 13, 2018 11:43 pm

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

[Math Revolution GMAT math practice question]

When n is a positive integer, is n / 4 an integer?

1) n - 1 is not divisible by 2
2) n + 1 is not divisible by 2
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

When n is a positive integer, is n / 4 an integer?

by fskilnik@GMATH » Fri Dec 14, 2018 1:40 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

When n is a positive integer, is n / 4 an integer?

1) n - 1 is not divisible by 2
2) n + 1 is not divisible by 2
$$n \ge 1\,\,{\mathop{\rm int}} $$
$${n \over 4}\,\,\mathop = \limits^? \,\,{\rm{int}}$$
$$\left( {1 + 2} \right)\,\,\,\mathop \Leftrightarrow \limits^{n\,\,{\mathop{\rm int}} } \,\,n\,\,{\rm{even}}\,\,\,\left\{ \matrix{
\,{\rm{Take}}\,\,{\rm{n = 2}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr
\,{\rm{Take}}\,\,{\rm{n = 4}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{E}} \right)$$

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
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 Dec 16, 2018 5:24 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.

Modifying the question:
Asking whether n/4 is an integer is equivalent to asking whether m is a multiple of 4.

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

Condition 1)
Since n - 1 is not divisible by 2, n - 1 is an odd number and n is an even number.
If n = 4, then n is a multiple of 4 and the answer is 'yes'.
If n = 2, then n is not a multiple of 4 and the answer is 'no'.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
Since n + 1 is not divisible by 2, n + 1 is an odd number and n is an even number.
If n = 4, then n is a multiple of 4 and the answer is 'yes'.
If n = 2, then n is not a multiple of 4 and the answer is 'no'.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Conditions 1) & 2):
If n = 4, then neither n - 1 nor n + 1 is divisible by 2, but n is a multiple of 4 and the answer is 'yes'.
If n = 2, then neither n - 1 nor n + 1 is divisible by 2, and n is not a multiple of 4 and the answer is 'no'.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

Therefore, the answer is E.
Answer: E

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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

by Jay@ManhattanReview » Mon Dec 17, 2018 8:58 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

When n is a positive integer, is n / 4 an integer?

1) n - 1 is not divisible by 2.
2) n + 1 is not divisible by 2.
For n/4 to be an integer, n must be divisible by 4.

Let's take each statement one by one.

1) n - 1 is not divisible by 2.

Since n and n - 1 are consecutive integer and n - 1 is not divisible by 2, it means that n is divisible by 2. Note that every second number is even, thus, divisible by 2. However, n may or may not be divisible by 4.

For example,

Case 1: Say n = 4. Thus, n - 1 = 3, not divisible by 2, but n = 4 is divisible by 4. The answer is yes.
Case 2: Say n = 2. Thus, n - 1 = 1, not divisible by 2, but n = 2 is not divisible by 4. The answer is no.

No unique answer. Insufficient.

2) n + 1 is not divisible by 2.

Sale analysis goes for this statement, too. Insufficient.

(1) and (2) together

Case 1: Say n = 4. Thus, n - 1 = 3 and n + 1 = 5: both not divisible by 2, but n = 4 is divisible by 4. The answer is yes.
Case 2: Say n = 2. Thus, n - 1 = 1 and n + 1 = 3: both not divisible by 2, but n = 2 is not divisible by 4. The answer is no.

No unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
_________________
Manhattan Review Test Prep

Locations: Manhattan Review Himayatnagar | Free GMAT Practice Test | GRE Prep Jayanagar | Madhapur GRE Coaching | 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
Post new topic Post Reply
• Page 1 of 1