GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Feb 2020, 21:15

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

SVP
Joined: 23 Feb 2015
Posts: 1542
If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)  [#permalink]

### Show Tags

23 Jan 2020, 08:16
00:00

Difficulty:

45% (medium)

Question Stats:

48% (01:15) correct 52% (01:56) wrong based on 21 sessions

### HideShow timer Statistics

If $$n$$ is an integer, is $$n$$ odd?
(1) $$\frac{n}{3}$$ is divisible by $$3$$
(2) $$2n$$ has twice as many factors as $$n$$

Posted from my mobile device
Intern
Joined: 27 Jul 2015
Posts: 40
Concentration: Technology, Entrepreneurship
GMAT 1: 750 Q50 V41
GPA: 2.2
WE: Information Technology (Computer Software)
If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)  [#permalink]

### Show Tags

Updated on: 24 Jan 2020, 13:05
If n/3=3, n is odd and n/3 is divisible by 3. If n/3=6, n is even and n/3 is divisible by 3. So statement 1 is insufficient.

The only way I can think for statement 2 to be true is prime numbers other than 2.
if n=5 (factors 1, 5); 2n=10 (factors 1, 2, 5, 10)
if n=7 (factors 1, 7); 2n=14 (factors 1, 2, 7, 14)
So, statement 2 alone is sufficient. answer is B.

Originally posted by s1lntz on 24 Jan 2020, 09:39.
Last edited by s1lntz on 24 Jan 2020, 13:05, edited 1 time in total.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8574
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)  [#permalink]

### Show Tags

24 Jan 2020, 10:56
If $$n$$ is an integer, is $$n$$ odd?
(1) $$\frac{n}{3}$$ is divisible by $$3$$
(2) $$2n$$ has twice as many factors as $$n$$

Posted from my mobile device

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

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)

We have an expression $$\frac{n}{3} = 3k$$ for some integer $$k$$.
Then we have $$n = 3^2k$$.
If $$k = 1$$, then $$n = 3^2 = 9$$, $$n$$ is an odd number and the answer is 'yes'.
If $$k = 2$$, then $$n = 3^2 \cdot 2 = 18$$, $$n$$ is an even number and the answer is 'no'.

Since condition 1) does not yield a unique solution, it is not sufficient.

Condition 2)

Assume $$n = p^a \cdot q^b \cdot r^c$$ where $$p, q$$ and $$r$$ are different prime numbers.
Then the number of factors of $$n$$ is $$(a+1)(b+1)(c+1)$$.

If $$p, q$$ and $$r$$ are odd prime numbers, then $$2n = 2^1 \cdot p^a \cdot q^b \cdot r^c$$ and the number of factors of $$2n$$ is $$(1+1)(a+1)(b+1)(c+1) = 2(a+1)(b+1)(c+1)$$ which is twice as many factors as $$n$$.

Assume $$p = 2$$ which means one of prime factors of $$n$$ is $$2$$.
Then $$2n = 2p^a \cdot q^b \cdot r^c = 2^{a+1} \cdot q^b \cdot r^c$$ and the number of factors of $$2n$$ is $$(a+2)(b+1)(c+1)$$.
We have $$(a+2)(b+1)(c+1) = 2(a+1)(b+1)(c+1)$$ or $$a+2 = 2a + 2$$. Then we have $$a = 0$$ and n is an odd number.

Since condition 2) yields a unique solution, it is sufficient.

Therefore, D is the answer.

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.
_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Re: If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)   [#permalink] 24 Jan 2020, 10:56
Display posts from previous: Sort by

# If n is an integer, is n odd? (1) n/3 is divisible by 3 (2)

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne