It is currently 25 Jun 2017, 00:29

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If n = p + r, where n, p, and r are positive integers and n

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 16 Jul 2009
Posts: 253
If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

08 Apr 2010, 03:56
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

61% (02:03) correct 39% (01:05) wrong based on 100 sessions

### HideShow timer Statistics

If n = p + r, where n, p, and r are positive integers and n is odd, does p equal 2?

(1) p and r are prime numbers.
(2) r ≠ 2
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39662
Re: If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

08 Apr 2010, 04:05
abhi758 wrote:
If n = p + r, where n, p, and r are positive integers and n is odd, does p equal 2?
(1) p and r are prime numbers.
(2) r ≠ 2

Given: $$odd=p+r$$, where $$p$$ and $$r$$ are positive integers. Question is $$p=2$$?

(1) The sum of two prime can be odd only if one of them is 2 (if 2, the only even prime, is not one of the primes, then the sum of the two primes will be odd+odd=even). But we don't know which one equals to 2. Not sufficient.

(2) $$r\neq{2}$$. Clearly insufficient.

(1)+(2) $$r\neq{2}$$, so $$p$$ must equal to $$2$$. Sufficient.

_________________
Manager
Joined: 11 Feb 2008
Posts: 90
Re: If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

08 Apr 2010, 11:29
abhi758 wrote:
If n = p + r, where n, p, and r are positive integers and n is odd, does p equal 2?
(1) p and r are prime numbers.
(2) r ≠ 2

n can be odd only if a prime number is 2

1)
p and r can take values(2,3,5,7 etc)
if 2 is not there then the sum is not odd
also either p or r can be 2
hence insuffcient

2)
now r not equals 2 but we do not know what p is. both r and n can take any positive valeu to give n as odd

combined 1 and 2
since r not equals 2 and for n to be odd we need 2, p equals 2

hence C
_________________

-------------------------------------------------------------------------------------------
Amar
http://amarnaik.wordpress.com

Manager
Joined: 04 Apr 2010
Posts: 89
Schools: UCLA Anderson
Re: If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

09 Apr 2010, 14:06
I agreed with both answers above.

It is easy to see that both S1 and S2 are insufficient.

When taken together, we know that n is odd, and r is a prime number greater than 2 such as 3,5,7,11,13, etc. For the sum of r and p to be odd, p must be even. The only even prime number is 2.

Hence C
_________________

CEO
Joined: 17 Jul 2014
Posts: 2524
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '20
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

17 Dec 2015, 07:35
If n = p + r, where n, p, and r are positive integers and n is odd, does p equal 2?
for n to be odd, p must be odd and r even or p even and r odd.

(1) p and r are prime numbers.
it might be that p=2 and r= some other prime number, different than 2, since n must be odd.
or r=2, and p an odd prime number. thus, statement 1 is insufficient.

(2) r ≠ 2
statement 2 alone is insufficient.

1+2
r is not 2, thus r is an odd prime number.
this means that p is 2.

1+2 is sufficient. C
Senior Manager
Joined: 17 Jun 2015
Posts: 263
GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
Re: If n = p + r, where n, p, and r are positive integers and n [#permalink]

### Show Tags

20 Dec 2015, 05:03
Odd +(-) Odd= Even
Even +(-) Even= Even
Odd + Even = Odd
Even + Odd = Even

n=p+r
and n is odd

So, either p or r is odd.

Statement 1. Although it indicates one of them is 2 (the only even prime number), it does not clarify whether its p or r. Insuff.
Statement 2. Numerous even and odd combinations would give odd. Insuff.

Combining the two, the air is clear in terms of which is not 2. R is not 2. That implies P is 2.

Hence, C
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Re: If n = p + r, where n, p, and r are positive integers and n   [#permalink] 20 Dec 2015, 05:03
Similar topics Replies Last post
Similar
Topics:
2 If n and p are positive integers, what is the ratio of n to p? (1) n 1 26 May 2017, 08:43
If P=S(1+r/100)^n where P is the amount from investment, S is principa 2 03 Apr 2016, 02:50
if N=p/q, where p and q are nozero integers, is n an 5 23 Jul 2011, 09:46
5 If p and n are positive integers and p > n, what is the remainder when 5 10 Dec 2014, 10:30
7 If n is a positive integer and r is the remainder when (n - 7 22 Apr 2017, 01:22
Display posts from previous: Sort by