GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Nov 2018, 19:56

### 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 November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

November 18, 2018

November 18, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score. November 18th, 7 AM PST
• ### How to QUICKLY Solve GMAT Questions - GMAT Club Chat

November 20, 2018

November 20, 2018

09:00 AM PST

10:00 AM PST

The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.

# If m and n are positive integers and mn = p + 1, is m + n = p ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 20 Nov 2009
Posts: 128
If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

Updated on: 04 Aug 2010, 22:19
1
00:00

Difficulty:

75% (hard)

Question Stats:

57% (01:58) correct 43% (02:17) wrong based on 164 sessions

### HideShow timer Statistics

If m and n are positive integers and mn = p + 1, is m + n = p ?

(1) Both m and n are prime numbers.
(2) p + 1 is even.

_________________

But there’s something in me that just keeps going on. I think it has something to do with tomorrow, that there is always one, and that everything can change when it comes.
http://aimingformba.blogspot.com

Originally posted by aiming4mba on 04 Aug 2010, 21:49.
Last edited by aiming4mba on 04 Aug 2010, 22:19, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

04 Aug 2010, 22:35
2
2
aiming4mba wrote:
If m and n are positive integers and mn = p + 1, is m + n = p ?
a. Both m and n are prime numbers.
b. p + 1 is even.

Given: $$mn=p+1$$. Question: is $$m+n=p$$?

(1) Both m and n are prime numbers. If $$m=n=2$$, then $$p=3$$ and the answer is NO, as $$m+n=2+2=4\neq{p=3}$$ but if $$m=2$$ and $$n=3$$ then $$p=5$$ and the answer is YES, as $$m+n=2+3=p=5$$. Not sufficient.

(2) p + 1 is even --> $$p=odd$$. No info about $$m$$ and $$n$$. Not sufficient.

(1)+(2) Examples from (1) are still valid (as in both examples $$p=odd$$), hence we still have two different answers. Not sufficient.

_________________
Intern
Joined: 15 Aug 2010
Posts: 13
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

03 Sep 2010, 03:48
Hi,
I dont know whether my approach is correct or wrong but I suspect anser is C.
From St1: i know they are prime numbers
and from St2: i get P as odd number -
mn = p + 1 from here, in order to p+1 to be even out of m and n one should be 2.
so i get m= (p+1)/2 (if n=2).
=> m+n =p => (p+1)/2 + 2 = p => defenitly not equal to P.

Please let me know if my approach was wrong.

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 50623
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

03 Sep 2010, 04:32
1
sikalvag wrote:
Hi,
I dont know whether my approach is correct or wrong but I suspect anser is C.
From St1: i know they are prime numbers
and from St2: i get P as odd number -
mn = p + 1 from here, in order to p+1 to be even out of m and n one should be 2.
so i get m= (p+1)/2 (if n=2).
=> m+n =p => (p+1)/2 + 2 = p => defenitly not equal to P.

Please let me know if my approach was wrong.

Thanks

OA is given in the first post, under the spoiler and it's E.

In my post above there are 2 cases given satisfying the stem and both statements and giving different answers to the question, thus proving that answer is E:
If $$m=n=2$$, then $$p=3=odd$$ and the answer is NO, as $$m+n=2+2=4\neq{p=3}$$;
If $$m=2$$ and $$n=3$$ then $$p=5=odd$$ and the answer is YES, as $$m+n=2+3=p=5$$.

Also why "(p+1)/2 + 2 = p => defenitely not equal to P" (the red part)? If you solve it for $$p$$ you'll get $$p=5$$ so $$n=2$$ and $$m=3$$.

Hope it helps.
_________________
Senior Manager
Joined: 18 Aug 2009
Posts: 361
Schools: UT at Austin, Indiana State University, UC at Berkeley
WE 1: 5.5
WE 2: 5.5
WE 3: 6.0
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

02 Feb 2011, 18:24
If m and n are positive integers and mn = p + 1, is m + n = p ?

S1: Both m and n are prime numbers.
S2: p + 1 and m are both even

A. S1 sf
B S2 sf
C both A and B together sf
D. Each sf
E. Neither sf nor together sf
_________________

Never give up,,,

Intern
Joined: 02 Feb 2011
Posts: 14
WE 1: Nonprofit
WE 2: Government
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

02 Feb 2011, 18:39
Test 1: M(2), N(3) P(5)

Meets criteria

Test 2: M(2), N(7) P(13)

Fails criteria

All criteria fail to meet test 2

Therefore (E)
Manager
Joined: 11 Sep 2009
Posts: 129
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

02 Feb 2011, 19:39
Let us analyze what the question is asking prior to looking at the statements given. We know that:

$$mn = p + 1$$

$$m + n = p?$$

Using what we know, we can rearrange this question as follows:

$$m + n = p?$$

$$m + n = mn - 1?$$

$$mn - m = n + 1?$$

$$m(n-1) = (n + 1)?$$

$$m = \frac{n+1}{n-1}?$$

Since we know that m and n are both positive integers, n can not be greater than 3, otherwise m will result in a value between 1 and 2. We also n can not be 1. Therefore, this leaves two distinct possibilities:

$$(m,n) = (2,3),(3,2)$$

Now let's move on to solving the question knowing these conditions.

Statement 1: Both m and n are prime numbers.

2 and 3 are both prime numbers, but so are 11 and 17. We need to know specifically that m and n are 2 and 3.

Therefore, not sufficient.

Statement 2: p + 1 and m are both even.

All this really tells us is that m is even. Given the initial condition that mn = p + 1, if either m or n are given to be even, it follows that p + 1 must be even as well. Hence, the distinct subset of (2,3) still exists, as well as various other possibilities of an even number and any other number.

Therefore, not sufficient.

Both Statements Together

We know that m and n are prime numbers, and that m is even. So m must be 2. Unfortunately, n is only defined to be a prime number. This could be 3 (in which case the statement is satisfied), but it could be any other prime number as well.

Therefore, not sufficient.

Retired Moderator
Joined: 20 Dec 2010
Posts: 1829
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

03 Feb 2011, 03:25
It took me between 3 and 4 minutes to think and answer this: Solved it using numbers eventually.

If m and n are positive integers and mn = p + 1,

Q: m + n = p ?

1. Both m and n are prime numbers.
2. p + 1 is even.

mn = p + 1

So, p is one less than mn

1. Started with lowest prime numbers
m=2, n=2 -> mn = 4, p=3: m + n = 4; 4<>3. Ans: No
m=2, n=3 -> mn= 6, p=5: m + n = 5; 5=5. Ans: Yes
Not sufficient.

2. p + 1 is even
p is odd.

Used the same data set and disapproved:

m=2, n=2 -> mn = 4, p=3(odd): m + n = 4; 4<>3. Ans: No
m=2, n=3 -> mn= 6, p=5(odd): m + n = 5; 5=5. Ans: Yes
Not sufficient.

Together:
Same data set. Not sufficient.

Ans: E
_________________
SVP
Joined: 06 Sep 2013
Posts: 1745
Concentration: Finance
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

05 Jan 2014, 12:40
aiming4mba wrote:
If m and n are positive integers and mn = p + 1, is m + n = p ?
a. Both m and n are prime numbers.
b. p + 1 is even.

This boils down to

Is m+n = mn-1

Statement 1

m,n are prime numbers
Let's number pick.

Mind you. if m and n are 2 and 3 then yes
If m and 3 are 2 and 5 then no

Insuff

Statement 2

p+1 is even, then p is odd

We get is mn even?

Both together

mn could be even as well as odd depending on whether the number 2 is included as one of both

Cheers!
J
Senior Manager
Joined: 15 Jan 2017
Posts: 359
Re: If m and n are positive integers and mn = p + 1, is m + n = p ?  [#permalink]

### Show Tags

12 Oct 2017, 13:30
If m and n are positive integers and mn = p + 1, is m + n = p ?
a. Both m and n are prime numbers.
m =2, n = 3; m = 3, n = 5...only (2)(3) = 5 + 1 suffices. (3)(5) = 14 +1; (2)(5) = 9 +1. Thus except, case 1 - but rest don't add up. So NOT SUFF.
b. p + 1 is even. No clue about m,n. Not Suff.

St 1 and 2: p +1 = even; m and n = both prime. Again only one case (2)(3) = 5 +1 works; rest don't - (2)(5) = 9 +1; (2)(13)= 26 (25 +1). So not sufficient. Ans E.
Re: If m and n are positive integers and mn = p + 1, is m + n = p ? &nbs [#permalink] 12 Oct 2017, 13:30
Display posts from previous: Sort by

# If m and n are positive integers and mn = p + 1, is m + n = p ?

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.