It is currently 18 Feb 2018, 18:12

### 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

# M10-29

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

15 Sep 2014, 23:43
Expert's post
10
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

35% (00:45) correct 65% (00:52) wrong based on 149 sessions

### HideShow timer Statistics

If $$x$$ and $$y$$ are prime numbers, what is $$|x - y|$$?

(1) $$x + y$$ is a prime number.

(2) Both $$x$$ and $$y$$ are less than 5.
[Reveal] Spoiler: OA

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

15 Sep 2014, 23:43
1
KUDOS
Expert's post
6
This post was
BOOKMARKED
Official Solution:

(1) $$x + y$$ is a prime number. Clearly insufficient, consider $$x=3$$, $$y=2$$ and $$x=5$$, $$y=2$$.

(2) Both $$x$$ and $$y$$ are less than 5. Also insufficient, consider $$x=3$$, $$y=2$$ and $$x=3$$, $$y=3$$. Note that on the GMAT, unless it is explicitly stated otherwise, different variables CAN represent the same number. So, $$x=y$$ is a valid scenario.

(1)+(2) Either $$x=3$$ and $$y=2$$ or vice versa. In any case $$|x-y|=1$$. Sufficient.

_________________
Intern
Joined: 20 Aug 2015
Posts: 2

### Show Tags

15 Jan 2016, 06:12
I think this is a poor-quality question and I don't agree with the explanation. If C is correct then it satisfies stat 1 and sat2...Now, the only case possible is x=y=3 or 2...but x+y=4 or 6 is not a prime no
Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

15 Jan 2016, 10:09
amritkumar05 wrote:
I think this is a poor-quality question and I don't agree with the explanation. If C is correct then it satisfies stat 1 and sat2...Now, the only case possible is x=y=3 or 2...but x+y=4 or 6 is not a prime no

Please read carefully: Either x=3 and y=2 or vice versa --> x + y = 5 = prime.
_________________
Intern
Joined: 30 May 2013
Posts: 5

### Show Tags

29 Jul 2016, 08:11
Wrong Solution: Please note if X=Y scenario is applicable the |x-y| will be zero, hence ambiguous as different values obtained in different cases.
Intern
Joined: 30 May 2013
Posts: 5

### Show Tags

29 Jul 2016, 08:12
sorry got it x+y=5....got it
Intern
Joined: 18 Sep 2014
Posts: 4

### Show Tags

02 Apr 2017, 20:43
what if x & y are negative?
Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

02 Apr 2017, 20:50
Hobbit20 wrote:
what if x & y are negative?

x and y cannot be negative because it's given in the stem that they are primes and only positive integers can be primes.

Check for more here: https://gmatclub.com/forum/math-number- ... 88376.html

Hope it helps.
_________________
Intern
Joined: 28 Apr 2016
Posts: 20

### Show Tags

04 Apr 2017, 09:17
Hi Bunuel,

When I was taking test I thought 2 is enough by itself because I thought x=3 and y=2 or vice versa.I guess I forgot about both number might be same. I mean 3-3 or 2-2, right?
Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

04 Apr 2017, 21:39
dyg wrote:
Hi Bunuel,

When I was taking test I thought 2 is enough by itself because I thought x=3 and y=2 or vice versa.I guess I forgot about both number might be same. I mean 3-3 or 2-2, right?

_______________
Yes, that's correct.
_________________
Intern
Joined: 24 Aug 2013
Posts: 11
GMAT 1: 710 Q50 V36

### Show Tags

09 Jun 2017, 23:55
Very good question. I forgot to include two pairs (2,2) and (3,3) for B.
Director
Joined: 18 Aug 2016
Posts: 628
Concentration: Strategy, Technology
GMAT 1: 630 Q47 V29
GMAT 2: 740 Q51 V38

### Show Tags

21 Jun 2017, 05:35
I think this is a high-quality question and I agree with explanation.
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse

Manager
Joined: 14 Jun 2016
Posts: 74
Location: India
GMAT 1: 600 Q49 V21
WE: Engineering (Manufacturing)

### Show Tags

27 Aug 2017, 09:45
Bunuel wrote:
Hobbit20 wrote:
what if x & y are negative?

x and y cannot be negative because it's given in the stem that they are primes and only positive integers can be primes.

Check for more here: https://gmatclub.com/forum/math-number- ... 88376.html

Hope it helps.

Why prime numbers need to be always positive?
-2,-3,-5 also have 1 and the number itself as factor.
Then why can't we consider them prime?
_________________

If you appreciate my post then please click +1Kudos

Math Expert
Joined: 02 Sep 2009
Posts: 43792

### Show Tags

27 Aug 2017, 10:01
buan15 wrote:
Bunuel wrote:
Hobbit20 wrote:
what if x & y are negative?

x and y cannot be negative because it's given in the stem that they are primes and only positive integers can be primes.

Check for more here: https://gmatclub.com/forum/math-number- ... 88376.html

Hope it helps.

Why prime numbers need to be always positive?
-2,-3,-5 also have 1 and the number itself as factor.
Then why can't we consider them prime?

By definition a prime number is a positive integer that has no positive integer divisors other than 1 and itself.

So just remember it and don't worry about it.

(The main reason we have this restrictions in definition is that if we remove them there will be some problems with fundamental theorem of arithmetic (unique prime factorization theorem), so removing them would require many other adjustment).
_________________
Re: M10-29   [#permalink] 27 Aug 2017, 10:01
Display posts from previous: Sort by

# M10-29

Moderators: chetan2u, Bunuel

 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®.