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

 It is currently 25 Jun 2018, 08:34

### 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 a,b, and c are prime numbers, do (a+b) and c have a common factor

Author Message
TAGS:

### Hide Tags

Intern
Joined: 15 Dec 2015
Posts: 5
Concentration: Sustainability, Strategy
If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

26 Apr 2016, 18:01
7
12
00:00

Difficulty:

35% (medium)

Question Stats:

68% (00:45) correct 32% (00:42) wrong based on 499 sessions

### HideShow timer Statistics

If a,b, and c are prime numbers, do $$(a+b)$$ and $$c$$ have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers
(2) $$c\neq{2}$$
Math Expert
Joined: 02 Aug 2009
Posts: 5951
If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

26 Apr 2016, 20:08
9
6
amitpaul527 wrote:
If a,b, and c are prime numbers, do $$(a+b)$$ and $$c$$ have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers
(2) $$c\neq{2}$$

Hi,

lets analyze the Q

1) If all three are same prime ans will be YES.. -- (3+3)=6 and 3-- factors 1 and 3

2) If all are different, and c is 2.. ans is YES -- (3+7) = 10, always be EVEN and 2--- 2 will be factor

3) If all are different and a or b is 2, ans can be both YES or NO..
(2+3) = 5 and c=5..YES
(2+7) =9 and c=11..NO

4) If all are different and none of them is 2.. ans will be again YES or NO..
(3+5)=8... c=7..NO
(3+7) = 10.. c=5.. YES

lets see the statements
(1) a,b, and c are all different prime numbers
Any of the above 3 conditions can exist -(2),(3)and (4)
Insuff

(2) $$c\neq{2}$$
any of the above cases (1), (3) and (4) can exist..
Insuff

Combined-
3 and 4 cases still exist
Insuff
E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Intern
Joined: 11 Apr 2015
Posts: 35
Location: Germany
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Project Management (Energy and Utilities)
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

27 Jun 2016, 04:55
chetan2u wrote:
amitpaul527 wrote:
If a,b, and c are prime numbers, do $$(a+b)$$ and $$c$$ have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers
(2) $$c\neq{2}$$

Hi,

lets analyze the Q

1) If all three are same prime ans will be NO.. -- (3+3)=6 and 3-- factors 1 and 3

chetan2u, can you please explain why the answer is no when the primes are all the same. 3 is the common factor of 3 and 6, so the answer should be yes. What am I missing? Sorry if the question is confusing, my brain is fried right now.
_________________

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times." Bruce Lee

"I hated every minute of training, but I said, "Don’t quit. Suffer now and live the rest of your life as a champion."" Muhammad Ali

Intern
Joined: 18 Jan 2012
Posts: 39
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

17 Jul 2016, 09:14
Each statement alone is not sufficient. Combined, two possibilities:
If (a+b) = (2+3) and c is 5 (c must be different from 2) they will have a common factor of 5
If (a+b) = 11+7 and c is 5, they will NOT have a common factor.

For Yes/No DS questions, we need to have a definitive Yes or a definitive No. Combined - not sufficient. Answer E.
Current Student
Joined: 18 Oct 2014
Posts: 882
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

17 Jul 2016, 11:06
amitpaul527 wrote:
If a,b, and c are prime numbers, do $$(a+b)$$ and $$c$$ have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers
(2) $$c\neq{2}$$

(1) a,b, and c are all different prime numbers
if a=3, b=2 and c=5, then no

if a = 3, b= 5 and c=7, then yes.

Not sufficient

(2) $$c\neq{2}$$[/quote]
if a=3, b=2 and c=5, then no

if a = 3, b= 5 and c=7, then yes.

Not sufficient.

Combining both statements is also not sufficient.

_________________

I welcome critical analysis of my post!! That will help me reach 700+

BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

21 Aug 2016, 10:25
Intern
Joined: 19 May 2016
Posts: 29
Location: United States
Concentration: Strategy, Human Resources
GMAT 1: 710 Q46 V41
GMAT 2: 730 Q49 V41
GMAT 3: 680 Q46 V37
WE: Operations (Manufacturing)
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

14 May 2017, 16:55
Hi Banuel,

I got this question right, but I was wondering if statement 2 said that neither a, b, or c could be 2, that would be sufficient, right?

Thank you!
Intern
Joined: 13 May 2017
Posts: 8
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

14 May 2017, 17:05
Example 17 , 19, 3
17+19= 36 which is divisible by 3
But 19+3 = 22 , not divisible by 17
Therefore statement 2 is not sufficient

Sent from my Coolpad 3600I using GMAT Club Forum mobile app
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

14 May 2017, 17:07
2
1
toby001 wrote:
Hi Banuel,

I got this question right, but I was wondering if statement 2 said that neither a, b, or c could be 2, that would be sufficient, right?

Thank you!

Nopes.
The answer would still be E.

Let us modify the question =-->

If a,b, and c are prime numbers, do (a+b) and c have a common factor that is greater than 1?
(1) a,b, and c are all different prime numbers
(2) c≠2

Statment 1 --> 2,3,5 => YES
3,5,13 => NO

Hence not sufficient,

Statment 2 --> What if the primes are equal ?
We need to consider the possibility when a=b=c
Say z=b=c=7
So a+b=14
c=7
Clearly GCD≠1
Hence not sufficient.

Now combing the two statements => as a,c,b≠2
They are all odd primes.
Still -> 3,5,7 => YES
3,5,11 => NO

Hence not sufficient.

_________________

MBA Financing:- INDIAN PUBLIC BANKS vs PRODIGY FINANCE!

Getting into HOLLYWOOD with an MBA!

The MOST AFFORDABLE MBA programs!

STONECOLD's BRUTAL Mock Tests for GMAT-Quant(700+)

AVERAGE GRE Scores At The Top Business Schools!

Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1315
Location: Malaysia
If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

14 May 2017, 19:03
amitpaul527 wrote:

TRICKY

If a,b, and c are prime numbers, do $$(a+b)$$ and $$c$$ have a common factor that is greater than 1?

(1) a,b, and c are all different prime numbers
(2) $$c\neq{2}$$

If you only know that they're all prime

You could have c = 2, a + b = 3 + 5 = 8

So they'd have a common factor

When S2 says c ≠ 2, that's a clue to try c = 2 in S1.

You could also try c = 3, a = 2, b = 7

Since c is prime, the question is whether c is a factor of ( a+b ), so you want to try to find ways to make c a factor of a+b.

If a = 2, b = 7, c = 3, then the answer is YES.

If a = 2, b = 11, c = 3, then the answer is NO.

So even with both statements you can't say.

_________________

"Be challenged at EVERY MOMENT."

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”

"Each stage of the journey is crucial to attaining new heights of knowledge."

Non-Human User
Joined: 09 Sep 2013
Posts: 7063
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

### Show Tags

15 May 2018, 03:02
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor   [#permalink] 15 May 2018, 03:02
Display posts from previous: Sort by