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

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
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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.
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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.

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.

(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.

E is the answer
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taking a=2 b=3 and c=7 we can discard both the statements as well as there combination
SMASH that E
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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!

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
Correct answer is E

Sent from my Coolpad 3600I using GMAT Club Forum mobile app

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.

Answer : E
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The two statements individually are not sufficient. When we combine the two statements, no additional information is provided.

Straightforward option E!!
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would you please explain this question without number picking? I mean using some theory and logic. Bunuel

Posted from my mobile device
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It's easier to step through this and test numbers.

We are asked whether the GCF between (a+b) and c is greater than 1.

Theory: if the GCF between (a+b) and c = 1 then (a+b) and c are consecutive integers
4,5 = GCF 1
5,6 = GCF 1 and so on...


Statement (1) a, b, c are all different primes
Firstly, take note of statement 2 as it gives us a reason for us to suspect that when c=2 different outcomes occur, so lets test c= 2 first
a= 3
b=5
c= 2
GCF (3+5), 2
GCF 8,2 = 2

is the GCF > 1? Yes

Now, lets test either a=2 or b=2
a= 2
b=3
c=5
GCF (a+b), c
= GCF (2+3), 5
= GCF 5,5 = 5 --- another Yes

What about
a=2
b=5
c=3

GCF(a+b),c
GCF(7,3) = 1
GCF > 1? NO

Therefore A is insufficient

Statement (2)
Just tells us that C is not equal to 2. There are heaps of possibilities for a, b and c, including repetitions since we don't have the restrictions of statement 1

Combined we know that when c is not equal 2 and a, b, and c are all different primes, then the two scenarios from above can occur:
GCF(7,3) = 1
OR
GCF (5,5) = 5

Producing NO and Yes answers respectively. Therefore E -->combined insufficient.

Bunuel, just to confirm that this is on GMATPrep, please add a tag, thanks!

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Added the tag. Thank you.
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Hi experts

If in this question we have CAN instead of DO then C can be the answer?

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