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

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

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New post 26 Apr 2016, 18:01
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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) \(c\neq{2}\)
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If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 26 Apr 2016, 20:08
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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
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 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.
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 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.
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 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.

E is the answer
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 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!
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 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
Correct answer is E

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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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New post 14 May 2017, 17:07
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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.

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

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New post 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.

Answer : E
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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor [#permalink]

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Re: If a,b, and c are prime numbers, do (a+b) and c have a common factor   [#permalink] 15 May 2018, 03:02
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