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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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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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26 Apr 2016, 20:08
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 numbersAny 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 Combined3 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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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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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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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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21 Aug 2016, 10:25



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



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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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14 May 2017, 17:07
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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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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