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06 Jul 2019, 09:02
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A
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Are \(a\) and \(b\) co-prime?
1) \(LCM (a,b)=ab\)
2) \(a-b\) is prime
1) \(LCM (a,b)=ab\)
2) \(a-b\) is prime
06 Jul 2019, 09:20
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Are a and b co-prime?
Meaning does a and b have a GCF of 1?
(1)LCM(a,b) =a•b
Say a=5,b= 3—> LCM(2,3)= 5•3
but a=2, b= 4 —> LCM(2,4) is not 2•4
.: a and b will always be co-prime (sufficient )
(2) a-b = prime
Say a=5 , b=3—> 5-3= 2(prime)
a and b co-prime
Again, a=6 ,b=4 —> 6-4=2(prime)
a and b not co-prime
(Not sufficient)
Answer A
Posted from my mobile device
Meaning does a and b have a GCF of 1?
(1)LCM(a,b) =a•b
Say a=5,b= 3—> LCM(2,3)= 5•3
but a=2, b= 4 —> LCM(2,4) is not 2•4
.: a and b will always be co-prime (sufficient )
(2) a-b = prime
Say a=5 , b=3—> 5-3= 2(prime)
a and b co-prime
Again, a=6 ,b=4 —> 6-4=2(prime)
a and b not co-prime
(Not sufficient)
Answer A
Posted from my mobile device
07 Jul 2019, 05:00
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You don't need to know what "co-prime" means on the GMAT, but two numbers are "co-prime" if their GCD is 1. Since
GCD(a, b) * LCM(a, b) = ab
is always true, then if LCM(a, b) = ab, the GCD must be 1, and Statement 1 is sufficient.
Statement 2 is not sufficient, since two consecutive even integers (4 and 6 say) differ by 2, a prime, but do not have a GCD of 1, while two consecutive odd integers (5 and 7 say) differ by 2, a prime, and do have a GCD of 1.
GCD(a, b) * LCM(a, b) = ab
is always true, then if LCM(a, b) = ab, the GCD must be 1, and Statement 1 is sufficient.
Statement 2 is not sufficient, since two consecutive even integers (4 and 6 say) differ by 2, a prime, but do not have a GCD of 1, while two consecutive odd integers (5 and 7 say) differ by 2, a prime, and do have a GCD of 1.
