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(1) x + y = 9

(Not Sufficient) as x+y can be 6+3 where 3 will be the GCD but if x+y is 5+4 where 1 will be the GCD.

(2) x and y are consecutive multiples of 3

(Sufficient) as the statement defines that x and y are consecutive multiples, whichever two numbers you take the GCD has to be 3.
Eg: (1) 3,6 (GCD: 3); (2) 18,21 (GCD: 3).

Thus the OA is B.
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What is the greatest common divisor of two positive integers x and y?

Stat1: x + y = 9, if x=1 and y=8 then HCF= 1; if x=3 and y=6 then HCF= 3. Not sufficient.

Stat2: x and y are consecutive multiples of 3; if x=3 and y=6 then HCF= 3; if x=9 and y=12 then HCF= 3 sufficient.

So, I think B. :)
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What is the greatest common divisor of two positive integers x and y?

(1) x + y = 9
X and Y can be 4 and 5 in which case there is no GCD
X and Y can be 3 and 6, in which case GCD is 3

We get 2 different answers, so Option 1 INSUFFICIENT

(2) x and y are consecutive multiples of 3
When X and Y are consecutive multiples of 3, 3 will always be the GCD of X and Y.

Option2 - SUFFICIENT

Ans B
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Wait, for statement 2, what if the consecutive multiples of 3 are 0 & 3? Since zero is technically a multiple of any integer.

I.e. zero divided by 3 is zero, which is an integer. Hence, zero is a multiple of 3.
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Commendlionel
Wait, for statement 2, what if the consecutive multiples of 3 are 0 & 3? Since zero is technically a multiple of any integer.

I.e. zero divided by 3 is zero, which is an integer. Hence, zero is a multiple of 3.

If x and y are 0 and 3, then still the greatest common divisor of 0 and 3 will be 3. But none of the unknowns can be 0 because we are told that x and y are positive integers, while 0 is neither positive not negative:

What is the greatest common divisor of two positive integers x and y?
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