Is there an easy way to approach problem like this/special pattern such as repharse the equation or picking a number?
Thanks
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Given x = 8y+12, where x and y are +ve integers and we need to find the GCD of (x,y)
Statement I: x = 12u, where u is an integer.
Now y= (x-12)/8 = 3(u-1)/2.
Since y is an integer, u-1 must be divisible by 2.
So for u = 3, we have x = 36 and y = 3 and GCD will be 3.
For u = 5, we have x =60 and y = 6 and GCD will be 6.
So statement I is not sufficient.
Statement II: y = 12z, where z is an integer.
Since x = 8y+1, we have x =12(8z+1)
Now GCD of x and y = GCD of 12(8z+1) and 12z.
Clearly the GCD of z and 8z+1 =1.
So GCD of x and y = 12
Hence II is sufficient