GMATinsight wrote:
If x and y are integers then Find unit digit of 22^x+ 37^y?
1) x*y is divisible by 16
2) x/y is an odd integer
2 and 7 have a cyclicity of a pattern of 4 when it comes to units digit
2 => 2,4,8,6
7 => 7,9,3,1
1) x*y is divisible by 16
x*y=16n.....We can say that at least one is a multiple of 4.
Both x and y are multiple of 4 => unit’s digit is 6+1=7
Only one is multiple of 4 and other not => unit’s digit will be different from 7
Insufficient
2) x/y is an odd integer
We can say that y is a factor of x.
x=ay, where a is an odd integer.
Insufficient
Combined
x*y=16n
ay*y=16n.....\(a*y^2=16*n\)
This tells us that y is surely a multiple of 4, as ‘a’ is odd.
Now x=ay, so x is also multiple of 4.
Since x and y are multiples of 4, the unit’s digit is 7.
Sufficient
C
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