Data Sufficiency (DS) | Re: If x, y and z are positive integers and x < y, what are the number of

Answer is A
as x,y,z all are positive and x<y, least value of y is 2 and x is 1

I did the following hit and trial
if y=2
Z=3 and x=1...Common factor..1

if y=3
Z=7 and x=1,2...Common factor 1

if y=4
z=25, x=1,2,3..common factor 1

if y=5 z=121..x=1,2,3,4..

if y=6 z=721..x=1,2,3,4,5....CF=1.

Seeing this pattern it is A... I am not able to deduce an algebraic solution but saw this pattern

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