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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.

If x and z are integers and:

how many instances are there for z to be 1 less than x?

is equivalent to:

and

is equivalent to:

Therefore z is an element of the set:

and x is an element of:

There are 12 values of z that are 1 less than some value of x.