x – 1

[logitech]

If x is a positive integer, is x – 1 a factor of 104?

(1) x is divisible by 3.

(2) 27 is divisible by x.

OA C

Source: MGMAT

[cramya]

Factors of 104 are

1 2 4 8 13 26 52 104



Stmt I) x is divisible by 3

6 is divisible by 3 but 6-1 is not a factor of 104
27 is dvivisible by 3 but 27-1 is a factor of 104

INSUFF

Stmt II

27 is divisible by x

27 divisible by 3 and 3-1 is a factor of 104
27 divisible by 1 but 1-1 = 0 is not a factor of 104

INSUFF

Stmt I and II together

27 is a cube of prime and it has only 4 factors 1,3,9,27

3 9, 27 fit the bill for x (satisfy statement I and II) and x-1 in each case is a factor of 104 or 104 is divisible by x-1 in each case

SUFF

Done C)