Is z/12 - 9 an integer? (1) (z + 24)/12 is an integer (2) z is a

The given expression \(\frac{z}{12}\) -9 can be an integer only if \(\frac{z}{12}\) is an integer. \(\frac{z}{12}\) is an integer only when z is divisible by 12.

From statement I alone, we have \(\frac{(z+24)}{12}\) = integer. This can be written as z+24 = 12*integer. The number on the RHS is a multiple of 12 and so is 24. Therefore, z = 12*integer – 24 which means that z is essentially a multiple of 12.

Since z is a multiple of 12, \(\frac{z}{12}\) will be an integer. Therefore, \(\frac{z}{12}\) – 9 will also be an integer. Statement I alone is sufficient to answer the question with a unique YES. Answer options B, C and E can be eliminated. The possible answer options are A or D.

From statement II alone, z is a multiple of 6. But, this does not mean that z is necessarily a multiple of 12. Therefore, \(\frac{z}{12}\) -9 is not necessarily an integer always and so we will get a YES AND a NO. Statement II alone is insufficient. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!