If Z is a positive integer less than 10 and Q = 4, 321 + Z, what is the value of Z?
(1) Q is divisible by 3.
(2) Q is divisible by 7.

From the given info, Z is between 1 & 9 (both included).
Which means Q can take the following values 4322 <= Q <= 4330

From (1)
Q is divisible by 3, means Q can be 4323, 4326 or 4329. Which means Z can be 2, 5 or 8. Not enough to determine unique value of Z.

From (2)
Q is divisible by 7. The only number in the range [4322, 4330] which is divisible by 7 is 4326. Which leads to Z = 5.

Hence the answer is (B).
What's the OA?

Here is another way to think about it.

(1) Q is divisible by 3.

A number will be divisible by three when you add us the digits in that number and they are divisible by 3.

4321, add up the digits and you get;

4+3+2+1=10

z will add values to ten that make this the sum divisible by three. So the possibilities of the value of z are;

2; 10+2=12
5; 10+5=15
8; 10+8=18

So Z must be equal to 2, 5 or 8.

(1) insufficient.

(2) Q is divisible by 7.

4321/7=617+2/7. The important thing to note here is that the remainder is 2/7. This means that you would have to add 5 to 4321 to get rid of the remainder. Because 0<z<10, then z can only be 5. (2) is sufficient.

IMO B is the answer.

From 1

sum of digits of 4321 is 4+3+2+1=10
so 10+z is divisible by 3..hence z can be 2,5,8...not sufficient

From 2
4321%7=2
hence 2+z is divisible by 7..hence z can only be 5..sufficient

Ans option B