Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?  Choose the correct option:
A) 14
B) 16
C) 18
D) 20
E) 22
Explanation :   The alarm tolls together twelves times a day. Therefore, they toll together once every 2 hours i.e in 120 minutes.   Since, no two alarms toll at equal intervals of time, the total number of distinct factors of 120, including 1 and 120 itself =23×3×5.   The number of factors =(3+1)×2×2=16.   Hence, the maximum value of X is 16.   Answer : 16
<result>B</result>
Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?