2.  The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:  
Answer: Option C Explanation:
Clearly, the numbers are (23 x 13) and (23 x 14). Larger number = (23 x 14) = 322. 
3.  Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?  
Answer: Option D Explanation:
L.C.M. of 2, 4, 6, 8, 10, 12 is 120. So, the bells will toll together after every 120 seconds(2 minutes).

4.  Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:  
Answer: Option A Explanation:
N = H.C.F. of (4665 – 1305), (6905 – 4665) and (6905 – 1305) = H.C.F. of 3360, 2240 and 5600 = 1120. Sum of digits in N = ( 1 + 1 + 2 + 0 ) = 4 
5.  The greatest number of four digits which is divisible by 15, 25, 40 and 75 is:  
Answer: Option C Explanation:
Greatest number of 4digits is 9999. L.C.M. of 15, 25, 40 and 75 is 600. On dividing 9999 by 600, the remainder is 399. Required number (9999 – 399) = 9600. 