When certain number of marbles are divided into groups of 4, one marble remained. When the same number of marbles are divided into groups of 7 and 12 then 4, 9 marbles remained. If the total marbles are less than 10,000 then find the maximum possible number of marbles.	Choose the correct choice from the following choices.
A) 9992  B) 9993  C) 9994  D) 9995  E) 9996
Ans: In this case the difference between the remainders and divisors is constant. i.e., 3. so N = K (LCM (4, 7, 12) - 3 = 84K - 3. Where K = natural number.   9993ut we know that 84K - 3 &lt; 10,000 ⇒⇒ 84 x 119 - 3 &lt; 10,000 ⇒⇒  9996 - 3= 
<gadget id="calculator"> 9996 - 3</gadget>
<output>9_993</output>
9993   Answer 9993
<result>B</result>
When certain number of marbles are divided into groups of 4, one marble remained. When the same number of marbles are divided into groups of 7 and 12 then 4, 9 marbles remained. If the total marbles are less than 10,000 then find the maximum possible number of marbles.