The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is :	Choose the correct choice from the following answers:  A) 8739  B) 9831  C) 9834  D) 9893  E) 8976
Solution   Greatest number of 4 digits is 9999. L.C.M. of 4, 7, and 13 = 364.   on dividing 9999 by 364, remainder obtained is 171.   So, greatest number of 4 digits divisible by 4,7, and 13 = (9999 - 171)= 
<gadget id="calculator">(9999 - 171)</gadget>
<output>9_828</output>
9828.   Hence, required number= (9828 + 3)= 
<gadget id="calculator">(9828 + 3)</gadget>
<output>9_831</output>
9831.Answer 9831
<result>B</result>
The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is :