Data Sufficiency

The answer should be E.

This is not a tough question,if you used numbers rather than tedious algebra.

Prompt says a ,when divided by 5,leaves remainder 3.

So a could be = 8,13,18,23... and so on

1) a when divided by 6 leaves remainder 1.

Think of no's that leave remainder 1:

7,13 [match with 13 in prompt].Go on to see whether its sufficient 19,25,31,37,43 [another match]

Divide 43 by 5 remainder = 3

Insufiicient

2) Same procedure 4:

5,9,13 [match],17,21,25,29,33 [match]

Insufficient.

1 and 2

6 -> 7,13 [Match],19,25,31,37,43,49,55,61,67,73 [match]
4 -> 5,9,13 [Match],17,21,25,29,33,37,41,45,49,53,57,61,65,69,73[Match]

a could be either 13 or 73.likewise there will be numerous other possible values of a.

You don't have to write down every value like I did above.you could have don the entire question mentally:just write down the matches on scratch paper so that you don't forget them.

What is the OA?

This is the main reason why I say algebra can be tedious.I solved this in under 45 seconds using this approach.GMAT doesn't check what you did on scratch paper.