Some tips on Quantitative Section:

The level of Math-skills required is of High-school level.
All the stuff tested here is on "the basics". One should be thorough in basic formulae and concepts to crack the Quantitative section of GMAT.

DS-Strategy:
DS Q' is a bit difficult in the sense that it requires a bit more time to solve when copmapred to a PS Q'. It requires a careful approach which deals a step by step elimination of the options.If one does not follow the process, there is a high chance of landing on a wrong choice.Weigh the two given statements independently to decide whether either one alone is enough to answer. If both the statements are not independently enough to solve the problem, then check whether both the statements together can do.
Time-Strategy:
Time may not be a big constraint while solving the 'Quantitative' section.
For Quantitative section, the given 75 minutes to solve 37 Q's leaves us a solid 2 minutes (or 120 seconds) time for each Q'. But as a PS problem generally takes lesser time than a DS one takes, there is no strict emphasis on limiting each problem to 2 minutes. One problem may take 150 seconds while the other may take 90 seconds only. So instead of keeping track on time taken for each problem, it is better to have an overall track on a bunch of problems (say 5 or 10 at a time). Keeping this in mind while practicing problems builds one's confidence in tackling any issues with time.
"Calculations performed in mind save a lot of time when compared to calculations put on paper"

Unless you do so on a regular basis, I would not recommend starting to do calculations in your head as part of your GMAT studies. Anything greater than a single number (such as 9 * 7 or 8 - 3) should be done on paper until you feel like you are just too good at this to keep doing calculations on paper.

Those who do math all the time and have done so for a really long time - the math specialists - enjoy doing the math in their heads. It is part of who they are. For them simple calculations are not very entertaining and so doing the calculations in their head makes it more interesting. And it can certainly be faster to calculate in your head, provided you are 100% on this with no mistakes.

The interesting thing is that I have taught many students who were much better at pure math than I am. They perform large calculations in their heads, something that I could probably do, but I do not risk it since I may make a small mistake. Yet, on the GMAT these people often score below the 75th percentile. That is because the section is "Quantitative Reasoning" not "Math." I would say that of the 37 problems on the Quantitative Reasoning side only 20 require actual calculations with numbers larger than 10 (many D.S. questions can be tested with small numbers less than 10).

So, for the average GMAT student - especially one who is seeking help in Quant - I would say that calculations greater than single digits should be done on paper. The GMAT puts a premium on tricking you, what you need to be looking out for is the "misdirection" where the GMAT funnels you into answering the wrong question or making an assumption. You need to be focused on these things and your math must be reliable.

Bottom line - if you normally do calculations in your head then by all means keep doing them there. But just for me I would say that if you are not already doing this on a daily basis it is better to be sure on test day and that means using the note paper. Remember, you can earn a 49 or even a 50 on Quant with only 25 correct answers out of 37. The premium needs to be on getting answers right, if that means a few more seconds in the calculations then that is what it means.