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At first glance, it appears that precise long division is necessary. The answer choices are very close together, making estimation difficult. However, with some manipulation and factoring, the solution is straightforward.

The key to factoring this fraction is to move the decimals of both the numerator and denominator three places to the right, so that we're dealing with integers. Then, we might notice that 3,507 is divisible by 7 (35 and 7 are both divisible by 7, providing a clue that we may be able to factor out 7). Moreover, 10,020 is divisible by 10 and by 2 (10,020 ends in a 0, and 1,002 is even):

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we can try to get an approximation first, 3.507 / 10.02 = 350.7/1002 this is slightly less than 0.3507. Just by doing this, we can eliminate C, D, and E.

now we are remained with A and B. I decided to do the long way, and got to 0.35 so A.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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