637 is an awkward number, we'll start by rounding up to 640: 640 * 2 = 1280, anyone in tech knows 2x that is 2560.

Make up the missing 3: 3 * 4 = 12, 2560 - 12 = 2548.

2548 * 10 = 25,480.

25,480 + 7 = 25,487

25,487 + 30 = 25,517

25,517 + 600 = 26,117.

That said, I did make a screw up when calculating it, and added the 637 before multiplying by 10 (which may have been the differentiating part of that question, combined with the intentional stress, to see how you cope with pressure? Although I didn't sleep last night, which might be the cause :D). I dunno if they wanted you to do it as quickly as 600/640 x 40 though, which obviously makes it much more difficult.

Afterthought, due to sleep deprived state, quicker way to solve:

600 x 40 = 24,000 40^2 = 1600 25,600 quick and dirty, for accuracy: 3 * 40 = 120 25,600 - 120 = 25,480 25,480 + 600 = 26,080 26,080 + 37 = 26,117.

Sorry, this comment turned into a bit of a ramble.