another way: logical reasoning.

1. "

machine X takes 2 days longer to produce w widgets than machine Y" - machine X works slowly that machine Y

2. If machine Y work simultaneously, both machine would produce >4w widgets (Y faster than X)

3. So, 5w/4 in 3 days and >4w in ----> >9.6 days

4. in ~10 day Y can produce ~ 4w*2/(10-2) ~ w more widgets than X

5. therefore, answer has to be close to 3*(4w+w)/ (5w/4) = 12

It took ~30sec in my mind and is one of fast ways for solving work problems along with back-solving.

_________________

HOT! GMAT TOOLKIT 2 (iOS) / GMAT TOOLKIT (Android) - The OFFICIAL GMAT CLUB PREP APP, a must-have app especially if you aim at 700+ | PrepGame