A software company named Hardsoft has three divisions, each staffed by

absolutely unsolvable under 2 mins for me 😒

Posted from my mobile device

Longer than two minutes, but if I get a question like this on an actual exam, I'm pretty sure I'll be at 50 or 51 Quant!

Maximizing the number of women looks like it'll be driven primarily by having as many people as possible in Marketing/Sales. The number of men in Marketing/Sales will be a multiple of 3 and it can't be larger than 85, since we still need to place at least 7 men in Finance/Administration and 8 men in Research/Development.
Could it be 84? Nope; there would be no way to add some multiple of 7 and some multiple of 8 and arrive at 100.
Could it be 81? Nope.
Could it be 78? Yep, we could add 7+7+8 and get to 100.
In this configuration, we have 26 "sets" of Marketing/Sales, 2 "sets" of Finance/Administration, and 1 "set" of Research/Development.
That's 26(4)+2(5)+1(7) = 121 women

Minimizing the number of women is the opposite. We want Marketing/Sales to be as small as possible and Finance/Administration to be as large as possible. The number of men in Finance/Administration will be a multiple of 7 and it can't be larger than 86, since we still need to place at least 8 men in Finance/Administration and 6 men in Marketing/Sales.
Could it be 84? Nope; there would be no way to add some multiple of 8 and some multiple of 3 (that is at least 6) and arrive at 100.
Could it be 77? Nope.
Could it be 70? Yep, we could add 8+8+8+3+3 and get to 100.
In this configuration, we have 2 "sets" of Marketing/Sales, 10 "sets" of Finance/Administration, and 3 "sets" of Research/Development.
That's 2(4)+10(5)+3(7) = 79 women

121-79 = 42

Answer choice D.

i never gott to the bottom of the question i had made a combimation and it had by chance culminated hence i answered it as it was a highly difficult 42 and more open was never in the realm of correct hence i nose dived into the second best option hence imo D this tokk around 4 min

­Could you please explain why "Maximizing the number of women looks like it'll be driven primarily by having as many people as possible in Marketing/Sales.", similarily why "Minimizing the number of women is the opposite. We want Marketing/Sales to be as small as possible and Finance/Administration to be as large as possible."Many thanks.