Data Sufficiency

swerve wrote:Four men and three women make up a seven-member committee. The committee has one male captain and one female captain. If all seven committee members are seated in a straight row of seven chairs, does at least one man sit next to another man?

(1) No woman sits next to another woman.
(2) The captains sit in the first and seventh chair.

The OA is B.

Source: Manhattan Prep

Let's take each statement one by one.

(1) No woman sits next to another woman.

Case 1: MFMFMFM. The answer is No, at least one man does NOT sit next to another man.
Case 2: MFMFMMF. The answer is Yes, at least one man sits next to another man.

Insufficient

(2) The captains sit in the first and seventh chair.

1. MMFMFMF
2. MFMMFMF
3. MFMFMMF
4. FMFMFMM

In each of the above cases, at least one man sits next to another man. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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Here's a good general rule: whenever you see "AT LEAST" in a DS question, it helps to think: "when would that NOT be the case?"

This question asks "does at least one man sit next to another man?" There are lots of ways to picture this happening, so how would it NOT happen? There's only 1 way for no men to sit next to each other: if they are exactly spaced out like this:


(N.b. I totally recommend drawing out slots in cases like this where there are fewer than 10 positions to work with. It really helps to visualize.)

Target question: do we have men in exactly positions 1, 3, 5, and 7, and women in 2, 4, and 6?

(1) No woman sits next to another woman.

Test this out. Clearly we can envision our target scenario, but is there anything else you can picture where women do NOT sit together, but men do? Here's one:


Since we can picture versions where men do NOT sit next to each other and ones where they do, this is insufficient.

(2) The captains sit in the first and seventh chair.

Since there is one male captain and one female captain, that means that a woman must occupy chair 1 or chair 7. That means that our target scenario of men in all the odd-numbered chairs and women in the even-numbered chairs must not be the case. Therefore, at least 2 men must sit next to each other. Sufficient.

The answer is B.

For more examples of "when you see 'at least', think of the opposite," see:
https://www.beatthegmat.com/can-someone ... 32360.html
https://www.beatthegmat.com/jury-select ... tml#698357
https://www.beatthegmat.com/probability ... tml#576756