A group of 9 people is traveling in two taxis. . .

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pm; Thanked: 6 times; Followed by:5 members

A group of 9 people is traveling in two taxis. . .

by Vincen » Wed Sep 20, 2017 7:10 am

A group of 9 people is traveling in two taxis from one destination to another. If the taxis have different passenger capacities, how many different ways can this group divide itself among the two taxis?

(1) The larger of the two taxis can hold no more than 5 people.

(2) The smaller of the two taxis can hold no more than 4 people.

The OA is A.

I am confused. I need any expert explain to me this DS question. Thanks.

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Source: Beat The GMAT — Data Sufficiency | Wed Sep 20, 2017 7:10 am

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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Wed Sep 20, 2017 10:19 am

Hi Vincen,

This prompt is worded in a 'quirky' way - if a question such as this were to show up on Test Day, it would likely be worded differently. Regardless, here is what you need to know to answer it.

We're given some facts in the prompt:
1) We're told that 9 people are taking 2 taxis. So we know that EACH of those 9 people got into one (or the other) of those 2 taxis.
2) The taxis have DIFFERENT capacities.

To figure out the number of different combinations of groups that could have gotten into those 2 taxis, we need to know the capacities of the two taxis.

1) The larger of the two taxis can hold no more than 5 people.

Since this is the LARGER taxi, and it can hold no more than 5 people, the OTHER taxi would have to hold the OTHER 4 people (and couldn't hold more than 4 because the LARGER taxi holds no more than 5).

This confirms that the taxis MUST hold "up to 5" and "up to 4" respectively - this accounts for all 9 people - so we could figure out the various combinations.
Fact 1 is SUFFICIENT

2) The smaller of the two taxis can hold no more than 4 people.

This tells us the capacity of the smaller taxi, so the larger taxi must hold AT LEAST 5, but could hold 6 or 7 or 8. Without knowing that value, there's no way to know how many people got into each taxi, so we cannot calculate the number of combinations.
Fact 2 is INSUFFICIENT.

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]