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

This topic has 1 expert reply and 0 member replies

### Top Member

Vincen Legendary Member
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#### A group of 9 people is traveling in two taxis. . .

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.

### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
Joined
23 Jun 2013
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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.

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

_________________
Contact Rich at Rich.C@empowergmat.com

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