A group of 9 people is traveling in two taxis from one

Question

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.

I am confused????

brandy96 · Accepted Answer

it should be A. if the max in one can be 5 which is larger, then the another one has to have 4. 
If the smallest can have max 4, it can have 3,2,1 and the larger can have 5,6,7,8

GMATmission · Answer

Its A.

Statement 1 says that the larger of taxis can hold a maximum of 5 people. So the smaller has to hold 4. we need to remember here that 9 people must travel in the two taxis. If the larger taxi can hold 5 people, there is no scope that the smaller taxi may hold 3 or 2 or 1 person. SUFFICIENT

Statement 2 tells us that the smaller taxi can hold a maximum of 4 people but we know nothing about the larger taxi. What if the larger taxi can hold all 9 people. So we can have multiple scenarios in this case. INSUFFICIENT

bhandariavi · Answer

Thanks brandy96 ..great idea ..1 Kudos for you.

subhashghosh · Answer

One question, where is this from ?

tgubbay1 · Answer

but if the larger has no more than 5, meaning a maximum of 5, how do we know the smaller can fit 4?
I chose B because if the smaller holds 4, then you know the 2nd one can hold 5 or more!

I know where I went wrong and why A is right, but I proceeded with the premise that we didn't know that less than 5 meant 4 or less (it could have been 1,2,3 and not sufficient space) I guess I was looking too much into the question -_-

EMPOWERgmatRichC · Answer

Hi tgubbay1,

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.

Fact 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

Fact 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

nisharma · Answer

The wording of this questions seems off. The questions asks the number of ways the group can divide itself in 2 taxis.
So B is sufficient. {L,S} = {{5,4},{6,3},{7,2},{8,1},{9,0}} -> 5 ways.
How is B insufficient?

rioacharya · Answer

I have a doubt. The question stem is talking about total no. of passengers (excluding driver) and the statements are talking about taxi capacity which should include the driver as well. One similar question I had seen and got wrong before also. Please search the following string to find the question.

john-has-5-friends-who-want-to-ride-in-his-new-car-that-can-accommodat-224828

kindly see the question above. In this DS question why should or shouldn't I take into account the driver?

atshy21saraf · Answer

I too thought in the same manner... 5 ways are coming... and number of ways is only asked..

Argo · Answer

What is the authenticity of the source? This doesn't seem to be a standard question.

syahasa2 · Answer

I don't know why I'm wrong here.

The first taxi can hold no more than 5 people.
Why the second taxi can't hold 6 people?

To put it more simply, how are we sure that if a taxi can hold 5 people it MUST reach max capacity?
For example, what if the taxi can hold 5 people, but it does not reach full capacity and there are 4 people in it.
Then the other one must have AT LEAST 5 people room.
 
How do we take for granted that the taxi has reached its maximum capacity?

I went with C. If we know that the first taxi's max passenger space is 5 people and the second one's 4 then the we know that the first one ACTUALLY HOLDS 5 people in it.

abhimahna · Answer

InAthens ,

You have missed the bolded word below :

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

So, if the larger can hold max 5 people, the smaller cannot hold more than 4 people.

Now, if you even consider 4 people in the larger one, then you will be left with 5 people. But the small has the capacity of 4 people, where would you adjust the last person then?

So, in order to have every person adjusted, we have to have 5 people in larger and 4 people in smaller.

I hope it is clear now.

syahasa2 · Answer

What a silly me ! Thanks a lot !

SVaidyaraman · Answer

This question tests one's most fundamental math. To put it more correctly it tests one's common sense. If the larger can hold no more than 5 people, it has to hold exactly 5 people because if it holds less than that means it cannot be called larger. Once we identify this, we know we can use the formula for combination to solve the problem. But (2) is not sufficient to answer the question because , larger may hold more than 5 people.

Victor19 · Answer

Answer is A.

Statement 1 : Larger of the 2 taxis can maximum carry 5 passengers. Since we have to accomodate 9 passengers the larger taxi should have 5 passengers and smaller taxi should have the remaining 4(9-5) passengers. We cannot have any other combination of passengers. Sufficient.

Statement 2 : Max number of passengers in smaller taxi does not give us a definite value. The passengers could be distributed as 4,5; 3,6; 2,7; 1,8. For each of these pairs we get different values as the answer. 
So insufficient.

Posted from my mobile device

jim441 · Answer

I think the wording of the question prompt is wrong!

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A group of 9 people is traveling in two taxis from one

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