tollbooths

the question asks if it is possible to have a pair of tollbooths which are < 10m away from each other.

1) and 2) are not sufficient by themselves.

combining, say it is not possible that any pair is <10m away from each other. so the minimum distance between the booths is 10m.there are 4 such booths, the max distance between the 1st and the 4th booth can be 30m. but it is given that the distance is 25m
=>our assumption is wrong, so there must be a pair which is <10m away from each other.

hence, C

ps: 5,10,12,20 wont work as it is given that 1st and the 4th booth are 25m away. in this case it is just 15.

hetavdave wrote:choice A says first and last tollbooths are 25 m apart. fine but not suff
choice B says there are total 4 tollbooths. not suff

how can we conclude that there's 10 m distance between two consecutive tollbooths?

why can't it be like 5,10,12,20 etc?

Here's another way to look at the statements in combination:

We have 4 tollbooths, which means that we have 3 distances between booths.

The total distance from 1st to last is 25.

Therefore, the average distance between booths is 25/3 = 8 1/3. If the average distance is less than 10, there must be at least one distance that's less than 10 as well: sufficient.

Hi Stuart, very good explanation! I was wondering, how would we know to find the average between the spaces if the Statements do not tell us that the booths are evenly spaced? What if the 1st 3 cones were 6m apart [spaced] from eachother = 12m, and the 4th cone were 13m from the 3rd cone? Thus, making one to believe the answer is "E". Are there certain assumptions that should be applied to DS problems such as this one? Thank you, Stuart.

P.S. I enjoy reading your posts, they are very clear and easy to understand, and enlightening!

BlindVision wrote:Hi Stuart, very good explanation! I was wondering, how would we know to find the average between the spaces if the Statements do not tell us that the booths are evenly spaced? What if the 1st 3 cones were 6m apart [spaced] from eachother = 12m, and the 4th cone were 13m from the 3rd cone? Thus, making one to believe the answer is "E". Are there certain assumptions that should be applied to DS problems such as this one? Thank you, Stuart.

P.S. I enjoy reading your posts, they are very clear and easy to understand, and enlightening!

Hi!

We don't know that the booths are evenly spaced and we're not assuming that they are. It's very dangerous to make any assumptions at all in data sufficiency and you should definitely avoid doing so!

The reason that we take the average is because we know that at least one member of every set will be at or below the average (after all, if every member of a set were above the average, then it couldn't very well be the average, could it?).

This questions asks us if at least one of the distances between booths is less than 10. Since the average is 8.33, we know for sure (i.e. we can answer a definite "yes" to the question) that at least one of the distances is less than or equal to 8.33.

That said, there are still an infinite number of possibilites for exactly how far apart the booths are - but we've answered the question posed.

a zillion thanks stuart.

now it's crystal clear.