Data Sufficiency

On her way home from work, Janet drives through several tollbooths. Is there a pair of these tollbooths that are less than 10 miles apart?

(1) The first tollbooth and the last tollbooth are 25 miles apart
(2) Janet drives through 4 tollbooths on her way home from work

OA is C, but I get E.
Could someone please explain how to get the answer?
Many thanks

Statement 1:
We don’t know how many tollbooths Janet drove through. Insufficient.

Statement 2:
We don’t know the how far apart the 4 tollbooths are. Insufficient.

Both statements combined.
We know the first and last are 25 miles apart, and there are 2 more tollbooths in between. Therefore there must be at least one pair of toll booths less than 10 miles apart. Sufficient.

Choose C.

-BM-

Obviously stmt 1 or 2 alone is not sufficient, so we are down to C or E.

There are 4 booths, suppose they are A-B-C-D. So there are 3 pairs:
A to B, B to C, C to D.

Question is asking, "Is there a pair of these tollbooths that are less than 10 miles apart?", it means "is there at least one pair of booths that are less than 10 miles apart?"

We assume there's not a single pair of booths that's less than 10 miles apart. So each pair of booths is 10 miles or more apart.

But 10+10+10=30 miles. If that's true, the minimum distance that Janet has to travel will be 30 miles, not 25 miles.

So there is at least one pair of booths that are less than 10 miles apart. Answer C is correct.

Thanks.
So just to understand this - to get to the answer, does one have to assume that the tollbooths are evenly spread?

Not at all Baldini. If the question doesn't say so, we can never assume.

I used 10 miles distance for each pair because it's the minimum distance, and the sum of all distance is still over 25 miles. You can use any 3 numbers that's over 10, such as 10+12+15. But minimum distance would be best to test the answer.

ok got it now - thanks again

pakaskwa wrote:Obviously stmt 1 or 2 alone is not sufficient, so we are down to C or E.

There are 4 booths, suppose they are A-B-C-D. So there are 3 pairs:
A to B, B to C, C to D.

Question is asking, "Is there a pair of these tollbooths that are less than 10 miles apart?", it means "is there at least one pair of booths that are less than 10 miles apart?"

I don't know if you can deduce from red to blue with at least. When I drew it on a number I got 2 options:

A-B: 10 + B-C: 5 + C-D: 10 = 25
A-B: 15 + B-C: 5 + C-D: 5 = 25

Maybe I am missing something, but don't know what. Grateful, id you can please elaborate.

Hi kanha81,
For the 2 scenarios you propsed:

A-B: 10 + B-C: 5 + C-D: 10 = 25
A-B: 15 + B-C: 5 + C-D: 5 = 25

In scenario one, 1 pair of booth is less than 10 miles apart (B-C);
In scenario two, 2 pairs of booths are less than 10 miles apart (B-C and C-D).

So they still meet the premise "at least 1 pair of booth is 10 miles apart".

I, too, initially selected E as the answer, but don't understand how we're assuming Janet's path home is a straight line (ie each segment from A-D). Although I thoroughly understand C, I answered E because if not a straight line and without information on total distance covered or additional information about the locations of specific toll booths, there is not enough information, without assuming, to conclude on C.

Any help to clarify would be appreciated!

Jim01234567890 wrote:I, too, initially selected E as the answer, but don't understand how we're assuming Janet's path home is a straight line (ie each segment from A-D). Although I thoroughly understand C, I answered E because if not a straight line and without information on total distance covered or additional information about the locations of specific toll booths, there is not enough information, without assuming, to conclude on C.

Any help to clarify would be appreciated!

The phrase 10 miles apart means -- at least to me -- 10 miles along the road being driven.

Pakaskwa used the strategy that I would use to solve this DS question.

When a question gives an upper or lower limit, plug in the limit in order to see how the problem is restricted.

The limit given in this problem is 10 miles: we're being asked whether the distance between any pair of tollbooths is less than this distance. So, in order to see how the problem is restricted, we should plug in 10 miles for the distance between each pair of tollbooths.
When the 2 statements are combined, we know from statement 2 that there are 4 tollbooths. If there are 10 miles between each pair, the total distance = 10+10+10 = 30. But statement 1 states that the total distance = 25. Thus, we know that the distance between at least one of the 3 pairs must be less than 10.

The correct answer is C.