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On her way home from work, Janet drives through several
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31 Mar 2008, 12:57
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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.
(1) The first tollbooth and the last tollbooth are 25 miles apart.
(2) Janet drives through 4 tollbooths on her way home from work.
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Re: On her way home from work, Janet drives through several
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20 Dec 2017, 08:02
20 Dec 2017, 08:02
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tarek99 wrote:
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.
(1) The first tollbooth and the last tollbooth are 25 miles apart.
(2) Janet drives through 4 tollbooths on her way home from work.
We are given that Janet drives through several tollbooths on her way home from work. We need to determine whether there is a pair of tollbooths that are less than 10 miles apart.
Statement One Alone:
The first tollbooth and the last tollbooth are 25 miles apart.
Since we do not know the number of tollbooths between her home and her work, we cannot determine whether there is a pair of these tollbooths that are less than 10 miles apart.
For example, if there are only two tollbooths, then they are 25 miles apart and thus greater than 10 miles apart. However, if there are three tollbooths, there could be a pair of tollbooths that are less than 10 miles apart. Statement one alone is not sufficient. We can eliminate answer choice A.
Statement Two Alone:
Janet drives through 4 tollbooths on her way home from work.
Since we do not know the distance between her home and her work, we cannot determine whether there is a pair of tollbooths that are less than 10 miles apart. Statement two alone is not sufficient. We can eliminate answer choice B.
Statements One and Two Together:
From statements one and two, we know that the distance between the 1st and 4th tollbooths is 25 miles, which means on average, approximately 8 miles are between each consecutive tollbooth. For example, it’s possible that the distances between the 1st and 2nd tollbooths, 2nd and 3rd tollbooths, and 3rd and 4th tollbooths are, respectively, 8 miles, 8 miles, and 9 miles. In this case, we have a pair (actually three pairs) of tollbooths that are less than 10 miles apart. Furthermore, regardless of how we adjust the number of miles for the three distances, there must be at least one pair of tollbooths less than 10 miles apart. For example, let’s say the distance between the 1st and 2nd tollbooths was increased to 10 miles and the distance between the 2nd and 3rd tollbooths was increased to 12 miles; then, the distance between the 3rd and 4th tollbooths would have to be 3 miles, which is less than 10 miles. Thus, the two statements together are sufficient.
Answer: C
On her way home from work, Janet drives through several
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24 Nov 2010, 11:35
24 Nov 2010, 11:35
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VeritasPrepKarishma wrote:
weakVerbal wrote:
janani wrote:
c
Very Tricky....
Since it is not mentioned in the question that the tollbooths are evenly spaced, you cannot assume it. Answer will be (E).
If it is indeed a GMAT Prep question, it would be a very very old question with no relevance now.
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
Even if we take several to mean more than 2, still (1) is not sufficient as we can have 3 tollbooths as shown below:
|---(12.5)---|---(12.5)---| (answer No)
|-(2.5)-|-----(22.5)-----| (answer Yes).
(2) Janet drives through 4 tollbooths on her way home from work. Clearly insufficient.
(1)+(2) We know that the first tollbooth and the last tollbooth are 25 miles apart AND that there are total of 4 tollbooths:
first-----(25)-----last
Now, we cannot place 2 more tollbooths between the first one and the last one (the fourth) so that at least one pair of tollbooths won't be less than 10 miles apart (no matter whether they are evenly spaced or not). Average distance, in case tollbooths are evenly spaced will be 8.(3), so at least one pair must be less than or equal to this distance as if all pairs are more than 8.(3) miles apart then the distance between the first and the last will be more than 25 miles. Sufficient.
Answer: C.
