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# On her way home from work, Janet drives through several

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I got this question from the GMATprep and scored 45 on the math section. I felt this question was tricky because I didn't know whether to assume that the tollbooths were evenly spaced. It would be a straight forward question if the tollbooths are evenly spaced. Should we assume that?
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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) alone doesnt answer the question as i donot know the no of booths shw passes on her way
2) alone doesnt anwer the ques as i donot know the distance she travels

both 1) and 2) taken together will also not answer the question as i dont know if the distance between the booths

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Is it just me, or does several indicate more than 2? Given that reasoning my answer is A.
I know the OA is C.

Any thoughts?
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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) 2 tollbooths=no. 50 toll booths between the 1st and last=yes (that's a lot of stopping!). INSUFFICIENT, eliminate A and D.
(2) 4 tollbooths each 11 miles apart=no. 4 toolbooths each 9 miles apart=yes. INSUFFICIENT, eliminate B.
(1)+(2) There's no way to partition 4 tollbooths where the first and last are 25 miles apart without putting 2 within 10 miles of each other. Eliminate E.

x-ALI-x wrote:
Is it just me, or does several indicate more than 2? Given that reasoning my answer is A.
I know the OA is C.

Any thoughts?

My interpretation of several is 2 or more.
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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.
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Oh yes of course. I got so lost in the 'evenly spaced' debate, I didn't focus on the actual question!
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Re: On her way home from work, Janet drives through several [#permalink]
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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.

Given: On her way home from work, Janet drives through several tollbooths.

Target question: Is there a pair of these tollbooths that are less than 10 miles apart?

Statement 1: The first tollbooth and the last tollbooth are 25 miles apart.
There are several scenarios that satisfy statement 1. Here are two:

Case a: There are exactly 2 toll booths, and they are 25 miles apart. In this case, the answer to the target question is NO, there are NOT two toll booths that are less than 10 miles apart
Case b: There are exactly 3 toll booths (A, B and C). Their distances are: A......(5 miles)...B.......(20 miles).....C. In this case, the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: Janet drives through 4 tollbooths on her way home from work
There are several scenarios that satisfy statement 2. Here are two:
Let the toll booths be A, B, C and D.

Case a: A......(5 miles)....B.......(5 miles).....C.......(5 miles)....D In this case, the answer to the target question is NO, there are NOT two toll booths that are less than 10 miles apart
Case b: A......(15 miles)....B.......(15 miles).....C.......(15 miles)....D In this case, the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Let's see if it is possible to satisfy both statements such that NO two toll booths are less than 10 miles apart.
So let's see what happens if we make every toll booth exactly 10 miles apart.
We get: A......(10 miles)....B.......(10 miles).....C.......(10 miles)....D
Since the total distance from the first and last toll booth is 30 miles (and not 25 miles as statement 1 suggests), we can be certain that at least one of the distance is above (between two adjacent tollbooths) MUST be less than 10 miles.
So, it must be the case that the answer to the target question is YES, there ARE two toll booths that are less than 10 miles apart

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Cheers,
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On her way home from work, Janet drives through several [#permalink]
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Interesting Ques.

To check: Is there a pair of these tollbooths that are less than 10 miles apart?

Statement 1: The first tollbooth and the last tollbooth are 25 miles apart.
Considering several as min 3 tollbooths, we can have a pair 12.5 miles apart OR 5-20 miles apart. No sufficient answer we are getting..... Insufficient

Statement 2: Janet drives through 4 tollbooths on her way home from work
That's it, no distance total or among booths given...only this much info. Can't deduce anything.......InSufficient

Combine S1 and S2:
Total tollbooths now: 4
Distance between first and last: 25 miles

- Assume all are equidistant, each would be ~8.3 miles apart --> Yes, there is a/are pair(s) of these tollbooths that are less than 10 miles apart.
- Assume one is more than 10, say 15 miles.. other would be total 10 or less than 10 miles each apart. ---> Yes, there is a/are pair(s) of these tollbooths that are less than 10 miles apart.
- Assume another case, distance of two booths is 12, 12... in this case last one would be 1 mile -->Yes, there is a/are pair(s) of these tollbooths that are less than 10 miles apart.

So overall, there is a pair of these tollbooths that are less than 10 miles apart..... Sufficient

Option C
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Re: On her way home from work, Janet drives through several [#permalink]
Bunuel 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 --> even if we take several to mean more than 2, still (1) is not sufficient as we can have 3 tollbooths as shown below:

(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.

­Why is the assumption here that toll booths are evenly spaced ?
Correct answer should be E. The toolbooths could be evenly spaced as you described above or say 1 mile apart in which case both options are possible.­
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Re: On her way home from work, Janet drives through several [#permalink]

boomer1ang wrote:
Bunuel 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 --> even if we take several to mean more than 2, still (1) is not sufficient as we can have 3 tollbooths as shown below:

(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.

­Why is the assumption here that toll booths are evenly spaced ?
Correct answer should be E. The toolbooths could be evenly spaced as you described above or say 1 mile apart in which case both options are possible.­

­The correct answer should be and is C, not E. The solution you quoted explicitly states that regardless of whether the tollbooths are evenly spaced or not, the answer would still be YES: there IS a pair of tollbooths that are less than 10 miles apart.­ I suggest reviewing the discussion above more carefully.
Re: On her way home from work, Janet drives through several [#permalink]
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