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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?

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

You dont have to assume here that the distance is equal. (1) not suff (2) not suf (1) (2) we know that The first tollbooth and the last tollbooth are 25 miles apart and there are 4 tollbooths on the way. Try to imagine the toolbooths: 2 at 11 miles, remain 14 miles but there is another tollbooths to put. So it has to be a pair with less than 10 miles between them.

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?

Should not assume anything if the text doesnt tell you!
_________________

Tricky question, I was also lured to pick C and this could happen, if these kinds of questions come at the end of GMAT questions. You are right sondenso

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.

Answer: C.

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.
_________________

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.
_________________

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) OR |-(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.

Re: On her way home from work, Janet drives through several [#permalink]

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14 May 2012, 02:08

nglekel wrote:

Would be great if the question stated that the road is a straight line

exactly what i thought... i was tempted to choose "C" but the above thought process gave me options of other irregular paths.... and chose "E" as a result...

because if the path is, say, zig-zag... the first and fourth tollbooth could still be positioned at a distance of 25 units between them... the others could be arranged anywhere along this irregular path...

don't know if am making any wrong judgment here.... or missing something between the lines.... or completely lost the plot...

Re: On her way home from work, Janet drives through several [#permalink]

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25 May 2013, 08:15

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.

when we consider the 1st statement .,we cannot judge as we dont know the number of tollbooths.. When we consider the 2nd statement alone...we dont know the distance between the tollbooths even we know the number of booths...

When we consider both the statements ... we know that the 1st and 2nd booth are 25miles apart even if we distribute 4 booths in between 25miles there should be any 2 booths that have a distance less than 10miles...

I chose A, I guess we interpret "several" on the GMAT as 2 or more...but the Oxford Dictionary does not.

sev•eral /sevrl/ det., pron., adj. det., pron. more than two but not very many

Either way, the answer is only C.

Lets assume means 2 or more. If 2, then distance is 25 miles. If 3, distance between any pair can range from 1 to 24 miles(if we asumme integer numbers only- although wrong assumption) and you can have both pairs >10 miles.

If 4, there has to be at least one pair with <10 miles if total distance is 25 miles.