On her way home from work, Janet drives through several

Question

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.

ScottTargetTestPrep · Accepted Answer

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

Bunuel · Answer

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.

tarek99 · Answer

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?

vinayn · Answer

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

so answer is cannot be answered

xALIx · Answer

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?

Yahsek · Answer

(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.

My interpretation of several is 2 or more.

KarishmaB · Answer

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.

KarishmaB · Answer

Oh yes of course. I got so lost in the 'evenly spaced' debate, I didn't focus on the actual question!

BrentGMATPrepNow · Answer

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

Answer: C

Cheers,
Brent

fauji · Answer

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

boomer1ang · Answer

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.

Bunuel · Answer

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.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

On her way home from work, Janet drives through several

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

On her way home from work, Janet drives through several

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards