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Janet drives through several tollbooths

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Janet drives through several tollbooths

by rsarashi » Thu Jul 27, 2017 9:14 am
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.

OAC

My doubt: I understand that A & B can be sufficient alone. How C is sufficient that I don't understand, because it is not mentioned that all tollbooths are equally apart. This might be possible that the distance between the 1 and 2nd tollbooths is more that 10 miles and the rest have less than 10 miles?

Please explain.

Thanks.
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by GMATGuruNY » Thu Jul 27, 2017 9:27 am
Test the THRESHOLD.
Here, the threshold =10 miles between successive tollbooths.

Statements combined:
Let the 4 tollbooths be A, B, C and D.
Let the distance between successive tollbooths = 10 miles.
The following figure is implied:
A<---10 miles--->B<---10 miles--->C<---10 miles--->D
In the figure above, the total distance = 10+10+10 = 30 miles.
But statement 1 requires that that the total distance be only 25 miles.
Implication:
To reduce the total distance in the figure above to 25 miles, at least one of the blue values must be LESS THAN 10 MILES.
SUFFICIENT.

The correct answer is C.
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by rsarashi » Fri Jul 28, 2017 1:02 am
GMATGuruNY wrote:Test the THRESHOLD.
Here, the threshold =10 miles between successive tollbooths.

Statements combined:
Let the 4 tollbooths be A, B, C and D.
Let the distance between successive tollbooths = 10 miles.
The following figure is implied:
A<---10 miles--->B<---10 miles--->C<---10 miles--->D
In the figure above, the total distance = 10+10+10 = 30 miles.
But statement 1 requires that that the total distance be only 25 miles.
Implication:
To reduce the total distance in the figure above to 25 miles, at least one of the blue values must be LESS THAN 10 MILES.
SUFFICIENT.

The correct answer is C.
Hi GMATGuruNY ,

Thank you so much for your reply sir.

All clear.
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by [email protected] » Sat Jul 29, 2017 10:17 am
Hi rsarashi,

In these types of DS questions, it's often useful to draw pictures of what COULD occur (based on the information that you've been given). This approach is similar to TESTing VALUES, in that you're looking to prove if a pattern occurs (and if the information 'limits' the possibilities in any way).

We're told that Janet drives through several tollbooths. We're asked if ANY pair of the tollbooths is LESS than 10 miles apart from one another. This is a YES/NO question.

1) The first tollbooth and the last tollbooth are 25 miles apart.

IF... there just these two tollbooths, then the answer to the question is clearly NO.
IF... there are four tollbooths, spread out "evenly", then the distance from one to the next would be 8 1/3 miles - and the answer to the question would be YES.
Fact 1 is INSUFFICIENT.

2) Janet drives through 4 tollbooths on her way home from work.

This Fact tells us NOTHING about the distances.
Fact 2 is INSUFFICIENT.

Combined we know:
-The first tollbooth and the last tollbooth are 25 miles apart.
-Janet drives through 4 tollbooths on her way home from work.

As mentioned in Fact 1, IF the four tollbooths are spread out "evenly", then the distance from one to the next would be 8 1/3 miles - and the answer to the question would be YES. Moving EITHER of the 'middle' tollbooths in any direction would increase the distance between two of them AND decrease the distance between two on the "other side." Thus, there will ALWAYS be at least one pair of tollbooths that are less than 10 miles apart from one another - and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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by Jeff@TargetTestPrep » Wed Aug 09, 2017 11:34 am
rsarashi 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.

OAC
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

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by Brent@GMATPrepNow » Wed Nov 20, 2019 10:40 am
rsarashi 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

Answer: C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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