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

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Director
Joined: 26 Mar 2006
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On her way home from work, Janet drives through several [#permalink]

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27 Mar 2006, 23:25
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On her way home from work, Janet drives through several booths. 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.
Director
Joined: 26 Mar 2006
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28 Mar 2006, 00:21
C seems to be the right choice. Please explain.

Thank You.
VP
Joined: 20 Sep 2005
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28 Mar 2006, 00:36
Let's say we have the first toll at distance 0 ,
the next toll at distance greater than 10 ( 10.1 ) ,
the next toll at distance greater than 10 of the last one ( 20.2)
....since the last one is at distance 25 from the first one...the distance from the third and fourth has to be less than 10.

Try other combinations and you will se...

Beyond700 wrote:
C seems to be the right choice. Please explain.

Thank You.
Director
Joined: 26 Mar 2006
Posts: 632
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Kudos [?]: 34 [0], given: 0

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28 Mar 2006, 01:31
As I suspected the assumption is that they are uniformly divided on a highway.

It need not be that way. 1 & 2 can be 5 miles apart and 2 & 3 can be 15 miles apart. Which means 1 & 3 are 20 miles apart.

The other scenario can be

1 - at 0 miles
2 - 7 -miles
3- 18 miles
4 - 25 miles

That is how it is in ASEAN and India. The toll is collected for the road or a bridge. Kindly enlighten me, bit blur here.
VP
Joined: 20 Sep 2005
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28 Mar 2006, 01:50
I don't see any assumption...the question is "Is there a pair of these tollbooths less than 10 miles apart ?"...the answer is always YES even in your cases. There is ONE pair atleast which is less than 10 miles apart.

Beyond700 wrote:
As I suspected the assumption is that they are uniformly divided on a highway.

It need not be that way. 1 & 2 can be 5 miles apart and 2 & 3 can be 15 miles apart. Which means 1 & 3 are 20 miles apart.

The other scenario can be

1 - at 0 miles
2 - 7 -miles
3- 18 miles
4 - 25 miles

That is how it is in ASEAN and India. The toll is collected for the road or a bridge. Kindly enlighten me, bit blur here.
Director
Joined: 13 Nov 2003
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Location: BULGARIA
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28 Mar 2006, 02:02
Read the Q carefully, in either scenario the distance between any 2 tollbooths will be <10 miles
Director
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28 Mar 2006, 03:08
Thank You Guys.

First lesson learnt - Read the question care fully.

Some how I miss-understood that the pair meant 2nd and 3rd tollbooth, but actually it meant any pair.
Senior Manager
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28 Mar 2006, 13:23
C.

SINCE THE DISTANCE BETWEEN FIRST AND LASTIS 25 MILES AND THERE ARE TWO IN BETWEEN THE FIRST NAD LAST MAKING IT 4, ONE PAIR OF TOLLBRIDGE HAS TO BE LESS THAN 10 MILES APART.

IF NONE OF THE PAIR IS LESS THAN 10, THE DISTANCE BETWEEN FIRST AND LAST MUST BE MORE THAN 30.
28 Mar 2006, 13:23
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