On her way fome from work, Janet drives through several

Question

On her way fome 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.




Please explain your answer

eschn3am · Answer

1. Doesn't tell us anything. Just that the furthest tollbooths are 25 miles apart.

2. Janet drives through 4 on her way home. Doesn't tell us anything about distance.

Together

4 tollbooths in 25 miles. There MUST be a pair of tollbooths less than 10 miles apart. To have 4 tollbooths on the way home without being less than 10 miles apart the first and last would have to be 40 miles apart.

 Answer C

tarek99 · Answer

the OA is indeed C. But how can you be sure? we don't even know whether they are equally spaced. if they are equally spaced, then we can concluded that C is complete. the way i saw it, the gaps between each tollbooths could be soo different. could you please explain? thanks

shubhampandey · Answer

If there are 4 tollbooth in 25 miles, there is atleast a pair of tollbooth that is less than 10 miles apart. 

Thats why C..

eschn3am · Answer

If they are equally spaced then that's the farther apart they can all be from each other.

Let's say we have 4tollbooths in 9 miles

Equally spaced they are at 

1---3---6---9

so they are all 3 miles apart. If we move two tollbooth farther away, the other ones have to get closer together to compensate.

1---5---7---9

so now 1---5 are further apart, but 5---7---9 got squished together


in the problem above there are 4 booths 25 miles away

1---8.33----16.67---25

so as you can see, when they are evenly spaced and all are less than 10 miles apart. We can shuffle them so a pair are more than 10 miles apart, but there will always be 1 pair that is.


1-----18---22---25

so now one pair is 17 miles apart, but the other ones are only 4 and 3 miles apart. The best chance we had at getting all of them more than 10 miles apart was having them spread out, and then the average was still less than 10.

vodyanoir · Answer

Can we assume, that the road is straight? If it is not the case, then the answer is E

eschn3am · Answer

We can assume the measurements are all based on distance traveled along the road. and since she's driving from Point A to Point B her route shouldn't look as twisted and confused as a bowl of spaghetti anyway

GMATBLACKBELT · Answer

C. 

Although I was wondering if several means more than 2? I was kinda physcin myself out for a minute.

On her way fome from work, Janet drives through several

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