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# Buses leave town B at 3pm and every 10 hours after that.

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Senior Manager
Joined: 07 Jul 2005
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Buses leave town B at 3pm and every 10 hours after that. [#permalink]

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08 Nov 2005, 20:16
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Buses leave town B at 3pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday what is the earliest day on which the bueses leave at the same time?

a) Tuesday
b) Wednesday
c) Thursday
d) Sunday
e) They will never leave at the same time.
Director
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09 Nov 2005, 16:42
I solved it using brute force and it seems to me that they will never meet..
What is OA??
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VP
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09 Nov 2005, 17:15
E.

I would panic if this kind of question comes in real test.
Would be interesting to know source.

well, here is the way to look at it. In order for these two buses to meet, the following condition need to be satisfied:

10 * x (mod 24) = 15*y + 1 (mod 24)

here:
x = Buse B is benning her xth trip
y = Buse C is beginning her yth trip

for above equation to be solvable:

10x - 15y = 1 should have positive integer solution. There is no solution for this.
Senior Manager
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09 Nov 2005, 22:12
This question is fromt thr Princeton Review. I highly doubt this type of question will be present on the actualy GMAT. GMAT tests concepts not ability to crunch numbers.

The OA is E. The correct way is too use mod... but who would do that on a test? =)
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13 Nov 2005, 11:54
rigger wrote:
Buses leave town B at 3pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday what is the earliest day on which the bueses leave at the same time?

a) Tuesday
b) Wednesday
c) Thursday
d) Sunday
e) They will never leave at the same time.

plz Rigger do you have any official explanation ?
thanks
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Re: PS: Buses   [#permalink] 13 Nov 2005, 11:54
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