A geyser in Yellowstone Park spouts at regular intervals .

Question

A geyser in Yellowstone Park  spouts at regular intervals . Will it spout more than 18 times in the seven day period beginning tonight at midnight?

(1) It spouted three times yesterday.
(2) It spouted three times the day before yesterday.

yezz · Answer

kEVIN SHOULD WE ASSUME THAT ...IT IS A PATTERN OR NOT??

kevincan · Answer

"Regular intervals" means that the time between two consecutive eruptions is always the same

kripalkavi · Answer

In that case the answer is  D  unless I'm missing something...

gauravgoyal_g · Answer

I think it should be D..

If x is the interval between spouts

6 hours < x <= 8 hours

There are 168 hours in a 7 day period.

Even if the first spout happens tomorrow morning at 7:59 am, it would still leave about 162 hours for 162/8 = approx 20 spouts.

Fig · Answer

I think it's (E)

Statment 1 & 2 alone are not sufficient:

 Case 1 :  We can consider the Period = 11h59 a spout

Thus,
o Day 1 (Yesterday or 2 days ago):
> Spout 1 at 00:01 am
> Spout 2 at 12:00 am
> Spout 3 at 11:59 pm

o Day 2 :
> Spout 4 at 11:58 am
> Spout 5 at 11:57 pm

o Day 3 :
> Spout 6 at 11:57 am
> Spout 7 at 11:56 pm

so on for the next day. Thus 2 a day for 7 days = 14 less than 18.

 Case 2 :  We can consider the Period = 8h00 a spout

o Day 1 (Yesterday or 2 days ago):
> Spout 1 at 7:59 am
> Spout 2 at 3:59 pm
> Spout 3 at 11:59 pm

o Day 2 :
> Spout 1 at 7:58 am
> Spout 2 at 3:58 pm
> Spout 3 at 11:58 pm

so on for the next day. Thus 3 a day for 7 days = 21 more than 18.

And why (E)? 
I believe, by pure guess, that the period in case (1) and case (2) still exists to create 2 cases even if they almost equal.

kevincan · Answer

Any more thoughts before we get the OA?

paddyboy · Answer

Agree and go with D.

Both cases appear to be giving the same information...

Fig · Answer

Sorry paddyboy.... But the problem is that we can have 3 spouts either Yesterday (Statment 1) or 2 days ago (Statment 2) and then have only 2 spouts (case 1) or 3 spouts (case 2) in a raw of much more than 7 days.

Thus,
o 2 spouts a day since today > 2*7 = 14 (< 18)
o 3 spouts a day since today > 3*7 = 21 (> 18)

The answer should be between C and E... and I prefer E

paddyboy · Answer

You caught the flaw in my reasoning... :-D

And I'm grateful to you for that. Yes, there could be 5 spouts in 48 hours (for Case 1), and 6 spouts every 48 hours, and 7 or 8 spouts in 72 hours (for Case 2) that make it impossible to predict with certainty whether there will be more than 18 spouts. Agree with E.

asaf · Answer

A geyser in Yellowstone Park spouts at regular intervals. Will it spout more than 18 times in the seven day period beginning tonight at midnight? 

(1) It spouted three times yesterday. 
(2) It spouted three times the day before yesterday.

1& 2) Ideally 3 spout a day will give us 7 * 3 = 21 spout but just one day is not enough to define the actual interval. So 1) is unsufficient. 
 So, answer is C or is it?

kevincan · Answer

I think it's clear that neither (1) nor (2) is sufficient by itself. The geyser could spout three times on a given day as long as the time between two eruptions is less than 12 hours (24/(3-1)) but more than 6 hours (24/(3+1)).

Combining (1) and (2), we know that the geyser erupted six times in a two day period (48 hours). Thus the time between two eruptions must be between  48/7  (48/(6+1)) and  48/5  (48/(6-1)) hours. In other words, the interval between two eruptions is less than 9 hours and 36 minutes. Let's see how many eruptions there could be in the 7 day period starting tonight at midnight if the time between two eruptions was 9 hours and 30 minutes.

If the first eruption occured tonight at midnight, the (n+1)th occured n*9.5 hours afterwards. The 19th occured 18*9.5=171 hours afterwards. Since in 7 days there are 168 hours, only 18 eruptions would occur. So together, (1) and (2) are not sufficient.

OA=E

The clever way to conclude that the answer is E is to say: All I know from (1) and (2) is that the geyser erupts more than 2.5 times a day. If it erupts 2.5000001 times a day, what I saw in the 48 hours begininning the day before yesterday was a freakish occurence, and in a 7 period, I can expect either 17 or 18 erputions.

I'm not sure that this question is GMAT calibre, but the concepts behind it are important in the business word- what can be inferred from a sample. If my job were making real GMAT questions, I would include such questions.

cicerone · Answer

Hey kevin what u said is absolutely fine.
I missed out on the upper limit.

paddyboy · Answer

:yikes 

Just joking, of course :wink:

A geyser in Yellowstone Park spouts at regular intervals .

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