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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie

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Director
Joined: 09 Aug 2006
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink]  06 Oct 2007, 04:20
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie II. Regine III. Brian

(A) I only
(B) II only
(C) III only
(D) I or II only
(E) I, II, or III
VP
Joined: 08 Jun 2005
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20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

Senior Manager
Joined: 27 Jul 2006
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KillerSquirrel wrote:
20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

another way to look at it.

If Brian ran at the speed of light (8mph) he would have made it in 2.5 hours and the combined time would be 4.5 hours, but this cannot be because 2x2.5 is 5, so Brian must have been running slower than 8mph and in any case the two other runners can be faster than him, but he can never be faster than the two runners.
VP
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defenestrate wrote:
KillerSquirrel wrote:
20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

another way to look at it.

If Brian ran at the speed of light (8mph) he would have made it in 2.5 hours and the combined time would be 4.5 hours, but this cannot be because 2x2.5 is 5, so Brian must have been running slower than 8mph and in any case the two other runners can be faster than him, but he can never be faster than the two runners.

Don't like to be a nitpicker but, the speed of light is 300,000 kph so it would take him less than one second hence = 0 time.

Intern
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Doen't
"Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours."
mean :

Ts+Tr = Tb + 2 ???

If this was the case then asnwer would be E.
VP
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hidalgo01 wrote:
Doen't
"Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours."
mean :

Ts+Tr = Tb + 2 ???

If this was the case then asnwer would be E.

No ! since if you run faster then someone you will arrive sooner. Hence negative value.

20/8 = 2.5
20/10 = 1

so the one who run faster (10 mph) will arrive 1.5 hour sooner.

Director
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KillerSquirrel wrote:
20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

KS, I didn't get the logic behind this. Can you pls. explain?

Firstly why do we assume that R = 0?
Secondly, even if we do, and S + 2 = B, then how is S = ~0??
Finally, why can B not be less than 2?
VP
Joined: 08 Jun 2005
Posts: 1146
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Kudos [?]: 136 [0], given: 0

GK_Gmat wrote:
KillerSquirrel wrote:
20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

KS, I didn't get the logic behind this. Can you pls. explain?

Firstly why do we assume that R = 0?
Secondly, even if we do, and S + 2 = B, then how is S = ~0??
Finally, why can B not be less than 2?

Since you cannot have two first places, then one has to be first one has to be second and the last one has to be third.

you are being asked who could have won the race ?

since you know that S+R = B-2 ---> Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

than even if it took Stephanie no time (she run at the speed of light) to finish the race. then 0+R = B-2 ---> R = B-2

this still holdes that Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

now lets assume that Regine came second (she run at the speed of sound) meaning also zero time but less the Stephanie.

0+0 = B-2 ---> B=2

still holds that Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

so Brian is the only one that cannot win this race.

Even if you decide that Stephanie and Regine's time is one hour each then 1+1 = B-2 and B = 4 ---> B will always be slower then either R or S.

since the max speed for R,S or B is 20/8 = 2.5 then:

2.5+S = B-2

0.5+S = B

B is slower then S !!! by helf an hour and cannot win the race.

CEO
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Re: PS: Race [#permalink]  08 Oct 2007, 11:00
GK_Gmat wrote:
Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

I. Stephanie II. Regine III. Brian

(A) I only
(B) II only
(C) III only
(D) I or II only
(E) I, II, or III

Ans has gotta be D.

Set up equations or rate chart as I like to do. And just try different values for Stephanie and Regine. I recommend rates of 4 and 5 b/c they are divisible by 20.

S || R || B
R: 4 || 5 || x
T: Ts || Tr || Ts+Tr-2=Tb
D: 20 || 20 || 20

First plug we get Ts=5 and Tr=4. So Tb=7hrs So Regine won the race.

Now since there is no bearing on S or R we can interchange 4 and 5 so that this time Stephanie wins the race.

So only 2 answer choices left D or E.

Brain will never be able to win the race. (just try more values if ur not certain)

So ans is D.
Director
Joined: 09 Aug 2006
Posts: 763
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KillerSquirrel wrote:
GK_Gmat wrote:
KillerSquirrel wrote:
20 miles race

time ---> no more then 20/8 = 2.5 hours

S+R = B-2 ---> in terms of time in hours.

lets assume R=0

so S+2 = B ---> S=~0 then B=~2

B cannot be less then two but --->S & R can !

KS, I didn't get the logic behind this. Can you pls. explain?

Firstly why do we assume that R = 0?
Secondly, even if we do, and S + 2 = B, then how is S = ~0??
Finally, why can B not be less than 2?

Since you cannot have two first places, then one has to be first one has to be second and the last one has to be third.

you are being asked who could have won the race ?

since you know that S+R = B-2 ---> Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

than even if it took Stephanie no time (she run at the speed of light) to finish the race. then 0+R = B-2 ---> R = B-2

this still holdes that Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

now lets assume that Regine came second (she run at the speed of sound) meaning also zero time but less the Stephanie.

0+0 = B-2 ---> B=2

still holds that Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

so Brian is the only one that cannot win this race.

Even if you decide that Stephanie and Regine's time is one hour each then 1+1 = B-2 and B = 4 ---> B will always be slower then either R or S.

since the max speed for R,S or B is 20/8 = 2.5 then:

2.5+S = B-2

0.5+S = B

B is slower then S !!! by helf an hour and cannot win the race.

KS: Thanks for the explanation!!! Very helpful.
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