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

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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 04 Feb 2012, 15:21
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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
D. only I or II only
E. I, II, or III
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 04 Feb 2012, 15:27
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arps 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
D. only I or II only
E. I, II, or III


Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.

To elaborate more: the least time one could complete the race is 20/8=2.5 hours, hence S+R\geq{5}. Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that S+B\geq{5}, so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.

Hope it's clear.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 05 Feb 2012, 02:52
Ans is D
since s=d/t or t=d/s so lower the speed more the time
since combined time of Stephanie and Regine exceeds that of Brian so Brian was the slowest.
Thus someone between Stephanie and Regine might have won the race
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Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 10 Sep 2012, 12:32
We don’t know who has won the race and who has come last. All we know is the fastest time is 2.5 hrs and the fastest speed is 8mi/hr.
Let’s us assume that Brain won the race. He took 2.5 hrs to complete the race. In this case
S + R = 4.5
Now the minimum possible time S and R could have taken would be 2.25 hrs to complete the race, since if they took any time less than 2.25 hrs (which is already less than 2.5hrs), then it would mean that Brian wasn’t the first to win the race.

Note that if S (or R) took more than 2.5 hrs, it means R (or S) took less than 2.5 hrs, and hence Brian wouldn’t be winner in that case.
Now even if they took 2.25 hrs, still the case is not possible, because Brian needs to take the lowest time in order to be winner. So we come to conclusion that Brian cannot be a winner in any case.

Let’s assume that Stephanie won the race in record time of 2.5 hrs. In that case
B = R + 0.5
Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.
The same is true with
B = S + 0.5
R came first, S and then B.
So we see that B is a loser in any case, however R or S have equal chances to win.
So (D) is the answer.

Thanks
Prashant
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 28 Aug 2013, 07:46
Bunuel wrote:
arps 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
D. only I or II only
E. I, II, or III


Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.

To elaborate more: the least time one could complete the race is 20/8=2.5 hours, hence S+R\geq{5}. Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that S+B\geq{5}, so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.

Hope it's clear.


Hi Bunuel

Why so S+R>=5 ?????

Rgds
Prasannajeet
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 28 Aug 2013, 08:30
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prasannajeet wrote:
Bunuel wrote:
arps 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
D. only I or II only
E. I, II, or III


Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.

To elaborate more: the least time one could complete the race is 20/8=2.5 hours, hence S+R\geq{5}. Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that S+B\geq{5}, so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.

Hope it's clear.


Hi Bunuel

Why so S+R>=5 ?????

Rgds
Prasannajeet


Nobody ran faster than 8 miles per hour --> the least time one could complete the race is 20/8=2.5 hours --> S+R>=2.5+2.5.

Hope it's clear.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 29 Aug 2013, 19:18
Thanx a ton Bunuel

Now its clear

Rgds
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 29 Aug 2013, 22:30
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arps 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
D. only I or II only
E. I, II, or III


It's a good conceptual question. Here are my thoughts on it:

8 mph implies that each person took at least 20/8 = 2.5 hrs. They could have taken more time too.
So Stephanie and Regina's combined time is at least 2.5*2 = 5 hrs. So Brian's time taken is at least 3 hrs. Can Brian win? No. The difference between S and R's combined time and Brian's time is 2 hrs but each person takes more than 2.5 hrs.

If S and R together took 5 hrs, B took 3 hrs. Both S and R must have taken 2.5 hrs each.
If S and R together took 6 hrs, B took 4 hrs. Both S and R must have taken less than 4 hrs since each person takes at least 2.5 hrs.
If S and R together took 10 hrs, B took 8 hrs. Both S and R must have taken less than 8 hrs since each person takes at least 2.5 hrs.
Brian could never win.
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie [#permalink] New post 02 Sep 2014, 02:08
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Re: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie   [#permalink] 02 Sep 2014, 02:08
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