Problem Solving

gmatmachoman 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

itsratul wrote:The answer is D

The fastest that any one could have ran and completed the race ,he would have taken 20 (miles) / 8 (miles per hr) = 2.5 hrs

Lets have Stephaine and Regine run with maximum speed then from the equation (coz thats when Brian's time will also be shortest):

StephaineTime+RegineTime = BrianTime+2
BrianTime =3 hrs

So Brian is the slowest.

Between Stephaine and regine we cannot find who was fastest as there is no more information.

therefore either Stephaine or Regine could have won the race.

singhpreet1 wrote:

gmatmachoman 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

i feel its C. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours therefore, Brian ran 20 miles at highest speed of 8 miles per hour and finished in 20/8= 2.5 hours as has already been mentioned by itsratul. now Stephanie and Regine took 2 more hours combined to finish the race, therefore, it is certain that they have to be slower than Brian to take more time to finish the race???

assuming that Stephanie and Regine both ran at 6 m/h they finished in 3.5 hours each which is 2 hours combined exceeded beyond Brian's time.

Alternatively, Stephanie ran at 5 m/h and Regine ran at 6m/h that would roughly suffice the condition as well.

hope that makes sense.

Preet

gmatmachoman wrote:

itsratul wrote:The answer is D

The fastest that any one could have ran and completed the race ,he would have taken 20 (miles) / 8 (miles per hr) = 2.5 hrs

Lets have Stephaine and Regine run with maximum speed then from the equation (coz thats when Brian's time will also be shortest):

StephaineTime+RegineTime = BrianTime+2
BrianTime =3 hrs

So Brian is the slowest.

Between Stephaine and regine we cannot find who was fastest as there is no more information.

therefore either Stephaine or Regine could have won the race.

Your approach is very much correct!!

In simpl,e we can say :

1.Determine the probable Minimum time any user can take.

Minimum Time : Distance/(Max speed)
20/8
:2.5 hrs

From the stem it is known that:

StephaineTime+RegineTime = BrianTime+2

So on Minimum terms , it will be

2.5+2.5= BrianTime+2
BrianTime = 3 hrs

So Maximum speed of Brian will be : 20/3
:6.67

On ordering speed of three players,

Stephaine>=Regine>Brian

So its clear that Brian could have NOT won the race in anyway!!

Pick D(May be S or R)

singhpreet1 wrote:

gmatmachoman wrote:

itsratul wrote:The answer is D

The fastest that any one could have ran and completed the race ,he would have taken 20 (miles) / 8 (miles per hr) = 2.5 hrs

Lets have Stephaine and Regine run with maximum speed then from the equation (coz thats when Brian's time will also be shortest):

StephaineTime+RegineTime = BrianTime+2
BrianTime =3 hrs

So Brian is the slowest.

Between Stephaine and regine we cannot find who was fastest as there is no more information.

therefore either Stephaine or Regine could have won the race.

Your approach is very much correct!!

In simpl,e we can say :

1.Determine the probable Minimum time any user can take.

Minimum Time : Distance/(Max speed)
20/8
:2.5 hrs

From the stem it is known that:

StephaineTime+RegineTime = BrianTime+2

So on Minimum terms , it will be

2.5+2.5= BrianTime+2
BrianTime = 3 hrs

So Maximum speed of Brian will be : 20/3
:6.67

On ordering speed of three players,

Stephaine>=Regine>Brian

So its clear that Brian could have NOT won the race in anyway!!

Pick D(May be S or R)

ok hand raised, question here!!!
Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

When Stephanie and Regine's combined time exceeded Brian's time. lets take another example. if i finished my soup in 1 hour and A&B finished their soups combined time exceeded my time by 2 hours. that means they took 3 hours in total, or if they ate at equal speed they finished in 1 1/2 hours each..they did not finish before me did they???

i hope i made sense.

Preet

singhpreet1 wrote: ok hand raised, question here!!!
Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

When Stephanie and Regine's combined time exceeded Brian's time. lets take another example. if i finished my soup in 1 hour and A&B finished their soups combined time exceeded my time by 2 hours. that means they took 3 hours in total, or if they ate at equal speed they finished in 1 1/2 hours each..they did not finish before me did they???

i hope i made sense.

Preet

sars72 wrote:

singhpreet1 wrote: ok hand raised, question here!!!
Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

When Stephanie and Regine's combined time exceeded Brian's time. lets take another example. if i finished my soup in 1 hour and A&B finished their soups combined time exceeded my time by 2 hours. that means they took 3 hours in total, or if they ate at equal speed they finished in 1 1/2 hours each..they did not finish before me did they???

i hope i made sense.

Preet

you are removing the conditions imposed by the original question... the question stem puts a limit on the minimum time taken by any the individuals.
we have a max speed of 8 mph --> min time of 20/8 = 2.5

if we removed this condition, then we could have a scenario where Stephanie and Regine's combined time was 3 hours.... don't want to continue blabbering... hope you get the gist

singhpreet1 wrote:[
calm down Sars..sorry im dumb..i wish i was smarter...but i can only try. i still dont seem to get it! Brian cant finish before 2.5 hours is that right?
and Stephanie and Regine's combined time exceeded 2 hours from Brian's time...so basically they ran in 4.5 hours in total and Brian's time was the slowest and Stephanie or Regine ran in 2.5 hours...thank God!

sorry everyone for eating your heads on this one!!!
Preet

singhpreet1 wrote:

sars72 wrote:

singhpreet1 wrote: ok hand raised, question here!!!
Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours.

When Stephanie and Regine's combined time exceeded Brian's time. lets take another example. if i finished my soup in 1 hour and A&B finished their soups combined time exceeded my time by 2 hours. that means they took 3 hours in total, or if they ate at equal speed they finished in 1 1/2 hours each..they did not finish before me did they???

i hope i made sense.

Preet

you are removing the conditions imposed by the original question... the question stem puts a limit on the minimum time taken by any the individuals.
we have a max speed of 8 mph --> min time of 20/8 = 2.5

if we removed this condition, then we could have a scenario where Stephanie and Regine's combined time was 3 hours.... don't want to continue blabbering... hope you get the gist

calm down Sars..sorry im dumb..i wish i was smarter...but i can only try. i still dont seem to get it! Brian cant finish before 2.5 hours is that right?
and Stephanie and Regine's combined time exceeded 2 hours from Brian's time...so basically they ran in 4.5 hours in total and Brian's time was the slowest and Stephanie or Regine ran in 2.5 hours...thank God!

sorry everyone for eating your heads on this one!!!

Preet

gmatmachoman 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