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Two cars start moving simultaneously in different directions from poin

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New post 08 Dec 2014, 05:16
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Two cars start moving simultaneously in different directions from point A at constant respective uniform speeds . What is the difference between their speeds (faster minus slower)?

(1) After 2 hours, the two cars are 140 miles apart

(2) When the faster car has covered a distance of 200 miles, the slower car has covered 150 miles
[Reveal] Spoiler: OA

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New post 08 Dec 2014, 07:53
statement 1: insufficient

Car 1 could be traveling at 70mph and car 2 could be traveling at 70 mph, giving us a difference of 0mph.
Car 1 could be traveling at 80mph and car 2 could be traveling at 60mph, giving us a difference of 20mph.

statement 2: insufficient

Car 1 could be traveling at 40mph and car 2 could be traveling at 30mph, giving us a difference of 10mph.
Car 1 could be traveling at 200mph and car 2 could be traveling at 150mph, giving us a difference of 50mph.

Down to answers C and E.

The statements together are sufficient. Statement (2) gives us a ratio to work with and statement (1) gives us a value to work with. I could take a couple minutes to try and figure out the answer but I love that date sufficiency doesn't require that :)

Answer C!

edit: oops! Forgot to check answer above, looks like E is OA

Last edited by DangerPenguin on 08 Dec 2014, 10:44, edited 1 time in total.

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New post 08 Dec 2014, 10:41
I'm getting C as well, are you sure the OA is E?

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New post 08 Dec 2014, 10:59
This is kind of a tricky one. Are you sure the OA is correct?

Situation (1):

You can set this up by saying distance = time * (V1+V2), where V1 is the speed of car 1 and V2 is the speed of car 2 (use + since they are moving in opp directions). Doesn't help you find V1-V2.

Situation (2):
Using same variables above, you can find distance of car 1 = V1(t), and distance of car 2 = V2(t) at some constant time t. You can take the ratio by saying d1/d2 = v1/v2, but that still doesn't give you enough to work with to find the difference.

Combined:
Seems like it should be sufficent, unless I'm missing something.

From (1), you can setup an equation such V2 = d/t - V1, and from (2) then (200/150) = V1/((140/2)-V1). Solve for V1, and then solve for V2.

Can one of the pros chime in? I admit DS is my worst topic on GMAT.

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New post 08 Dec 2014, 20:42
I also marked C as the answer. But OA was given as E. OE was not provided.

Dear Bunuel :- Please confirm the OA.

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New post 09 Dec 2014, 23:39
i think the catch in this question is that it says cars move in different directions that i think could be opposite direction or moving perpendicular... but i am not sure about this.

P.S--Bunnel please help.

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desaichinmay22 wrote:
Two cars start moving simultaneously in different directions from point A at constant respective uniform speeds . What is the difference between their speeds (faster minus slower)?

(1) After 2 hours, the two cars are 140 miles apart

(2) When the faster car has covered a distance of 200 miles, the slower car has covered 150 miles


Yes, different directions doesn't necessarily imply opposite direction. They could move away from each other at any angle.

Statement 1 only tells you the distance between them. It doesn't tell us the distance covered by them together. If they moved in opposite directions, 140 would be the distance covered by them. If they moved perpendicular to each other, together they would have covered distance more than 140.

Statement 2 only tells us that the ratio of their speed is 200:150 = 4:3. We don't know what their actual speeds are.

Using both, we don't know the distance traveled by them together so we don't know their individual speeds. We cannot find the difference between their speeds. e.g.
Say they travel opposite to each other, their combined speed is 140/2 = 70 miles/hr. So their independent speeds are 40 miles/hr and 30 miles/hr. Difference in their speeds = 40 - 30 = 10 miles/hr
Say they travel perpendicular to each other, the distance between them is the hypotenuse of the right triangle and is 140. The distance traveled by them will be in the ratio 4:3 (legs of the triangle) so the 140 represents the side 5. Multiplier is 140/5 = 28. So the legs of the triangle are 4*28 and 3*28. Their speeds then are 4*28/2 = 56 miles/hr and 3*28/2 = 42 miles/hr. Difference between their speeds is 56 - 42 = 14 miles/hr

Answer (E)
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VeritasPrepKarishma wrote:
desaichinmay22 wrote:
Two cars start moving simultaneously in different directions from point A at constant respective uniform speeds . What is the difference between their speeds (faster minus slower)?

(1) After 2 hours, the two cars are 140 miles apart

(2) When the faster car has covered a distance of 200 miles, the slower car has covered 150 miles


Yes, different directions doesn't necessarily imply opposite direction. They could move away from each other at any angle.

Statement 1 only tells you the distance between them. It doesn't tell us the distance covered by them together. If they moved in opposite directions, 140 would be the distance covered by them. If they moved perpendicular to each other, together they would have covered distance more than 140.

Statement 2 only tells us that the ratio of their speed is 200:150 = 4:3. We don't know what their actual speeds are.

Using both, we don't know the distance traveled by them together so we don't know their individual speeds. We cannot find the difference between their speeds. e.g.
Say they travel opposite to each other, their combined speed is 140/2 = 70 miles/hr. So their independent speeds are 40 miles/hr and 30 miles/hr. Difference in their speeds = 40 - 30 = 10 miles/hr
Say they travel perpendicular to each other, the distance between them is the hypotenuse of the right triangle and is 140. The distance traveled by them will be in the ratio 4:3 (legs of the triangle) so the 140 represents the side 5. Multiplier is 140/5 = 28. So the legs of the triangle are 4*28 and 3*28. Their speeds then are 4*28/2 = 56 miles/hr and 3*28/2 = 42 miles/hr. Difference between their speeds is 56 - 42 = 14 miles/hr

Answer (E)


+1. Thank you for the explanation.

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Unnecessarily tricky question. If the cars are travelling on road and we measure road distance between points, then 'C'.
If the cars are moving on a vacant plain and we measure 'crow flies' distance, then E.

This seems to be more of lateral thinking question to me.

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New post 03 Oct 2016, 00:47
This question is tricky because it seems as though you have enough information to solve for CAR_A_SPEED and CAR_B_SPEED. However, you do not but you can solve for their speeds combined. Considering the question is against C and E I'll just go through these scenarios.

Quote:
Two cars start moving simultaneously in different directions from point A at constant respective uniform speeds . What is the difference between their speeds (faster minus slower)?

(1) After 2 hours, the two cars are 140 miles apart

(2) When the faster car has covered a distance of 200 miles, the slower car has covered 150 miles


1+2) We know that Va = Da/t and Vb = Db/t as such we can write two equations
1. Va(2)+Vb(2) = 140
2. 200/Va = 150/Vb

We can then solve Va and Vb which are 40 miles/hr and 30 miles/hr respectively. Now then this should be QED solved BUT if you reread the questions carefully it says two cars start moving in different directions simultaneously it doesn't say in opposite directions.

As such you could have assumed one car went north and the other went west or one of the cars was moving away from the other at a 2 degree inclination from the origin (A).

As such the equations become very different and more unknowns are thrown into the mix.

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