Three friends A, B and C decide to run around a circular track. They

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Edited. Thank you.

Bunuel I am sorry to bother you again but C option doesn't fit with question conditions while Option D fits

Suppose Track length is 4
As per option C
WHen A completes one LAP i.e. 4 unit distance then B is at 3 (at 3/4) the mark of track length and C is at 2

After 3 laps
A completes 12 units B completes 9 units and C travels 6 units

i.e. C is at the midpoint of the track i.e. C is not at mark where B was when A completed first lap

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Edited. Thank you.

At the end of A's 3rd lap, the distance between A and C must be

Track length + Distance between A and B at the end of 1st lap

If the track length is 500m and the speed ratio is 5:4:3

A's first lap, A:B:C=500:400:300
A's second lap, A:B:C=1000:800:600
A's third lap, A:B:C=1500:1200:900

So the distance between A and C at the end ofnA's third lap is 1500-900=600=500+100 (track length + Distance between A and B at the end of A's first lap)

This perfectly matches our requirement.

Answer is (D)

Posted from my mobile device

Let length of the track be 1
Speed of A, B and C = a, b, c respectively

Time instant 1:
Distance covered by A= 1
by B= 1-x
by C= 1-2x

Time ratio: A:B:C= 1/a : (1-x)/b : (1-2x)/c
Speed ratio: a:b:c = 1:1-x:1-2x

Time instant 2:
Distance covered by A= 3
by C= 2-x (cannot be 3-x as relative distance between A-C must increase)

Time ratio: A:C= 3/a : (2-x)/c
Speed ratio: a:c = 3:2-x

Therefore, a/c = 1/(1-2x) = 3/(2-x)
x= 1/5

So, a:b:c = 1: 4/5 : 3/5 = 5:4:3

Ans D

The question states "When A completes 3 laps, C is at the exact same point on the circular track as B was when A finished the first lap."
So why do we need to measure distances?
Looking at firas92 explanation, C's position when A finished the third lap is in 900M point/mark and why is it not simply B's point/mark when A finished its first lap?

Slightly copying firas92's diagram here - isnt the question saying
A's 1st Lap - A:500M point === B:400M point === C:300M point
A's 2nd Lap - A:xxx === B:xxx === C:xxx
A's 3rd Lap - A:xxx === B: xxx === C: 400M Point

?

Cheers

gorbyrodo

That would mean that C is not maintaining constant speed and so the ratio between the speeds of A and C will not be the same throughout the race.

Hope its clear

Posted from my mobile device

A's 1st Lap - A:500M point === B:400M point === C:300M point
A's 2nd Lap - A:xxx === B:xxx === C:xxx
A's 3rd Lap - A:xxx === B: xxx === C: 400M Point

?

Cheers[/quote]


That would mean that C is not maintaining constant speed and so the ratio between the speeds of A and C will not be the same throughout the race.

Hope its clear

Posted from my mobile device[/quote]

HI firas92. sorry for the late reply mate.

Thats the thing though, with the way the question is laid out it doesnt seem that constant speed is not maintained by C.
If we were to assume that C's speed is maintained, then wouldnt the illustration looks like this?

A's 1st Lap - A:500M point === B:300M point === C:100M point
A's 2nd Lap - A:xxx === B:xxx === C:xxx
A's 3rd Lap - A:xxx === B: xxx === C:300M Point

C is maintaining 100M throughout A's run. Thus the ratio would be 5:3:1

That would mean that C is not maintaining constant speed and so the ratio between the speeds of A and C will not be the same throughout the race.

Hope its clear

Posted from my mobile device[/quote]

HI firas92. sorry for the late reply mate.

Thats the thing though, with the way the question is laid out it doesnt seem that constant speed is not maintained by C.
If we were to assume that C's speed is maintained, then wouldnt the illustration looks like this?

A's 1st Lap - A:500M point === B:300M point === C:100M point
A's 2nd Lap - A:xxx === B:xxx === C:xxx
A's 3rd Lap - A:xxx === B: xxx === C:300M Point

C is maintaining 100M throughout A's run. Thus the ratio would be 5:3:1[/quote]

I get your point now. 5:3:1 could be an answer as explained by GMATinsight above.

I just worked with the given options and D was the only one that fit so I didn't consider 5:3:1

Bunuel chetan2u IanStewart VeritasKarishma GMATinsight
Is there any specific reason why A/C = 5/1 is rejected, and 5/3 is the OA
I feel both the options are viable.
Please help.

Also, in the real GMAT exam, is it possible to get questions which have multiple answers as per multiple cases, but OA is specific to only one case ?

Thanks!

You're right -- the question has two correct answers (one of which is not among the choices). That can't happen on the GMAT, at least when a question asks for an exact answer.

But there are several real GMAT questions that are phrased in this way:

If |x - 3| = 7, what could be the value of x?
A) -10
B) -7
C) -4
D) 4
E) 7

When the question asks what x "could" be, that phrasing indicates that the question may (and probably does) have more than one right answer, but you'll only find one of those answers among the choices. Here the absolute value equation has two solutions for x, 10 and -4, but only one of those is among the choices. But on the actual GMAT, the question above could never ask "What is the value of x?" because x does not have a unique value, so it would be mathematically incorrect to phrase the question that way.

Both 5:3:1 and 5:4:3 are valid answers. The question is faulty in that it suggests there is only one solution: What is the ratio of the speeds of A, B and C?
So, if someone gets 5:3:1 through a certain method, it would surely hamper his speed, concentration and mind frame. Thai is not something GMAT would want, so you can safely assume that in GMAT, with such wordings, you should get only one answer.

Questions wherein there is a possibility of more than one answers the question would be phrased accordingly: Which COULD be a value and so on.

EDIT: It seems Ian too has answered the query in similar way while I was posting my thoughts. I agree with Ian completely on this issue.

You can use the options to solve the question.

"when A finishes the first lap lap, C is as much behind B as B is behind A"
So the difference between the speed of A and B is the same as difference between the speed of B and C. Hence options (A) and (B) are out.

As per option (E), when A completes 3 laps, C would have completed 1 lap and would be at starting point too. But that is not possible. So (E) is out.

Now, check for option (C):
When A completes 1 lap, B completes 3/4 (three quarters of circle) and C completes 2/4 (Half of circle).
When A completes 3 laps, B completes 9/4 (quarter of circle) and C completes 6/4 (Half of circle)
C is not at the same position as B was.

Answer (D)

Let's check anyway:
When A completes 1 lap, B completes 4/5 and C completes 3/5 .
When A completes 3 laps, B completes 12/5 and C completes 9/5
Since 9/5 is (1 + 4/5), C is at the same position as B was.

firas92 @VeritasKarishma
GMATinsight
How did we deduce the equation

At the end of A's 3rd lap, the distance between A and C must be
Track length + Distance between A and B at the end of 1st lap

Why have we added Track length here, if I go based on algebraic equation it should
Assuming Track length as 100, At the end of 1st lap,
A = 100
B = 100-x
C = 100-2x
At 3rd Lap, A=300 , C=3(100-2x) = 300-6x
What am I missing here?
Again, By solving the same equation that says
When A completes 3 laps, C is at the exact same point on the circular track as B was when A finished the first lap.
300-6x = 100-x
x=40
I get the laps as
1st---- 100,60,20
2nd--- 200,120,40
3rd--- 300,240,60
and speed ratio as 5:4:1

You are not wrong RajatGMAT777 (except for some calculation mistakes you have done in your last two steps)

I get the laps as
1st---- 100,60,20
2nd--- 200,120,40
3rd--- 300,240,60 (This should be 300, 180, 60)
and speed ratio as 5:4:1 (This should be 5:3:1)

That said, there are two possitibilites - C could have covered an entire track length and reached B's previous point or C may not have covered even one track length by the time A covers 3 laps.
So speeds of 5:4:3 as well as 5:3:1 are possible. The question mentions "could be the ratio" and that is why I would typically use the options to see which option "could" be the ratio. Now that I see other responses above, I guess the question started out by looking for an exact value and was later on updated.

Instead of calculating the ratio through algebra, this approach felt faster to me -

Observation 1 - Since A has to land back into it's starting position after 3 laps, the speed of A is a number divisible by 3. You can add all ratios given in each option and check the sum of the three ratios given (ratio1:ratio2:ratio3) should be divisible by 3, that narrows down our possible answer choices to C,D and E.

Now you can pick each Ratio and apply both scenarios and see what are the relative positions coming for A, B, C in each scenario. For instance -

Picking C (4:3:2) -
We know A will always come back to it's starting position so it's easier to comprehend the relative position w.r.t A, therefore we can write the ratio as 1:3/4:2/4. Notice that this is exactly satisfies scenario 1 - "They start at the same time, from the same point and run in the same direction. A is the quickest and when A finishes the first lap lap, C is as much behind B as B is behind A."

If we multiply this ratio by 3 = 3: 9/4 : 3/2, B should have been at A's starting position (should be a whole number)

Therefore we can eliminate C.


Picking E (3:2:1) -
E = 1 : 2/3 : 1/3 (this also perfectly satisfies scenario 1)

Let's multiply the ratio by 3 and see what are the relative positions of A, B and C -
E' = 3 : 2 : 1 (B comes to A starting position, however C also comes at the came exact position since it's a whole number. But Scenario to explains that C should have been on B's place aka 2/3rd mark of the circle)

Therefore we can eliminate E.

We are left with D, which is our answer.