Two Cars A And B Start From Diametrically Opposite Points Of GMAT Data Sufficiency

Question: Two cars A and B start at same time from diametrically opposite points of a circular track in opposite direction, with A moving clockwise and B moving anti-clockwise. If they meet each other for first time after A has traveled 20 miles, what is the length of circular track?

(1) The ratio of speed of A to B is 4:1.
(2) When A and B meet for the second time, B has traveled another 10 miles after meeting A for the first time.

Correct Answer: (D)

Approach Solution : 1

Working for the distance traveled as a portion of the total when they meet would be a very logical and simple method.

Both have traveled half the distance of the track when they first cross paths.
A travels 20 while B travels x, making the half-track value x+20 and the total value as 2(x+20).

Statement - 1 : The ratio of speed of A to B is 4:1

Both of them have been traveling for the same amount of time when they first meet.

As a result, if A travels 20 miles and the speed ration of A:B is 4:1, B will cover 20/4 = 5 miles.
Consequently, half track = 20+x = 20+5 = 25.

Finally, the total track = 2 * 25 = 50.

Therefore this statement is sufficient.

Statement - 2 : When A and B meet for the second time, B has traveled another 10 miles after meeting A for the first time

When they meet again, determine how far they have traveled. After the initial meeting, they travel the entire track.

B covers 10 miles in this full track, so in half that distance, he would travel 10/2=5 miles.

As a result, the combined half-track distance of 20+5 = 25.

Respectively the full track distance will be, 2*25 = 50 miles.

Therefore this statement is sufficient.

Approach Solution : 2

Let A and B travel at speeds of u and v, respectively. Initial movement from diametrically opposed points means that when they eventually meet, they will have traveled half of the circumference.

=> πr = (u+v)∗t, where t is considered as the time take to meet
We can write that from the given information, t = 20/u

And so, πr = (u+v)∗(20/u) -------------------(1)
Thus, length of the track which is the circumference of a circular track will be, 2πr = 40 + [(40)*(v/u)]

In order to determine the length, we must know the speed ratio between A and B.

Statement - 1 : The ratio of speed of A to B is 4:1

The ratio is provided here in a direct way.

Therefore this statement is sufficient.

Statement - 2 : When A and B meet for the second time, B has traveled another 10 miles after meeting A for the first time

When they cross paths again, they will have traveled the entire circular route and the time taken is 10/v .

And now we can write, 2πr = (u+v)∗(10/v).

Divide the above equation by equation (1) to get, 2 =(10u) / (20v)
=> v/u = 14.
Finally the speed ration is determined.

Therefore this statement is sufficient.

Approach Solution : 3

This question is based on the idea of relative speed, which depends on how distance changes with respect to speed when time is held constant.
Distance and speed are directly proportional when time is constant. In other words, the ratio of the speeds of two objects will match the ratio of the distances they travel.

The question mentions that A traveled 20 miles before first encountering B. Now let us assess the statements.

Statement - 1 : The ratio of speed of A to B is 4:1

The speed ratio is available. We can say that A and B traveled at the same time because they both began at the same location and ended up there when they met.
Time being a constant, the distances they travel will be proportional to their speeds.

So, Da:Db=4:1
Da is 20, though, and we know that. Therefore, we will be able to determine Db. Consequently, we will be able to determine half the length of the track. By multiplying that by 2, we can find the full length.
Therefore this statement is sufficient.

Statement - 2 : When A and B meet for the second time, B has traveled another 10 miles after meeting A for the first time

By the time they cross paths again, B has reportedly traveled a distance of 10 miles. The ratio of their speeds, however, will not change regardless of whether they meet for the first or second time.
Let the track's length be 2πr. After that, the distance traveled by A between the first and second meetings is equal to 2πr - 10.
So, [(2πr–10) / 10] = [ 20 / (πr–20)]

Finding a special value for 2πr will be made possible by solving the equation above.
Therefore this statement is sufficient.

“Two cars A and B start from diametrically opposite points of” - is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

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Two Cars A And B Start From Diametrically Opposite Points Of GMAT Data Sufficiency

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