Pls explain with a diagram-what is diametrically Opposite

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Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500

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by Stuart@KaplanGMAT » Tue Dec 10, 2013 11:37 pm
[email protected] wrote:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
Hi! This seems like a somewhat insanely complicated question! However, our old friend backsolving will save us from having to do crazy math.

First, "diametrically opposed" means, literally, "at opposite ends of a diameter of the circle". In other words, they're directly across the circle from each other. Thinking geometrically, if one of the two starts at 0 degrees, the other starts at 180 degrees.

You could set up some pretty complicated equations to solve this problem, but backsolving will be much quicker. Since there's no quick reason to eliminate choices based on logic, let's start with (B).

If the distance were 300, then since they run in opposite directions (i.e. directly toward each other), they'll have jointly covered 150m when they meet. We're told that Brenda has run 100m at this time, which means that S has only covered 50m.

They next meet after S covers 150m. Well, if the track were 300m long, then that means that B has also covered 150m (they meet after jointly running 1 full circle). However, we know that B is faster than S (since B covered 100 to S's 50 in the first part), so that makes no sense! (B)300 is too small.

Next let's try (D)400. If the total distance is 400, then the first meet after 200m. B has run 100m, which means that S has also run 100 - so they have to be running at the same speed. They next meet when S has run 150m.. but wait, that's not 1/2 of 400, that makes no sense! So, (D) goes too far in the opposite direction.

(B) is too small, (D) is too big - breathe a sigh of relief and choose (C)!

Again, this is a VERY high level Q.

* * *

Now, what should you do when you're done the question and reviewing? Practice! So, even though on test day we'd pick (C) and move on, let's actually backsolve (C) just to make sure we know how to backsolve properly.

If d=350, then 1/2d = 175. So, when they meet the first time B has gone 100 and S has gone 75.

They meet again after S runs 150, which means that B runs 350-150=200.

The first time, B ran 100 and S ran 75... that's a 100:75 ratio.
The second time, B ran 200 and S ran 150... that's also a 100:75 ratio.

Since the ratios are the same both times, (C) is in fact the correct answer.
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by sanju09 » Tue Dec 10, 2013 11:55 pm
Stuart Kovinsky wrote:
[email protected] wrote:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
Hi! This seems like a somewhat insanely complicated question! However, our old friend backsolving will save us from having to do crazy math.

First, "diametrically opposed" means, literally, "at opposite ends of a diameter of the circle". In other words, they're directly across the circle from each other. Thinking geometrically, if one of the two starts at 0 degrees, the other starts at 180 degrees.

You could set up some pretty complicated equations to solve this problem, but backsolving will be much quicker. Since there's no quick reason to eliminate choices based on logic, let's start with (B).

If the distance were 300, then since they run in opposite directions (i.e. directly toward each other), they'll have jointly covered 150m when they meet. We're told that Brenda has run 100m at this time, which means that S has only covered 50m.

They next meet after S covers 150m. Well, if the track were 300m long, then that means that B has also covered 150m (they meet after jointly running 1 full circle). However, we know that B is faster than S (since B covered 100 to S's 50 in the first part), so that makes no sense! (B)300 is too small.

Next let's try (D)400. If the total distance is 400, then the first meet after 200m. B has run 100m, which means that S has also run 100 - so they have to be running at the same speed. They next meet when S has run 150m.. but wait, that's not 1/2 of 400, that makes no sense! So, (D) goes too far in the opposite direction.

(B) is too small, (D) is too big - breathe a sigh of relief and choose (C)!

Again, this is a VERY high level Q.

* * *

Now, what should you do when you're done the question and reviewing? Practice! So, even though on test day we'd pick (C) and move on, let's actually backsolve (C) just to make sure we know how to backsolve properly.

If d=350, then 1/2d = 175. So, when they meet the first time B has gone 100 and S has gone 75.

They meet again after S runs 150, which means that B runs 350-150=200.

The first time, B ran 100 and S ran 75... that's a 100:75 ratio.
The second time, B ran 200 and S ran 150... that's also a 100:75 ratio.

Since the ratios are the same both times, (C) is in fact the correct answer.
This is stupendous illustration for such a tricky problem. Only experts of the likes of my old favourites Stuart Kovinsky and Ian Stewart could do justice with such problems. Nice to see Stuart Kovinsky's post after long period of time. Not sure where's Ian Stewart these days. Hats Off!
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by GMATSUCKER » Wed Dec 11, 2013 5:43 am
Stuart Kovinsky wrote:
[email protected] wrote:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
Hi! This seems like a somewhat insanely complicated question! However, our old friend backsolving will save us from having to do crazy math.

First, "diametrically opposed" means, literally, "at opposite ends of a diameter of the circle". In other words, they're directly across the circle from each other. Thinking geometrically, if one of the two starts at 0 degrees, the other starts at 180 degrees.

You could set up some pretty complicated equations to solve this problem, but backsolving will be much quicker. Since there's no quick reason to eliminate choices based on logic, let's start with (B).

If the distance were 300, then since they run in opposite directions (i.e. directly toward each other), they'll have jointly covered 150m when they meet. We're told that Brenda has run 100m at this time, which means that S has only covered 50m.

They next meet after S covers 150m. Well, if the track were 300m long, then that means that B has also covered 150m (they meet after jointly running 1 full circle). However, we know that B is faster than S (since B covered 100 to S's 50 in the first part), so that makes no sense! (B)300 is too small.

Next let's try (D)400. If the total distance is 400, then the first meet after 200m. B has run 100m, which means that S has also run 100 - so they have to be running at the same speed. They next meet when S has run 150m.. but wait, that's not 1/2 of 400, that makes no sense! So, (D) goes too far in the opposite direction.

(B) is too small, (D) is too big - breathe a sigh of relief and choose (C)!

Again, this is a VERY high level Q.

* * *

Now, what should you do when you're done the question and reviewing? Practice! So, even though on test day we'd pick (C) and move on, let's actually backsolve (C) just to make sure we know how to backsolve properly.

If d=350, then 1/2d = 175. So, when they meet the first time B has gone 100 and S has gone 75.

They meet again after S runs 150, which means that B runs 350-150=200.

The first time, B ran 100 and S ran 75... that's a 100:75 ratio.
The second time, B ran 200 and S ran 150... that's also a 100:75 ratio.

Since the ratios are the same both times, (C) is in fact the correct answer.
Hey, Is this a GMAT Question ? What's the source ?
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by GMATGuruNY » Wed Dec 11, 2013 6:42 am
[email protected] wrote:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
Here's an alternate approach.

1st meeting:
Image
Here, B and S together travel HALF THE CIRCLE.
It is given that B's distance = 100 meters.

2nd meeting:
Image
Here, B and S together travel the ENTIRE CIRCLE.
It is given that S's distance = 150 meters.
Since B runs 100 meters when she and S together travel half the circle, B must run 200 meters when she and S together travel the entire circle.
Thus, B's distance = 200 meters.
Result:
Circumference = (S's distance) + (B's distance) = 150+200 = 350 meters.

The correct answer is C.
Last edited by GMATGuruNY on Wed Dec 18, 2013 2:43 am, edited 1 time in total.
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by GmatGreen » Wed Dec 11, 2013 8:45 am
diametrically opposite means completely opposite. Two people have diametrically opposite characters if they are different in every way.

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by [email protected] » Tue Dec 17, 2013 5:54 pm
Hi Mitch,

I have a question if the second time around B runs 200 total why are we not adding to the distance run by Sally? I mean can we assume he was standing still?

=150+200

Could you please explain this part once?

Thanks



GMATGuruNY wrote:
[email protected] wrote:Brenda and Sally run in opposite direction on a circular track, starting at diametrically opposite points. They first meet after Brenda has run 100 meters. They next meet after Sally has run 150 meters past their first meeting point. Each girl runs at a constant speed. What is the length of the track in meters?

A. 250
B. 300
C. 350
D. 400
E. 500
Here's an alternate approach.

1st meeting:
Image
Here, B and S together travel HALF THE CIRCLE.
It is given that B's distance = 100 meters.

2nd meeting:
Image
Here, B and S together travel the ENTIRE CIRCLE.
It is given that S's distance = 150 meters.
Since B runs 100 meters when half the circle is traveled, she must run 200 meters when the entire circle is traveled.
Thus, B's distance = 200 meters.
Result:
Circumference = (S's distance) + (B's distance) = 150+200 = 350 meters.

The correct answer is C.

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by vipulgoyal » Tue Dec 17, 2013 9:45 pm
experts "I DONT GET IT WHATS THE BIG DEAL"

since its clearly mentioned both running aat there constant rate

First time they run half of the circumference.
Second time they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters for the full circle thus the circumference is 200 + 150 = 350

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by [email protected] » Tue Dec 17, 2013 9:52 pm
Hi Vipul,

I can understand your concern!




vipulgoyal wrote:experts "I DONT GET IT WHATS THE BIG DEAL"

since its clearly mentioned both running aat there constant rate

First time they run half of the circumference.
Second time they run full circumference.

First time Brenda runs 100 meters, thus second time she runs 2*100 = 200 meters.

Since second time (when they run full circumference) Brenda runs 200 meters and Sally runs 150 meters for the full circle thus the circumference is 200 + 150 = 350

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by GMATGuruNY » Wed Dec 18, 2013 3:00 am
[email protected] wrote:Hi Mitch,

I have a question if the second time around B runs 200 total why are we not adding to the distance run by Sally? I mean can we assume he was standing still?

=150+200

Could you please explain this part once?

Thanks
Correct!
In the 2nd meeting:
S travels 150 meters, B travels 200 meters.
The sum of the two distances is equal to the circumference of the circle:
150+200 = 350 meters.

In my solution, note the phrases in red:
Here, B and S together travel the ENTIRE CIRCLE.
It is given that S's distance = 150 meters.
Since B runs 100 meters when half the circle is traveled, she must run 200 meters when the entire circle is traveled.
Thus, B's distance = 200 meters.
Result:
Circumference = (S's distance) + (B's distance) = 150+200 = 350 meters.
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I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

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