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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar

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parkhydel
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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   27 Apr 2020, 15:48
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Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483


PS12151.02
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B
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BrentGMATPrepNow
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   01 May 2020, 12:08
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parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483

Before solving the question, let's make sure we fully understand what the question tells us AND the implications.

Given: Candice can complete one lap in 42 seconds.
So, after 42 seconds, Candice will be at the starting point (and she will have completed 1 lap).
After 84 seconds, Candice will be at the starting point (and she will have completed 2 laps).
After 126 seconds, Candice will be at the starting point (and she will have completed 3 laps).
After 168 seconds, Candice will be at the starting point (and she will have completed 4 laps).
etc...
If we let C = the number of laps Candice has completed, then 42C = Candice's total running time


Given: Sabrina can complete one lap in 46 seconds.
So, after 46 seconds, Sabrina will be at the starting point (and she will have completed 1 lap).
After 92 seconds, Sabrina will be at the starting point (and she will have completed 2 laps).
After 138 seconds, Sabrina will be at the starting point (and she will have completed 3 laps).
After 184 seconds, Sabrina will be at the starting point (and she will have completed 4 laps).
etc...
If we let S = the number of laps Sabrina has completed, then 46S = Sabrina's total running time

How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?
If Candice and Sabrina were together at the starting point, then we know that : 42C = 46S
Aside: Keep in mind that, in order for both people to be at the starting point, C and S must both be positive integers

So, we're looking for the smallest possible integer value of C such that: 42C = 46S
To make things a bit easier on ourselves, let's divide both sides of the equation by 2 to get: 21C = 23S
At this point, we can see that the smallest possible (positive) values of C and S are C = 23 and S = 21.

In other words, after Candice completes 23 laps, and Sabrina completes 21 laps, both runners will be together at the starting point.

Answer: B

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Brent
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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   27 Apr 2020, 16:53
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Candice —42 seconds
Sabrina —46 seconds
—> LCM ( 42, 46) = 2*21*23 = 966 seconds

They will meet together at the starting point after 966 seconds.
—> 966/42 = 23 laps ( for Candice)

Answer (B)

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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   01 May 2020, 04:24
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parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483


PS12151.02

Candice completes each round in 42 seconds, so she will be back at the starting point after every 42 seconds, so after 42*1, then 42*2 and so on.
Similarly Sabrina will be back at the starting point after every 46 seconds..46*1 , then 46*2 and so on.

So we look for TIME that would be multiple of 42 and 46, or in other words we are looking for the LCM.
LCM(42,46) = LCM({2*3*7},{2*23})=2*3*7*23=42*23=21*46

Now, Candice would have done \(\frac{42*23}{42}\) or 23 laps at the rate of 42 secs per lap.
Similarly, Sabrina would have done \(\frac{46*21}{46}\) or 21 laps at the rate of 46 secs per lap.


B. 23
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   02 May 2020, 08:02
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If Candice had taken 1 second and Sabrina 2 seconds to complete a lap then the ratio of their speeds would have been 2:1 (inverse of their respective timings) and they would have met at the starting point after Candice had completed 2 laps and Sabrina 1 lap. By the same token:
Candice's speed: Sabrina's speed = 46:42 = 23:21 and they will meet at the starting point after Candice and Sabrina complete 23 and 21 laps respectively.
ANS: B
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   04 May 2020, 23:19
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parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483


PS12151.02

They both start together from S.

At what time points will candice reach S again?

Candice reaches S again after: 42 sec (1 lap done), 2*42 secs (2 laps done), 3*42 secs (3 laps done), 4*42 secs ... (all multiples of 42)
Sabrina reaches S again after: 46 sec (1 lap done), 2*46 sec (2 laps done), 3*46 secs (3 laps done), 4*46 secs ... (all multiples of 46)

When will they both reach S together again? At a time which is the first common multiple of 42 and 46.
LCM of 42 and 46 is 42 * 23. At this time, Candice would have completed 23 laps.

Answer (B)
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   25 Jul 2020, 14:29
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parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483


PS12151.02

Solution:

Let’s let C = the integer number of laps that Candice completes; since her rate is 42 seconds per lap, then the expression 42C is the time when Candice passes the starting point. For example, when C = 1, then 42C = 42, and she has passed the starting point at the 42-second mark. When C = 2, then 42C = 84, and she has again passed the starting point at the 84-second mark.

Similarly, if we let S = the integer number of laps that Sabrina completes, then 46S is the time when Sabrina passes the starting point. For example, when S = 2, then 46S = 92, and she has passed the starting point at the 92-second mark.

We want to ascertain the number of laps that Candice has completed when the two runners again pass the starting point simultaneously. Thus, we equate the two expressions:

42C = 46S

21C = 23S

We see that we have equality if C = 23 and S = 21. Thus, Candice will have completed 23 laps when the two women pass the starting point simultaneously.

Answer: B
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   10 Sep 2020, 22:34
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Concept: They will both meet at the Starting Point at the Exact Time that is the LCM of the Time it takes them to complete 1 lap Each

Find the LCM (42 seconds and 46 seconds) = 2 * 3 * 7 * 23 = 966 seconds will pass when they meet at the Starting Point.


In Those 966 Seconds, at a Speed of 42 Seconds per lap, Candice will finish 23 laps (966 / 42 = 23)

-B-
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   04 Aug 2021, 02:37
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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   27 Oct 2023, 03:08
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parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483


PS12151.02

Check out this video discussing the basics of circular motion and a one minute solution to this problem:

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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   02 Jun 2024, 03:46
 
BrentGMATPrepNow
parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A.  21
B.  23
C.  42
D.  46
E. 483

 
Before solving the question, let's make sure we fully understand what the question tells us AND the implications.

Given: Candice can complete one lap in 42 seconds.
So, after 42 seconds, Candice will be at the starting point (and she will have completed 1 lap).
After 84 seconds, Candice will be at the starting point (and she will have completed 2 laps).
After 126 seconds, Candice will be at the starting point (and she will have completed 3 laps).
After 168 seconds, Candice will be at the starting point (and she will have completed 4 laps).
etc...
If we let C = the number of laps Candice has completed, then 42C = Candice's total running time


Given: Sabrina can complete one lap in 46 seconds.
So, after 46 seconds, Sabrina will be at the starting point (and she will have completed 1 lap).
After 92 seconds, Sabrina will be at the starting point (and she will have completed 2 laps).
After 138 seconds, Sabrina will be at the starting point (and she will have completed 3 laps).
After 184 seconds, Sabrina will be at the starting point (and she will have completed 4 laps).
etc...
If we let S = the number of laps Sabrina has completed, then 46S = Sabrina's total running time

How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?
If Candice and Sabrina were together at the starting point, then we know that : 42C = 46S
Aside: Keep in mind that, in order for both people to be at the starting point, C and S must both be positive integers

So, we're looking for the smallest possible integer value of C such that: 42C = 46S
To make things a bit easier on ourselves, let's divide both sides of the equation by 2 to get: 21C = 23S
At this point, we can see that the smallest possible (positive) values of C and S are C = 23 and S = 21.

In other words, after Candice completes 23 laps, and Sabrina completes 21 laps, both runners will be together at the starting point.

Answer: B

Cheers,
Brent
­
Hi BrentGMATPrepNow ,

could you please explain why "If Candice and Sabrina were together at the starting point, then we know that : 42C = 46S"?
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Re: Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   03 Jul 2024, 15:45
I don't know if my approach is correct but this how I solved, please let me know if it is just a fluke that I got the answer right or this logic makes sense:

Difference in time for C & S = 46-42 = 4 seconds

Now, to find when will Candice meet Sabrina, C has to do 4 * X laps such that 46 is divisible by X. So, I tried 46/4 is non-Interger, thus (A) eliminated. Next, 46*2/4 = 23 (Integer) so (B) is the answer

Request inputs from experts!
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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink] Yesterday, Candice and Sabrina trained for a bicycle race by riding ar   26 Aug 2024, 04:55
LCM of 42 and 46 = 23*42 (I didn't calculate it fully because I knew this isn't imp and would save time)

Then ques is asking about Candice, her time was 42 seconds only. So Laps = 23*42/42 which is 23.

20 seconds to ans hardly. Give Kudoss
parkhydel
Yesterday, Candice and Sabrina trained for a bicycle race by riding around an oval track. They both began riding at the same time from the track's starting point. However, Candice rode at a faster pace than Sabrina, completing each lap around the track in 42 seconds, while Sabrina completed each lap around the track in 46 seconds. How many laps around the track had Candice completed the next time that Candice and Sabrina were together at the starting point?

A. 21
B. 23
C. 42
D. 46
E. 483


PS12151.02
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Yesterday, Candice and Sabrina trained for a bicycle race by riding ar [#permalink]
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