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

Question

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

A. 21
B. 23
C. 42
D. 46
E. 48

PS12151.02

lacktutor · Accepted Answer

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)

BrentGMATPrepNow · Answer

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  42   C   = 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  46   S   = 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 :  42   C   =  46   S  
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:  42   C   =  46   S  
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

chetan2u · Answer

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

KarishmaB · Answer

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)

effatara · Answer

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

ScottTargetTestPrep · Answer

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

Fdambro294 · Answer

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-

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=Ca_GMY_B_V4

KarishmaB · Answer

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

https://www.youtube.com/watch?v=Jz-mSB1xNFY

egmat · Answer

This is a classic "meeting point" problem that trips up a lot of students. Let me walk you through how to think about this systematically.

Here's the key insight you need:  Candice and Sabrina will be together at the starting point again when both have completed  whole numbers of laps  at exactly the same moment. This isn't about one catching up to the other on the track—it's about finding when their lap times sync up perfectly.

Let's work through this step by step:

Step 1: Understand what we're looking for

We need a time when:
 
 Candice completes some whole number of laps (let's call it C laps) 
 Sabrina completes some whole number of laps (let's call it S laps)  
 They both finish at exactly the same moment

This means:  C 	imes 42 = S 	imes 46

The smallest such time is the Least Common Multiple (LCM) of their lap times.

Step 2: Find the LCM of 42 and 46

First, let's break down each number into prime factors:
 
  42 = 2 	imes 3 	imes 7  
  46 = 2 	imes 23

For the LCM, take the highest power of each prime factor that appears:
 LCM = 2 	imes 3 	imes 7 	imes 23 = 966  seconds

So after 966 seconds, both cyclists will be at the starting point together for the first time.

Step 3: Calculate Candice's laps

Since Candice completes each lap in 42 seconds:
 Number\ of\ laps = \frac{966}{42} = 23  laps

Step 4: Verify (always a good habit!) 
 
 Candice:  23 	imes 42 = 966  seconds ✓ 
 Sabrina:  966 \div 46 = 21  laps, so  21 	imes 46 = 966  seconds ✓

Answer: B (23)

Watch out for this trap:  Notice that Sabrina completes 21 laps in the same time. Don't accidentally pick answer choice A—the question asks specifically about Candice!

---

While this solution gets you to the right answer, there's a much deeper systematic framework for recognizing and solving all LCM timing problems efficiently. You can check out the  complete step-by-step solution on Neuron by e-GMAT  to understand the underlying patterns and learn how to spot these problem types instantly. You can also explore detailed solutions for  hundreds of other GMAT official questions on Neuron , with comprehensive explanations, common faltering points, and practice quizzes that help you build systematic accuracy.

Hope this helps!

Amazingakhil · Answer

They meet at the starting point again when time is LCM of lap times (42 and 46).
Factor: 42 = 2×3×7, 46 = 2×23 ⇒ LCM = 2×3×7×23 = 966 seconds.
In 966 seconds, Candice completes = 966 ÷ 42 = 23 laps.

So, when they next meet at the start, Candice has done 23 laps.

BongBideshini · Answer

Since Candice is faster, she will complete more laps in the same total timeframe. 
Candice's Laps × Candice's Time = Sabrina's Laps × Sabrina's Time
Candice's Laps × 42 = Sabrina's Laps × 46
Candice's Laps / Sabrina's Laps = 46 / 42 =  2  3 / 21 
 Candice completed 23 laps.

Ans B

topnotch123 · Answer

I got this wrong because I took Candice's speed as L/42 and Sabrina's speed as L/46, then used the difference in their speeds as their relative speed. I divided the total distance L by that relative speed and got 21×23 = 483 seconds.
I didn't realize that 483 seconds is just the time until they meet each other again, not the time until they meet at the starting point. At 483 seconds, Candice is one lap ahead of Sabrina, but they are both halfway around the track. They need another 483 seconds to be together at the starting point, giving 966 seconds.
So my mistake was specifically using relative speed to answer a starting-point question?

Bunuel · Answer

Yes. Your relative-speed calculation is correct, but it answers a different question:  when will they next meet anywhere on the track?
 
At 483 seconds, Candice has completed 483/42 = 11.5 laps and Sabrina 483/46 = 10.5 laps, so they meet halfway around the track.

The question asks when they are next together  at the starting point , so each must have completed a whole number of laps. That occurs at 483 * 2 = 966 seconds.

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

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