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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:
This means: \(C \times 42 = S \times 46\)
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:
For the LCM, take the highest power of each prime factor that appears:
\(LCM = 2 \times 3 \times 7 \times 23 = 966\) 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!)
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!
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: \(C \times 42 = S \times 46\)
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:
- \(42 = 2 \times 3 \times 7\)
- \(46 = 2 \times 23\)
For the LCM, take the highest power of each prime factor that appears:
\(LCM = 2 \times 3 \times 7 \times 23 = 966\) 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: \(23 \times 42 = 966\) seconds ✓
- Sabrina: \(966 \div 46 = 21\) laps, so \(21 \times 46 = 966\) 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!
