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Justin and Joe started driving eastwards from point A and point B respectively, where point B was 8 kilometres east of point A. If Justin stopped for a break after every 12 kilometres and Joe stopped for a break after every 10 kilometres, what was the number of points within a distance of 230 kilometres east of point A at which both Justin and Joe stopped for a break?
- a)1
- b)2
- c)3
- d)4
- e)5
Correct answer is option 'D'. Can you explain this answer?
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Justin and Joe started driving eastwards from point A and point B resp...
Given:
- Justin started from point A and Joe started from point B traveling eastwards
- Point B was 8 kilometres eastwards of point A
- Justin stopped for break after every 12 kilometres
- Joe stopped for break after every 10 kilometres
To Find: Number of common points within a distance of 230 kilometres from point A where Justin and Joe both stopped for a break?
Approach:
- Had both Justin and Joe started from the same point, they would have taken a break at the same point at an interval of every LCM (10, 12) kilometres.
- However as Joe started from a point, that was 8 kilometres east of Justing, our first task would be to find the first common point at which Justin and Joe stopped.
- From the first common point, Justin and Joe would break at the common points at an interval of every LCM (10, 12) kilometres.
Working out:
- Justin would take a break at 12, 24, 36, 48, 60..kilometres from point A
- Joe would take a break at 10, 20, 30, 40, 50, 60…. Kilometres from point B
- However, as point B is 8 kilometres east of point A, Joe would take a break at (10+8, 20+8, 30+8, 40+8…) kilometres from point A
- Comparing the points at which Justin and Joe take a break, we can see that the first common point at which both of them took a break is 48 kilometres from point A.
- Now, LCM(10, 12) = 60
- So, Justin and Joe would take a break at points (48+60), (48+120), (48+180) kilometres from point A. All the other points would be outside the range of 230 kilometres from point A
- So, Justin and Joe took a break at 48, 108, 168, 228 kilometres from point A, i.e. a total of 4 points.
Answer : D
Most Upvoted Answer
Justin and Joe started driving eastwards from point A and point B resp...
Understanding the Problem
To find the points where both Justin and Joe stop for a break within 230 kilometers east of point A, we first need to establish their stopping points based on their respective distances.
Justin's Stopping Points
- Justin starts at point A (0 km) and stops every 12 kilometers.
- His stopping points are: 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228.
Joe's Stopping Points
- Joe starts at point B (8 km) and stops every 10 kilometers.
- His stopping points are: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168, 178, 188, 198, 208, 218, 228.
Finding Common Stopping Points
Now, we need to find the common stopping points within the range of 0 to 230 kilometers:
- Justin's points: 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228.
- Joe's points: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168, 178, 188, 198, 208, 218, 228.
Common Points
The common points where both Justin and Joe stop are:
- 48, 108, 168, 228.
Conclusion
- There are 4 points within a distance of 230 kilometers east of point A where both Justin and Joe stopped for a break. Thus, the correct answer is option D.
To find the points where both Justin and Joe stop for a break within 230 kilometers east of point A, we first need to establish their stopping points based on their respective distances.
Justin's Stopping Points
- Justin starts at point A (0 km) and stops every 12 kilometers.
- His stopping points are: 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228.
Joe's Stopping Points
- Joe starts at point B (8 km) and stops every 10 kilometers.
- His stopping points are: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168, 178, 188, 198, 208, 218, 228.
Finding Common Stopping Points
Now, we need to find the common stopping points within the range of 0 to 230 kilometers:
- Justin's points: 0, 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228.
- Joe's points: 8, 18, 28, 38, 48, 58, 68, 78, 88, 98, 108, 118, 128, 138, 148, 158, 168, 178, 188, 198, 208, 218, 228.
Common Points
The common points where both Justin and Joe stop are:
- 48, 108, 168, 228.
Conclusion
- There are 4 points within a distance of 230 kilometers east of point A where both Justin and Joe stopped for a break. Thus, the correct answer is option D.
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Justin and Joe started driving eastwards from point A and point B respectively, where point B was 8 kilometres east of point A. If Justin stopped for a break after every 12 kilometres and Joe stopped for a break after every 10 kilometres, what was the number of points within a distance of 230 kilometres east of point A at which both Justin and Joe stopped for a break?a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?
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Justin and Joe started driving eastwards from point A and point B respectively, where point B was 8 kilometres east of point A. If Justin stopped for a break after every 12 kilometres and Joe stopped for a break after every 10 kilometres, what was the number of points within a distance of 230 kilometres east of point A at which both Justin and Joe stopped for a break?a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Justin and Joe started driving eastwards from point A and point B respectively, where point B was 8 kilometres east of point A. If Justin stopped for a break after every 12 kilometres and Joe stopped for a break after every 10 kilometres, what was the number of points within a distance of 230 kilometres east of point A at which both Justin and Joe stopped for a break?a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Justin and Joe started driving eastwards from point A and point B respectively, where point B was 8 kilometres east of point A. If Justin stopped for a break after every 12 kilometres and Joe stopped for a break after every 10 kilometres, what was the number of points within a distance of 230 kilometres east of point A at which both Justin and Joe stopped for a break?a)1b)2c)3d)4e)5Correct answer is option 'D'. Can you explain this answer?.
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