GMAT Exam > GMAT Questions > Circular gears P and Q start rotating at the ...
Start Learning for Free
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?
- a)6
- b)8
- c)10
- d)12
- e)15
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Circular gears P and Q start rotating at the same time at constant spe...
Understanding Gear Revolutions
To solve the problem, we need to determine the number of revolutions made by each gear over time.
Revolutions per Minute
- Gear P: 10 revolutions per minute (rpm)
- Gear Q: 40 revolutions per minute (rpm)
Revolutions per Second
- Gear P: \( \frac{10 \text{ revolutions}}{60 \text{ seconds}} = \frac{1}{6} \text{ revolutions per second} \)
- Gear Q: \( \frac{40 \text{ revolutions}}{60 \text{ seconds}} = \frac{2}{3} \text{ revolutions per second} \)
Revolutions Over Time
- Let \( t \) be the time in seconds after the gears start rotating.
- Revolutions by Gear P: \( \text{Revolutions}_P = \frac{1}{6}t \)
- Revolutions by Gear Q: \( \text{Revolutions}_Q = \frac{2}{3}t \)
Finding the Difference in Revolutions
- We want to find when Gear Q has made exactly 6 more revolutions than Gear P.
- Set up the equation:
\[ \text{Revolutions}_Q = \text{Revolutions}_P + 6 \]
\[ \frac{2}{3}t = \frac{1}{6}t + 6 \]
Solving the Equation
1. Clear the fractions by multiplying the entire equation by 6:
\[ 6 \cdot \frac{2}{3}t = 6 \cdot \frac{1}{6}t + 36 \]
\[ 4t = t + 36 \]
2. Isolate \( t \):
\[ 4t - t = 36 \]
\[ 3t = 36 \]
\[ t = 12 \]
Conclusion
Thus, Gear Q will have made exactly 6 more revolutions than Gear P after **12 seconds**. The correct answer is option **D**.
To solve the problem, we need to determine the number of revolutions made by each gear over time.
Revolutions per Minute
- Gear P: 10 revolutions per minute (rpm)
- Gear Q: 40 revolutions per minute (rpm)
Revolutions per Second
- Gear P: \( \frac{10 \text{ revolutions}}{60 \text{ seconds}} = \frac{1}{6} \text{ revolutions per second} \)
- Gear Q: \( \frac{40 \text{ revolutions}}{60 \text{ seconds}} = \frac{2}{3} \text{ revolutions per second} \)
Revolutions Over Time
- Let \( t \) be the time in seconds after the gears start rotating.
- Revolutions by Gear P: \( \text{Revolutions}_P = \frac{1}{6}t \)
- Revolutions by Gear Q: \( \text{Revolutions}_Q = \frac{2}{3}t \)
Finding the Difference in Revolutions
- We want to find when Gear Q has made exactly 6 more revolutions than Gear P.
- Set up the equation:
\[ \text{Revolutions}_Q = \text{Revolutions}_P + 6 \]
\[ \frac{2}{3}t = \frac{1}{6}t + 6 \]
Solving the Equation
1. Clear the fractions by multiplying the entire equation by 6:
\[ 6 \cdot \frac{2}{3}t = 6 \cdot \frac{1}{6}t + 36 \]
\[ 4t = t + 36 \]
2. Isolate \( t \):
\[ 4t - t = 36 \]
\[ 3t = 36 \]
\[ t = 12 \]
Conclusion
Thus, Gear Q will have made exactly 6 more revolutions than Gear P after **12 seconds**. The correct answer is option **D**.
|
Explore Courses for GMAT exam
|
|
Similar GMAT Doubts
Top Courses for GMATView all
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer?
Question Description
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer?.
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? for GMAT 2025 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GMAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer?.
Solutions for Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for GMAT.
Download more important topics, notes, lectures and mock test series for GMAT Exam by signing up for free.
Here you can find the meaning of Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute and Gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P ?a)6b)8c)10d)12e)15Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice GMAT tests.
|
|
Explore Courses for GMAT exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup