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GMAT Inequalities is a high-frequency topic in GMAT Quant, but many students struggle because the concepts behave differently from standard algebra. Understanding the right rules, patterns, and edge cases can significantly improve both speed and accuracy.- May 06
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16 Feb 2025, 09:47
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A factory has three machines: A, B, and C.
- Machine A alone can complete a task in 6 hours.
- Machine B alone can complete the same task in 4 hours.
- Machine C alone can complete it in 3 hours.
All three machines start working together, but after 1 hour, Machine C breaks down and stops. Machine A and B continue working for another 2 hours, after which Machine A also stops. How much longer will it take for Machine B to finish the remaining work?
Solution Approach:
Step 1: Work Done Per Hour
- Machine A’s rate: 1/6 of the task per hour
- Machine B’s rate: 1/4 of the task per hour
- Machine C’s rate: 1/3 of the task per hour
- Together, their combined rate:
1/6 + 1/4 + 1/3
Finding a common denominator (12):
2/12 + 3/12 + 4/12 = 9/12 = 3/4
So, when all three machines work together, they complete 3/4 of the task per hour
Step 2: Work Done in 1 Hour (Before C Breaks Down)
1 × 3/4 = 3/4
So, 3/4 of the task is completed, and 1/4 of the task remains
Step 3: Work Done in the Next 2 Hours (Only A and B Working)
- A and B together work at a rate of:
1/6 + 1/4 = 2/12 + 3/12 = 5/12
- In 2 hours, they complete:
2 × 5/12 = 10/12 = 5/6
Step 4: Remaining Work
- The total task was 1, and so far, we've completed:
3/4 + 5/6
Converting to a common denominator (12):
9/12 + 10/12 = 19/12
But since the task is only 1 whole unit, we see they’ve overcompleted the task
Final Answer:
After 1 hour of all machines working together and 2 hours of A & B working together, the task is already completed
Takeaway:
This problem highlights the importance of checking your work carefully before assuming a final step is needed. The GMAT loves to test whether you’re blindly following a formula or actually thinking through the problem logically.
Would you have caught this before continuing? Let me know in the comments!
- Machine A alone can complete a task in 6 hours.
- Machine B alone can complete the same task in 4 hours.
- Machine C alone can complete it in 3 hours.
All three machines start working together, but after 1 hour, Machine C breaks down and stops. Machine A and B continue working for another 2 hours, after which Machine A also stops. How much longer will it take for Machine B to finish the remaining work?
Solution Approach:
Step 1: Work Done Per Hour
- Machine A’s rate: 1/6 of the task per hour
- Machine B’s rate: 1/4 of the task per hour
- Machine C’s rate: 1/3 of the task per hour
- Together, their combined rate:
1/6 + 1/4 + 1/3
Finding a common denominator (12):
2/12 + 3/12 + 4/12 = 9/12 = 3/4
So, when all three machines work together, they complete 3/4 of the task per hour
Step 2: Work Done in 1 Hour (Before C Breaks Down)
1 × 3/4 = 3/4
So, 3/4 of the task is completed, and 1/4 of the task remains
Step 3: Work Done in the Next 2 Hours (Only A and B Working)
- A and B together work at a rate of:
1/6 + 1/4 = 2/12 + 3/12 = 5/12
- In 2 hours, they complete:
2 × 5/12 = 10/12 = 5/6
Step 4: Remaining Work
- The total task was 1, and so far, we've completed:
3/4 + 5/6
Converting to a common denominator (12):
9/12 + 10/12 = 19/12
But since the task is only 1 whole unit, we see they’ve overcompleted the task
Final Answer:
After 1 hour of all machines working together and 2 hours of A & B working together, the task is already completed
Takeaway:
This problem highlights the importance of checking your work carefully before assuming a final step is needed. The GMAT loves to test whether you’re blindly following a formula or actually thinking through the problem logically.
Would you have caught this before continuing? Let me know in the comments!
16 Feb 2025, 10:14
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Thanks for sharing and posting!
Does the question have answer choices by chance?
Does the question have answer choices by chance?
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