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The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?
- a)36
- b)25
- c)640
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The owner of a local jewellery store hired 3 watchmen to guard his di...
At last thief is left with one diamond.
Hence, the number of diamonds before he gave some diamonds to the third watchman,
x − 42 = 1
or x = 6
Hence, he had 6 diamonds before he gave 5 to the third watchman.
Similarly number of diamonds before giving to second watchman,
or, x = 16
And number of diamonds before giving to the first watchman,
x − 42 = 16
or, x = 36
∴ The thief has stolen 36 diamonds originally
Hence, the correct option is (A).
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The owner of a local jewellery store hired 3 watchmen to guard his di...
Problem:
The owner of a local jewelry store hired 3 watchmen to guard his diamonds, but a thief still managed to steal some diamonds. On the way out, the thief met each watchman, one at a time. To each watchman, he gave half of the diamonds he had then and 2 more besides. The thief managed to escape with just one diamond. How many diamonds did he steal originally?
Solution:
Let's assume the number of diamonds the thief stole originally is 'x'.
Meeting with the first watchman:
When the thief met the first watchman, he gave him half of the diamonds he had then and 2 more besides. Therefore, the first watchman received (x/2) + 2 diamonds.
Meeting with the second watchman:
When the thief met the second watchman, he again gave him half of the diamonds he had then and 2 more besides. Therefore, the second watchman received [(x/2) + 2]/2 + 2 diamonds.
Meeting with the third watchman:
When the thief met the third watchman, he once again gave him half of the diamonds he had then and 2 more besides. Therefore, the third watchman received [[(x/2) + 2]/2 + 2]/2 + 2 diamonds.
Thief's escape:
The thief managed to escape with just one diamond, so the number of diamonds he had when he met the third watchman was 1.
Equation:
We can set up an equation to solve for 'x', the original number of diamonds stolen:
[[[(x/2) + 2]/2 + 2]/2 + 2] = 1
Solving the equation:
Simplifying the equation step by step:
1. [[(x/2) + 2]/2 + 2]/2 + 2 = 1
2. [(x/2) + 2]/2 + 2 = 1
3. (x/2) + 2 = 1 - 2
4. (x/2) + 2 = -1
5. (x/2) = -1 - 2
6. (x/2) = -3
7. x = -3 * 2
8. x = -6
Conclusion:
The solution 'x = -6' means that the thief stole negative 6 diamonds, which is not possible in this scenario since the thief cannot steal a negative number of diamonds. Therefore, the correct answer is 'None of these' (option D).
The owner of a local jewelry store hired 3 watchmen to guard his diamonds, but a thief still managed to steal some diamonds. On the way out, the thief met each watchman, one at a time. To each watchman, he gave half of the diamonds he had then and 2 more besides. The thief managed to escape with just one diamond. How many diamonds did he steal originally?
Solution:
Let's assume the number of diamonds the thief stole originally is 'x'.
Meeting with the first watchman:
When the thief met the first watchman, he gave him half of the diamonds he had then and 2 more besides. Therefore, the first watchman received (x/2) + 2 diamonds.
Meeting with the second watchman:
When the thief met the second watchman, he again gave him half of the diamonds he had then and 2 more besides. Therefore, the second watchman received [(x/2) + 2]/2 + 2 diamonds.
Meeting with the third watchman:
When the thief met the third watchman, he once again gave him half of the diamonds he had then and 2 more besides. Therefore, the third watchman received [[(x/2) + 2]/2 + 2]/2 + 2 diamonds.
Thief's escape:
The thief managed to escape with just one diamond, so the number of diamonds he had when he met the third watchman was 1.
Equation:
We can set up an equation to solve for 'x', the original number of diamonds stolen:
[[[(x/2) + 2]/2 + 2]/2 + 2] = 1
Solving the equation:
Simplifying the equation step by step:
1. [[(x/2) + 2]/2 + 2]/2 + 2 = 1
2. [(x/2) + 2]/2 + 2 = 1
3. (x/2) + 2 = 1 - 2
4. (x/2) + 2 = -1
5. (x/2) = -1 - 2
6. (x/2) = -3
7. x = -3 * 2
8. x = -6
Conclusion:
The solution 'x = -6' means that the thief stole negative 6 diamonds, which is not possible in this scenario since the thief cannot steal a negative number of diamonds. Therefore, the correct answer is 'None of these' (option D).
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The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?a)36b)25c)640d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?a)36b)25c)640d)None of theseCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?a)36b)25c)640d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The owner of a local jewellery store hired 3 watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/2 of the diamonds he had then and 2 more besides. He escaped with one diamond. How many did he steal originally?a)36b)25c)640d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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