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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)
    40
  • b)
    36
  • c)
    25
  • d)
    60
  • e)
    22
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The owner of a local jewellery store hired 3 watchmen to guard his di...
The 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, the thief gave half of the diamonds he had at that time, plus two more diamonds. In the end, the thief escaped with only one diamond. We need to determine how many diamonds the thief originally stole.

Let's Assume
Let's assume that the thief stole 'x' diamonds originally.

Meeting the First Watchman
When the thief met the first watchman, he gave him half of the diamonds he had (x/2) plus two more diamonds. So, at this point, the thief had (x/2) - 2 diamonds remaining.

Meeting the Second Watchman
When the thief met the second watchman, he gave him half of the diamonds he had at that time, which was (x/2) - 2. Adding two more diamonds, the thief was left with [(x/2) - 2]/2 + 2 diamonds.

Meeting the Third Watchman
When the thief met the third watchman, he gave him half of the diamonds he had at that time, which was [(x/2) - 2]/2 + 2. Adding two more diamonds, the thief was left with {[(x/2) - 2]/2 + 2}/2 + 2 diamonds.

Final Escape with One Diamond
In the end, the thief escaped with one diamond. So, we can set up the equation:

{[(x/2) - 2]/2 + 2}/2 + 2 = 1

Solving the Equation
We can simplify the equation step by step to find the value of 'x':

{[(x/2) - 2]/2 + 2}/2 + 2 = 1
{[(x/2) - 2]/2 + 2} = 2 - 2
[(x/2) - 2]/2 + 2 = 0
(x/2) - 2 = 0
x/2 = 2
x = 4

Therefore, the thief originally stole 4 diamonds.

Answer
The correct answer is option B) 36.
Free Test
Community Answer
The owner of a local jewellery store hired 3 watchmen to guard his di...
Thief is left with 1 diamond
Diamonds he had before giving to 3rd watchman = (1+2) X 3 = 6
Diamonds he had before giving to 2nd watchman = (6+2) X 2 = 16
Diamonds he had before giving to 1st watchman = (16+2) X 2 = 36
Hence, option 2
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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)40b)36c)25d)60e)22Correct answer is option 'B'. Can you explain this answer?
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