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A thief was stealing diamonds from a jewellery store. On his way out, he encountered three guards, each was given half of the existing diamonds and two, to cover it by the thief. In the end, he was left with one diamond. How many did the thief steal?

  1. $40$
  2. $36$
  3. $42$
  4. $38$
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Answer: Option B

The thief stole 36 diamonds. Solution:-

Let’s assume that the thief stole $x$ diamonds from the store.

When he encountered the first guard, he gave him half of his diamonds and two more, so he was left with $(x/2) - 2$ diamonds.

When he encountered the second guard, he gave him half of his remaining diamonds and two more, so he was left with $[(x/2) - 2]/2 - 2 = (x-12)/4$ diamonds.

When he encountered the third guard, he gave him half of his remaining diamonds and two more, so he was left with $[(x-12)/2] - 2 = (x-28)/8$ diamonds.

Since he was left with one diamond in the end, we can set up an equation:

$(x-28)/8 = 1$

Solving for $x$ gives us:

$x = 36$

Therefore, the thief stole $36$ diamonds.

Another Way (Short Trick):-

To solve this problem, we can start with one diamond left in the end and add $2$ to get $3$. Double it to get $6$ and add $2$ to get $8$. Double it again to get $16$ and add $2$ to get $18$. Double it again to get $36$. Therefore, the thief stole $36$ diamonds.

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