Question: 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 then, and 2 more besides. He escaped with one diamond. How many did he steal originally?

(a) 40
(b) 30
(c) 25
(d) 30
(e) None of these

Correct Answer: (E)
Solution and Explanation:
Approach Solution 1:

Let x be the total number of diamond thieves at any given time.
As a result, each time a watchman receives a diamond, he will always have =x - (x/2+2) = ( x - 4) / 2.
2

We can state: (x - 4)/2 = 1
X = 6 when the moment following the third witness is taken into account.
Before running into the third watchman, the robber had six gems.

We can state: (x- 4) / 2 = 6
(x = 16) when the second watchman is encountered.
Before coming across the second watchman, the burglar had 16 gems.

We can state: (x - 4) / 2 = 16
x=36 when the first watchman is encountered.
Before coming across the first watchman, the robber had 36 gems.

Approach Solution 2:
Given that, despite having three watchmen on duty to protect his diamonds, the owner of a nearby jewellery store nonetheless had some diamonds stolen. The thief encountered each watchman individually as they were leaving. He gave each person half of the gems they already possessed plus an additional two. He got away with just one diamond.

The thief left with 1 diamond at the end
Ao at last watchmen, Thief had (1+2)*2= 6 diamonds
At 2nd watchmen, he had = (6+2)*2 = 16 Diamonds
At 1st watchmen, he had = (16+2)*2 = 36 Diamonds

Approach Solution 3:
Let’s assume the total number of diamonds be x

Then the thief offers to watchman one = 1/2x + 2
Therefore, Remaining : x - 1/2x - 2 = 1/2x - 2

The thief offers to watchman two:
1/2(1/2x - 2)+ 2 = 1/4x - 1 + 2 = 1/4 x + 1
Therefore, Remaining : 1/2x - 2 - 1/4x - 1 = 1/4x - 3

The thief offers to watchman 3:
= 1/2(1/4x - 3) + 2 = 1/8x - 1.5 + 2 = 1/8x + 0.5
Therefore, Remaining : 1/4x - 3 - 1/8x - 0.5 = 1/8x - 3.5

1/8x - 3.5 = 1
1/8x = 4.5
x = 4.5 × 8
x = 36
Therefore, the total number of diamonds was 36 diamonds.

“The owner of a local jewellery store hired 3 watchmen to guard his diamonds" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”. To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The candidates must go through GMAT Quant practice papers that will enable them to enhance their mathematical understanding.

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