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First, I prepared the grignard reagent then performed nucleophilic addition to the carbonyl carbon and then did hydrolysis.

So basically in my product, $\ce{-Br}$ is replaced by $\ce{-CH2OH}$

But answer given is:

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Why is my mechanism wrong?

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Grignard reagents are capable of rearranging, especially in this situation where there is significant strain. The specific vinyl bromide you drew here has been studied: J. Org. Chem., 1974, 39 (10), pp 1411–1416. The table of data shown below is hard to read without including more of the text, but it was found that at 66 C in THF, after 5-10 minutes, 41% of the initial Grignard had undergone rearrangement, so this is a fairly likely process.

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A potential mechanism for the rearrangement is: enter image description here

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