Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining

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Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

(1) The investor owns 100 shares of Company Y stock.
(2) The investor owns 200 more shares of Company X stock than of Company Y stock.



OA D

Source: GMAT Prep

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BTGmoderatorDC wrote:
Wed Oct 05, 2022 4:54 pm
Of the shares of stock owned by a certain investor, 30 percent are shares of Company X stock and 1/7 of the remaining shares are shares of Company Y stock. How many shares of Company X stock does the investor own?

(1) The investor owns 100 shares of Company Y stock.
(2) The investor owns 200 more shares of Company X stock than of Company Y stock.



OA D

Source: GMAT Prep
Let \(N\) be the number of total shares the investor owns.
\(0.3 N =\) number of Company \(X\) stock he owns
\(1/7\) of \(0.7 N\) (the remaining shares) \(= 0.1 N =\) number of Company \(Y\) stock he owns

Goal is to calculate \(N\). \(X\) is \(30\%\) of \(N\) (which is what we are asked to calculate).

Statement 1:
\(100 Y\) shares and we know \(Y\) shares are \(10\%\) of the total \(N\).
\(0.1 N = 100\). \(N\) is therefore \(1,000\). Sufficient \(\Large{\color{green}\checkmark}\)

Statement 2:
He owns \(30\%\) \(N\) shares and \(10\%\) \(Y\) shares. And that differential is \(200\).
\(0.3 N - 0.1 N = 200\). \(N\) is therefore \(1,000\). Sufficient \(\Large{\color{green}\checkmark}\)

Hence, D