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

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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

1. X is 300 shares

2. X is 300 shares

Explanation:

Going by the fact that the investor has a portfolio containing three companies' shares, the shares owned in company X can ascertained as follows:

In the first instance, the investor had 100 shares of company Y:

the shares in company Y is 1/7 after 30% held in company X has been deducted, i. e 1/7 * (1-30%) = 1/7*0.7=0.1

0.1 is 10%, the shares in company Y is 10% of the entire portfolio

The entire portfolio is = 100/0.1=1000 shares

Number of shares held in company X = 1000*30%=300 shares

In the second instance:

The investor had 200 more shares in X than Y, which can be interpreted mathematically thus:

0.3*entire portfolio-200 shares=0.1*entire portfolio

let entire portfolio be P

0.3P-200 shares=0.1P

0.3P-0.1P=200 shares

0.2P = 200 shares

P=200 Shares/0.2

P=1000 shares

X is 30% of P=1000*30%=300 shares