An investment manager is considering 3 stocks, P, Q, and R for her portfolio. For the cost of 1 share of P, she could buy 3 shares of Q or 5 shares of R. If she invested an amount equal to the cost of 4500 shares of Q but purchased equal numbers of shares of P and R and no shares of Q, how many shares of R did she buy?

Correct answer marked below

250

625

1250

Correct

3,650

3,750

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Explanation

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Official Explanation

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According to the question,

P=3Q=5R

Investment manager is investing 4500Q amount in 2 parts. Let's say x in stock P and 4500Q - x in stock R.

According to the question,

\frac{x}{P}=\frac{4500Q-x}{R}

⇒\frac{x}{3Q}=\frac{4500Q-x}{\frac{3Q}{5}}

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What this question tests

Your ability to convert between fractions, ratios, and decimals and to reason proportionally.

Cross-multiplying incorrectly or mixing up the ratio parts — a part:part ratio is not a fraction of the whole.