The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is

## Concept & Logic When you have the product and the quotient of two numbers, multiplying these two values together cleverly cancels out the smaller number, giving you the square of the larger number directly. $$ (x \times y) \times \left(\frac{x}{y}\right) = x^2 $$ ## Step-by-Step Solution * **Given:** Let the larger number be $x$ and the smaller number be $y$. Product: $xy = 9375$ Quotient: $\frac{x}{y} = 15$ * **Calculation / Deduction:** * From the quotient, we can express $x$ in terms of $y$: $x = 15y$. * Substitute this into the product equation: * $(15y) \times y = 9375$ * $15y^2 = 9375$ * Divide by 15: * $y^2 = \frac{9375}{15}$ * $y^2 = 625$ * Take the square root (ignoring the negative root as aptitude questions typically assume positive numbers unless stated otherwise): * $y = 25$ * Now find $x$: $x = 15 \times 25 = 375$. * The question asks for their sum: $x + y = 375 + 25 = 400$. ## Exam Strategy & Shortcut **Direct Multiplication Method:** Multiply the product by the quotient to get the square of the larger number: $9375 \times 15$. To avoid huge numbers, divide the product by the quotient to get the square of the smaller number: $9375 / 15 = 625$. Immediately you know $y = 25$. Then $x$ is just $15$ times that ($375$). Sum is $400$. ## Common Pitfall Finding the two numbers ($375$ and $25$) and then hastily looking for $375$ in the options, forgetting that the final question asks for the **sum** of the two numbers. Always re-read the final sentence of the prompt before selecting an option. ## Final Answer **Therefore, the correct answer is 400.**