Question

The following question accompanied by three statements I, II and III. We have to determine which statements is/are sufficient to answer the question.

What is the sum of two numbers?

I. The bigger of these two numbers is $6$ more than the smaller number.

II. $40\%$ of the smaller number is equal to $30\%$ of the bigger number.

III. The ratio between half of the bigger number and one-third of the smaller number is $2:1.$

• A. Only II and II are sufficient
• B. Only I and II are sufficient
• C. I and either II or III is sufficient
• D. All, I, II, and III together are sufficient

Answer 1

Answer: (C)

I and either II or III is sufficient

From the given statements we can make the following equations.
(I) $y=x+6$
(II) $0.4x=0.3y$
$\Rightarrow$ $\frac{x}{y}=\frac{3}{4}$
(III) $\Rightarrow \frac{\frac{y}{2}}{\frac{x}{3}}=\frac{2}{1}\Rightarrow \frac{y}{x}=\frac{4}{3}\Rightarrow \frac{x}{y}=\frac{3}{4}$
Obviously, question can be solved by using (I) and either (II) or (III)
because equations (II) and (III) are same.