GMAT Quantitative Reasoning Practice Test 1

Let $\mathit{x}=$ the smaller integer. The ratio of 1 to 4 can be written as $1\mathit{x}$ to $4\mathit{x}$ or $\mathit{x}∕4\mathit{x}$. Add 6 to the smaller integer, set the ratio equal to $1∕2$, and solve: $\frac{\mathit{x}+6}{4\mathit{x}}=\frac{1}{2}$
Cross-multiply to get $2\mathit{x}+12=4\mathit{x}$. Subtract $2\mathit{x}$ from both sides of the equation. $2\mathit{x}-2\mathit{x}+12=4\mathit{x}-2\mathit{x}.12=2\mathit{x}$, so $6=\mathit{x}$. If the smaller integer is 6 , then the larger integer is $6\times 4=24$.