SAT Mathematics Practice Test 5

Let n be the number of novels and m be the number of magazines that Sadie purchased. If Sadie purchased a total of $\mathrm{\$}11$ novels and magazines, then $\mathit{n}+\mathit{m}=11.$ It is given that the combined price of 11 novels and magazines is $\mathrm{\$}20$. Since each novel sells for $\mathrm{\$}4$ and each magazine sells for $\mathrm{\$}1$,it follows that $4\mathit{n}+\mathit{m}=20.$ So the system of equations below must hold$4\mathit{n}+\mathit{m}=20$
$\mathit{n}+\mathit{m}=11$Subtracting side by side the second equation from the first equation yields $3\mathit{n}=9$, so $\mathit{n}=3$. Therefore, Sadie purchased 3 novels.
Choice A is incorrect. If 2 novels were purchased, then a total of $\mathrm{\$}8$ was spent on novels. That leaves $\mathrm{\$}12$ to be spent on magazines, which means that $12$ magazines would have been purchased. However, Sadie purchased a total of $11$ novels and magazines. Choices C and D are incorrect. If $4$ novels were purchased, then a total of $\mathrm{\$}16$dollars was spent on novels. That leaves $\mathrm{\$}4$ to be spent on magazines, which means that $4$ magazines would have been purchased. By the same logic, if Sadie purchased 5 novels, she would have no money at all ($\mathrm{\$}0$) to buy magazines. However, Sadie purchased a total of 11 novels and magazines.