SAT · Math · Problem-Solving and Data Analysis
Porcentajes, aumentos y descuentos sucesivos, y porcentaje de cambio.
Un precio sube un 20 % y luego baja un 20 %: $100\times1{,}2\times0{,}8=96$ → termina un 4 % por debajo del original.
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
The number $63$ is $140\%$ of what number?
Respuesta numérica (escribes el número).
Respuesta: 45
Let the number be $n$. Then $1.4n=63$, so $n=\frac{63}{1.4}=45$.
Check: $140\%$ of $45$ is $45+0.4(45)=45+18=63$.
The price of a desk lamp dropped from $\$80$ to $\$68$. By what percent did the price decrease?
Respuesta correcta: B. $15\%$
The price dropped by $80-68=12$ dollars. As a percent of the original price: $\frac{12}{80}=0.15=15\%$.
$17.6\%$ divides by the new price, $68$. $12\%$ treats the $\$12$ drop as the percent. $85\%$ is the new price as a percent of the old one.
At a high school, $45\%$ of the students belong to exactly one club, and the other students do not belong to any club. Of the students who belong to a club, $40\%$ belong to a sports club. The number of students who belong to a club that is not a sports club is $54$ greater than the number of students who belong to a sports club. How many students are at the school?
Respuesta numérica (escribes el número).
Respuesta: 600
Let $n$ be the number of students at the school. Then $0.45n$ students belong to a club. Of these, $40\%$, or $0.40(0.45n)=0.18n$, belong to a sports club, and the other $60\%$, or $0.60(0.45n)=0.27n$, belong to a club that is not a sports club. The difference is $0.27n-0.18n=0.09n$, so $0.09n=54$ and $n=600$.
Check: $270$ students are in clubs, $108$ in sports clubs and $162$ in other clubs, and $162-108=54$.