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A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, $p$ people chose the first picture in the set. If more than $20 \%$ of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of $p$ ?

SAT · Math · previous-year question

  1. A.$p>0.20(300-36)$, where $p \leq 150$
  2. B.$p>0.20(300+36)$, where $p \leq 150$
  3. C.$p-36>0.20(300)$, where $p \leq 150$
  4. D.$p+36>0.20(300)$, where $p \leq 150$correct

Answer

D. $p+36>0.20(300)$, where $p \leq 150$

Explanation

Choice D is correct. Of the first 150 participants, 36 chose the first picture in the set, and of the 150 remaining participants, $p$ chose the first picture in the set. Hence, the proportion of the participants who chose the first picture in the set is $\frac{36+p}{300}$. Since more than $20 \%$ of all the participants chose the first picture, it follows that $\frac{36+p}{300}>0.20$. This inequality can be rewritten as $p+36>0.20(300)$. Since $p$ is a number of people among the remaining 150 participants, $p \leq 150$.Choices A, B, and $C$ are incorrect and may be the result of some incorrect

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