Question

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?

• A. $p>0.20(300-36),wherep\le 150$
• B. $p>0.20(300+36),wherep\le 150$
• C. $p-36>0.20\left(300\right),wherep\le 150$
• D. $p+36>0.20\left(300\right),wherep\le 150$

Answer 1

The correct option is D $p+36>0.20\left(300\right),wherep\le 150$

Given that among the first 150 participants, 36 chose the first picture in the set. Of the remaining 150, p people chose the first picture in the set $(p\le 150)$. Hence, the total number of people who chose the first picture in the set is (p + 36), $p\le 150$.
If the number of participants who chose the first picture is more than the total number of participants i.e. 300, then, it is represented by the following inequality
$(p+36)\ge 0.20\left(300\right)$, where $p\le 150$