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Linear inequalities in one or two variables SAT question
Math · Algebra · Hard · Answer it here, explanation included.
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 ?
ExplanationShow
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 
. Since more than 20% of all the participants chose the first picture, it follows that 
.
This inequality can be rewritten as 
. Since p is a number of people among the remaining 150 participants, 
.
Choices A, B, and C are incorrect and may be the result of some incorrect interpretations of the given information or of computational errors.
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