An exam is given in a certain class. The average (arithmetic mean) of the highest score and the lowest score is equal to x. If the average score for the entire class is equal to y and there are z students in the class, where z > 5, then in terms of x, y, and z, what is the average score for the class excluding the highest and lowest scorers?
Correct answer: D
Explanation
Highest: H
Lowest: L
Number of students in the class: Z
Number of students in the class excluding the highest and lowest : Z-2
Average of Highest and Lowest: (H + L)/2=X => H+L=2X
Average of Entire Class : (H+L+Others)/Z=Y => Others= ZY-2X
Average of the others in the class: (ZY-2X)/(Z-2)
D
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AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.