<em><u>Question:</u></em>
Brian, Chris, and Damien took a math test that had 20 questions. The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right. Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly. If Brian and Damien have the same score, which statement is true?
A) Brian and Damien both answered 2 fewer questions correctly than Chris did.
B) Brian and Damien both answered 4 more questions correctly than Chris did.
C) Brian and Damien both answered 2 more questions correctly than Chris did.
D) Brian and Damien both answered 4 fewer questions correctly than Chris did.
<em><u>Answer:</u></em>
Option C
Brian and Damien both answered 2 more questions correctly than Chris did
<em><u>Solution:</u></em>
Let "x" be the number of correct answers of Brian
Let "y" be the number of correct answers of Chris
Let "z" be the number of correct answers of Damien
<em><u>The number of questions Brian got right is 14 more than 1/4 the number of questions Chris got right</u></em>
---------- eqn 1
<em><u>Damien correctly answered 2 less than 5/4 the number of questions Chris answered correctly</u></em>
---------- eqn 2
<em><u>Brian and Damien have the same score</u></em>
x = z -------- eqn 3
Therefore,
<em><u>Substitute y = 16 in eqn 1</u></em>
Therefore, by eqn 3,
z = 18
Thus we get,
Number of correct answers of Brian = 18
Number of correct answers of chris = 16
Number of correct answers of Damien = 18
Therefore, correct statement is:
Brian and Damien both answered 2 more questions correctly than Chris did
