GMAT Practice Question: In a field day at a school, each child who competed in n events and scored a total of p...
Question
In a field day at a school, each child who competed in n events and scored a total of p points was given an overall score of \frac{p}{n}+n. Andrew competed in 1 event and scored 9 points. Jason competed in 3 events and scored 5, 6, and 7 points, respectively. What was the ratio of Andrew's overall score to Jason's overall score?
- \frac{10}{23}
- \frac{7}{10}
- \frac{4}{5}
- \frac{10}{9}
- \frac{12}{7}
Topics: word problems, ratios, simultaneous equations, translations
Solution
Step 1
We first name the variables for Andrew's number of events and total points.
n_A = 1 p_A = 9
Step 2
We then calculate Andrew's overall score by applying the formula \frac{p}{n}+n.
\text{Andrew's score} = \frac{p_A}{n_A} + n_A = \frac{9}{1} + 1 = 9 + 1 = 10
Step 3
Next we name the variables for Jason's number of events and total points.
n_J = 3 p_J = 5 + 6 + 7 = 18
Step 4
We then calculate Jason's overall score using the same formula.
\text{Jason's score} = \frac{p_J}{n_J} + n_J = \frac{18}{3} + 3 = 6 + 3 = 9
Step 5
Finally, we form the ratio of Andrew's overall score to Jason's overall score.
\frac{\text{Andrew's score}}{\text{Jason's score}} = \frac{10}{9}
Answer
The ratio is \frac{10}{9}, which corresponds to option D.
