In a field day at a school, each child who competed in n events and sc

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?

A. \(\frac{10}{23}\)

B. \(\frac{7}{10}\)

C. \(\frac{4}{5}\)

D. \(\frac{10}{9}\)

E. \(\frac{12}{7}\)

A.  \frac{10}{23}

B.  \frac{7}{10}

C.  \frac{4}{5}

D.  \frac{10}{9}

E.  \frac{12}{7}

BrentGMATPrepNow · Accepted Answer

Given: Score = p/n + n

Andrew competed in 1 event and scored 9 points  
Here, n = 1 and p = 9
So, Andrew's score = 9/1 + 1 = 9 + 1 =  10

Jason competed in 3 events and scored 5, 6, and 7 points, respectively  
5 + 6 + 7 = 18
So, n = 3 and p = 18
Jason's score = 18/3 + 3 = 6 + 3 =  9

What was the ratio of Andrew's overall score to Jason's overall score?   
Ratio =  10 / 9

Answer: D

Cheers,
Brent

jedit · Answer

It should be  D

For readers, denominator for P is just 1 n. The fraction then adds into so you can rewrite it as  n + \frac{p}{n}  for a clearer understanding.

Andrew:

1 + \frac{9}{1}   = 1 + 9 = 10

Jason:
 3 + \frac{(5+6+7)}{3}   = 3 + \frac{18}{3} = 9

Andrew : Jason  = 10 : 9

Devbek · Answer

Answer D

Andrew: n=1, p=9 So: 9/1+1=10
Jason: n=3, p=5+6+7=18 So: 18/3+3=9
Ratio: 10/9

TimeTraveller · Answer

Andrew's overall score =  \frac{9}{1} + 1 = 10 .

Jason's overall score  = \frac{5+6+7}{3} + 3 = 6+3 = 9 .

Ratio =  10:9 . Ans - D.

ScottTargetTestPrep · Answer

Since Andrew competed in 1 event and received 9 points, his overall score was:

9/1 + 1 = 10

Since Jason completed in 3 events and scored 5, 6, and 7 points, he scored a total of 18 points and his overall score was:

18/3 + 3 = 9 
 
Thus, the ratio of Andrew’s score to Jason’s score is 10/9.

Answer: D

CyberStein · Answer

Andrew / Jason = X = Ratio of andrews overall over Jason's overall

Andrew = P/n + n = 9/1 + 1 = 1 9/1 = 10/1 =  10  = Andrews overall score
Jason = 18/3 + 3 = 3 18/3 = 27/3 =  9  = Jason's overall score
 X = 10/9

Therefore, the correct answer is (D) 10/9

Good warm up question. I wonder what level it is.

sandysilva · Answer

Is there really a need of word " respectively" in the question?
What difference will it make with or without this word?

The reason i ask is this word made me calculate the three rates Separately at first and then re-do my calculations again.

AkshdeepS · Answer

Word "respectively" adds emphasize that you need to calculate each set of point i.e, 5, 6 , and 7 for 1 game only. Means 5/1, 6/1, and 7/. And not 5/1 + 1, 6/1 + 1 etc.

Though I did it wrong.

QZ

Basshead · Answer

Andrew's overall score = 9/1 + 1 = 10

Jason's overall score = 18/3 + 3 = 9

10/19

Answer is D.

woohoo921 · Answer

ScottTargetTestPrep 
Had a similar question to the other users on the threat. "Respectively" led me to calculate Jason's points separately for a total of 21. Thankfully, this was not an answer to select from, so I went back to redo the problem. How did you know to group the scores rather than do the work out for each game for Jason? Thank you!

egmat · Answer

Hi  woohoo921  
Thanks for your query.

Your query clearly shows that you did not get the translation of the question correctly.

Let me begin by telling you that “TRANSLATION” plays a key role in Quant questions. Correctly translating a question from English to Math will take you halfway toward the correct answer.

Now, let’s see how correct translation would have saved precious time for you in this question.

READ AND TRANSLATE THE 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 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?

Firstly, I would suggest you stop reading my response further and try to focus on the parts I highlighted in the question above. This time, pause at each such part and try to translate again.

I hope you have tried it yourself! Now, see the below explanation to check whether your translations were correct this time or not.

-  “Each child who   competed in ‘n’ events  ”  - ‘n’ represents the  TOTAL  number of events competed in by one child.

-  “Scored a   total of p points  ”  - ‘p’ represents the  TOTAL  points someone earns. This is the sum of all points scored in these ‘n’ events.   (This is one part you understood wrong!)

-  “was given an   overall score of (p/n) + n. ” - Here the word  “OVERALL”  is the key word. It shows there are not multiple scores someone will get. Each child will get only one overall score.   (You assumed that the overall score would be the sum of scores obtained in each event separately).

And that’s it! Once you understand this, you will be able to confidently say that n = 3 and p = 18 for Jason. Nothing will confuse you after this. 😊

Hope this helps!

Best, 
Aditi Gupta 
Quant expert, e-GMAT

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