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# Martha obtained an average score of y in a total of x mandatory papers

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Math Expert
Joined: 02 Sep 2009
Posts: 59572
Martha obtained an average score of y in a total of x mandatory papers  [#permalink]

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25 Nov 2019, 02:54
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Difficulty:

(N/A)

Question Stats:

44% (02:42) correct 56% (02:22) wrong based on 16 sessions

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Martha obtained an average score of y in a total of x mandatory papers. She also obtained a score of z in an additional optional paper. Does Martha’s average score on all the x + 1 papers exceed her average score on the x mandatory papers by more than 50%?

(1) 3x = y
(2) 2z – 3y = xy

Are You Up For the Challenge: 700 Level Questions
Math Expert
Joined: 02 Aug 2009
Posts: 8284
Re: Martha obtained an average score of y in a total of x mandatory papers  [#permalink]

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26 Nov 2019, 19:23
Bunuel wrote:
Martha obtained an average score of y in a total of x mandatory papers. She also obtained a score of z in an additional optional paper. Does Martha’s average score on all the x + 1 papers exceed her average score on the x mandatory papers by more than 50%?

(1) 3x = y
(2) 2z – 3y = xy

Are You Up For the Challenge: 700 Level Questions

Let us form equations.
Martha obtained an average score of y in a total of x mandatory papers...Total =xy
She also obtained a score of z in an additional optional paper.
...Total =xy+z

We have to find whether $$\frac{xy+z}{x+1}>y*1.5......xy+z>1.5xy+1.5y......2xy+2z>3xy +3y.....2z-3y>xy$$

Statement II gives us exactly what we are looking for
The answer is NO, it doesn’t exceed by MORE than 50%.

B
_________________
Re: Martha obtained an average score of y in a total of x mandatory papers   [#permalink] 26 Nov 2019, 19:23
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