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Martha obtained an average score of y in a total of x mandatory papers
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Bunuel
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Martha obtained an average score of y in a total of x mandatory papers [#permalink] New post  25 Nov 2019, 01:54
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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


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chetan2u
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Re: Martha obtained an average score of y in a total of x mandatory papers [#permalink] New post  26 Nov 2019, 18:23
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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



If you start without any clue, you can just discard A as z is must to get to answer.

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
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satya2029
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Re: Martha obtained an average score of y in a total of x mandatory papers [#permalink] New post  02 Jan 2020, 05:58
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


Say sum of scores received is S
Y=S/X
\(Y'=(S+Z)/(X+1)\)
\(Y'=(XY+Z)/(X+1)\)
Question is \(Y'>1.5Y\)?
\(Y'>3/2Y\)?
\((XY+Z)/X+1>3/2Y\)?
\(2XY+2Z>3Y(X+1)\)?
\(2Z-3Y>XY\)?
after Rephrasing
is \(2Z-3Y>XY\)?
B:)
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Re: Martha obtained an average score of y in a total of x mandatory papers [#permalink]
02 Jan 2020, 05:58
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