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# The average score of x number of exams is y. When an additional exam

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Math Expert
Joined: 02 Sep 2009
Posts: 54543
The average score of x number of exams is y. When an additional exam  [#permalink]

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08 Oct 2014, 14:23
00:00

Difficulty:

65% (hard)

Question Stats:

62% (02:25) correct 38% (02:52) wrong based on 161 sessions

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Tough and Tricky questions: Statistics

The average score of x number of exams is y. When an additional exam of score z is added in, does the average score of the exams increase by 50%?

(1) 3x = y
(2) 2z - 3y = xy

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Re: The average score of x number of exams is y. When an additional exam  [#permalink]

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08 Oct 2014, 23:00
1
Bunuel wrote:

Tough and Tricky questions: Statistics

The average score of x number of exams is y. When an additional exam of score z is added in, does the average score of the exams increase by 50%?

(1) 3x = y
(2) 2z - 3y = xy

B.

The questions can be mathematically represented as:

(xy+z)/(x+1) = 1.5y --- (A)

1) 3x=y
clearly insufficient as we have no info about z.

2) 2z-3y=xy
this is nothing but the simplified form of equation (A)
sufficient.
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The average of a set of x exam scores is y. When an additional exam of  [#permalink]

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23 Mar 2017, 23:55
The average of a set of x exam scores is y. When an additional exam of score z is added to the set, does the average score of the exams increase by 50%?

(1) $$3 x = y$$
(2) $$2 z – 3 y = xy$$
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Re: The average of a set of x exam scores is y. When an additional exam of  [#permalink]

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24 Mar 2017, 00:16
Sum of the exam scores = xy
When new score z is introduced, sum is xy+z
Avg =( xy+z)/x+1
Question is asking if (xy+z)/x+1 = 150% of y
On solving, we get xy = 2z-3y, which is given in statement b
Hence B.
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Posts: 54543
Re: The average score of x number of exams is y. When an additional exam  [#permalink]

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24 Mar 2017, 01:06
ziyuen wrote:
The average of a set of x exam scores is y. When an additional exam of score z is added to the set, does the average score of the exams increase by 50%?

(1) $$3 x = y$$
(2) $$2 z – 3 y = xy$$

Merging topics. Please refer to the discussion above.
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Re: The average score of x number of exams is y. When an additional exam  [#permalink]

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24 Mar 2017, 02:01
1
Alternate method:

Let number of exams = x = 10
average = y = 50

Question: Is (500 + z)/11 = 75?

St1: x = 3y --> Clearly insufficient as we do not know anything about z.

St2: z = (xy + 3y)/2 = (500 + 150)/2
We know the value of z.
Sufficient.

Answer: B
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Re: The average score of x number of exams is y. When an additional exam  [#permalink]

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11 Sep 2017, 05:31
Bunuel wrote:

Tough and Tricky questions: Statistics

The average score of x number of exams is y. When an additional exam of score z is added in, does the average score of the exams increase by 50%?

(1) 3x = y
(2) 2z - 3y = xy

St 1

We know nothing about Z

St 2

Holds true for all scenarios for example

x=3 ,y=4

x=5, y=6

B
Re: The average score of x number of exams is y. When an additional exam   [#permalink] 11 Sep 2017, 05:31
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# The average score of x number of exams is y. When an additional exam

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