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# The average score of x number of exams is y

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SVP
Joined: 24 Sep 2005
Posts: 1816
The average score of x number of exams is y  [#permalink]

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13 Oct 2005, 23:05
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73% (01:15) correct 27% (00:39) wrong based on 74 sessions

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Question
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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.

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GMAT Club Legend
Joined: 29 Jan 2005
Posts: 5062

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13 Oct 2005, 23:12
B.

I just picked numbers for X, Y, and Z. But the problem is probably much more difficult than this...

OA?
Manager
Joined: 03 Aug 2005
Posts: 132

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14 Oct 2005, 02:57
1
To get a 50% increase:

(xy+z)/(x+1)=1'5y and this is exactly what (2) says
Manager
Joined: 04 May 2005
Posts: 133
Location: Chicago

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14 Oct 2005, 10:38
I did GMATT's way. Anyone got a better way? Anyone? Anyone?

jdto, could you elaborate?
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Christopher Wilson

Senior Manager
Joined: 26 Jul 2005
Posts: 306
Location: Los Angeles

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14 Oct 2005, 10:53
Can someone explain the approach in a little more detail?

Thanks!
Director
Joined: 21 Aug 2005
Posts: 763

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14 Oct 2005, 11:13
2
2
B

Sum of all numbers = xy
New number = z
New Average = xy+z/(x+1)
We need to find if xy+z/(x+1) = 3y/2 --- (1)

A) We don't have z. So Insufficient
B) Simplify (1),
we get 2xy+2z=3xy+3y => 3z-3y=xy which the same as (B)
Hence Suff.
VP
Joined: 22 Aug 2005
Posts: 1090
Location: CA

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14 Oct 2005, 11:21
In order for 50% increase in ang scope, z has to be equal to difference between old score sum (x * y) and new score sum ((x+1) * 1.5 y). OR

z = (x+1) * 1.5 y - xy or
z = 0.5 y (x +3) or
z = 1/2 y (x + 3)

(1) tells relationship between x and y only insufficient

(2) simplifying we get:
z = 1/2y(x+3)
exactly what we want.
ans: yes, sufficient
Senior Manager
Joined: 26 Jul 2005
Posts: 306
Location: Los Angeles

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14 Oct 2005, 11:24
Cool - thanks for the detailed steps!
SVP
Joined: 24 Sep 2005
Posts: 1816

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14 Oct 2005, 20:12
OA is B. OE is the same to gsr's.
Director
Joined: 10 Feb 2006
Posts: 647

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11 Jun 2008, 06:59
1. 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

(A) Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is not.
(B) Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is not.
(C) Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient to answer the question.
(E) Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question.
_________________

GMAT the final frontie!!!.

Director
Joined: 01 Jan 2008
Posts: 600

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11 Jun 2008, 07:37
average after adding z is (xy+z)/(x+1) and compare to 1.5*y

1) insufficient (z can be anything)
2) sufficient z = (xy+3y)/2 => (xy+z)/(x+1) = 3*(xy+y)/2/(x+1)=1.5y -> sufficient

Director
Joined: 10 Feb 2006
Posts: 647

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11 Jun 2008, 07:55
great stuff, how long did it take you to solve this ?
_________________

GMAT the final frontie!!!.

Director
Joined: 01 Jan 2008
Posts: 600

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11 Jun 2008, 08:31
great stuff, how long did it take you to solve this ?

it was fairly straight-forward for me primarily because of lots of practice long-long time ago.
Manager
Joined: 09 Jun 2011
Posts: 95

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01 Sep 2011, 05:42
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) 3x = y
(2) 2z – 3y = xy

Hey Guys! I need Help, what would be the best answer, please explain.
Intern
Joined: 16 Apr 2010
Posts: 28
Location: United States (AL)
Concentration: Technology, Entrepreneurship
GMAT 1: 680 Q44 V37
GPA: 3.91
WE: Information Technology (Energy and Utilities)

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01 Sep 2011, 11:05

The question asks if the new average, with z, greater than the old average(y) by 50%?

We know that the sum of the numbers in the set is xy (no. of terms x average of terms).
so when a new term,z, is added to the set, the new average becomes (xy+z)/(x+1).
Plugging this in to the question, we get : is (xy+z)/(x+1) = 1.5y ?
Simplifying both sides, the answer is 2z – 3y = xy viz B.

bholakc 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) 3x = y
(2) 2z – 3y = xy

Hey Guys! I need Help, what would be the best answer, please explain.
Non-Human User
Joined: 09 Sep 2013
Posts: 8154
Re: The average score of x number of exams is y  [#permalink]

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14 Feb 2018, 07:03
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--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

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Re: The average score of x number of exams is y &nbs [#permalink] 14 Feb 2018, 07:03
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