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The average score of x number of exams is y [#permalink]
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13 Oct 2005, 23:05
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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.
Answer



Current Student
Joined: 29 Jan 2005
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B.
I just picked numbers for X, Y, and Z. But the problem is probably much more difficult than this...
OA?



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To get a 50% increase:
(xy+z)/(x+1)=1'5y and this is exactly what (2) says



Manager
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I did GMATT's way. Anyone got a better way? Anyone? Anyone?
jdto, could you elaborate?
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Can someone explain the approach in a little more detail?
Thanks!



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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 => 3z3y=xy which the same as (B)
Hence Suff.



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Joined: 22 Aug 2005
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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
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Cool  thanks for the detailed steps!



SVP
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OA is B. OE is the same to gsr's.



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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.
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Re: average [#permalink]
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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
B is the answer



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Re: average [#permalink]
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11 Jun 2008, 07:55
great stuff, how long did it take you to solve this ?
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Re: average [#permalink]
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11 Jun 2008, 08:31
alimad wrote: great stuff, how long did it take you to solve this ? it was fairly straightforward for me primarily because of lots of practice longlong time ago.



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ADVANCED DATA SUFFICIENCY [#permalink]
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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.



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Re: ADVANCED DATA SUFFICIENCY [#permalink]
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01 Sep 2011, 11:05
The answer is B. 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.



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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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Re: The average score of x number of exams is y
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