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# time n work again

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Manager
Joined: 19 Aug 2009
Posts: 79
Followers: 1

Kudos [?]: 223 [0], given: 46

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20 Aug 2009, 14:00
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Q.
Mini and Vinay are quiz masters preparing for a quiz.In 'x' minutes, Mini makes 'y' questions more than Vinay. If it were possible to reduce the time needed by each to make a question by 2 mins, then in 'x' minutes Mini would make '2y' questions more than Vinay. How many questions does Mini make in 'x' minutes?
1] 1/4[ 2(x+y) - ( 2 x^2 + 4 y^2 )^1/2 ]
2] 1/4[ 2(x-y) - ( 2 x^2 + 4 y^2 )^1/2 ]
3] Either option 1 or 2
4] 1/4[ 2(x-y) - ( 2 x^2 - 4 y^2 )^1/2 ]
Senior Manager
Joined: 23 Jun 2009
Posts: 361
Location: Turkey
Schools: UPenn, UMich, HKS, UCB, Chicago
Followers: 5

Kudos [?]: 130 [1] , given: 80

Re: time n work again [#permalink]

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21 Aug 2009, 14:55
1
KUDOS
Very hard question. Not for gmat I think.

In x minutes mini makes a questions.
i.e.Mini makes a question in x/a minutes.
In x minutes vinay makes a-y questions.
Vinay makes a question in x/(a-y) minutes
if mini makes a question in x/a-2 minutes (is equal to (x-2a)/a )and vinay makes a question in x/(a-y)-2 minutes is equal to ((x-2a+2y)/(a-y))than in x minutes mini makes 2y questions more.
That is to say problem wants a in this equation
ax/(x-2a)-(a-y).x/(x-2a+2y)=2y
ax/(x-2a)-2y=(a-y).x/(x-2a+2y)
(ax-2yx+4ay)/(x-2a)=(ax-yx)/(x-2a+2y)
(ax-2yx+4ay).(x-2a+2y)-(x-2a)(ax-yx)=0
(x-2a)(ax-2yx+4ay-ax+yx)+2y(ax-2yx+4ay)=0
(x-2a)(4ay-yx)+2y(ax-2yx+4ay)=0
(x-2a).y.(4a-x)+2y.(ax-2yx+4ay)=0
(4ax-x^2-8a^2+2ax).y+y.(2ax-4yx+8ay)=0
y(8ax-x^2-8a^2+8ay)=0
y(8a(x-a+y)-x^2)=0
8ay(x+y-a)=yx^2
a(x+y-a)=yx^2/8y
a(x+y-a)=x^2/8
a^2-ax-ay+x^2/8=0
a^2-a(x+y)+x^2/8=0
solving for a for 2nd degree equations. (b^2-4ac formula)
a1=((x+y)+sqrt((x+y)^2-4.x^2/8))/2 or
a2=((x+y)-sqrt((x+y)^2-4.x^2/8))/2
Manager
Joined: 19 Aug 2009
Posts: 79
Followers: 1

Kudos [?]: 223 [0], given: 46

Re: time n work again [#permalink]

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26 Aug 2009, 01:45
maliyeci wrote:
Very hard question. Not for gmat I think.

In x minutes mini makes a questions.
i.e.Mini makes a question in x/a minutes.
In x minutes vinay makes a-y questions.
Vinay makes a question in x/(a-y) minutes
if mini makes a question in x/a-2 minutes (is equal to (x-2a)/a )and vinay makes a question in x/(a-y)-2 minutes is equal to ((x-2a+2y)/(a-y))than in x minutes mini makes 2y questions more.
That is to say problem wants a in this equation
ax/(x-2a)-(a-y).x/(x-2a+2y)=2y
ax/(x-2a)-2y=(a-y).x/(x-2a+2y)
(ax-2yx+4ay)/(x-2a)=(ax-yx)/(x-2a+2y)
(ax-2yx+4ay).(x-2a+2y)-(x-2a)(ax-yx)=0
(x-2a)(ax-2yx+4ay-ax+yx)+2y(ax-2yx+4ay)=0
(x-2a)(4ay-yx)+2y(ax-2yx+4ay)=0
(x-2a).y.(4a-x)+2y.(ax-2yx+4ay)=0
(4ax-x^2-8a^2+2ax).y+y.(2ax-4yx+8ay)=0
y(8ax-x^2-8a^2+8ay)=0
y(8a(x-a+y)-x^2)=0
8ay(x+y-a)=yx^2
a(x+y-a)=yx^2/8y
a(x+y-a)=x^2/8
a^2-ax-ay+x^2/8=0
a^2-a(x+y)+x^2/8=0
solving for a for 2nd degree equations. (b^2-4ac formula)
a1=((x+y)+sqrt((x+y)^2-4.x^2/8))/2 or
a2=((x+y)-sqrt((x+y)^2-4.x^2/8))/2

Yes Sir, aftr lookin at the solution and the time constraint in the exam i too think it wont be asked in real exam..though it was put up in a mock test.
Re: time n work again   [#permalink] 26 Aug 2009, 01:45
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