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# A scholarship committee awarded scholarships in the $1250,  Question banks Downloads My Bookmarks Reviews Important topics Author Message Manager Joined: 17 Jul 2006 Posts: 50 Followers: 0 Kudos [?]: 4 [0], given: 0 A scholarship committee awarded scholarships in the$1250, [#permalink]  21 Oct 2006, 19:01
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1. A scholarship committee awarded scholarships in the $1250,$2500, and $4000. The committee awarded twice as many$2500 scholarships as $4000 scholarship, and three times as many$1250 as $2500 scholarship. If total$37500 awarded in $1250, how many$4000 are award?

A) 5
B) 6
C) 9
D) 10
E) 15

2. Why f(x) = x^2(1 â€“ x^2) is equal to f(x) = f (1-x) for all x?

3. Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many second after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P?
A) 6
B) 8
C) 10
D) 12
E) 15
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Joined: 08 Oct 2006
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Kudos [?]: 5 [0], given: 0

Solution for the first problem [#permalink]  22 Oct 2006, 02:56
Solution for the first problem is following:

$1250 - x scholarships$2500 - y scholarships
$4000 - z scholarships if total x scolarships =$37500, then $37500/1250 = 30 scolarships x= 2* z then z = x/2= 15 scholarships for$4000

Intern
Joined: 08 Oct 2006
Posts: 30
Followers: 0

Kudos [?]: 5 [0], given: 0

Solution for the first problem:

missed one point

y=2*z
x=3*y=6*z

if x=30, then z =5

Intern
Joined: 08 Oct 2006
Posts: 30
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Kudos [?]: 5 [0], given: 0

Solution for problem #2 [#permalink]  22 Oct 2006, 03:20
It's impossible to solve problem #2. Maybe there is some mistake or missing invormation in the text of the problem.
Intern
Joined: 08 Oct 2006
Posts: 30
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Kudos [?]: 5 [0], given: 0

Solution for problem #3 [#permalink]  22 Oct 2006, 03:31
Solution for problem #3:

sign V means speed, sign t means time and sign R means amount of rotations.

V(P) = 10 rotations per minute = 10/60 rotations per second = 1/6 r per s
V(Q) = 40 rotations per minute = 40/60 rotations per second = 2/3 r per s

R=V*t

2/3*t - 6 = 1/6*t

4/6*t - 1/6*t = 6

1/2*t = 6

t = 12 seconds

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1. A scholarship committee awarded scholarships in the $1250,$2500, and $4000. The committee awarded twice as many$2500 scholarships as $4000 scholarship, and three times as many$1250 as $2500 scholarship. If total$37500 awarded in $1250, how many$4000 are award?

A) 5 B) 6 C) 9 D) 10 E) 15

4000 scholarships = x

2500 scholars = 2x

1250 scholars = 6x = 37500 / 1250 = 30 thus x = 5

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