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Plz help

by Mani_mba » Sat Jul 19, 2008 11:28 pm
Please help me with the following two questions:

1) The points R,T,U lie on a circle that has a radius 4. If the length of arc RTU is 4Pi/3, what is the length of line segment RU ?

A) 4/3
B) 8/3
C) 3
D) 4
E) 6

OA. D

2) If P is the product of the integers from 1 to 30 inclusive, what is the greatest integer k for which 3^k is a factor of P ?

A) 10
B) 12
C) 14
D) 16
E) 18

OA. C

Please justify your answers.

Thanks,
Mani
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by sudhir3127 » Sun Jul 20, 2008 12:27 am
my answer is 4.

lets assume O is centre of the circle

length of the (Arc) = 2(Pi) r * (x/360)= 4/3 Pi

8 Pi *x /360 = 4/3 Pi

If we solve this we get x= 60

RU is part of a triangle in a circle with centre O

We know that the triangle has two sides equal OR and OU =4, and central angle =60, therefore the other two angles must be equal and since the sum of all the angles in a triangle =180 , the other two angles = 60.

the triangle is an equilateral triangle and the length of the third side is also 4
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by sudhir3127 » Sun Jul 20, 2008 12:34 am
My answer 14.

1 to 30 means 30 !

hence here it goes
Now in 30!, we need to find all multiples of 3

3
6=3*2
9=3^2
12=3*4
15=3*5
18=3^2*2
21=7*3
24=8*3
27=3^3
30=3*10
if we count all the 3's we get 14.
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by Mani_mba » Sun Jul 20, 2008 3:43 am
THanks for the explanations.
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