(5^2006)/(3^2004+5^2005) is a number between;

A) 1 and 2

B) 2 and 3

C) 3 and 4

D) 4 and 5

E) 5 and 6

### 1 Answer | Add Yours

`y = (5^2006)/(3^2004+5^2005)`

Divide the whole by `5^2005`

`(5)/((3^2004)/(5^(2005))+1)`

`= (5)/((3^2004)/(5^(2004))xx(1/5)+1)`

`= 5/((3/5)^2004xx1/5+1)`

Here we can say `((3/5)^2004xx1/5+1)>1` .

Therefore `5/((3/5)^2004xx1/5+1)<5 ` OR `y<5`

`(3/5)^(2004)<1`

`(3/5)^2004xx1/5<1/5`

`(3/5)^2004xx1/5+1<1/5+1`

So now we can say;

`5/((3/5)^2004xx1/5+1)>5/(1/5+1)`

`y > 25/6`

So definitely `y>4`

*So we have obtained y<5 and y>4*

*Now we know that y is between 5 and 4.*

*So the answer is D*

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