exponents

nisha.menon294 wrote:Question from Gmat prep . i would like to know an easier way to solve it if possible. thanks

what is the closest value of 10^8-10^2\10^7-10^3

a)0
b)1
c)10
d)10^2
e)10^3

When they talk about the closest value in such cases, take a judicious look at the choices. In the present case, the choices are far apart in most of the cases.

Try with the smaller degrees of 10 for comparison, as the difference between 10^0 and 10^1 is close to 10^1, hence the difference between 10^0 and 10^2 will be incredibly close to 10^2, and so on. We can now safely predict that 10^8 – 10^2 is incredibly close to 10^8, and that 10^7 – 10^3 is incredibly close to 10^7, such that

(10^8 – 10^2)\(10^7 – 10^3) is incredibly close to 10^8/10^7 = [spoiler]10.

C[/spoiler]

thanks .. that was helpful. i wasted a lot of time trying to get to that answer

10^8 - 10² / 10^7 - 10³
10²(10^6 -1) / 10³(10^4-1)
(10^6 -1) /10(10^4-1)
app 10^6/10^5 or 10