Problem Solving

10^9 – 10^4
-------------------
10^8 - 10^5

is closest to which of the following?

A) 1
B) 10
C) 10^2
D) 10^3
E) 10^4

Source: GMAC practice test - Note that numbers have been changed to respect copywright restrictions.

I did this problem in every way possible and come up with an answer of 1 however the answer is 10. Can anyone break down there steps and explain why the answer is 10?

Thanks

10^4(10^5 – 1) / 10^5(10^3 – 1)

(10^5 – 1) / (10^4-10)

The one and the 10 are irrelevant so we have 10^5/10^4 = 10

10^9 – 10^4
------------------- = 10^4(10^5-1)/10^5(10^3-1)=(99999/999)/10=appx 10
10^8 - 10^5

10^9 – 10^4
-------------------
10^8 - 10^5

is closest to which of the following?

10^9
-------
10^8


= 10 That's it!

Thanks guys - I guess I just got hung up with the 10^4/10^5

To me I was calculating it after simplifying the exponent as 10^1 - 10^-1 or 1/10^1 so that gave me 9/10 which is closer to one. I treated them as two fractions. My bad. Thanks.

10^9-10^4 / 10^8-10^5

Take 10^4 out as common factor in Nr and Dr

10^4(10^5 - 1) / 10^4 ( 10^4- 1)

= 10^5 / 10^4 (10^5-1 ~=10^5 10^4-1~= 10^4)
= 10

cramya wrote:10^9-10^4 / 10^8-10^5

Take 10^4 out as common factor in Nr and Dr

10^4(10^5 - 1) / 10^4 ( 10^4- 1)

= 10^5 / 10^4 (10^5-1 ~=10^5 10^4-1~= 10^4)
= 10

Cramya has all the time in this world!

Cramya has all the time in this world!

Seriously, how much time do u think it will take if u were to take 10^4 as the common factor(1 sec at the max) in the numerator and denominator and make the approximation even clearer to the original poster of this thread or whover visits this thread?

Come on man! We can do it ourselves anyway we want but the explanation we provide must be understandable by all (alteast try our best so that it does)

Speaking generally here(applies to both of us also):

Its doesnt matter to people if xyz or abc can solve a problem in a way only they can understand but whether th people looking through these posts understand the concept behind the problem and solve it the next time they see such a problem

Woudln't we want the same in a solution or explanation provided by someone else??

Something to think about for sure........