The value of 10^8 - 10^2 / 10^2 - 10^3 is...

[Guest]

... 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

[Guest]

please use this version as I made a mistake in the first equation.

10^8 - 10^2 / 10^7 - 10^3

Thanks

[RR]

You have to remember the question says 'closest'. So approximation is allowed
So 10^8 - 10^2 / 10^7 - 10^3
=
10^2 (10^6 - 1)
------------------
10^2 (10^5 - 10)

1 and 10 are small in comparison to 10^6 and 10^5 respectively. So they can be ignored. This reduces to 10^6 / 10^5 which is 10

[RonPurewal]

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

you don't have to alter problems from the GMATPREP software; you can post those verbatim.

it's official guide problems that you're not allowed to post.
and live questions from the actual test? yeah, don't even think about posting those, even in altered form. just don't.
but, again, practice test problems (from the official gmatprep software) - those are fine.

[RonPurewal]

You have to remember the question says 'closest'. So approximation is allowed
So 10^8 - 10^2 / 10^7 - 10^3
=
10^2 (10^6 - 1)
------------------
10^2 (10^5 - 10)

1 and 10 are small in comparison to 10^6 and 10^5 respectively. So they can be ignored. This reduces to 10^6 / 10^5 which is 10

perfect.

remember to make simplifying approximations when you see words like "approximately" or "closest".

alternatively, you could actually perform long division here (it's 99,999,900 / 9,999,000). after the first step or so, it's going to be easy to see that you're going to get an answer that's really, really, really close to 10.
in fact, depending on how accustomed you are to staring at numbers, you may be able to tell that the answer is 10 just by writing out the above fraction, since it becomes a lot more obvious that the fraction is, essentially, (about 100 million) / (about 10 million).