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GMAT Prep Questions

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GMAT Prep Questions

by stratcat03 » Mon Jun 04, 2007 8:31 am
Hey guys, need some brushing up on my work with exponents. Ran across these questions on a practice test and could use some help. Thanks in advance.


1) (10^8 - 10^2) / (10^7 - 10^3) is closest to which of the following?

a) 1
b) 10
c) 10^2
d) 10^3
e) 10^4


2) If (2^x)(3^y) = 288, where x and y are positive integers, then (2^x-1)(3^y-2) equals which of the following?

a) 16
b) 24
c) 48
d) 96
e) 144
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by mschling52 » Mon Jun 04, 2007 9:53 am
(1) I think the answer is B. In a problem like this, the 10^2 and 10^3 that are subtracted are very small relative to the 10^8 and 10^7 and can be ignored for the purpose of an approximation. For example, the numerator is 100,000,000 - 100. This is very close to 100 million. Likewise the denominator is very close to 10 million. Therefore, the ratio will be very close to 10 (100 million/10 million).

(2) Is this one A? Break 288 into its prime factors, which gives

288 = 2^5 * 3^2

so x=5 and y=2. Then we know that

2^(x-1) * 3^(y-2) = 2^4 * 3^0 = 16 (anything to the zero power = 1).
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by stratcat03 » Mon Jun 04, 2007 1:32 pm
good stuff, you nailed them both. thanks a lot for the explanations
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