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Logic behind two practice exam q on factors and exponents

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by [email protected] » Fri Aug 20, 2010 1:39 pm
I can't understand the logic behind these two questions from a practice exam. Can anyone help?
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Picture 10.png
Why is it 2^9?
Picture 11.png
How do you solve this to get 20?
Last edited by [email protected] on Sat Aug 21, 2010 7:32 am, edited 2 times in total.
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by beatthegmatinsept » Fri Aug 20, 2010 1:41 pm
What exactly is the question here? Is picture 10 related to Picture 11?
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by Makushr1 » Fri Aug 20, 2010 2:33 pm
[email protected] wrote:I can't figure the logistics behind these questions from a practice exam. Can anyone help?
Well, for the 2nd one, you can see the exponent is just adding 1 (except for the first 2). So, try this:

2+2+2^2+2^3=2 + 2 + 4 + 8 = 16

16 is also the next one in the order, 2^4, so you should be able to guess that after 2^8 is 2^9.
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by GMATGuruNY » Fri Aug 20, 2010 7:31 pm
For an algebraic solution to the first problem, please see the attached document.

An easier approach would be to ballpark:

[Sqrt(9 + Root80) + Sqrt(9 - Root80)]^2
=[Sqrt(9 + almost 9) + Sqrt(9 - almost 9)]^2
= [Sqrt(18) + Sqrt(fraction)]^2 approximately
=[Sqrt(18) + Sqrt(fraction)]*[Sqrt(18) + Sqrt(fraction)]
= 18 + more

The only answer choice larger than 18 is E.
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Algebra_Roots.doc
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by anantbhatia » Sat Aug 21, 2010 1:05 am
Logistics and logic are two different terms. Don't use them interchangeably. Might be helpful for your essays in VA. Similar to Vegan and vegetarian. Vegan is not a shorter term for vegetarian. Sorry.. off the topic but though might be helpful for someone.
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