exponents
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Source: Beat The GMAT — Problem Solving |
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nikhilagrawal
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csandeepreddy
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99,999^2 - 1^2 can be written as
(100,000 - 1)^2 - 1^2
=>(10^5 - 1)^2 - 1^2
=>10^10 + 1 - 2*10^5 - 1 -----------using (a - b)^2 = a^2 + b^2 - 2ab
=>10^10 - 2*10^5
=>10^5(10^5 - 2)
IMO E
(100,000 - 1)^2 - 1^2
=>(10^5 - 1)^2 - 1^2
=>10^10 + 1 - 2*10^5 - 1 -----------using (a - b)^2 = a^2 + b^2 - 2ab
=>10^10 - 2*10^5
=>10^5(10^5 - 2)
IMO E
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lunarpower
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you could do that, and you would be fine.csandeepreddy wrote:99,999^2 - 1^2 can be written as
(100,000 - 1)^2 - 1^2
=>(10^5 - 1)^2 - 1^2
=>10^10 + 1 - 2*10^5 - 1 -----------using (a - b)^2 = a^2 + b^2 - 2ab
=>10^10 - 2*10^5
=>10^5(10^5 - 2)
IMO E
BUT
you should notice that THIS IS ALREADY A DIFFERENCE OF SQUARES.
it's just so ... perfect. it's like a nice juicy steak on a silver platter, at the perfect temperature for human consumption; the solution above, while 100% correct, is somewhat akin to putting that perfect steak back into the microwave for 30 more seconds.
here's how to take a nice big juicy bite:
99,999^2 - 1^2
= (99,999 - 1)(99,999 + 1)
= (99,998)(100,000)
= (10^5 - 2)(10^5)
done
notice that you have to pick up on the fact that 10^5 is the same thing as 100,000.
but you should know that.
put it on a flash card if you don't.
while you're at it, also make a flash card for the difference of squares.
and if you didn't recognize the difference of squares within 3 seconds, then drop and give me 100 pushups. right now.
flash cards are your friends.
Ron has been teaching various standardized tests for 20 years.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
