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165)^2 - (164)^2 = a. 1 b. 100 c. 229 d. 329

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165)^2 - (164)^2 = a. 1 b. 100 c. 229 d. 329 [#permalink] New post 04 Nov 2003, 11:55
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(165)^2 - (164)^2 =

a. 1
b. 100
c. 229
d. 329
e. 349
any short cut?
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shubhangi

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 [#permalink] New post 04 Nov 2003, 12:05
(165*165)-(164*164)=
((165*164)+165)-(164*164)=
((164*164)+165+164)-(164*164)

So as a general rule on these problems (difference of squares of consecutive nonnegative integers), I <i>think </i>the answer will always be the sum of the two terms being squared.
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 [#permalink] New post 04 Nov 2003, 12:11
? :cry:
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 [#permalink] New post 04 Nov 2003, 12:56
What did you do Stoolfi.. ?? its more confusing.. that way..
i guess the best method is to add up both the terms.
165+164??
what do you think?
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 [#permalink] New post 04 Nov 2003, 13:24
subhangi: 165^2 is equal to 165 * 165. It is also equal to (165 * 164)+165.

That's all I did.

I think it makes sense, but it's a wee bit roundabout, maybe...
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 [#permalink] New post 05 Nov 2003, 00:42
165┬▓-164┬▓ = (164+1)┬▓ -164┬▓ =164┬▓ +2*164+1-164┬▓ =2*164+1=328+1=329

OR

165┬▓ -164┬▓ =(165+164)(165-164)=329
  [#permalink] 05 Nov 2003, 00:42
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165)^2 - (164)^2 = a. 1 b. 100 c. 229 d. 329

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