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Exponents on steroids...

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Current Student
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Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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GMAT Tests User
Exponents on steroids... [#permalink] New post 06 Sep 2005, 10:36
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
If (a+b)^x=a^x + y(a^(x-1)*b^(x-4)) + z(a^(x-2)*b^(x-3)) + z(a^(x-3)*^(x-2)) + y(a^(x-4)*b^(x-1)) + b^x, what is the value of yz?

(A) 24
(B) 30
(C) 36
(D) 42
(E) 50


please show working....
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 [#permalink] New post 06 Sep 2005, 11:20
The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50
Current Student
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Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 158 [0], given: 2

GMAT Tests User
 [#permalink] New post 06 Sep 2005, 12:55
hmm could you shed some light on this?

I figured out what y is, but had hard time figuring z....

basically I know that x =5, then I know that the coefficient of y will also be 5....figuring out z is the hard part...

zag1979 wrote:
The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50
Current Student
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Joined: 28 Dec 2004
Posts: 3405
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 158 [0], given: 2

GMAT Tests User
 [#permalink] New post 06 Sep 2005, 12:57
actually this is a nice chart to remember whenever you have (a+b)^x...

depending on x..you can build out this chart...nice indeed....

can someone show how we can expand the pascal plot...to more than 6...
Manager
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GMAT Tests User
 [#permalink] New post 06 Sep 2005, 15:16
Just add the two numbers above each number when in the normal isosceles triangle design.

Or use the nCr formula.

Try looking up Pascal's triangle on a search engine on the internet.
Senior Manager
Senior Manager
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GMAT Tests User
 [#permalink] New post 06 Sep 2005, 21:09
zag1979 wrote:
The factors y & z follow the below shown triangle of values (can't remember its name):

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1

For the equation given, y=5 & z =10...answer is 50


Zag! Pretty d@mn good! I totally forgot that from high school. That makes these kind of problems a piece of cake.
  [#permalink] 06 Sep 2005, 21:09
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