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Problem Solving — algebra and arithmetic
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by sanju09 » Wed Aug 25, 2010 8:51 pm
A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
The mind is everything. What you think you become. –Lord Buddha



Sanjeev K Saxena
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by phillybeat » Wed Aug 25, 2010 9:06 pm
sanju09 wrote:A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
answer is 3^8 = 27*27*9 = 6561

solution is

just take first part of the prob

3+3+3+2*3^2 = 9+2*3^2= 3^2+2*3^2= 3^3.
the last one is 3^7 so total is 3^8.


whats the right answer..
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by sanju09 » Wed Aug 25, 2010 10:00 pm
phillybeat wrote:
sanju09 wrote:A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
answer is 3^8 = 27*27*9 = 6561

solution is

just take first part of the prob

3+3+3+2*3^2 = 9+2*3^2= 3^2+2*3^2= 3^3.
the last one is 3^7 so total is 3^8.


whats the right answer..
whatever, but you rock
The mind is everything. What you think you become. –Lord Buddha



Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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by BastiG » Fri Aug 27, 2010 4:02 pm
phillybeat wrote:
sanju09 wrote:A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
answer is 3^8 = 27*27*9 = 6561

solution is

just take first part of the prob

3+3+3+2*3^2 = 9+2*3^2= 3^2+2*3^2= 3^3.
the last one is 3^7 so total is 3^8.


whats the right answer..
Pls go more into detail. What is with the middle part 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 ?
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by phillybeat » Fri Aug 27, 2010 4:31 pm
BastiG wrote:
phillybeat wrote:
sanju09 wrote:A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
answer is 3^8 = 27*27*9 = 6561

solution is

just take first part of the prob

3+3+3+2*3^2 = 9+2*3^2= 3^2+2*3^2= 3^3.
the last one is 3^7 so total is 3^8.


whats the right answer..
Pls go more into detail. What is with the middle part 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 ?
here you go..

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???


To make it simple I will use ()

(3 + 3 + 3) + (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 9+ (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^2 + (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^2 (1+2)+ ( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^3 +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

=3^3 (1+2)+ (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^4(1+2) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^5(1+2) +( 2 × 3^6) + (2 × 3^7)

= 3^6 (1+2) + (2 × 3^7)
= 3^7(1+2)
= 3^8 is the answer..

I hope I made it clear..
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by BastiG » Fri Aug 27, 2010 6:05 pm
Thanks a lot for your detailed explanation. :D
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by sanju09 » Sat Aug 28, 2010 3:23 am
phillybeat wrote:
BastiG wrote:
phillybeat wrote:
sanju09 wrote:A very very interesting question, which was no doubt tricky and difficult.

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???



[spoiler]Source: somewhere on this page https://railgaadi.wordpress.com/[/spoiler]
answer is 3^8 = 27*27*9 = 6561

solution is

just take first part of the prob

3+3+3+2*3^2 = 9+2*3^2= 3^2+2*3^2= 3^3.
the last one is 3^7 so total is 3^8.


whats the right answer..
Pls go more into detail. What is with the middle part 2 X 3^3 + 2 X 3^4 + 2 X 3^5 + 2 X 3^6 ?
here you go..

3 + 3 + 3 + 2 × 3^2 + 2 × 3^3 + 2 × 3^4 + 2 × 3^5 + 2 × 3^6 + 2 × 3^7 =???


To make it simple I will use ()

(3 + 3 + 3) + (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 9+ (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^2 + (2 × 3^2) +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^2 (1+2)+ ( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^3 +( 2 × 3^3) + (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

=3^3 (1+2)+ (2 × 3^4) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^4(1+2) + (2 × 3^5) +( 2 × 3^6) + (2 × 3^7)

= 3^5(1+2) +( 2 × 3^6) + (2 × 3^7)

= 3^6 (1+2) + (2 × 3^7)
= 3^7(1+2)
= 3^8 is the answer..

I hope I made it clear..
many congratulations
The mind is everything. What you think you become. –Lord Buddha



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Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com
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by jagger » Sat Nov 27, 2010 5:45 am
another way could be to use the sum of G.P (geometric progressions) formula...
the expression can be written as 3 + 2(3) + 2(3^2) + 2(3^3)...+2(3^7). Leave out the first term of 3 (you can add it later) and simplify the remaining terms as 2[3 ^1 + 3^2 + ...3^7]. The expression in the bracket is a GP and you can find its sum easily. Remember to add the 3 you removed earlier and you get the same answer: 3^8.
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