tricky and difficult

[sanju09]

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]

[phillybeat]

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..

[sanju09]

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

[BastiG]

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 ?

[phillybeat]

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..

[BastiG]

Thanks a lot for your detailed explanation.

[sanju09]

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

[jagger]

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.