Problem Solving

If a 5-year construction project is structured to double the investment every succeeding year, what percentage of the total cost was invested in the first year?

a 12.5%
b 10%
c 8.25%
d 5%
e 3%


OA - E

Here's what I did;

Investment in the first year - 100 => 200 => 400 => 800 => 1600.

% of total cost = 100/1600=6.25%

However, OE says that total cost = 100+200+400+800+3100 ...Not sure why is OE adding all investments. Essentially, for a five year, perpetuity (Say), one cannot withdraw the investment in the middle of timeframe. Secondly, $200 get re-invested. Why are we considering it cost? Can anyone please explain?

thanks

The question says "What percentage of the total costs was invested in the first year. Hence, we add the investments of all 5 years

1st year=x; 2nd year=2x; 3rd year=4x; 4th year=8x; 5th year=16x

Total investment = 31x

(x/31x)*100 =~ 3.2%

voodoo_child wrote:If a 5-year construction project is structured to double the investment every succeeding year, what percentage of the total cost was invested in the first year?

a 12.5%
b 10%
c 8.25%
d 5%
e 3%


OA - E

Here's what I did;

Investment in the first year - 100 => 200 => 400 => 800 => 1600.

% of total cost = 100/1600=6.25%

However, OE says that total cost = 100+200+400+800+3100 ...Not sure why is OE adding all investments. Essentially, for a five year, perpetuity (Say), one cannot withdraw the investment in the middle of timeframe. Secondly, $200 get re-invested. Why are we considering it cost? Can anyone please explain?

thanks

Investments-

Year 1 = x

Year 2 = 2x

Year 3 = 4x

Year 4 = 8x

Year 5 = 16 x


Total Investment in these 5 years is x + 2x + 4x +8x + 16x = 31x

Now we are asked to find out :

what percentage of the total cost was invested in the first year

Investment in Year 1 / Total Investment * 100

x /31x *100 = ~ 3.xxx%

voodoo_child wrote:If a 5-year construction project is structured to double the investment every succeeding year, what percentage of the total cost was invested in the first year?

a 12.5%
b 10%
c 8.25%
d 5%
e 3%


OA - E

Here's what I did;

Investment in the first year - 100 => 200 => 400 => 800 => 1600.

% of total cost = 100/1600=6.25%

However, OE says that total cost = 100+200+400+800+3100 ...Not sure why is OE adding all investments. Essentially, for a five year, perpetuity (Say), one cannot withdraw the investment in the middle of timeframe. Secondly, $200 get re-invested. Why are we considering it cost? Can anyone please explain?

thanks

Well your mistake is 1600 is 5th year cost, the percentage should be summation of all 5 year projects.

As per your calculation - the total cost is 3100. not 1600...

Just a suggestion as your mistake in this problem - Read very carefully the question. That's the greatest GMAT trick used