Hi,

How would you approach those two excersises below? I am preparing alone (without a tutor and math/ GMAT prep. background) so I found those tasks rather difficult for me..

I've found suggestion here: https://www.preplounge.com/en/consulting-forum/math-prep-cagr-without-excel-any-tips-750#a1460 to use Taylor series - but that approach seems not to be applicable for all the cases (i.e. if the (1+x)^a=V is (1+(-x))^a - decreasing by 1 p.p. is not helpful at all)..

I am looking for several generic&fast approaches to cover all possible cases (i.e. solutions are too close to each other, growth rate is negative, etc.)

1. The Revenue in Y0 = 11.64. We project annual growth to be 7%. Which of the foll. is the closest estimate of the projected Revenue in Y5?

- a) 15.2
- b) 16.3
- c) 17.4
- d) 18.5

My approach:

1) 11.64(1+0.07)^5 = y

then either:

2) use binomial formula: (1+x)^5 = 1+5x+10x^2+10x^3+5x^4+x^5 => x = 1.403

or

3) (1+0.07)^5 = 1.07^4 * 1.07 = 1.15*1.15*1.07=1.323*1.07 = 1.42

4) y = 11.64*1.4 = 16.3 => **b)**

2. Number of cows 3 years ago - 2 150 000, now - 500 000. Assuming cows declining at a constant rate, which of the foll. is the closest estimate of the annual % drop in the number?

- a) 20%
- b) 25%
- c) 40%
- d) 55%

My approach:

1) 2 150 000 (1-x)^3 = 500 000

(1-x)^3 = 0.232

2) x=20%:

0.8^3 = 0.64*0.8 = 0.512 => wrong

3) x=25%: too close to 20% => wrong

4) x=40%:

0.6^3 = 0.36*0.6 = 0.216 ~ 0.232

5) x = 55%:

0.45^3 = 0.20*0.45 = 0.09 => wrong.

6) **c)**

Thank you in advance!