Interesting GMATFix Problem-32

[arora007]

The Richter magnitude scale quantifies the amount of energy released by an earthquake. An earthquake of magnitude m+1 releases 900% more energy than an earthquake of magnitude m. The energy released by an earthquake of magnitude 4.7 is approximately how many times the energy released by an earthquake of magnitude 3.2?
A)150
B)100
C)55
D)32
E)15

[fatalityish]

The answer of this has to be (E) 15 times.

Solution:-

let energy released for mag. m be e
hence energy for m+1 = 900% excess of e
i.e.
(900/100)*e + e = 10e

hence
energy for m ->e
energy for m+1->10e

now assume energy for mag 3.2 be e

4.7 = 3.2 + 1 + 0.5
therefore energy for mag. 4.7 -> 10e + 5e = 15e

hence energy for mag. 4.7 is 15e/e = 15 times the energy of mag. 3.2

Ishaan

[arora007]

Ishaan I hope you get that the intensity increases exponentially!

[saurabhmahajan]

i dont know if i am right.... please dont get angry if i am doing it in stupid way

m+1 releases 900% more energy than m....i.e 9 times more for an increase by 1.
therefore for an increase by 1.5 * 9 = 13.5
approx equal to 15 times

[fatalityish]

Ishaan I hope you get that the intensity increases exponentially!

so is 15 not the answer???

[gmatmachoman]

i dont know if i am right.... please dont get angry if i am doing it in stupid way

m+1 releases 900% more energy than m....i.e 9 times more for an increase by 1.
therefore for an increase by 1.5 * 9 = 13.5
approx equal to 15 times

ebergy released by M : x

energy released by m+1 : 10 X

So for 3.2 units X units of energy is released

for 4.2 units 10 X units of Energy is released

for 5.2 units 100 X units of energy is released

So for 4.7 units , the value will be mean of 5.2 & 4.2 units

Pick C-- 55 units of energy .

I dont think this a foolproof method.. I felt like i am using some conventional milkmaid method used by my grandma! LOL

[fatalityish]

hey machoman good one. arora i didnt think about the geometric increase of the energy with the growth.

Ishaan