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Consulting Interview Mental Math
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Gravity
Terms in this set (53)
1/3
0.33
1/4
0.25
1/5
0.2
1/6
.167
1/7
.143
1/8
.125
1/9
.11
1/11
.0909
1/12
.083
1/13
.077
1/14
.071
1/15
.067
1/16
.0625
1/17
.059
1/18
.056
1/19
.053
1/20
.05
1,000 * 1,000
1,000,000 (One Million)
100 * 10,000
1,000,000 (One Million)
25,000 * 20,000
500,000,000 (500 Million)
[25*2=50; add 7 zeros]
18,000,000 / 6,000
3,000 (Three Thousand)
[Simplified to 18,000/6 = 3,000]
5
18,000
1,000,000
90,000,000,000 (90 Billion)
[5*18=90; add 9 zeros]
How long does it take an investment with annual return 6% to double?
12 years
[Rule of 72: 72/6=12 years]
How long does it take an investment with annual return 20% to double?
Approximately 3.5 years
[Rule of 72: 72/20≈3.5 years]
An investor purchased an asset for 120,000 45 years ago. The asset has appreciated by 8% per year. What is the investment worth today?
3.84M
[Rule of 72: 72/8 = doubles every 9 years]
[45/9 = has doubled 5 times]
[Investment worth 120,000*2⁵ = 3.84M]
How many people in the United States?
300M
Population of EU
750M
Population of Asia
4.5B
Population of China
1.4B
Population of Middle East
200M
Population of Africa
1B
How many deaths per year assuming life expectancy is 75 years and population is 300M?
4M
[If uniform distribution, 1/75 of population dies each year]
[1/75*300=4]
12*16
192
[12*10 + 12*6]
[120 + 72]
19*19
361
[20*20=400]
[400-1*20-1*19=361]
17*17
289
[20*20=400]
[400-3*20-3*17=289]
18*18
324
[20*20=400]
[400-2*20-2*18=324]
16*16
256
13*13
169
[10*10=100]
[100+3*10+3*13=169]
A company is looking for 12% annual ROI on a $50M upfront investment. What is the minimum required return
$6M/year
[50M*12%=6M]
A company is looking for 20% ROI on a $50M upfront investment over a period of 5 years. What annual return would they need to see?
$2M/year
[50M*20%=10M = aggregate return]
[10M/5 years = 2M/year]
33,000,000 / 5000
6,600
[Simplifies to 33,000/5]
[=30,000/5 + 3,000/5]
[=6,000 + 600]
[=6,600]
17,000/320,000
Approximately 5%
[17,000/32,000 would be 50%]
[Move one decimal to the left = 5%]
Specifically 5.3%
[16,000/320,000 = 5%]
[1,000/320,000 = 1/320]
[1/32 = 1/16/4≈.06/2=0.3]
[=5.3%]
3/5
60%
7/12
58.3%
3/8
37.5%
5/16
31.25%
(1/4)*(1/3) [in decimal format]
.083 (1/12)
14*11
154
[Multiplication by 11 trick:]
[ 11*AB={1}{A+B}{B}]
[11*14=154]
11*25
275
[Multiplication by 11 trick:]
[ 11*AB={1}{A+B}{B}]
11*36
396
[Multiplication by 11 trick:]
[ 11*AB={1}{A+B}{B}]
8*16
128
132/X = 10
X = 13.2
120*x = 30
X=0.25
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