An Interview question @UBS for a quant job - can u solve it?

nanosensor

An interviewee at UBS for a math-heavy quant job was asked one of the toughest Wall Street interview questions we've seen yet.

Can you write your own math formula given a set of conditions on the spot?

If you want to be a quant at UBS, you'll have to.

To test your skills, try to answer this question posed to an interviewee a couple of years ago:

The number 1978 is such a number that if you add the first 2 sets of numbers, you'll will get the middle 2 sets of numbers. So in 1978, 19+78=97; so the question is write a formula that can find numbers that satisfy these conditions.

超级潜水员

Number: a3a2a1a0
a3*10+a2+a1*10+a0=a2*10+a1
10a3-9a2+9a1+a0=0

silicon_beaver

mark.

ysc

mlif

超级潜水员 发表于 2011-9-9 21:17
Number: a3a2a1a0
a3*10+a2+a1*10+a0=a2*10+a1
10a3-9a2+9a1+a0=0

a3+a0=9*(a2-a3-a1)
0<a3+a0<19=>a2-a3-a1=1 (if a3=a0=9, a2>9)
so (a3,a0)=(8,1) (7,2) (6,3) (5,4) (4,5) (3,6) (2,7) (1,8)
and you can list all possible (a2,a1) for each (a3,a0)

gummykitty

suppose the number is abcd, a = 1..9, all other 3 can be 0..9
from the given conditions, you will have 9*(b-c) = 10*a + d
the right is positive (a>=1), so (b-c) must be positive, and (10*a+d) has to be 9's multiple
now all possible combinations -
  a = 1, d = 8, b-c = 2
  a = 2, d = 7, b-c = 3
  ...
  a = 8, d = 1, b-c = 9  

ppteam

too simple to spend time on it. lol

mlif

Now my turn to kill some time for you guys
Compare these 2 w/o access to a calculator
sqrt(2)^sqrt(5) & sqrt(3)^sqrt(3)
sqrt as square root and ^ as power