which one is bigger?

[ustado]

Column A
100, 210 x 90,021

column b
100,021 x 90,210

[kobe317]

A=(100,000+210)(90,000+21)=100,000*90,000+210*21+( 100,000*21 +90,000*210)
B=(100,000+21) (90,000+210)=100,000*90,000+210*21+(100,000*210 +90,000*21)

So we can just compare x,y
x=10^5*21+9*10^4*210=21(10^5+9*10^5)=21*10^6
y=10^5*210+9*10^4*21==21*10^6+10^4*21

So x<y A<B
exactly, B-A= 21*10^4

[chestnut.cc]

A100, 210 x 90,021

B100,021 x 90,210

B can be simplified as:

(90,021 + 10,000) * (100,210 - 10,000)
90,021*100,210 + 10,000(100,210 - 90,021 -1)
ie A + (some positive term)

A<B

[kobe317]

chestnut.cc
well done!

[rokxal]

no need for explicit calculations here. Think of it this way, given sets of quantities ab and (a-c)(b+c) and imagine a,b to be lengths of a rectangle. You are essentially comparing areas of 2 different rectangles... Knowing that squares maximize area (by optimization or linear algebra principles), its easy to see that column b is correct. You can also generalize this problem to extremes, e.g. 99*1 vs (99-49)(1+49) since the principles still applies.

[sporty.arjun]

there is a very simple method in these kinda sums....between the two columns whichever smaller number is greater that column is the greater column eg.Col A has 90,021 and col B has 90,210....col b will b greater

[e.cartman]

I think rokxal nailed it.