a comparison q

[astral glow]

1.
col a:19^20
col b:20^19

[priyankagre2005]

Column A will be greater because 19 is being multiplied 20 times whereas 20 is being multiplies only 19 times.
This is similar to the question: Compare: 3⁵ 5³; 3⁵ > 5³

[manwiththemission2005]

For such questions, except 2^3 is < 3^2 , all other increasing order values satisfy the ans A.

3^4 > 4^3
4^5 > 5^4
and so on
So Ans is A

[Dimas]

I will provide a general way to solve this type of questions:

You are comparing a^b to c^d
a^b : c^d
Ln(a^b) : Ln( c^d)
b Ln a : d Ln c
b/Ln c : d / Ln a

Whatever a,b,c, and d are, keep in mind this inequality:

x/Lnx > y/lny if x > y > 2.71 which is e
x/Lnx < y/lny if 2.71 > x > y > 0
x/Lnx < y/lny if 2.71 > x > y > 1

For this problem, 20 and 19 are both > 2.71 so the problem is easy.
19^20 : 20^19
20 Ln 19 : 19 Ln 20
20/Ln20 : 19/Ln19
A for sure.

[gre1600]

good dimas very helpful formula

[xeley]

thanks! it's very helpful to have those tricks in mind without thinking how they are derived- especially only a few days before the test! my GRE is on august 30 and i hope to learn some similar facts- that can help save time and nerves. thank you again