PowerPrep Math Question (Math concepts) Taking GRE on Thursday

[gakgx6]

Attached are some Powerprep math question that I didn't understand. Will someone be able to explain me how to solve them?

Thanks In advance
Gakgx6

[Reza2011]

Simply,
1st term = 100210 x 90021
= (10000 + 210) x (90000 + 21 )
= 9000000000 + 2100000 + 21 x 210 + 21x90000x10
2nd Term = 100021 x 90210
= (10000 + 21) x (90000 + 210 )
= 9000000000 + 2100000 x 10 + 21 x 210 + 21x90000

the bolded numbers are the same for both term so,eliminating bolted term from both side and rearranging we can get

1st term = 2100000 + 21 x 90000 + 21 x 90000 x 9
2nd term = 2100000 + 21 x 90000 + 2100000 x 9
eliminating again :
1st term = 1890000 x 9
2nd term = 2100000 x 9
Now it is easily perceivable that, Column B > Column A,
I think anybody knows easier way to solve this type of problem.
Normally I solve this type of problem, in the following way:
* firstly looking at the biggest number of each four: the column containing biggest number is the smaller column.
For example :
(1)Column A : 1060 x 120 Column B : 1020 x 160
Ans : Column B > Column A

(2)Column A : 10099 x 100 Column B : 10100 x 99
Ans : Column A > Column B
It is not the actual procedure but may be used as a quicker way to find the right answer.

[Reza2011]

For Geometry, Circle :
Radius of circular flower bed including walk way = r + r/2 = 3r/2
Area of flower bed = pie x sqr (r)
Area of walk way = pie x sqr (r) - pie x sqr (3r/2)
= 5/4 x pie sqr (r)

So, Area of walk way > Area of flower bed
Please correct me if I am wrong.

[Reza2011]

For Reflection problem :
please see at following :
http://www.urch.com/forums/gre-math/...e-explain.html (PowerPrep Problem(Please solve and explain))

[Reza2011]

There are formula :
Sum of first n odd numbers: 1 + 3 + 5 + .... upto n terms = n^2
Sum of first n even numbers: 2 + 4 + 6 + ... upto n terms = n(n+1)
As there are 24 odd and 24 even term :
So, V = 24 x (24 + 1)
=24 x 24 + 24
D = 24^2 =24x24

So, V > D+23
Ans : A

[Reza2011]

For Equation of line :

we know if the equation of line is , y = mx + c , slope is = m
So, we get slope of the line, y=ax + b, is = a
Now, for y intersection, x = 0, it gives, y = b
for x intersection, y = 0, it gives, x = -b/a
According to question , both intersection are equal,
-b/a = b
so, a = -1
Hence, Ans : C