GMAT paper test DS

I got C
but would appreciate if someone can suggest a faster way.

So it is either a C or E.

from stmt 1
2(l +w) = 28
=> l + w = 14 ------------- (1)

Squaring both sides
(l +2)^2 = 196
l^2 + w^2 +2lw = 196.
From the figure
l^2 + w^2 = 10^2 (from stmt 2)

simplifying, lw = 48 ------------(2)


substitute 2 in 1
l + 48/l = 14
=> l^2 -14l +48 = 0
solving this l = 6 or 8.
Now from the problem we get the longer side is l = 8 so
shorter side = 6 ( coz l + w = 14)

from this diameter of circle = 6 = length of shorter side .

area of semi circle = 1/2 * 22/7 * (6/2)^2.
Add this value to 48 from stmt 2
to get the answer.


Long process!!!! .

hope someone can provide a faster better procedure.
I took more than 2 mins to figure out.

Also any thoughts on the problem level ??
I think this is a 600 - 700 level problem.

What do u guys think?

St 1: 2(l+b) = 28
l+b = 14-------equ 1

Insuff

St 2: l^2 + b^2 = 100-------equ 2

Insuff

Combining 1+2

Every time you see an equation in the form of a^2 + b^2 = 10^2 think of special triangle 3-4-5

So using the special triangles concept, l = 8 and b = 6 (l>b)
These values also satisfy both equ 1 and equ 2.

So C is suff.

Okay, I find this apropriate forum for DS questions I faced in GMATPrep test1.

This DS questions asks to check co-ordinates for given equation. I dont get how the answer can be C. Can anybody solve this?

Thanks in advance

mals24 wrote:St 1: 2(l+b) = 28


Every time you see an equation in the form of a^2 + b^2 = 10^2 think of special triangle 3-4-5

.

Yes!!! good tip. somehow forgot about using that!!!.
thanks for the tip

rgds
-V