Dear yousufa,
I'm happy to help with these.

These are two bodacious questions, so I am going to treat each as a separate entry. First, the one about the architect and the spherical stones.

This is a question screaming out for approximations. The answers are widely spaced, and the question even says "select the value that is closest to ...", which is practically an engraved invitation to approximate. See this blog:
https://magoosh.com/gmat/2012/the-power- ... mat-quant/

First of all, one tricky thing --- the formula for surface area is given in terms of radius, but they give us circumferences. We ourselves need to know

c = 2(pi)r

Rearrange this to

r = c/[2(pi)]

Substitute this into the surface area formula:

SA = 4(pi)(r^2) = 4(pi)[(c^2)/[4((pi)^2)] = (c^2)/(pi)

Now, multiply that surface area times $92 for the cost

Cost = (92)*(c^2)/(pi)

Right away, I am going to approximate --- pi = something a little over three, so 92 (a little over 90) divided by something a little over three is approximately 90/3 = 30, so we can approximate

Cost = 30*(c^2)

For c = 5.5
Avoid the temptation to use the calculator. The calculator is a waste of time. What is 5.5 squared? Well, 5^2 = 25, and 6^2 = 36. We are just approximating, so let's say (c^2) is about halfway between 25 and 36, around 30. (Good to pick a nice round number in estimating.)
Cost = 30*30 = 900
There's the answer for the first column.

For c = 7.85.
Well, 7^2 = 49 and 8^2 = 64, and 7.85 is much closer to 8 than to 7, so approximate (c^2) is closer to 64 than to 49, so around 60 (just to pick a nice round number).
Cost = 30*60 = 1800
There's the answer for the second column.

Does this approach make sense?
Mike

Dear yousufa,

Now, let's go step by step through the flowchart. BTW, you can do another flowchart practice problem here:
https://magoosh.com/gmat/2013/gmat-ir-nu ... -problems/
Also, you may find this useful:
https://magoosh.com/gmat/2012/gmat-integ ... ing-ebook/

Question #1:
Start with
(a = 24, b = 35)

We start with T = 0
We enter (a = 24, b = 35)
Is b odd? YES. Go up.
T = T + a = 0 + 24 = 24
Right there, that's the first non-zero value for T, T = 24

Question #2:
Start with
(a = 35, b = 27)

We start with T = 0
We enter (a = 35, b = 27)
Is b odd? YES. Go up.
T = T + a = 0 + 35 = 35
move right
b = b - 1 = 26
move down
a = 2a = 2*35 = 70
move right
b = b/2 = 26/2 = 13 (this is the first time we do the b/2 operation)
Does b = 1? NO. Follow the long arrow back
Is b odd? YES. Go up.
T = T + a = 35 + 70 = 105
move right
b = b - 1 = 12
move down
a = 2a = 2*70 = 140
move right
b = b/2 = 12/2 = 6
That was the second time we got to the b/2 box, so that's the answer, b = 6.

Does all this make sense?
Mike