tough questions

[sukh]

A certain board game has a row of squares numbered 1 to 100.
If a game piece is placed on a random square and then moved
7 consecutive spaces in a random direction, what is the
probability the piece ends no more than 7 spaces from the
square numbered 49?
(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

The inside dimensions of a rectangular wooden box are 4
meters by 5 meters by 6 meters. A cylindrical drum is to be
placed inside the box so that it stands upright when the closed
box rests on one of its six faces. Of all such drums that could
be used, what is the volume, in cubic meters, of the one that
has maximum volume?
(A) 20
(B) 24
(C) 25
(D) 96
(E) 100
Why the answer isn't 45 pi

[cans]

A certain board game has a row of squares numbered 1 to 100.
If a game piece is placed on a random square and then moved
7 consecutive spaces in a random direction, what is the
probability the piece ends no more than 7 spaces from the
square numbered 49?
(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

No more than 7 spaces from 49 means no. lies between 42 and 56 (including these). Thus possible no. = 15.
Now if original no. on 49 - 100%
less than 35 or more than 63= 0%
35-48 and 50-63 = 50% (total numbers = 28) = 14%
thus final = 15%
IMO D

[cans]

The inside dimensions of a rectangular wooden box are 4
meters by 5 meters by 6 meters. A cylindrical drum is to be
placed inside the box so that it stands upright when the closed
box rests on one of its six faces. Of all such drums that could
be used, what is the volume, in cubic meters, of the one that
has maximum volume?
(A) 20
(B) 24
(C) 25
(D) 96
(E) 100

4*5*6.
Volume = pi*r*r*h
if base = 4*6, height = 5 and r = 2. Vol = 20pi
if base = 5*6, h=4 and r=2.5, Vol = 25pi
if base = 4*5, h=6 and r=2, vol = 24pi
thus 25pi.
IMO C

[sunman]

A certain board game has a row of squares numbered 1 to 100.
If a game piece is placed on a random square and then moved
7 consecutive spaces in a random direction, what is the
probability the piece ends no more than 7 spaces from the
square numbered 49?
(A) 7%
(B) 8%
(C) 14%
(D) 15%
(E) 28%

No more than 7 spaces from 49 means no. lies between 42 and 56 (including these). Thus possible no. = 15.
Now if original no. on 49 - 100%
less than 35 or more than 63= 0%
35-48 and 50-63 = 50% (total numbers = 28) = 14%
thus final = 15%
IMO D

Thanks for the mathematical explanation. It makes sense now.

I selected the correct answer as well, but my theory was much more simplistic (and admittedly, a little bit of intuition more than mathematical calculation):

42-56 = 15 squares out of 100.

No matter what square you land on, and how many consecutive spaces you move in 1 direction or another, your chances of landing on one of those squares will always be 15/100. So 15%.