gmAT PAPER CODE 28 S3 Q14,16

[rb90]

Q14)
In a certain school, 40 more than 31 of all the students are taking a science course and 41 of those taking a science course are taking physics. If 81 of all the students in the school are taking physics, how many students are in the school?

(A) 240
(B) 300
(C) 480
(D) 720
(E) 960

OA is A.

Q16)
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister 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 canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

OA is B.


Please explain the working in both the cases here.
Thanks in advance!

[GMATGuruNY]

The first question was reproduced incorrectly. Here is the correct version:

In a certain school, 40 more than 1/3 of all the students are taking a science course and 1/4 of those taking a science course are taking physics. If 1/8 of all the students in the school are taking physics, how many students are in the school?

A)240
B)300
C)480
D)720
E)960

We can plug in the answer choices, which represent the total number of students. Since 1/8 of the students take physics, the correct answer must be divisible by 8. Eliminate B.

Answer choice C: 480 students
40 more than 1/3 of all the students are taking a science course: 40 + (1/3)*480 = 200
1/4 of those taking a science course are taking physics: (1/4)*200 = 50.
1/8 of all the students in the school are taking physics: (1/8)*480 = 60.
50 ≠ 60.
Eliminate C. Need a smaller answer choice.

The correct answer is A.

Answer choice A: 240 students.
40 more than 1/3 of all the students are taking a science course: 40 + (1/3)*240 = 120
1/4 of those taking a science course are taking physics: (1/4)*120 = 30.
1/8 of all the students in the school are taking physics: (1/8)*240 = 30.
30 = 30. Success!

[shovan85]

Q16)
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister 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 canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?

(A) 3
(B) 4
(C) 5
(D) 6
(E) 8

OA is B.

Volume of cylinder = (pie)*(Radius)^2 *(Height)

We need this volume to be maximized.

As we have 6 faces of the Box out of which 3 will be distinctly different from one another (as facing faces are same)

So these 3 faces are 6 by 8, 8 by 10, and 10 by 6

When base Area (on which canister stands) is 6 by 8 the radius of the cylinder at best can be 3
When base Area (on which canister stands) is 10 by 8 the radius of the cylinder at best can be 4
When base Area (on which canister stands) is 6 by 10 the radius of the cylinder at best can be 3

Thus answer is 4.

See the below diagram if you have any feelings for why it cannot be 5? You can never dram a circle of radius 5 inch inside a rectangle of 8 by 10.