Uva@90 wrote:A computer manufacturer claims that a perfectly square computer monitor
has a diagonal size of 20 inches. However, part of the monitor is made up of
a plastic frame surrounding the actual screen. The area of the screen is three
times the size of that of the surrounding frame. What is the diagonal of the
screen?

A) √125
B) 20/3
C) 20/√3
D) √150
E) √300

Diagonal of a square = s√2.
Let S = a side of the entire monitor and s = a side of the screen.

The monitor has a diagonal size of 20 inches.
Since S√2 = 20, S = 20/√2.
Thus, the area of the entire monitor = S² = (20/√2)² = 400/2 = 200.

The area of the screen is three times the size of that of the surrounding frame.
Implication:
If the area of the screen is 3 square inches, then the area of the frame is 1 square inch, with the result that the screen area is equal to 3/4 of the total area.
Since the monitor has a total area of 200, the screen area = (3/4)(200) = 150.
Since s² = 150, s = √150.
Thus:
diagonal = s√2 = √150 * √2 = √300.

The correct answer is E.

[email protected] wrote:Hi Uva@90,

What is the source of this question? I ask because the 'design' of the question (and the answers) isn't quite a match for proper GMAT 'style.' We're meant to assume that the plastic frame has a uniform width, although the prompt does not explicitly state that (and if the width is not uniform, then the answer to the question changes). Also, the answer choices have not been properly 'reduced/rewritten.'

If this question comes from an old (or unreliable) source, then you might be better off working with more realistic materials.

GMAT assassins aren't born, they're made,
Rich

Rich,

It is from Veritas Prep

Regards,
Uva.

GMATGuruNY wrote:

Uva@90 wrote:A computer manufacturer claims that a perfectly square computer monitor
has a diagonal size of 20 inches. However, part of the monitor is made up of
a plastic frame surrounding the actual screen. The area of the screen is three
times the size of that of the surrounding frame. What is the diagonal of the
screen?

A) √125
B) 20/3
C) 20/√3
D) √150
E) √300

Diagonal of a square = s√2.
Let S = a side of the entire monitor and s = a side of the screen.

The monitor has a diagonal size of 20 inches.
Since S√2 = 20, S = 20/√2.
Thus, the area of the entire monitor = S² = (20/√2)² = 400/2 = 200.

The area of the screen is three times the size of that of the surrounding frame.
Implication:
If the area of the screen is 3 square inches, then the area of the frame is 1 square inch, with the result that the screen area is equal to 3/4 of the total area.
Since the monitor has a total area of 200, the screen area = (3/4)(200) = 150.
Since s² = 150, s = √150.
Thus:
diagonal = s√2 = √150 * √2 = √300.

The correct answer is E.

Thanks Mitch,
I failed to notes this part
"If the area of the screen is 3 square inches, then the area of the frame is 1 square inch, with the result that the screen area is equal to 3/4 of the total area."

Thanks a lot.

Regards,
Uva

Uva@90 wrote:A computer manufacturer claims that a perfectly square computer monitor
has a diagonal size of 20 inches. However, part of the monitor is made up of
a plastic frame surrounding the actual screen. The area of the screen is three
times the size of that of the surrounding frame. What is the diagonal of the
screen?

A) √125
B) 20/3
C) 20/√3
D) √150
E) √300

Since the diagonal = side√2, we have:

20 = side√2

20/√2 = side

Multiplying by √2/√2, we have:

10√2 = side

If we let each side of the monitor, not counting the frame = n, then we can create the following equation:

n^2 = 3[(10√2)^2 - n^2]

n^2 = 3[200 - n^2]

n^2 = 600 - 3n^2

4n^2 = 600

n^2 = 150

n = √150

So, the diagonal of the screen is √150 x √2 = √300.

Alternate Solution:

Since the diagonal = side√2, a side of the monitor is 20/√2 = 10√2. Thus, the area of the monitor, including the screen and the surrounding frame, is (10√2)^2 = 200.

If we let A denote the area of the surrounding frame, the area of the screen is 3A and thus, the total area of the monitor is 3A + A = 4A. Since 4A = 200, we find that A = 50 and the area of the screen is 3A = 150. Then, a side of the screen is √150 = 5√6. Finally, the diagonal of the screen is (5√6) x √2 = 5√12 = √300.

Answer: E