The ratio of the area of a square mirror to its frame is 16 to 33. If

Question

The ratio of the area of a square mirror to its frame is 16 to 33. If the frame has a uniform width (c) around the mirror, which of the following could be the value, in inches, of c ?

I. 2
II. 3 1/2
III. 5

A. I only
B. III only
C. I and II only
D. I and III only
E. I, II, and III

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CareerGeek · Accepted Answer

Since ratio of area of mirror to frame = 16/33
Let the area of mirror = 16*k^2
—> Area of mirror + frame = 33k^2 + 16k^2 = 49k^2
—> Side of mirror = 4k 
Side of mirror + frame = 7k
—> 4k + 2c = 7k
—> 2c = 3k
—> c = 3/2k

We can get all the values 2, 3 1/2 & 5 of c for certain values of k

IMO Option E

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Archit3110 · Answer

giving a try
ratio given
x^2/(x+2a)^2 = 16/33
solve for x & a
for each value of given a = 2,3.5 and 5
we can check for area of square which should be < the frame
IMO E ; is valid

Thekingmaker · Answer

pure luck and brute force examintion and determination is all it takes to get tot the answer hence imo E

Fdambro294 · Answer

We can set up the Ratio of the Inner Square’s Area to the Entire Square’s Area

Inner Square Area in ratio units = 16

Entire Square Area in ratio units = 16 + 33 = 49

Call the side of the Inner Square = X ——> Area = (X)^2

This means the side of the Entire Square = X + 2C ———> Area = (X + 2C)^2

Rule: since all squares are similar shapes, if we take the Square Root of the Ratio of the (Area of Inner Square) / (Area of Entire Square)

———> we will get the Ratio of the: (Side of the Inner Square) / (Side of Entire Square)

(X)^2 / (X + 2*C)^2 = 16/49

Take the square root of each side: since we are dealing with lengths, we only need to take the positive root of the unknown Variable squared and the binomial squared

X / (X + 2C) = 4/7 = Ratio of (Inner square’s side) / (Entire square’s side)

7X = 4X + 8C

3X = 8C

You can plug in any of the values of C given by the Roman numerals and you will get a corresponding value of X

Since there is no constraint on what type of value X can take, any positive value of C is possible because there will always be a corresponding positive value of X that will keep the two Areas in the correct ratio.

(E) all three

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abhiramguddeti · Answer

Method 1:

= 33/16

{X+2C}^2/X^2 - X^2/X^2 = 33/16

{X+2C}^2/X^2 - 1 = 33/16

{X+2C}^2/X^2 = 49/16

{X+2C}/X = 7/4

7X = 4X + 8C

According to this equation, all the values can be true. Hence answer E.

Method 2:

For anyone who wonders how to solve this question if it comes in the real GMAT exam:
Since there are no restrictions on X and C mentioned in the question other than the fact that they are X, C>0 and it is just a mere ratio, any values should be okay. Hence option E.

DISCLAIMER: I would use this method only if I was running out of time. Otherwise please follow the methods suggested above.

bumpbot · Answer

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The ratio of the area of a square mirror to its frame is 16 to 33. If

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