If a Carton Containing a Dozen Mirrors is Dropped GMAT Problem Solving

Question: If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

1. 2:1
2. 3:1
3. 3:2
4. 1:1
5. 7:5

“If a carton containing a dozen mirrors is dropped,”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide Quantitative Review". To solve GMAT Problem Solving questions a student must have knowledge about a good number of qualitative skills. GMAT Quant section consists of 31 questions in total. The GMAT quant topics in the problem-solving part require calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:

Approach Solution 1:

Given to us in the question, a carton containing a dozen mirrors is dropped and it is asked which could not be the ratio of broken mirrors to unbroken mirrors.
A dozen means 12. Therefore there are 12 mirrors in the carton.

We have to check all the five options to know which ratio is not possible.
The idea is that whatever may be the number of broken mirrors, it will always be an integer.
In the first option,
Ratio = 2:1
This means 2/2+1 of total mirrors are broken
Or ⅔ * 12 mirrors = 8 mirrors are broken.
As 8 is an integer this could be possible.

In second option.
Ratio = 3:1
This means 3/(3+1) of total mirrors are broken.
Or ¾ * 12 mirror are broken
=> 9 mirrors are broken and the rest 3 are not broken.

As 9 is an integer this could be possible.

In third option,
Ratio = 3:2
This means 3/(3+2) of total mirrors are broken
=> ⅗ of 12 mirrors are broken
=> 7.2 mirror are broken.
But the number of mirrors cannot be a fraction.
Therefore this ratio is not possible.

In fourth option
Ratio = 1:1
This means 1/(1+1) of total mirrors are broken
=> 1/2 of 12 mirrors are broken
=> 6 mirror are broken.
As 6 is an integer this could be possible.

In the fifth option,
Ratio = 7:5
Ratio = 1:1
This means 7/(7+5) of total mirrors are broken
=> 7/12 of 12 mirrors are broken
=> 7 mirrors are broken and the rest 5 are not broken.
As 7 is an integer this could be possible.

Therefore we can finally see that there is only one ratio which is not an integer and therefore not possible.

Correct Answer: C

Approach Solution 2:

Let us assume that the ratio of broken to unbroken mirrors is m:n
Then (m+n) * p must be equal to 12, where p is some integer.
This implies that 12 must have a factor of m+n
Now by checking the options it is clear that option C
3:2
Here m = 3 and n = 2
M+n = 3+2 = 5 is not a factor of 12.

Correct Answer: C

Approach Solution 3:

Considert that there are m:n broken mirrors compared to unbroken mirrors.
Then (m+n)*p, where p is an integer, must equal 12.
This suggests that 12 must be multiplied by m+n.
Now that we have checked the alternatives, we can see that option C
3:2
Here, m is 3 and n is 2.
It is not a factor of 12 for M+n = 3+2 = 5.

Correct Answer: C

Suggested GMAT Problem Solving Question

• Metropolis Corporation has 4 Shareholders GMAT Problem Solving 
• If x and y are positive integers and (1/7)^x * (1/8)^12 = (1/8)^1/18y, then what is the value of y-x? GMAT Problem Solving 
• At Springfield High, three-fourths of the male students and half of the female students speak a foreign language GMAT Problem Solving 
• What is the number of integers from 1 to 1000, inclusive that are not divisible by 11 or by 35? GMAT Problem Solving 
• If m is Three Times n, and if 2n + 3 is 20% of 25, What is the value of m? GMAT Problem Solving 
• If Ben Were to Lose the Championship, Mike would be the Winner GMAT Problem Solving 
• A Train Travelling at a Certain Constant Speed takes 30 seconds GMAT Problem Solving 
• A conference room is equipped with a total of 45 metal or wooden chairs. GMAT Problem Solving 
• A welder received an order to make a 1 million litre cube-shaped tank. GMAT Problem Solving 
• After 6 games, Team B had an average of 61.5 points per game. GMAT Problem Solving 
• If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a three-percent vinegar solution, GMAT Problem Solving 
• A contractor estimated that his 10-man crew could complete the construction in 110 days if there was no rain GMAT Problem Solving 
• A circle is inscribed in a square with the diagonal of 4 centimeters. GMAT Problem Solving 
• At a dog competition, a dog is awarded 10 points if it runs through 4 pipes, makes 10 jumps, and walks on 2 beams. GMAT Problem Solving 
• Two consultants, Mary and Jim, can type up a report in 12.5 hours and edit it in 7.5 hours. GMAT Problem Solving 
• What is the value of k if the sum of consecutive odd integers from 1 to k equals 441? GMAT Problem Solving 
• A circle with a radius R is inscribed into a square with a side K. GMAT Problem Solving 
• Machine A can do a certain job in 12 days working 2 full shifts while Machine B can do the same job in 15 days working 2 full shifts. GMAT Problem Solving 
• The square of \(5^\sqrt2)\ =? GMAT Problem Solving 
• The population of the bacteria colony doubles every day. GMAT Problem Solving