Explanation

Use the overlapping sets formula for two groups: Total = Group 1 + Group 2 – Both + Neither. (Adding the two groups—in this case Latin and Spanish—double-counts the students who
study both languages, so the formula subtracts the “both” students.)

Set up your equation:

150 = 75 + 110 – B + 11

150 = 196 – B

46 = B

Careful! This is not the value of Quantity A. Since 46 students study both Latin and Spanish, subtract 46 from the total who study Latin to find those who study only Latin:

75 – 46 = 29

Thus, Quantity A is 29. Therefore Quantity B is greater.
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Just make a table
The numbers written in black is what were given
The numbers written in red are the calculations based on what was given

If there are 150 students in total, but 110 taking spanish, then there are 40 people not taking Spanish
Also, if there are 150 students, and 75 students take Latin, then 75 Students dont take latin
Out of 75 students who dont take Latin, 11 take neither latin nor spanish, which means there are 75-11=64 students who take spanish but not latin
out of the 110 studetns that take spanish, there are 110-64=46 students who also take latin
Out of the 75 students that take latin, 75-46 =29 that take only latin.

This table, on paper, takes about 50 seconds to complete if you are good with simple math, and don't want to learn anything
that may seem too complicated.

Answer: B
First Approach:
Total number of people: 150
Neither Spanish, nor Latin: 11
Spanish or Latin or both: 150-11 = 139 ->
Specifically Spanish + Specifically Latin Both Latin and Spanish = 139
Latin : 75
Spanish: 110
139 - 110 =19 Those who don’t speak Spanish and speak just Latin. (Specifically Latin)
139-75 =54 Those who don’t speak Latin and study just Spanish (Specifically Spanish)

Specifically Spanish + Specifically Latin + Both Latin and Spanish = 139
19 + 54 + both = 139 -> both = 46
A: The number of students who study only Latin: 19
B: 46
B is bigger

Second Approach:
If we think of a venn diagram we will see: the total numbers in the union would be 150-11=139
There is an intersection and a specific Latin and a specific Spanish:

Spanish + Latin - intersection = 110 + 75 - intersection = 139 -> intersection = 46
A: Just Latin = 75 - 46 = 19 which is less than B. And the asnwer is B.
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I hope to hear from GreenLightTestPrep for a Good Approach.
_________________

The approaches above are perfectly fine.

Difficult to find the shortest way to the solution

Regards
_________________

Wow, this is a good task for a skilled math person. Sadly I need essay help at https://www.aresearchguide.com/essay-help.html to complete this kind of task. Hope that soon I become a real professional.

Great

I just needed it. Thanks for sharing.

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