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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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.
_________________

Follow your heart

The approaches above are perfectly fine.

Difficult to find the shortest way to the solution

Regards
_________________

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