350 students at High School are currently enrolled in French, Spanish,

Official Explanation

Although you could draw a Venn diagram or a double-set matrix to answer this question, there is a formula for overlapping sets that will save you time:

Total = Group 1 + Group 2 + Neither – Both

In words, the total number of items equals the number of items in the first group, plus the number of items in the second group, plus the number of items in neither group, minus the number of items in both groups. (That last subtraction is necessary because the “both” items have been counted twice, as part of the first group and as part of the second group.) Apply the formula to the current problem:

Total = Spanish + French + Neither – Both

The total number of students is 350 and the number of students currently enrolled in Spanish is 230. Furthermore, all students are taking either French or Spanish or both, so the Neither category equals 0.

230 + French + 0 – Both = 350

French – Both = 120

Find 2 choices that differ by 120, with the larger number representing the total number of students currently enrolled in French and the smaller number representing the number of student enrolled in both French and Spanish. 260 and 140 are the only numbers in the list that have a difference of 120.

Column 1: The correct answer is (E).
Column 2: The correct answer is (A).