All the fourth-graders in a certain elementary school took a standardized test. A total of 85% of the students were found to be

Answer:

a. 13%

b. 20%

c. 2%

Step-by-step explanation:

To tackle this problem effectively, drawing a Venn diagram is recommended. Create a rectangle representing all fourth-graders, and include two overlapping circles within it. One circle should indicate reading proficiency, occupying 85% of the total area (including the overlap), while the other represents math proficiency, covering 78% of the area (including overlap). The intersection accounts for 65% of the total.

a. Given that 65% is the overlap and 78% are proficient in math, the percentage of students proficient in math but not in reading is calculated by:

78% − 65% = 13%

b. Since the overlap is 65% and 85% are proficient in reading, the percentage proficient in reading but not math is obtained by:

85% − 65% = 20%

c. To find the percentage of students who are not proficient in either reading or math, subtract the percentages of those proficient in only reading, only math, and both from 100%:

100% − 20% − 13% − 65% = 2%

Refer to the diagram provided (not to scale).