Out of 600 students who complete the proficiency test, 423 were found to be proficient in reading, 398 were found to be proficient in math, and 512 were found to be proficient in either reading or math. How many were proficient in both reading and math?

309 students

Step-by-step explanation:

Out of 600 students who complete the proficiency test, 423 were found to be proficient in reading, 398 were found to be proficient in math, and 512 were found to be proficient in either reading or math. How many were proficient in both reading and math?

We solve the above question using the formula below:

Where R = Proficiency in reading

M = Proficiency in maths

n ( R ∪ M) = n(R) + n ( M) - n ( R ∩ M)

n ( R ∪ M) = 512 students

n(R) = 423

n ( M) = 398

n ( R ∩ M) = ??

Hence:

512 = 423 + 398 - n ( R ∩ M)

n ( R ∩ M) = 423 + 398 - 512

= 821 - 512

= 309

The number of people proficient in both reading and math [n ( R ∩ M)] = 309 students