A law school admissions office sent letters to each of its

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A law school admissions office sent letters to each of its 200 applicants, but because of an error in the mail room the acceptance and denial letters did not all go to the proper recipients. 40% of those who should have received denial letters received acceptance letters instead, and 10% of those who were supposed to receive acceptances received denial letters. If 160 applicants received acceptance letters, how many applicants who should have received acceptance letters instead received denial letters?

A. 16
B. 20
C. 24
D. 28
E. 32

We can let r = the number of applicants who should have received acceptance letters; thus, (200 - r) = the number of applicants who should have received denial letters.

Thus, 0.9r = the number of applicants who should have received acceptance letters and received acceptance letters, and 0.1r = the number of applicants who should have received acceptance letters but received denial letters instead. Similarly, 0.6(200 - r) = the number of applicants who should have received denial letters and received denial letters, and 0.4(200 - r) = the number of applicants who should have received denial letters but received acceptance letters instead.

Therefore, we can create the following equation for the total number of applicants who received acceptance letters:

0.9r + 0.4(200 - r) = 160

9r + 4(200 - r) = 1600

9r + 800 - 4r = 1600

5r = 800

r = 160

Since 10% of the 160 applicants who should have received acceptance letters received denial letters, 16 of them received denial letters.

Answer: A