Bunuel wrote:

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

Another very nice problem in which "blending" the

k technique and the

grid (double-matrix) "shields" the problem fast and clear!

(At least to my students) Study this problem asking yourself why start putting in the grid the

10k "value" was a smart move.

\(? = {1 \over {10}}\left( {200 - 10k} \right) = 20 - k\)

\(160 - {2 \over 5}\left( {10k} \right) = {9 \over {10}}\left( {200 - 10k} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,160 - 4k = 180 - 9k\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,5k = 20\)

\(? = 16\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

_________________

Fabio Skilnik :: GMATH method creator (Math for the GMAT)

Our high-level "quant" preparation starts here: https://gmath.net