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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

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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

OA A

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Let x be the number of applicants who should have received acceptance letters.
Let y be the number of applicants who should have received denial letters.

Therefore we know that x+y=200
Now,
10% of those who were supposed to receive acceptances received denial letters. This means that 90% of the accepted candidates got their correct letters, which is 0.9x.
40% of those who should have received denial letter got acceptance letters instead, which is 0.4y

Since 160 applicants received acceptance letters
0.9x+0.4y=160.

Now we can solve the 2 equations

Solve this we have x=160 and y=40.

Thus 0.1x = 16

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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
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.

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Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

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AAPL wrote:
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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

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Scott Woodbury-Stewart Founder and CEO

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