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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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A law school admissions office sent letters to each of its
This topic has expert replies
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
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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fskilnik@GMATH
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Another very nice problem in which "blending" the k technique and the grid (double-matrix) "shields" the problem fast and clear!AAPL wrote:Veritas Prep
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
(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)
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Scott@TargetTestPrep
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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.AAPL wrote:Veritas Prep
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
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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