A law school admissions office sent letters to each of its 200 applica

Question

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

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

broall · Accepted Answer

Call  x  is the number of applicants who should have received acceptance letters
Call  y  is the number of applicants who should have received denial letters
We have  x+y=200

10% of those who were supposed to receive acceptances, or  0.1x , received denial letters. This leads to 90% of those who were supposed to receive acceptances, or  0.9x , received acceptances letters.
40% of those who should have received denial letters, or  0.4y , received acceptance letters instead.

Since there are 160 applicants received acceptance letters, we have  0.9x+0.4y=160 .

Now we have:
 \begin{cases}
x+y=200\
0.9x+0.4y=160\
\end{cases}

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

The number of applicants who should have received acceptance letters instead received denial letters is  0.1x=16 .

The answer is A

munnabhaimbbs · Answer

I would go with B.160 applicants received the letters which represent the 40 percent of the total number of students.So 100 percent is 400 students.Now,the ratio of letters sent to applicants to total applicants is 200/400.It implies that the applicants who should have received acceptance letters instead received denial letters would be 400*10%*200/400=20

Please correct me if I am incorrect.
Cheers

JeffTargetTestPrep · Answer

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

fskilnik · Answer

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.

https://preview.ibb.co/g90DT0/14-Oct18-11b.gif

? = {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.

saukrit · Answer

Let us assume the actual candidates to be denied as D and those accepted as A

Now as per question:
0.4D + 0.9 A=160
0.4(200-A) +0.9A=160 {As A+D=200}
Hence A=160

Applicants who should have received acceptance letters instead received denial letters =0.1*A =16

Hence Answer is A

Paras96 · Answer

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

Let the no. of correct acceptance letters = x
Let the no. of correct denial letters = y

therefore, x + y = 200

As per actual condition,
the no. of actual acceptance letters = 0.9x + 0.4y = 160
the no. of actual denial letters = 0.6y + 0.1x = 200-160=40

Solving,
=> y =40
=> x = 160
=> Answer = 0.1x = 16

Hence A

Malar95 · Answer

Im seeing lengthy calculations.
My marker pen rn is running out of ink to share a clear pic.
But once I inputted all the numbers in the table, it all just adds up to 10% of 160 = 16. Correct me if I am wrong or maybe doing this super late at night is blurring me.

Pratham_Patil24 · Answer

Hi  Bunuel ,

Could you please share similar questions to practice ?

Bunuel · Answer

Overlapping Sets

Theory: 
 
  Overlapping Sets Made Easy!  
  How to draw a Venn Diagram for problems  
  ADVANCED OVERLAPPING SETS PROBLEMS  
  Formulae for 3 overlapping sets

Questions: 
 
  The E-GMAT Sets Triad: 3 Exciting Sets Questions!  
  The Word “Or” in GMAT Math  
  DS Questions  
  PS Questions

For more: 
 
  ALL YOU NEED FOR QUANT ! ! !  
  Ultimate GMAT Quantitative Megathread

Hope it helps.

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