NEW HERE? LEARN MORE
closeclose
Last visit was: 10 May 2024, 13:14 It is currently 10 May 2024, 13:14
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93155
Own Kudos [?]: 622687 [50]
Given Kudos: 81828
Send PM
CAT Tests Forum Quiz Mode
A law school admissions office sent letters to each of its 200 applica [#permalink] New post   24 Nov 2016, 02:42
4
Kudos
46
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

45% (medium)

Question Stats:

74% (03:06) correct 26% (03:02) wrong based on 359 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
broall
Retired Moderator
Joined: 10 Oct 2016
Status:Long way to go!
Posts: 1144
Own Kudos [?]: 6162 [7]
Given Kudos: 65
Location: Viet Nam
Send PM
GMAT ToolKit User
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   24 Nov 2016, 03:41
5
Kudos
2
Bookmarks
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


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
General Discussion
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3043
Own Kudos [?]: 6334 [1]
Given Kudos: 1646
Send PM
Forum Quiz Mode
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   25 Jul 2018, 17:34
1
Bookmarks
Expert Reply
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


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
User avatar
D
saukrit
Senior Manager
Senior Manager
Joined: 05 Jul 2018
Status:Current student at IIMB
Affiliations: IIM Bangalore
Posts: 384
Own Kudos [?]: 405 [1]
Given Kudos: 326
Location: India
Concentration: General Management, Technology
Schools: IIMB EPGP'22 (A)
GMAT 1: 600 Q47 V26
GRE 1: Q162 V149
GPA: 3.6
WE:Information Technology (Consulting)
Send PM
Reviews Badge
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   14 Oct 2018, 15:05
1
Bookmarks
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
User avatar
B
munnabhaimbbs
Intern
Intern
Joined: 17 Jul 2016
Posts: 24
Own Kudos [?]: 11 [0]
Given Kudos: 141
Send PM
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   24 Nov 2016, 02:57
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

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
User avatar
P
fskilnik
Tutor
Joined: 12 Oct 2010
Status:GMATH founder
Posts: 892
Own Kudos [?]: 1379 [0]
Given Kudos: 56
Send PM
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   14 Oct 2018, 14:47
Expert Reply
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.
User avatar
S
Paras96
Director
Director
Joined: 11 Sep 2022
Posts: 500
Own Kudos [?]: 154 [0]
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Send PM
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   15 Aug 2023, 09:17
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?

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
User avatar
B
Malar95
Senior Manager
Senior Manager
Joined: 29 Oct 2023
Posts: 331
Own Kudos [?]: 162 [0]
Given Kudos: 11
Location: Malaysia
Send PM
Re: A law school admissions office sent letters to each of its 200 applica [#permalink] New post   09 Jan 2024, 09:53
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.
GMAT Club Bot
gmatclubot
Re: A law school admissions office sent letters to each of its 200 applica [#permalink]
09 Jan 2024, 09:53
Moderators:
Bunuel
Math Expert
93155 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions