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RenB
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In a certain meatpacking plant, one-fifth of the shipments are tainted 20 Sep 2023, 18:49
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61% (03:21) correct 39% (03:20) wrong based on 568 sessions

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In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
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E
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In a certain meatpacking plant, one-fifth of the shipments are tainted 13 Jun 2026, 11:30
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RenB
In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
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GMATNinja Video Solution:



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In a certain meatpacking plant, one-fifth of the shipments are tainted 20 Sep 2023, 23:46
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RenB
In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?
(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
Show more

We can plot the information on a 2 * 2 matrix and solve the question. The detailed solution to the question is shown below -

Attachment:
Screenshot 2023-09-21 121453.jpg
Screenshot 2023-09-21 121453.jpg [ 83.89 KiB | Viewed 9564 times ]

Option E
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In a certain meatpacking plant, one-fifth of the shipments are tainted 23 Sep 2023, 12:36
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RenB
In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
Show more

Really good question.

Let's take 150 as total shipments. T=150.

S = Stained (salmonella)
SR1 = Stained (salmonella) Rejected
SR2 = Stained (salmonella) Not Rejected

U = Unstained
UR1 = Unstained (salmonella) Rejected
UR2 = Unstained (salmonella) Not Rejected

Total = 150
Stained = \(\frac{1}{5}*150\) = 30
Unstained = 120

80% of S is rejected.
SR1 = 24.
SR2 = 6.

We know that U = 120.

So, UR1 = x and UR2 = 120-x

Given: the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected.

Translating to the equation:

SR1 + UR1 = \(\frac{1}{3}*UR2\)
24 + x = \(\frac{1}{3}*(120-x)\)
x = 12

Question is asking for: \(\frac{x}{SR1+US1}\)
\(\frac{12}{24+12}\) = \(\frac{1}{3}\)

Answer = E: 33.3%
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In a certain meatpacking plant, one-fifth of the shipments are tainted 24 Sep 2023, 12:37
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RenB
In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
Show more

If T is the total number of shipments, we have:

#Salmonella = #Rejected Salmonella + #Not-rejected Salmonella
(1/5)T = (4/5)(1/5)T + (1/5)(1/5)T
T/5 = 4T/25 + T/25

#Not-salmonella = #Rejected Not-salmonella + #Not-rejected Not-salmonella
(4/5)T = [4T/5 – x] + x

Since the total number of rejected shipments is equal to one-third of the number of untainted shipments that are not rejected, we have:

4T/25 + 4T/5 – x = x/3
24T/25 = 4x/3
T/x = 25/18

The percentage of the rejected shipments that are not tainted with salmonella is:

[(4T/5 – x)/(x/3)]100% = [(12/5)(T/x) – 3]100% =
[(12/5)(25/18) – 3]100% =
[10/3 – 3]100% =
[100/3]% ≈ 33.3%

Answer: E
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In a certain meatpacking plant, one-fifth of the shipments are tainted 21 Nov 2024, 14:01
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I've solved this using values—check out the detailed video solution here. Hope you find it helpful!



Smart Prep (Tutor)

RenB
In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

(A) 8%
(B) 16%
(C) 20%
(D) 24%
(E) 33.3%
Show more
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In a certain meatpacking plant, one-fifth of the shipments are tainted 27 Nov 2024, 03:51
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In a certain meatpacking plant, one-fifth of the shipments are tainted with salmonella, and 80 percent of the shipments with salmonella are rejected. If the total number of rejected shipments is equal to one-third of the number of untainted shipments that are NOT rejected, approximately what percent of the rejected shipments are NOT tainted with salmonella?

Tainted with SalmonellaNot Tainted with SalmonellaTotal
Rejected80%*20%=16%x%-16%x%
Not Rejected4%96%-x%100%-x%
Total20%80%100%

x% = 1/3 (96%-x%)
3x% = 96% - x%
x% = 96%/4 = 24%


Tainted with SalmonellaNot Tainted with SalmonellaTotal
Rejected80%*20%=16%x%-16%=8%x%=24%
Not Rejected4%96%-x%=72%100%-x%=76%
Total20%80%100%

The percent of the rejected shipments are NOT tainted with salmonella = 8%/24% = 33.33%

IMO E
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In a certain meatpacking plant, one-fifth of the shipments are tainted 21 Jul 2025, 10:20
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I wonder why can't we answer it 8%? ... 8% is nothing but Rejected & Non Tainted Kinshook
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In a certain meatpacking plant, one-fifth of the shipments are tainted 21 Jul 2025, 11:01
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BinodBhai
I wonder why can't we answer it 8%? ... 8% is nothing but Rejected & Non Tainted Kinshook
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Because we want to find percentage of the rejected shipments that are NOT tainted with salmonella, thus 8/24 = 33.33%

8% is the percentage of total shipments that are rejected and not tainted with salmonella

Hope it helps.
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