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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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E
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Difficulty:

85% (hard)

Question Stats:

62% (03:18) correct 38% (03:19) wrong based on 439 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 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 8644 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, 12:43
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GMATNinja - this one's yours I think...

Could be 'solved' (or rather, guessed) within 10 seconds. I've seen this also with some OG Questions in the newest edition.

They ask you 'approximately' but then go on to provide 4 terminating fractions and one that is an approximation... Could be risky but worked every single time I've seen it.
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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%
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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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