In a certain meatpacking plant, one-fifth of the shipments are tainted

Question

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%

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

gmatophobia · Answer

We can plot the information on a 2 * 2 matrix and solve the question. The detailed solution to the question is shown below - Screenshot 2023-09-21 121453.jpg Option E

RiyazAhamed · Answer

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%

JeffTargetTestPrep · Answer

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 =   + 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:

100% =  100% =
 100% =
 100% =
 % ≈ 33.3%

Answer: E

akwenok · Answer

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.

QuantMadeEasy · Answer

I've solved this using values—check out the detailed video solution here. Hope you find it helpful!

https://www.youtube.com/watch?v=nvG-z7oFJec

Smart Prep (Tutor)

Kinshook · Answer

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%

Tainted with Salmonella 
 Not Tainted with Salmonella 
 Total 
 
  Rejected 
 80%*20%=16% 
 x%-16% 
 x% 
 
  Not Rejected 
 4% 
 96%-x% 
 100%-x% 
 
  Total 
 20% 
 80% 
 100%

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

Tainted with Salmonella 
 Not Tainted with Salmonella 
 Total 
 
  Rejected 
 80%*20%=16% 
 x%-16%=8% 
 x%=24% 
 
  Not Rejected 
 4% 
 96%-x%=72% 
 100%-x%=76% 
 
  Total 
 20% 
 80% 
 100%

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

IMO E

BinodBhai · Answer

I wonder why can't we answer it 8%? ... 8% is nothing but Rejected & Non Tainted  Kinshook

Krunaal · Answer

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.

In a certain meatpacking plant, one-fifth of the shipments are tainted

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	Tainted with Salmonella	Not Tainted with Salmonella	Total
Rejected	80%*20%=16%	x%-16%	x%
Not Rejected	4%	96%-x%	100%-x%
Total	20%	80%	100%

GMAT Problem Solving (PS) Questions

In a certain meatpacking plant, one-fifth of the shipments are tainted

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

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My Rewards