In a certain shipment of T-shirts, 20 percent are red. Of those shirts

Question

Tough and Tricky questions: Overlapping Sets.

In a certain shipment of T-shirts, 20 percent are red. Of those shirts, 30 percent are size small. If there are 366 red, small T-shirts, how many T-shirts in total were in the original shipment?

A. 732
B. 1220
C. 1830
D. 4806
E. 6100

Kudos for a correct  solution .

gillesalex07 · Answer

If N is the total number of T-shirts, we have 20*N/100 red T-shirts and 30/100*20*N/100=6/100*N small red T-shirts.
We have 6/100*N=366 so N=6100.

Answer (E)

NATABERI · Answer

0.3*0.2=0.06 --- 6%

so 366 is 6%
366/0.06=6100

Answer: E

PareshGmat · Answer

Answer = E = 6100

a% of b = \frac{ab}{100}

a% of (b% of c) = \frac{abc}{100*100} and so on........

Back to the problem,

Let the total shirts = x

20 percent are red. Of those shirts, 30 percent are size small

\frac{20*30 * x}{100*100} = 366

x = 6100

Vetrik · Answer

20 % are red and of that 30% are small. So the small red is 30*20/100 = 6% of the total shipment.

If 6% is 366, what is 100%,

(100/6)*366 = 6100.

Hence Answer E.

Bunuel · Answer

Official Solution:

In a certain shipment of T-shirts, 20 percent are red. Of those shirts, 30 percent are size small. If there are 366 red, small T-shirts, how many T-shirts in total were in the original shipment?

A. 732
B. 1220
C. 1830
D. 4806
E. 6100
 
We are trying to find  t , the total number of T-shirts in the original shipment. The problem says that  20%  of these T-shirts are red. Recall that the word "of" entails multiplication, so we can represent the number of red T-shirts as  20% 	imes t . Converting the percent to a decimal, we get:  0.2t .

Of these red shirts,  30%  are small, so the number of small T-shirts is  30% 	imes 0.2t = 0.3(0.2t) . Since there are 366 of these red, small T-shirts, we can formulate the equation:  0.3(0.2t) = 366 .

Now we solve for  t , the number of total T-shirts in the shipment.  0.3(0.2) = 0.06 , so  0.06t = 366 . Since  0.06 = \frac{6}{100} = \frac{3}{50} , we have  \frac{3}{50} 	imes t = 366 . Multiplying both sides by  \frac{50}{3} , we get  \frac{50}{3}(0.06t) = 366 	imes \frac{50}{3} , so  t = 366\leftarrow(\frac{50}{3}ightarrow) . To avoid large numbers, we divide by 3 first:  t = 366 	imes \frac{50}{3} = 122 	imes 50 = 6100 .
 
Answer: E.

ScottTargetTestPrep · Answer

We can create the equation:

0.2 x 0.3 x n = 366

0.06n = 366

n = 6,100

Answer: E

Kinshook · Answer

T=366/.2/.3 = 6100

IMO E

Posted from my mobile device

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In a certain shipment of T-shirts, 20 percent are red. Of those shirts

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