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A box contains n shirts, of which 60% are white in color. Three out of

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Kushchokhani
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A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   11 Sep 2021, 09:01
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A box contains n shirts, of which 60% are white in color. Three out of every four non-white shirts have a tailoring defect. What percentage of white shirts do not have a tailoring defect?

(1) If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
(2) The probability that a shirt with tailoring defect will be white in color is 2/5
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D
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   13 Jul 2022, 04:36
OA = D

Let's say, n=100
So, Total white shirts = 60 % of n = 60
Total non-white shirts = 40

now, three out of every four non-white shirts have a tailoring defect
so, non-white shirts with defect = [3/4]*40= 30
non-white shirts without defect = 10

Statement 1)

If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5

\(\frac{ Total defective shirts }{Total shirts } = 0.5\)
total defective shirts = 0.5*[total shirts] = 0.5*100 = 50

now , total defective shirts = [white defective shirts] + [non-white defective shirts]

so, white defective shirts = [total defective shirts] - [non-white defective shirts] = 50-30= 20

now, total white shirts = [ defective white shirts]+[not defective white shirts]

so, not defective white shirts = [total white shirts]-[defective white shirts] = 60 -20=40

percentage of white shirts do not have a tailoring defect = [40/60]*100, required answer

statement 1 is sufficent

statement 2)

\( \frac{white defective shirts}{total defective shirts} = \frac{2}{5}\)
so, let's say white defective shirts = 2x , then total defective shirts = 5x
now, total defective shirts = [white defective shirts] + [non-white defective shirts]
so , 5x = 2x + 30 , then x = 10

white defective shirts = 2x = 20

now, total white shirts = [ defective white shirts]+[not defective white shirts]

so, not defective white shirts = [total white shirts]-[defective white shirts] = 60 -20=40

percentage of white shirts do not have a tailoring defect = [40/60]*100, required answer

statement 2 is sufficent
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   05 Dec 2022, 19:12
Kushchokhani
A box contains n shirts, of which 60% are white in color. Three out of every four non-white shirts have a tailoring defect. What percentage of white shirts do not have a tailoring defect?
(1) If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
(2) The probability that a shirt with tailoring defect will be white in color is 2/5

A solution to this would be really helpful to evaluate
Thank you
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   06 Dec 2022, 01:24
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Kushchokhani
A box contains n shirts, of which 60% are white in color. Three out of every four non-white shirts have a tailoring defect. What percentage of white shirts do not have a tailoring defect?
(1) If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
(2) The probability that a shirt with tailoring defect will be white in color is 2/5

Solution:
Pre Analysis:
  • Total number of shirts \(= n\)
  • Total number of white shirts \(=60\% \text{ of } n=0.6n\)
    • white shirts with no tailoring defect \(=a\) (assuming)
    • white shirts with tailoring defect \(=0.6n-a\)
  • Total number if non-white shirts \(=n-0.6n=0.4n\)
    • non-white shirt with no tailoring defect \(=0.1n\)
    • non-white shirt with tailoring defect \(=0.3n\) (3 out of every 4)
Attachment:
tailor.png
tailor.png [ 8.31 KiB | Viewed 2737 times ]
  • We are asked the percentage of white shirts that do not have a tailoring defect i.e., the value of \(\frac{a}{0.6n}\) or \(\frac{a}{n}\)

Statement 1: If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
  • According to this diagram, \(\frac{0.6n-a+0.3n}{n}=\frac{1}{2}\)
    \(⇒\frac{0.9n-a}{n}=\frac{1}{2}\)
    \(⇒0.9-\frac{a}{n}=\frac{1}{2}\)
  • From this, we can very easily get the value of \(\frac{a}{n}\)
  • Thus, statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2: The probability that a shirt with tailoring defect will be white in color is 2/5
  • According to this diagram, \(\frac{0.6n-a}{0.6n-a+0.3n}=\frac{2}{5}\)
  • From this, we can very easily get the value of \(\frac{a}{n}\)
  • Thus, statement 2 alone is also sufficient

Hence the right answer is Option D
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   30 Jun 2023, 21:58
Kushchokhani
A box contains n shirts, of which 60% are white in color. Three out of every four non-white shirts have a tailoring defect. What percentage of white shirts do not have a tailoring defect?
(1) If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
(2) The probability that a shirt with tailoring defect will be white in color is 2/5

Good question! IMO D as well.

We know that 60% of n shirts are white in colour. So 3n/5 shirts are white. And 2n/5 shirts are non-white.
p(non white shirt with tailoring defect) = 3/4
So total non white shirts with tailoring defects are 3/4*2n/5 = 3n/10.

Statement 1: If one shirt is selected at random from the box, the probability that it will have a tailoring defect is 0.5
So total defect shirts(white+non white) = n/2. Out of these n/2 shirts defect shirts, 3n/10 shirts are non white defects. So shirts with white defects = \(\frac{n}{2}-\frac{3n}{10} = 0.2n\) shirts.
% of white defect shirts: \((\frac{0.2n}{n})*100=20\)%

Statement 2: The probability that a shirt with tailoring defect will be white in color is 2/5
White shirts=3n/5, Non white shirts=2n/5
Non white shirts with defects= \(\frac{3}{4}*\frac{2n}{5}=\frac{3n}{10}\)

Given: p(white shirt with tailoring defect)=2/5
# white shirts with tailoring defect/All shirts with tailoring defect = 2/5
Let # white shirts with tailoring defect=a
\(\frac{a}{(3n/10+a)}=\frac{2}{5}\).....(Non white shirts with defects=3n/10)
\(5a=\frac{6n}{10}+2a\)
\(a=\frac{2n}{10}\)
% of white defect shirts: (0.2n/n)*100=20%

Thus, option D.
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink] A box contains n shirts, of which 60% are white in color. Three out of   27 Aug 2024, 11:08
it is good strategy to prepare the tree diagram for such questions
n
White shirts Non white shirts
(0.6n) (0.4n)
Def Non Def Def Non-Def
x ? 0.3n 0.1n
statement 1 : 0.3n+x = 0.5n
x = 0.2n therefore non defective white shirt is 0.4n but we were asked %of non defective shirts out of white shirts
so required % = 0.4/0.6 = 66.67%

statement 2 : x/(0.3n+x) = 2/5
it gives x = 0.2n
and this statement is sufficient alone
hence answer is D
(be careful about what has been asked. Since this is DS question, option D could be selected without much calculation but this would have been the PS question in quant, it is necessary to know what percent has been asked)
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Re: A box contains n shirts, of which 60% are white in color. Three out of [#permalink]
27 Aug 2024, 11:08
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