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01 Jan 2025, 01:30
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D
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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
(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
01 Jan 2025, 03:11
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Bunuel
Let n = 100 and W be white, NW be not white, D be defect and ND be no defect then we are given below details in the question
| W | NW | T | |
| D | 40*3/4 = 30 | ||
| ND | ? | 10 | |
| T | 60 | 40 | 100 |
Calculate \(\frac{100 * ND_W}{T_W}\)?
Statement 1 => D = 50
| W | NW | T | |
| D | 20 | 30 | 50 |
| ND | 40 | 10 | |
| T | 60 | 40 | 100 |
Percentage = 100*40/60 = 66.67%
Hence, this statement is sufficient.
Statement 2 => Let total shirts with tailoring defect be x, then
| W | NW | T | |
| D | 2x/5 | 30 | x |
| ND | ? | 10 | |
| T | 60 | 40 | 100 |
2x/5 + 30 = x
30 = 3x/5
x = 50
| W | NW | T | |
| D | 20 | 30 | 50 |
| ND | 40 | 10 | |
| T | 60 | 40 | 100 |
Percentage = 100*40/60 = 66.67%
Hence, this statement is sufficient.
IMO: D
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