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24 Mar 2022, 06:45
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E
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Difficulty:
25%
(medium)
Question Stats:
82% (02:03) correct
18%
(02:54)
wrong
based on 188
sessions
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A group of items was studied to determine whether or not each item possessed characteristic A and whether or not each item possessed characteristic B. Among the items possessing characteristic A, 17 items possessed characteristic B while 31 items did not possess characteristic B. If 60 percent of the items did not possess characteristic A, how many items were in the group?
A. 48
B. 71
C. 96
D. 108
E. 120
A. 48
B. 71
C. 96
D. 108
E. 120
thkkrpratik
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24 Mar 2022, 07:04
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A group of items was studied to determine whether or not each item possessed characteristic A and whether or not each item possessed characteristic B. Among the items possessing characteristic A, 17 items possessed characteristic B while 31 items did not possess characteristic B. If 60 percent of the items did not possess characteristic A, how many items were in the group?
Items possessing ONLY characteristic A = x
Items possessing ONLY characteristic B = y
Items possessing BOTH characteristics A and B = z
As per the given info:
z = 17
x = 31
Total = x+z = 48
Given info - 60 percent of the items did not possess characteristic A
Therefore, y = 60 % of the items and remaining, i.e. x + z = 40 % of the items.
We know, x + z = 48.
40% of total items = 48, therefore total items = 120.
Option E.
Items possessing ONLY characteristic A = x
Items possessing ONLY characteristic B = y
Items possessing BOTH characteristics A and B = z
As per the given info:
z = 17
x = 31
Total = x+z = 48
Given info - 60 percent of the items did not possess characteristic A
Therefore, y = 60 % of the items and remaining, i.e. x + z = 40 % of the items.
We know, x + z = 48.
40% of total items = 48, therefore total items = 120.
Option E.
10 Oct 2024, 21:26
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Problem is based on Overlapping Sets with 2 variables
Let's draw a 2x2 table to represent the problem as below:
2x2 table.jpg [ 18.41 KiB | Viewed 1350 times ]
Let T = x
Among the items possessing characteristic A, 17 items possessed characteristic B while 31 items did not possess characteristic B.
=> AB = 17 and AB ̅ = 31
=> Total A = 17 + 31 = 48
If 60 percent of the items did not possess characteristic A
=> 60% of Total = A ̅
=> 0.6 * x = A ̅
=> A ̅ = 0.6x
2x2 solution.jpg [ 17.69 KiB | Viewed 1270 times ]
=> A = x - A ̅ = x - 0.6x = 0.4x = 48
=> x = \(\frac{48}{0.4}\) = 120
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Overlapping Sets
Let's draw a 2x2 table to represent the problem as below:
Attachment:
2x2 table.jpg [ 18.41 KiB | Viewed 1350 times ]
- A represents the items possessing characteristics A
- B represents the items possessing characteristics B
- AB represents the items possessing characteristics A and B
- AB ̅ represents the items possessing characteristics A but not B
- A ̅ B represents the items possessing characteristics B but not A
- A ̅ B ̅ represents the items not possessing characteristics A and B
- A ̅ represents the items not possessing characteristics A
- B ̅ represents the items not possessing characteristics B
- T represents total items considered
Let T = x
Among the items possessing characteristic A, 17 items possessed characteristic B while 31 items did not possess characteristic B.
=> AB = 17 and AB ̅ = 31
=> Total A = 17 + 31 = 48
If 60 percent of the items did not possess characteristic A
=> 60% of Total = A ̅
=> 0.6 * x = A ̅
=> A ̅ = 0.6x
Attachment:
2x2 solution.jpg [ 17.69 KiB | Viewed 1270 times ]
=> A = x - A ̅ = x - 0.6x = 0.4x = 48
=> x = \(\frac{48}{0.4}\) = 120
So, Answer will be E
Hope it helps!
Watch the following video to MASTER Overlapping Sets
