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18 Feb 2025, 01:30
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
84% (01:03) correct
16%
(01:11)
wrong
based on 81
sessions
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Each of the 850 local villagers in Lucia owns either a Golden Retriever or a Bernard. How many people own both?
(1) The number of villagers who own a Golden Retriever only is 300.
(2) The number of villagers who own a Bernard only is 280.
(1) The number of villagers who own a Golden Retriever only is 300.
(2) The number of villagers who own a Bernard only is 280.
18 Feb 2025, 02:43
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Let:
- G = total number of villagers who own a Golden Retriever
- B = total number of villagers who own a Bernard
- x = number of villagers who own both
Given:
G + B - x = 850 (Total villagers equation)
Statement (1):
G - x = 300 (Golden Retriever only)
Insufficient alone.
Statement (2):
B - x = 280 (Bernard only)
Insufficient alone.
Combining (1) and (2):
1. G - x = 300
2. B - x = 280
3. G + B - x = 850 (given)
Adding (1) and (2):
G + B - 2x = 580
Subtracting from (3):
(G + B - x) - (G + B - 2x) = 850 - 580
-x = -270
x = 270
Since x is uniquely determined, both statements together are sufficient.
Answer: (C) Both statements together are sufficient, but neither alone.
- G = total number of villagers who own a Golden Retriever
- B = total number of villagers who own a Bernard
- x = number of villagers who own both
Given:
G + B - x = 850 (Total villagers equation)
Statement (1):
G - x = 300 (Golden Retriever only)
Insufficient alone.
Statement (2):
B - x = 280 (Bernard only)
Insufficient alone.
Combining (1) and (2):
1. G - x = 300
2. B - x = 280
3. G + B - x = 850 (given)
Adding (1) and (2):
G + B - 2x = 580
Subtracting from (3):
(G + B - x) - (G + B - 2x) = 850 - 580
-x = -270
x = 270
Since x is uniquely determined, both statements together are sufficient.
Answer: (C) Both statements together are sufficient, but neither alone.
18 Feb 2025, 08:00
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T = 850
N= 0
B=?
g = Golden Retriever
b = Bernard
T = g + b - B + N
850 = g + b - B - (1)
g only = g - B
b only = b - B
Statement 1
g only = 300
Plugging this in the equation 1
850 = 300 +b
b= 550 - (2)
No way to know value of B here
Insufficient
Statement 2
b only = 280
Plugging this in the equation 1
850 = g +280 - (3)
No way to know value of B here
Insufficient
Combined
We have
b = 550 from (equation 2)
b only = 280
B = b - b only = 550 - 280 = 270
Sufficient
N= 0
B=?
g = Golden Retriever
b = Bernard
T = g + b - B + N
850 = g + b - B - (1)
g only = g - B
b only = b - B
Statement 1
g only = 300
Plugging this in the equation 1
850 = 300 +b
b= 550 - (2)
No way to know value of B here
Insufficient
Statement 2
b only = 280
Plugging this in the equation 1
850 = g +280 - (3)
No way to know value of B here
Insufficient
Combined
We have
b = 550 from (equation 2)
b only = 280
B = b - b only = 550 - 280 = 270
Sufficient
Bunuel
