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22 Dec 2023, 07:01
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C
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Difficulty:
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80% (01:20) correct
20%
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wrong
based on 169
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12 Days of Christmas 🎅 GMAT Competition with Lots of Questions & Fun
Elvin has sent wish lists to both Santa and Mrs. Claus. What is the probability that he will receive gifts from neither of them?
(1) The probability that he will receive gifts from both Santa and Mrs. Claus is 1/4.
(2) The probability that he will receive gifts from exactly one of them is three times the probability that he will receive gifts from both.
Elvin has sent wish lists to both Santa and Mrs. Claus. What is the probability that he will receive gifts from neither of them?
(1) The probability that he will receive gifts from both Santa and Mrs. Claus is 1/4.
(2) The probability that he will receive gifts from exactly one of them is three times the probability that he will receive gifts from both.
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23 Dec 2023, 05:59
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GMAT Club Official Explanation:
Elvin has sent wish lists to both Santa and Mrs. Claus. What is the probability that he will receive gifts from neither of them?
We have:
{Sant only} + {Mrs. Claus only} + {Both} + {Neither} = 1
The question asks to find the probability of {Neither}.
(1) The probability that he will receive gifts from both Santa and Mrs. Claus is 1/4.
This implies that {Both} = 1/4. Not sufficient.
(2) The probability that he will receive gifts from exactly one of them is three times the probability that he will receive gifts from both.
This implies that {Sant only} + {Mrs. Claus only} = 3*{Both}. Not sufficient.
(1)+(2) Since from (1) {Both} = 1/4 and from (2) {Santa only} + {Mrs. Claus only} = 3*{Both}, then {Santa only} + {Mrs. Claus only} = 3/4. Thus, we have that 3/4 + 1/4 + {Neither} = 1, which yields {Neither} = 0. Of course, Elvin won't be left without gifts on Christmas! Sufficient.
Answer: C.
General Discussion
22 Dec 2023, 07:26
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Total components
Gift from santa and mrs. claus both = x
Git from only one of them = y
Gift from neither of them = z
x+y+z = 1
Statement 1:
x = 1/4
insufficient
Statement 2:
x = p
y = 3p
z = 1-4p
Insufficient
Both together,
p = 1/4
z = 0
C
Gift from santa and mrs. claus both = x
Git from only one of them = y
Gift from neither of them = z
x+y+z = 1
Statement 1:
x = 1/4
insufficient
Statement 2:
x = p
y = 3p
z = 1-4p
Insufficient
Both together,
p = 1/4
z = 0
C
