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15 Jul 2024, 07:00
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C
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Difficulty:
35%
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Question Stats:
75% (01:14) correct
25%
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wrong
based on 363
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In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
(1) The probability that the mouse will find only one of the two treats is 1/5.
(2) The probability that the mouse will find both treats is 3/10.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
(1) The probability that the mouse will find only one of the two treats is 1/5.
(2) The probability that the mouse will find both treats is 3/10.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
D. EACH statement ALONE is sufficient to answer the question asked.
E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
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15 Jul 2024, 08:15
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In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
This is an overlapping problem in disguise, so let's treat it as such:
Essentially, we need to find the value of the green box given that the sum of the four colored boxes is 1.
(1) The probability that the mouse will find only one of the two treats is 1/5.
The above gives the sum of the values of the red boxes, which is not sufficient to find the value of the green box.
(2) The probability that the mouse will find both treats is 3/10.
The above gives the value of the yellow box, which is not sufficient to find the value of the green box.
(1)+(2) Together, we have the combined value of the red boxes (1/5) and the value of the yellow box (3/10). Thus, the value of the green box is 1 - (1/5 + 3/10) = 1/2. Sufficient.
Answer: C.
GMAT-Club-Forum-ndlh5sy1.png [ 4.21 KiB | Viewed 896 times ]
GMAT Club Official Explanation:
In a science experiment, a mouse is placed in a labyrinth with two different treats hidden in it. What is the probability that the mouse will find neither of the treats?
This is an overlapping problem in disguise, so let's treat it as such:
Essentially, we need to find the value of the green box given that the sum of the four colored boxes is 1.
(1) The probability that the mouse will find only one of the two treats is 1/5.
The above gives the sum of the values of the red boxes, which is not sufficient to find the value of the green box.
(2) The probability that the mouse will find both treats is 3/10.
The above gives the value of the yellow box, which is not sufficient to find the value of the green box.
(1)+(2) Together, we have the combined value of the red boxes (1/5) and the value of the yellow box (3/10). Thus, the value of the green box is 1 - (1/5 + 3/10) = 1/2. Sufficient.
Answer: C.
Attachment:
GMAT-Club-Forum-ndlh5sy1.png [ 4.21 KiB | Viewed 896 times ]
General Discussion
Oppenheimer1945
Joined: 16 Jul 2019
Last visit: 14 Nov 2025
Posts: 784
Given Kudos: 223
Location: India
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80 
GPA: 7.81
Schools: INSEAD '26 (D) ISB '27 (D) IIMB '26 (A) IIMA '26 (A) HEC '26 (D) LBS '26 IESE '27 (D) Fuqua '27 (WL) Tepper '27 (WL)
GMAT Focus 1: 645 Q90 V76 DI80
Posts: 784
15 Jul 2024, 07:21
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let a be prob of finding 1st treat, b be prob of finding 2nd treat
what is (1-a)(1-b)=1-a-b+ab?
S1) a(1-b)+b(1-a)=1/5
=>1+a+b-2ab=1/5 (not suff)
S2) ab=3/10 (not suff)
S1+S2) putting ab in S1, gives a+b,
hence you can find 1-a-b+ab=0.5 (Suff)
what is (1-a)(1-b)=1-a-b+ab?
S1) a(1-b)+b(1-a)=1/5
=>1+a+b-2ab=1/5 (not suff)
S2) ab=3/10 (not suff)
S1+S2) putting ab in S1, gives a+b,
hence you can find 1-a-b+ab=0.5 (Suff)
