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E
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Difficulty:
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61% (01:39) correct
39%
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At a shipping center, every package in a certain batch is either domestic or international, and each package is either insured or uninsured. If one package is selected at random from the batch, what is the probability that the package selected is a domestic insured package?
(1) Three-eighths of the packages in the batch are domestic.
(2) Two-fifths of the packages in the batch are insured.
(1) Three-eighths of the packages in the batch are domestic.
(2) Two-fifths of the packages in the batch are insured.
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26 Apr 2026, 01:00
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GMAT Club Official Solution:
At a shipping center, every package in a certain batch is either domestic or international, and each package is either insured or uninsured. If one package is selected at random from the batch, what is the probability that the package selected is a domestic insured package?
(1) Three-eighths of the packages in the batch are domestic.
Knowing that three-eighths of the packages are domestic tells us only the probability that a randomly selected package is domestic. It gives no information about how many of those domestic packages are insured. Not sufficient.
(2) Two-fifths of the packages in the batch are insured.
Knowing that two-fifths of the packages are insured tells us only the probability that a randomly selected package is insured. It gives no information about how many of those insured packages are domestic. Not sufficient.
(1)+(2) Take the total number of packages to be 40, the least common multiple of 8 and 5.
Then 3/8 of 40 = 15, so 15 packages are domestic and the remaining 25 are international.
Also, 2/5 of 40 = 16, so 16 packages are insured and the remaining 24 are uninsured.
But this still does not determine how many packages are both domestic and insured.
For example, one possible arrangement is:
15 domestic insured
0 domestic uninsured
1 international insured
24 international uninsured
In this case, the probability of selecting a domestic insured package is 15/40 = 3/8.
Another possible arrangement is:
0 domestic insured
15 domestic uninsured
16 international insured
9 international uninsured
In this case, the probability of selecting a domestic insured package is 0/40 = 0.
Not sufficient.
Answer: E.
At a shipping center, every package in a certain batch is either domestic or international, and each package is either insured or uninsured. If one package is selected at random from the batch, what is the probability that the package selected is a domestic insured package?
(1) Three-eighths of the packages in the batch are domestic.
Knowing that three-eighths of the packages are domestic tells us only the probability that a randomly selected package is domestic. It gives no information about how many of those domestic packages are insured. Not sufficient.
(2) Two-fifths of the packages in the batch are insured.
Knowing that two-fifths of the packages are insured tells us only the probability that a randomly selected package is insured. It gives no information about how many of those insured packages are domestic. Not sufficient.
(1)+(2) Take the total number of packages to be 40, the least common multiple of 8 and 5.
Then 3/8 of 40 = 15, so 15 packages are domestic and the remaining 25 are international.
Also, 2/5 of 40 = 16, so 16 packages are insured and the remaining 24 are uninsured.
But this still does not determine how many packages are both domestic and insured.
For example, one possible arrangement is:
15 domestic insured
0 domestic uninsured
1 international insured
24 international uninsured
In this case, the probability of selecting a domestic insured package is 15/40 = 3/8.
Another possible arrangement is:
0 domestic insured
15 domestic uninsured
16 international insured
9 international uninsured
In this case, the probability of selecting a domestic insured package is 0/40 = 0.
Not sufficient.
Answer: E.
General Discussion
19 Apr 2026, 22:43
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Let P(domestic and insured) be what we need to find
Statement (1) tells us that 3/8 of packages are domestic. But knowing how many packages are domestic tells us nothing about how many of those are insured. Insufficient
Statement (2) tells us that 2/5 of packages are insured. But knowing how many packages are insured tells us nothing about how many of those are domestic. Insufficient
Combining both statements, we know 3/8 are domestic and 2/5 are insured, but we still cannot determine the overlap between the two groups. We would need to know either the actual number of domestic insured packages, or that the two characteristics are independent of each other.
Neither is given. —— insufficient
The answer is E
Statement (1) tells us that 3/8 of packages are domestic. But knowing how many packages are domestic tells us nothing about how many of those are insured. Insufficient
Statement (2) tells us that 2/5 of packages are insured. But knowing how many packages are insured tells us nothing about how many of those are domestic. Insufficient
Combining both statements, we know 3/8 are domestic and 2/5 are insured, but we still cannot determine the overlap between the two groups. We would need to know either the actual number of domestic insured packages, or that the two characteristics are independent of each other.
Neither is given. —— insufficient
The answer is E
