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Difficulty:
15%
(low)
Question Stats:
85% (01:11) correct
15%
(00:44)
wrong
based on 62
sessions
History
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In a group of 42 college students, how many were juniors who landed summer internships?
(1) Of the 42 college students, 29 found summer internships.
(2) Of the 42 college students, 24 were juniors.
(1) Of the 42 college students, 29 found summer internships.
(2) Of the 42 college students, 24 were juniors.
01 Feb 2026, 23:37
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In a group of 42 college students, how many were juniors who landed summer internships?
(1) Of the 42 college students, 29 found summer internships.
(2) Of the 42 college students, 24 were juniors.
Let's look at each statement individually and then at both of them together (if required):
Statement 1: Of the 42 college students, 29 found summer internships.
Through this statement, we get to know the number of total interns in the college, but nothing about how many of them were juniors can be inferred.
Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Of the 42 college students, 24 were juniors.
Through this statement, we get to know the number of total juniors in the college, but nothing about how many of them were interns can be inferred.
Hence, Statement 2 is insufficient alone.
Now, let's take a look at the combination of both statements - Statement 1 and Statement 2:
We know:
Total number of college students = 42
Total number of interns = 29
Total number of juniors = 24
However, the total number of junior interns could vary. Let's understand this through this example:
Case 1 - Total number of junior interns = 24 (all juniors could have internships). This can also be thought of as the case of Maximum Overlap.
Case 2 - Now, let's try to minimize the overlap:
Total students = 42
If there was no overlap, we would have => 24 + 29 = 53
Since 52 is more than 42, some overlap is necessarily present.
For Minimum Overlap/Intersection => Juniors + Interns - Total = 24 + 29 - 42 = 11
Thus, atleast 11 students must be junior interns.
Therefore, the total number of junior interns could range from 11 to 24.
Since we cannot arrive at a single answer for the number of junior interns, we cannot answer the question uniquely.
Hence, the correct answer is Option E - Statements (1) and (2) TOGETHER are NOT sufficient.
Hope this helps!
(1) Of the 42 college students, 29 found summer internships.
(2) Of the 42 college students, 24 were juniors.
Let's look at each statement individually and then at both of them together (if required):
Statement 1: Of the 42 college students, 29 found summer internships.
Through this statement, we get to know the number of total interns in the college, but nothing about how many of them were juniors can be inferred.
Hence, Statement 1 is insufficient alone.
Now, let's take a look at Statement 2 closely:
Statement 2: Of the 42 college students, 24 were juniors.
Through this statement, we get to know the number of total juniors in the college, but nothing about how many of them were interns can be inferred.
Hence, Statement 2 is insufficient alone.
Now, let's take a look at the combination of both statements - Statement 1 and Statement 2:
We know:
Total number of college students = 42
Total number of interns = 29
Total number of juniors = 24
However, the total number of junior interns could vary. Let's understand this through this example:
Case 1 - Total number of junior interns = 24 (all juniors could have internships). This can also be thought of as the case of Maximum Overlap.
Case 2 - Now, let's try to minimize the overlap:
Total students = 42
If there was no overlap, we would have => 24 + 29 = 53
Since 52 is more than 42, some overlap is necessarily present.
For Minimum Overlap/Intersection => Juniors + Interns - Total = 24 + 29 - 42 = 11
Thus, atleast 11 students must be junior interns.
Therefore, the total number of junior interns could range from 11 to 24.
Since we cannot arrive at a single answer for the number of junior interns, we cannot answer the question uniquely.
Hence, the correct answer is Option E - Statements (1) and (2) TOGETHER are NOT sufficient.
Hope this helps!
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