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14 Oct 2024, 01:30
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University U has 13,472 undergraduate students, 37.5 percent of whom are upperclassmen. The rest are underclassmen. What percent of its undergraduate students are in the College of Liberal Arts?
(1) The number of upperclassmen who are not in the College of Liberal Arts is three times the number of upperclassmen who are in the College of Liberal Arts.
(2) The number of upperclassmen in the College of Liberal Arts is three times the number of underclassmen not in the College of Liberal Arts.
(1) The number of upperclassmen who are not in the College of Liberal Arts is three times the number of upperclassmen who are in the College of Liberal Arts.
(2) The number of upperclassmen in the College of Liberal Arts is three times the number of underclassmen not in the College of Liberal Arts.
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14 Oct 2024, 03:56
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The number of upperclassmen is 0.375 * (13, 472) = 5,052
Statement 1.
Let's assume x is the number of upperclassmen in the College of Liberal Arts. According to the statement, the number of upperclassmen not in the College of Liberal Arts is 3x. Thus, the total number of upperclassmen is x + 3x = 4x, which equals 5,052
Using this information, we know how many upperclassmen are in the College of Liberal Arts. However, this doesn't directly tell us the percentage of the total undergraduate students in the College of Liberal Arts because we don't know how many underclassmen are in the College of Liberal Arts.
INSUFFICIENT
Statement 2
x = 3y, where y is the number of underclassmen not in the College of Liberal Arts.
Since we know the total number of underclassmen is 13,472 − 5,052 = 8,420, we can find the number of underclassmen in the College of Liberal Arts by subtracting y from 8,420.
However, we don't have enough information to directly find the total number of students in the College of Liberal Arts from this statement alone.
INSUFFICIENT
Both Together
x = 1,263 (the number of upperclassmen in the College of Liberal Arts), y = 421 (the number of underclassmen not in the College of Liberal Arts)
Since the total number of underclassmen is 8,420, the number of underclassmen in the College of Liberal Arts is 8,420 - 421 = 7,999
Now, we can find the total number of students in the College of Liberal Arts:
1,263 upperclassmen + 7,999 underclassmen = 9,262 students. SUFFICIENT
Answer C.
Statement 1.
Let's assume x is the number of upperclassmen in the College of Liberal Arts. According to the statement, the number of upperclassmen not in the College of Liberal Arts is 3x. Thus, the total number of upperclassmen is x + 3x = 4x, which equals 5,052
Using this information, we know how many upperclassmen are in the College of Liberal Arts. However, this doesn't directly tell us the percentage of the total undergraduate students in the College of Liberal Arts because we don't know how many underclassmen are in the College of Liberal Arts.
INSUFFICIENT
Statement 2
x = 3y, where y is the number of underclassmen not in the College of Liberal Arts.
Since we know the total number of underclassmen is 13,472 − 5,052 = 8,420, we can find the number of underclassmen in the College of Liberal Arts by subtracting y from 8,420.
However, we don't have enough information to directly find the total number of students in the College of Liberal Arts from this statement alone.
INSUFFICIENT
Both Together
x = 1,263 (the number of upperclassmen in the College of Liberal Arts), y = 421 (the number of underclassmen not in the College of Liberal Arts)
Since the total number of underclassmen is 8,420, the number of underclassmen in the College of Liberal Arts is 8,420 - 421 = 7,999
Now, we can find the total number of students in the College of Liberal Arts:
1,263 upperclassmen + 7,999 underclassmen = 9,262 students. SUFFICIENT
Answer C.
