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06 Aug 2026, 07:43
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A course advisor is paid a monthly enrollment bonus. In any month in which she enrolls at least 10 students, she earns a total bonus of \(b\) dollars for the first 10 students enrolled, plus \(0.05b\) dollars for each additional student enrolled, where \(b\) is positive. If she enrolled at least 10 students last month, did she enroll at least 25 students last month?
(1) Last month, her total enrollment bonus was \(1.75b\) dollars.
(2) Last month, her total enrollment bonus was $1,050.
(1) Last month, her total enrollment bonus was \(1.75b\) dollars.
(2) Last month, her total enrollment bonus was $1,050.
06 Aug 2026, 07:43
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Official Solution:
A course advisor is paid a monthly enrollment bonus. In any month in which she enrolls at least 10 students, she earns a total bonus of \(b\) dollars for the first 10 students enrolled, plus \(0.05b\) dollars for each additional student enrolled, where \(b\) is positive. If she enrolled at least 10 students last month, did she enroll at least 25 students last month?
Let \(n\) be the number of students the course advisor enrolled last month. Since she enrolled at least 10 students, her total bonus was:
\(b + 0.05b(n - 10)\)
The question asks whether \(n \geq 25\).
(1) Last month, her total enrollment bonus was \(1.75b\) dollars.
So:
\(b + 0.05b(n - 10) = 1.75b\)
\(1 + 0.05(n - 10) = 1.75\)
\(n = 25\)
So the answer to the question is YES.
Sufficient.
(2) Last month, her total enrollment bonus was $1,050.
So:
\(b + 0.05b(n - 10) = 1,050\)
This does not determine \(n\).
For example, if \(n = 20\):
\(b + 0.05b(10) = 1,050\)
\(b = 700\)
So \(n = 20\) is possible, and the answer is NO.
But if \(n = 25\):
\(b + 0.05b(15) = 1,050\)
\(b = 600\)
So \(n = 25\) is possible, and the answer is YES.
Both values of \(b\) are positive, so both cases are allowed.
Not sufficient.
Answer: A
A course advisor is paid a monthly enrollment bonus. In any month in which she enrolls at least 10 students, she earns a total bonus of \(b\) dollars for the first 10 students enrolled, plus \(0.05b\) dollars for each additional student enrolled, where \(b\) is positive. If she enrolled at least 10 students last month, did she enroll at least 25 students last month?
Let \(n\) be the number of students the course advisor enrolled last month. Since she enrolled at least 10 students, her total bonus was:
\(b + 0.05b(n - 10)\)
The question asks whether \(n \geq 25\).
(1) Last month, her total enrollment bonus was \(1.75b\) dollars.
So:
\(b + 0.05b(n - 10) = 1.75b\)
\(1 + 0.05(n - 10) = 1.75\)
\(n = 25\)
So the answer to the question is YES.
Sufficient.
(2) Last month, her total enrollment bonus was $1,050.
So:
\(b + 0.05b(n - 10) = 1,050\)
This does not determine \(n\).
For example, if \(n = 20\):
\(b + 0.05b(10) = 1,050\)
\(b = 700\)
So \(n = 20\) is possible, and the answer is NO.
But if \(n = 25\):
\(b + 0.05b(15) = 1,050\)
\(b = 600\)
So \(n = 25\) is possible, and the answer is YES.
Both values of \(b\) are positive, so both cases are allowed.
Not sufficient.
Answer: A
