MathRevolution wrote:
[GMAT math practice question]
A teacher distributes \(n\) apples to some students. If she gives \(4\) apples to each student, \(7\) apples remain. If she tried to give \(5\) apples to each student, \(3\) students would not get anything. What is the range of possible values of \(n\)?
A. \(14\)
B. \(16\)
C. \(18\)
D. \(20\)
E. \(22\)
Let k be the number of students. Since 7 apples remain when each student is given 4 apples, we have:
n = 4k + 7
Suppose all but three of the students get 5 apples when the teacher tries to give each student 5 apples. Then, we have:
n = 5(k - 3)
Substituting n = 5(k - 3) into n = 4k + 7, we get:
5(k - 3) = 4k + 7
5k - 15 = 4k + 7
k = 22
In this scenario, there are 22 students and 5(22 - 3) = 5(19) = 95 apples.
To find an upper bound for the number of apples, suppose all but four students get 5 apples, one student gets only one apple and three students get no apples. Thus, we have:
n = 5(k - 4) + 1
Again substituting n = 4k + 7 in n = 5(k - 4) + 1, we get:
4k + 7 = 5(k - 4) + 1
4k + 7 = 5k - 20 + 1
k = 26
In this scenario, there are 26 students and 5(26 - 4) + 1 = 111 apples.
So, the number of apples can be any number between 95 and 111, inclusive. The range for the number of apples is 111 - 95 = 16.
Answer: B
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