IMAT 2012 Q35 [Loans]

A student gives his friends small, short-­term loans for periods of 1, 2 or 3 weeks after which time they must be repaid in full. He always lends on a Friday afternoon. He starts with €120 and loans out the following amounts each week:

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What is the smallest amount of money he has by the end of the 4th Friday?

A. €82
B. €12
C. €77
D. €100
E. €57

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By analyzing the table we can see that by the 4th Friday, the only loan that must be paid back would be that of Week 1- as it exceeds the deadline for repayment.

For the student to hold the least amount of money by the end of the 4th Friday, it must mean that no one has paid him back- with the exception of the first loan (nobody from week 2 and onwards has repaid him.)

Therefore, his costs must look like this:

€120 -€45 +€45 -€25 -€18 -€20 = €57, our answer is E.