Question

Over the period of a year, Sam’s net worth increased. Which of the following could be true?
a.
Sam’s assets and liabilities decreased by the same amount.
b.
Sam’s assets and liabilities increased by the same amount.
c.
Sam’s assets increased by more than his liabilities.
d.
Sam’s assets decreased by more than his liabilities.

Answer 1

Net worth = assets − liabilities. Over the year, change in net worth = Δassets − Δliabilities. For net worth to increase we need Δassets − Δliabilities > 0, i.e. Δassets > Δliabilities.

a) If both decreased by the same amount, Δassets = Δliabilities → no change. (Not possible.)
b) If both increased by the same amount, Δassets = Δliabilities → no change. (Not possible.)
c) If assets increased by more than liabilities, Δassets > Δliabilities → net worth increases. (Possible.)
d) If assets decreased by more than liabilities, then Δassets < Δliabilities → net worth decreases. (Not possible.)

Answer: c only.