Marge received a certain amount of money as a gift. She spent half of

Let's assume that Marge received $\(2x\) as a gift

The amount she spends the first week = \(x\)

The amount she spends the second week = \(\frac{x}{2}\)

The amount she spends the third week = \(\frac{x}{4}\)

The amount she spends the fourth week = \(\frac{x}{8}\)
.
.
so on

Question: What was the first week in which the total amount of the gift that Marge had spent was greater than \(\frac{19}{20}\) of the amount of the gift?

Expenses by Marge = {\(x\), \(\frac{x}{2}\), \(\frac{x}{4}\), \(\frac{x}{8}\), ...}

The expenses by Marge represent a Geometric progression with a common ratio of \(\frac{1}{2}\)

\(\frac{19}{20} * 2x < x * \frac{(1-(\frac{1}{2})^n)}{1-\frac{1}{2}}\)

\(\frac{19}{20} * 2x < 2x(1-(\frac{1}{2})^n)\)

Dividing both sides of the equation by \(2x\)

\(\frac{19}{20} < 1-(\frac{1}{2})^n\)

\( (\frac{1}{2})^n < 1 - \frac{19}{20}\)

\( (\frac{1}{2})^n < \frac{1}{20}\)

Hence, the minimum value of n for which \( (\frac{1}{2})^n < \frac{1}{20}\) is \(5\)

Option B­