A budget planner allocates \frac{1}{3} of a monthly stipend to housing expenses and \frac{… — GRE General Test

A budget planner allocates $\frac{1}{3}$ of a monthly stipend to housing expenses and $\frac{2}{5}$ of the stipend to food. If no other expenses are incurred from these two categories, what fraction of the total monthly stipend remains unallocated?

A
$\frac{3}{8}$
$\frac{4}{15}$ Answer
C
$\frac{5}{8}$
D
$\frac{7}{15}$
E
$\frac{11}{15}$

Answer

\frac{4}{15}

of the total monthly stipend remains unallocated.

To find the remaining unallocated fraction, first determine the total fraction spent by adding

\frac{1}{3}

and

\frac{2}{5}

using the common denominator

15

, yielding

\frac{5}{15} + \frac{6}{15} = \frac{11}{15}

. Subtracting this total from

1

gives

1 - \frac{11}{15} = \frac{4}{15}

. Thus, the option equal to

\frac{4}{15}

is correct.

Step-by-Step Solution

Calculate the total fraction allocated to housing and food.

\frac{1}{3} + \frac{2}{5} = \frac{5}{15} + \frac{6}{15} = \frac{11}{15}

Find a common denominator (15) to combine the fractions.

Subtract the allocated fraction from 1 to determine the unallocated portion.

1 - \frac{11}{15} = \frac{15}{15} - \frac{11}{15} = \frac{4}{15}

The total stipend is represented by 1 whole.

Key Concept

Adding and subtracting rational numbers using common denominators

Estimated Time:1m 0s

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