A military logistics center is distributing its annual fuel reserve among different divisi… — Armed Services Vocational Aptitude Battery (ASVAB)

A military logistics center is distributing its annual fuel reserve among different divisions:

- The Aviation division receives $\frac{3}{8}$ of the total reserve.
- The Ground Transport division receives $22.5\%$ of the total reserve.
- A Naval detachment receives a portion equivalent to the decimal $0.125$ of the total reserve.
- The remainder of the fuel is stored in the emergency depot.

Which of the following fractions correctly represents the ratio of the amount of fuel stored in the emergency depot to the amount of fuel allocated to the Aviation division?

$\frac{11}{15}$ Answer
B
$\frac{11}{40}$
C
$\frac{7}{5}$
D
$\frac{31}{30}$

Answer

The correct ratio is

\frac{11}{15}

To find the ratio, all given quantities must first be converted into a common format, such as decimals. The Aviation division's

\frac{3}{8}

is equivalent to

0.375

. The Ground Transport's

22.5\%

is equivalent to

0.225

. The Naval detachment is already given as

0.125

. Adding these distributed portions together gives

0.375 + 0.225 + 0.125 = 0.725

. Because the total fuel reserve represents

1

whole (

100\%

), the remainder stored in the emergency depot is

1 - 0.725 = 0.275

. The question asks for the ratio of the emergency depot (

0.275

) to the Aviation division (

0.375

). This creates the ratio

\frac{0.275}{0.375}

, which can be rewritten as

\frac{275}{375}

. Dividing both the numerator and the denominator by their greatest common divisor of

25

simplifies the fraction to

\frac{11}{15}

Step-by-Step Solution

Convert all the distributed fuel allocations into a single format (decimals) to allow for easy addition.

Aviation =

0.375

; Ground =

0.225

; Naval =

0.125

Fractions, decimals, and percentages must be in the same format before they can be summed.

Sum the converted allocations to find the total distributed portion of the reserve.

0.375 + 0.225 + 0.125 = 0.725

This establishes what portion of the whole (

1.0

) has already been assigned.

Subtract the total distributed portion from the whole (

1.0

) to find the portion stored in the emergency depot.

1.0 - 0.725 = 0.275

The emergency depot contains whatever is left over from the original reserve.

Set up the requested ratio (Emergency Depot to Aviation Division) using their decimal values.

\frac{0.275}{0.375}

The stem asks for the ratio of the emergency depot to the Aviation division.

Simplify the decimal ratio into a proper fraction in its lowest terms.

\frac{275}{375} = \frac{11}{15}

Multiplying numerator and denominator by

1000

removes the decimals, and dividing both by their greatest common divisor (

25

) yields the simplest fraction.

Key Concept

To compare quantities given in mixed formats (fractions, decimals, and percentages), they must first be converted into a common format. After finding unknown quantities using a consistent format, their relative sizes can be expressed as a ratio and simplified into a final fraction.

Estimated Time:2m 0s

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