Match each military and logistics operational scenario to the correct final mathematical r… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each military and logistics operational scenario to the correct final mathematical ratio. Read the conditions carefully, as some require calculating a new ratio after a change occurs.

A naval strike group contains cruisers, destroyers, and frigates. For every $2$ cruisers, there are $5$ destroyers. The number of frigates equals the combined number of cruisers and destroyers. Find the ratio of destroyers to the total number of ships. $5:14$
A unit has $60$ personnel total, with an initial officer to enlisted ratio of $3:7$ . After $6$ officers are transferred out (while enlisted numbers remain unchanged), find the new ratio of officers to enlisted personnel. $2:7$
A fuel mixture correctly requires $3$ parts additive per $8$ parts base fuel. A technician mistakenly uses $4$ parts additive per $10$ parts base fuel instead. If both scenarios use exactly $40$ gallons of base fuel, find the ratio of the correct additive amount to the mistakenly used additive amount. $15:16$
A supply convoy's ratio of cargo trucks to escort vehicles is $5:2$ . The convoy has $35$ total vehicles. If $1$ escort vehicle breaks down and leaves the convoy, find the new ratio of escort vehicles to cargo trucks. $9:25$

Answer

The correct matches are: Scenario 1 maps to 5:14, Scenario 2 maps to 2:7, Scenario 3 maps to 15:16, and Scenario 4 maps to 9:25.

Each scenario involves distinct ratio logic: Scenario 1 requires combining parts to find a whole. Scenarios 2 and 4 require breaking a total into parts using an initial ratio, subtracting from one part, and writing a new simplified ratio. Scenario 3 requires using part-to-part logic to find an unknown part given a specific base, then comparing the two results.

Step-by-Step Solution

Calculate the ratios for the Naval Strike Group (Scenario 1).

The total proportion is

2

(cruisers) +

5

(destroyers) +

7

(frigates) =

14

. The ratio of destroyers to total ships is

5:14

You must establish the total baseline by summing the parts before finding the part-to-whole ratio.

Determine the new personnel ratio (Scenario 2).

Initially, officers =

18

and enlisted =

42

. Subtracting

6

officers leaves

12

. The new ratio is

12:42

, simplified to

2:7

Changes to one subset of a population require determining the original absolute values first.

Compare the fuel additive amounts (Scenario 3).

Correct additive is

\frac{3}{8} \times 40 = 15

. Mistaken additive is

\frac{4}{10} \times 40 = 16

. The ratio is

15:16

Scaling both ratios up to the common base fuel amount of

40

reveals the exact additive quantities to compare.

Adjust the convoy vehicles ratio (Scenario 4).

Initially, cargo =

25

and escort =

10

. Subtracting

1

escort leaves

9

. The required ratio of escort to cargo is

9:25

Calculating initial absolute quantities is necessary before applying the subtraction of

1

vehicle and interpreting the final specific order requested.

Key Concept

Applying part-to-part and part-to-whole ratio relationships to calculate absolute values, applying condition changes, and then re-evaluating and simplifying the final ratios.

Alternative Method

For Scenario 2, you can also calculate the fractional drop without finding absolute enlisted numbers. The officer count drops from

18

12

, which is exactly

\frac{2}{3}

of the original amount. Thus, the new ratio must simply be

\frac{2}{3}

of the original officer portion (

3

) against the same enlisted portion (

7

), resulting directly in a

2:7

ratio.

Estimated Time:2m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

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