Advanced Military Math Aptitude Quiz

Math

Military Training

ASTB

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| By Thames

Thames

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Quizzes Created: 7153 | Total Attempts: 9,523,263

| Questions: 22 | Updated: Nov 6, 2025

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Question 1 / 22

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1. Which of the following fractions is the largest?

1/2

23/32

11/16

3/4

The correct answer is 3/4 because it is equivalent to 0.75, which is greater than 0.5, 0.6875, and 0.71875, the decimal equivalents of the incorrect answers respectively.

Explanation

The correct answer is 3/4 because it is equivalent to 0.75, which is greater than 0.5, 0.6875, and 0.71875, the decimal equivalents of the incorrect answers respectively.

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About This Quiz

This comprehensive preparation tool targets math skills essential for aspiring military officers. It integrates questions from multiple authoritative sources, enhancing mathematical proficiency and test readiness for various military aptitude assessments.

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2. What is the total number of degrees in 3 angles of a triangle?

180

100

120

The sum of the internal angles of a triangle is always 180 degrees, regardless of the type of triangle. This is a fundamental property of Euclidean geometry.

Explanation

The sum of the internal angles of a triangle is always 180 degrees, regardless of the type of triangle. This is a fundamental property of Euclidean geometry.

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3. A marine fired X rounds of ammunition, gave 2X to his buddy, and had 27 remaining in a magazine. If this accounted for 120 rounds in all, then X =

To solve this problem, you need to set up an equation. X (rounds fired) + 2X (rounds given to buddy) + 27 (remaining rounds) = 120 (total rounds). By solving this equation, you find X = 31.

Explanation

To solve this problem, you need to set up an equation. X (rounds fired) + 2X (rounds given to buddy) + 27 (remaining rounds) = 120 (total rounds). By solving this equation, you find X = 31.

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4. In the figure, if ACD is a straight line and AB = BC, then X =

180

135

145

In the given scenario, when ACD is a straight line and AB = BC, the angles opposite to the equal sides are also equal by the properties of isosceles triangles. Therefore, angle X would be equal to 135 degrees.

Explanation

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5. Which is true?

2/25 < 1/10

5/13 = 4/5

1/10 > 3/30

2/28 < 3/35

In the given options, 2/25

Explanation

In the given options, 2/25

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6. What is the result of X/4 + X?

X/4

5x/4

2x/4

To find the result of X/4 + X, you first need to combine the terms. X/4 + X can be simplified to (X + 4X)/4 = 5X/4.

Explanation

To find the result of X/4 + X, you first need to combine the terms. X/4 + X can be simplified to (X + 4X)/4 = 5X/4.

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7. What is the result of X-X/2?

X/2

3x/2

To solve X-X/2, first perform the division X/2 and then subtract that result from X to get X/2.

Explanation

To solve X-X/2, first perform the division X/2 and then subtract that result from X to get X/2.

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8. Perimeter of a rectangle is 180 ft, the width is 1/2 of the length, what is the length?

To find the length of the rectangle, we first need to calculate the width. Given that the width is 1/2 of the length, we can say width = length / 2. From the perimeter of the rectangle (180 ft) = 2(length + width), we can substitute the width value to find the length.

Explanation

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9. If 3 times X exceeds 1/3 of y by 9, which of the following is the equation that shows the relationship between x and y?

X - 3y =3

3x > 1/3y + 9

9x > y +27

3x - 1/3y = 9

The correct equation is derived from the statement '3 times X exceeds 1/3 of y by 9', which translates to 3x - 1/3y = 9.

Explanation

The correct equation is derived from the statement '3 times X exceeds 1/3 of y by 9', which translates to 3x - 1/3y = 9.

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10. What is the average of 1/25 and 1/100?

1/50

1/40

1/20

5/100

To find the average of two numbers, you add them together and then divide by 2. In this case, (1/25 + 1/100) / 2 = (4/100 + 1/100) / 2 = 5/100 / 2 = 1/40.

Explanation

To find the average of two numbers, you add them together and then divide by 2. In this case, (1/25 + 1/100) / 2 = (4/100 + 1/100) / 2 = 5/100 / 2 = 1/40.

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11. The destruction of a particular bridge requires 3 1/2 tons of C4 explosive. How many tons of C4 would be required to destroy 1/3 of the bridge?

3/4

2 3/4

1 1/6

To find out how many tons of C4 would be required to destroy 1/3 of the bridge, we need to multiply 3 1/2 tons by 1/3. This will give us 7/2 * 1/3 = 7/6 = 1 1/6 tons of C4 needed.

Explanation

To find out how many tons of C4 would be required to destroy 1/3 of the bridge, we need to multiply 3 1/2 tons by 1/3. This will give us 7/2 * 1/3 = 7/6 = 1 1/6 tons of C4 needed.

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12. If (Y*Y*Y)/(Y+Y) = 2, then Y =

To solve the equation, we can simplify the expression on the left side by dividing Y^3 by 2Y. This simplifies to Y^2/2, which equals 2. Therefore, Y = 2.

Explanation

To solve the equation, we can simplify the expression on the left side by dividing Y^3 by 2Y. This simplifies to Y^2/2, which equals 2. Therefore, Y = 2.

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13. 74 - (12-20)=

In the given expression, first we need to solve the inner brackets i.e. 12-20 = -8. Now, the expression becomes 74 - (-8) which is equivalent to 74 + 8 = 82.

Explanation

In the given expression, first we need to solve the inner brackets i.e. 12-20 = -8. Now, the expression becomes 74 - (-8) which is equivalent to 74 + 8 = 82.

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14. If 100 times x is between 50 and 100, then x could be

.75

.50

.25

1.00

To find x, we need to solve the inequality 50

Explanation

To find x, we need to solve the inequality 50

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15. If 20% of a number is 2.5, what is the number?

12.5

1.25

To find the number, you can set up the equation 20% of x = 2.5. Multiplying both sides by 5 to eliminate decimals gives 20% of x = 12.5. Therefore, x = 12.5.

Explanation

To find the number, you can set up the equation 20% of x = 2.5. Multiplying both sides by 5 to eliminate decimals gives 20% of x = 12.5. Therefore, x = 12.5.

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16. What is the area, in square ft, of the figure?

To find the area of a figure, you need to use the correct formula or measurements. The correct answer for this question is calculated based on a specific figure with the area being 63 square feet. The incorrect answers are choices that do not align with the correct calculation.

Explanation

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17. The equation x= 1/2 t(y-z) is equivalent to the equation y=

1/2x + zt

2x/t - z

2x/t + z

1/2t( y - z )

To get the equation in terms of y, first multiply both sides of x= 1/2 t(y-z) by 2 to get rid of the fraction. Then move z to the other side by adding it to both sides, and finally divide by t to isolate y.

Explanation

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18. Two ammo cans contain various numbers of live bullets and blank bullets. Ammo can X contains 60 live bullets and 30 blank bullets, ammo can Y contains 90 live bullets and 30 blank bullets. If one bullet is selected randomly from each ammo can, which bullet would most likely be a live bullet?

The one selected from ammo can X

It cannot be determined from the information given

Since can Y has a higher ratio of live bullets to blank bullets compared to can X, the one selected from can Y is more likely to be a live bullet.

Explanation

Since can Y has a higher ratio of live bullets to blank bullets compared to can X, the one selected from can Y is more likely to be a live bullet.

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19. In the square WXYZ figure, AX = 1, YZ =2 and XB =BY. What is the perimeter of polygon WABYZ?

8 + ?2

6 + ?2

To find the perimeter, we need to add the lengths of all sides of polygon WABYZ. Since AX = 1, XB = BY, and YZ = 2, we have two sides of length 1 and one side of length 2. The perimeter of the square would be the sum of these three sides plus two additional equal sides due to the square's properties. Therefore, the perimeter would be 2(1) + 2(2) + 1 = 6 + ?2.

Explanation

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20. While assaulting a fortified machine gun bunker, a marine fired 2000 rounds during two engagements. If he fired 800 rounds more in his first engagement than in his 2nd, how many rounds did he fire during his 1st engagement?

600

2000

1200

1400

In order to find the number of rounds fired during the 1st engagement, we can set up an equation. Let x be the number of rounds fired in the 2nd engagement. Then, the number of rounds fired in the 1st engagement is x + 800. The total rounds fired in both engagements is 2000, so x + (x + 800) = 2000. Solving for x, we get x = 600. Therefore, the number of rounds fired during the 1st engagement is 600 + 800 = 1400.

Explanation

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21. It will take 4 hrs 32 min 30 sec to dig one part of a mortar pit. If the other part will take three quarters the time, how long will the second part take?

3 hrs 24 min 22.5 sec

2 hrs 24 min 22.5 sec

3 hrs 46 min 36 sec

1 hr 56 min 39 sec

To find the time for the second part, we need to take three quarters of the time taken for the first part (4 hrs 32 min 30 sec). This gives us 3 hours 24 minutes and 22.5 seconds.

Explanation

To find the time for the second part, we need to take three quarters of the time taken for the first part (4 hrs 32 min 30 sec). This gives us 3 hours 24 minutes and 22.5 seconds.

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22. At a mess night, there are only captains, 2nd lieutenants, and 1st lieutenants. If the total number of 2nd lieutenants and 1st lieutenants is 30, the total number of 2nd lieutenants and captains is 45, and the total number of 1st lieutenants and captains is 35, what is the total number of company grade officers at the mess night?

110

220

To solve this problem, we can set up a system of equations. Let x be the number of captains, y be the number of 2nd lieutenants, and z be the number of 1st lieutenants. From the given information, we have: y + z = 30, x + y = 45, and x + z = 35. Solving these equations simultaneously, we get x = 10, y = 15, and z = 15. Therefore, the total number of company grade officers is x + y + z = 10 + 15 + 15 = 40.

Explanation

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