Advanced Mathematics Aptitude Test Preparation Quiz

1) Arrange these fractions in order of size from largest to smallest: 1/3, 2/5, 4/15

2/5, 1/3, 4/15

4/15, 2/5, 1/3

1/3, 2/5, 4/15

1/3, 4/15, 2/5

To compare fractions, you can either find a common denominator and then compare the numerators, or you can convert all fractions to decimals. In this case, converting to decimals: 1/3 = 0.333, 2/5 = 0.4, 4/15 = 0.267. Therefore, from largest to smallest: 2/5, 1/3, 4/15.

Explanation

To compare fractions, you can either find a common denominator and then compare the numerators, or you can convert all fractions to decimals. In this case, converting to decimals: 1/3 = 0.333, 2/5 = 0.4, 4/15 = 0.267. Therefore, from largest to smallest: 2/5, 1/3, 4/15.

2) 300% is the same as

300

3

.03

.3

When converting a percentage to a decimal, you move the decimal point two places to the left. Therefore, 300% is equivalent to 3 in decimal form.

Explanation

When converting a percentage to a decimal, you move the decimal point two places to the left. Therefore, 300% is equivalent to 3 in decimal form.

3) 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?

2000

1400

600

1200

To determine how many rounds were fired in the first engagement, we can use algebra. Let x be the rounds fired in the 2nd engagement. Since the marine fired 800 rounds more in the first engagement, the rounds fired in the 1st engagement would be x + 800. The total rounds fired in both engagements equals 2000, so x + (x + 800) = 2000. Solving for x gives x = 600. Therefore, the marine fired 1400 rounds in the 1st engagement.

Explanation

To determine how many rounds were fired in the first engagement, we can use algebra. Let x be the rounds fired in the 2nd engagement. Since the marine fired 800 rounds more in the first engagement, the rounds fired in the 1st engagement would be x + 800. The total rounds fired in both engagements equals 2000, so x + (x + 800) = 2000. Solving for x gives x = 600. Therefore, the marine fired 1400 rounds in the 1st engagement.

4) Which of the following fractions is the largest?

11/16

1/2

5/8

3/4

To determine the largest fraction, we need to compare the numerators and denominators of each fraction. In this case, 3/4 has a larger numerator and denominator compared to the other fractions provided.

Explanation

To determine the largest fraction, we need to compare the numerators and denominators of each fraction. In this case, 3/4 has a larger numerator and denominator compared to the other fractions provided.

5) What is the total number of degrees in 3 angles of a triangle?

180

100

120

90

The sum of the interior angles of a triangle is always 180 degrees, regardless of the type of triangle. Each angle has a specific measure which adds up to a total of 180 degrees in any triangle.

Explanation

The sum of the interior angles of a triangle is always 180 degrees, regardless of the type of triangle. Each angle has a specific measure which adds up to a total of 180 degrees in any triangle.

6) 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 =

29

31

32

30

To solve the question, you need to set up the equation: X + 2X + 27 = 120. Combine like terms to get 3X + 27 = 120. Subtract 27 from both sides to get 3X = 93. Divide by 3 to find X = 31.

Explanation

To solve the question, you need to set up the equation: X + 2X + 27 = 120. Combine like terms to get 3X + 27 = 120. Subtract 27 from both sides to get 3X = 93. Divide by 3 to find X = 31.

7) Which is true?

5/13 = 4/5

2/28 < 3/35

1/10 > 3/30

2/25 < 1/10

In order to compare fractions, you can find a common denominator and then compare the numerators. In this case, for 2/25

Explanation

In order to compare fractions, you can find a common denominator and then compare the numerators. In this case, for 2/25

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

100

60

30

90

To find the length, we need to set up the equation 2(Length) + 2(Width) = Perimeter. Since the width is half of the length, we can represent the width as 0.5(Length). Substituting the values into the equation, we get 2(Length) + 2(0.5*Length) = 180. Solving this equation gives us Length = 60 feet.

Explanation

To find the length, we need to set up the equation 2(Length) + 2(Width) = Perimeter. Since the width is half of the length, we can represent the width as 0.5(Length). Substituting the values into the equation, we get 2(Length) + 2(0.5*Length) = 180. Solving this equation gives us Length = 60 feet.

9) What is the average of 1/25 and 1/100?

5/100

1/20

1/40

1/50

To find the average of two fractions, you add them together and then divide by 2. Therefore, (1/25 + 1/100) / 2 = 0.04 which in fraction form simplifies to 1/40.

Explanation

To find the average of two fractions, you add them together and then divide by 2. Therefore, (1/25 + 1/100) / 2 = 0.04 which in fraction form simplifies to 1/40.

10) If (Y*Y*Y)/(Y+Y) = 2, then Y =

2

4

0

1

To solve the given equation, we can simplify (Y*Y*Y)/(Y+Y) = 2. After simplification, we get Y^2 = 2, which means Y = 2.

Explanation

To solve the given equation, we can simplify (Y*Y*Y)/(Y+Y) = 2. After simplification, we get Y^2 = 2, which means Y = 2.

11) If 100 times x is between 50 and 100, then x could be

.50

1.00

.25

.75

To find x for the given condition, we can set up the inequality 50

Explanation

To find x for the given condition, we can set up the inequality 50

12) If 20% of a number is 2.5, what is the number?

10

12.5

1.25

25

To find the original number, you can set up the equation: 20% of x = 2.5. This simplifies to 0.2x = 2.5. Solving for x gives x = 2.5 / 0.2 = 12.5.

Explanation

To find the original number, you can set up the equation: 20% of x = 2.5. This simplifies to 0.2x = 2.5. Solving for x gives x = 2.5 / 0.2 = 12.5.

13) 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 blank?

The one selected from ammo can Y

It cannot be determined from the information given.

Both bullets have an equal likelihood of being blank.

The one selected from ammo can X

In ammo can X, there are a higher percentage of blank bullets compared to live bullets, increasing the likelihood of selecting a blank bullet from this can.

Explanation

In ammo can X, there are a higher percentage of blank bullets compared to live bullets, increasing the likelihood of selecting a blank bullet from this can.

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

8 + ?2

8

10

6 + ?2

The perimeter of polygon WABYZ can be calculated as follows: WABYZ = WX + WY + YZ + ZA + AB. Since WXYZ is a square, all sides are equal in length. Given that AX = 1, then XW = 1 as well. With YZ = 2, we know that WY = 2. Since XB = BY, this gives us XB = 2. The perimeter can now be calculated as 1 + 2 + 2 + 2 + 1 = 6 + ?2.

Explanation

The perimeter of polygon WABYZ can be calculated as follows: WABYZ = WX + WY + YZ + ZA + AB. Since WXYZ is a square, all sides are equal in length. Given that AX = 1, then XW = 1 as well. With YZ = 2, we know that WY = 2. Since XB = BY, this gives us XB = 2. The perimeter can now be calculated as 1 + 2 + 2 + 2 + 1 = 6 + ?2.

15) 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?

1 hr 56 min 39 sec

3 hrs 24 min 22.5 sec

2 hrs 24 min 22.5 sec

3 hrs 46 min 36 sec

The correct answer can be found by multiplying the time for the first part (4 hrs 32 min 30 sec) by 3/4 to get the time for the second part.

Explanation

The correct answer can be found by multiplying the time for the first part (4 hrs 32 min 30 sec) by 3/4 to get the time for the second part.

16) 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 (2ndLts, 1stLts, and Capts) at the mess night?

220

55

60

110

To solve the problem, we can set up three equations based on the given information and solve for the total number of company grade officers. After solving the equations, we can determine that the total number of company grade officers is 55.

Explanation

To solve the problem, we can set up three equations based on the given information and solve for the total number of company grade officers. After solving the equations, we can determine that the total number of company grade officers is 55.

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

90

135

180

145

In the given situation, since AB = BC, ∠ABC and ∠BCA are equal. Therefore, ∠X = 180 - 45 = 135 degrees.

Explanation

In the given situation, since AB = BC, ∠ABC and ∠BCA are equal. Therefore, ∠X = 180 - 45 = 135 degrees.

18) What is the result of X/4 + X?

2x/4

X/4

4x

5x/4

To solve the expression X/4 + X, we can first simplify X/4 to get 1/4 times X. Adding this to X results in 5/4 times X, which can be written as 5x/4.

Explanation

To solve the expression X/4 + X, we can first simplify X/4 to get 1/4 times X. Adding this to X results in 5/4 times X, which can be written as 5x/4.

19) Simplify the expression X-X/2.

2x

X/2

3x/2

4x

To simplify the expression X-X/2, we need to first perform the division X/2 which results in X/2. Therefore, the correct answer is X/2.

Explanation

To simplify the expression X-X/2, we need to first perform the division X/2 which results in X/2. Therefore, the correct answer is X/2.

20) 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?

3x - 1/3y = 9

X - 3y = 3

9x > y + 27

3x > 1/3y + 9

The correct equation derived from the given question is 3x - 1/3y = 9 where 3 times X exceeds 1/3 of y by 9.

Explanation

The correct equation derived from the given question is 3x - 1/3y = 9 where 3 times X exceeds 1/3 of y by 9.

21) 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?

1 1/3

1

1 1/6

2 1/4

To find out how many tons of C4 would be required to destroy 1/3 of the bridge, we need to calculate 1/3 of 3 1/2 tons. 1/3 of 3 1/2 tons is equal to 1 1/6 tons.

Explanation

To find out how many tons of C4 would be required to destroy 1/3 of the bridge, we need to calculate 1/3 of 3 1/2 tons. 1/3 of 3 1/2 tons is equal to 1 1/6 tons.

22) 74 - (12-20)=

66

56

42

82

To solve this problem, first perform the operation inside the parentheses: 12-20=-8. Then subtract this result from 74 to get 74 - (-8) = 82.

Explanation

To solve this problem, first perform the operation inside the parentheses: 12-20=-8. Then subtract this result from 74 to get 74 - (-8) = 82.

23) What is the area, in square ft, of the figure?

32

72

54

63

To find the area of the figure, the correct calculation should be provided to arrive at the answer of 63 square ft.

Explanation

To find the area of the figure, the correct calculation should be provided to arrive at the answer of 63 square ft.

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

2x/t - z

2x/t + z

1/2x + zt

1/2t( y - z )

To find the equivalent equation, we need to isolate y in the given equation x= 1/2 t(y-z). By performing the necessary operations, we arrive at y= 2x/t + z.

Explanation

To find the equivalent equation, we need to isolate y in the given equation x= 1/2 t(y-z). By performing the necessary operations, we arrive at y= 2x/t + z.