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  • Armed Services Vocational Aptitude Battery

ASVAB

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Solve for [imath]x[/imath] when [imath]x^2 - 6 = 0[/imath]

A) [imath]-3[/imath]
B) [imath]\sqrt{3}[/imath]
C) [imath]\sqrt{6}[/imath]
D) [imath]3[/imath]



Step-by-step Explanation

Step 1: Start with the equation
[imath]x^2 - 6 = 0[/imath]

Step 2: Add [imath]6[/imath] to both sides
[imath]x^2 - 6 + 6 = 0 + 6[/imath]
[imath]x^2 = 6[/imath]...
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What is [imath]x + 4z - 5 - 3x[/imath], when [imath]x = 2[/imath] and [imath]z = 3x[/imath]?

A) [imath]15[/imath]
B) [imath]17[/imath]
C) [imath]23[/imath]
D) [imath]26[/imath]



Step-by-step Explanation

Step 1: Use the given value of [imath]x = 2[/imath]
Then [imath]z = 3x = 3 \cdot 2 = 6[/imath]

Since we know z=6, just replace z with 6 in the...
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Evaluate the expression [imath]4a - 2x + 3y[/imath] if [imath]a = -2[/imath], [imath]x = 5[/imath], and [imath]y = 6[/imath]:
[imath]\text{(A) } 0 \quad \text{(B) } -10 \quad \text{(C) } 8 \quad \text{(D) } 12[/imath]

Answer: A

We are given:
[imath]4a - 2x + 3y[/imath]
where:
[imath]a = -2,\quad x = 5,\quad y = 6[/imath]


Step 1: Substitute...
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50
0 Votes
Evaluate
[imath]\frac{(m - n)^2 - 2p}{(-n)^3}[/imath]
when [imath]m = 7[/imath], [imath]n = 3[/imath], and [imath]p = 5[/imath]

A) [imath]\frac{1}{27}[/imath]
B) [imath]-\frac{1}{27}[/imath]
C) [imath]\frac{2}{9}[/imath]
D) [imath]-\frac{2}{9}[/imath]



Step-by-step Explanation

Step 1: Substitute values
[imath]\frac{(7 - 3)^2 -...[/imath]
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The sum of two angles in a triangle is [imath]136^\circ[/imath].
How many degrees is the third angle?

A) [imath]44^\circ[/imath]
B) [imath]90^\circ[/imath]
C) [imath]134^\circ[/imath]
D) [imath]224^\circ[/imath]



Step-by-step Explanation

Step 1: Use the triangle angle sum rule
The interior angles of any triangle always...
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If [imath]\sqrt{x} + 6 = 16[/imath], then [imath]x[/imath] could equal:

A) [imath]1[/imath]
B) [imath]4[/imath]
C) [imath]10[/imath]
D) [imath]100[/imath]



Step-by-step Explanation

Step 1: Isolate the square root
[imath]\sqrt{x} + 6 = 16[/imath]

Subtract 6 from both sides:
[imath]\sqrt{x} + 6 - 6 = 16 - 6[/imath]

Then we get
[imath]\sqrt{x}...[/imath]
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Which of the following pairs of numbers represents a perfect square and its square root?

A) [imath]16[/imath] and [imath]\sqrt{8}[/imath]
B) [imath]25[/imath] and [imath]\sqrt{5}[/imath]
C) [imath]125[/imath] and [imath]25[/imath]
D) [imath]256[/imath] and [imath]16[/imath]



Step-by-step Explanation

Step 1: Understand the question
We need a...
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4
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Simplify:
[imath]e^{ax} \cdot e^{-ax} - e^{2ax}[/imath]

A) [imath]e^{-2ax}[/imath]
B) [imath]e - e^{2ax}[/imath]
C) [imath]1 - e^{2ax}[/imath]
D) [imath]e^{-2a2x} - e^{2ax}[/imath]



Step-by-step Explanation

Step 1: Use exponent multiplication rule
When multiplying like bases, add the exponents:

[imath]e^{ax} \cdot...[/imath]
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Which of the following expressions is equivalent to
[imath]92x^2 + x - 1 + xy + \frac{2x^3}{x}[/imath]?

A) [imath]94x^2 + x + xy - 1[/imath]
B) [imath]92x^2 + 3x + xy - 1[/imath]
C) [imath]2x^2 + 92x + y - 1[/imath]
D) [imath]2x^3 + 92x^2 + 2x + xy - 1[/imath]



Step-by-step Explanation

Start with the given...
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What is the reciprocal of [imath]15\frac{2}{3}[/imath]?

A) [imath]15\frac{3}{2}[/imath]
B) [imath]3\frac{2}{15}[/imath]
C) [imath]\frac{45}{3}[/imath]
D) [imath]\frac{3}{47}[/imath]



Step-by-step Explanation

Step 1: Convert the mixed number to an improper fraction

[imath]15\frac{2}{3}[/imath] means:

[imath]15 + \frac{2}{3} =...[/imath]
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Which of these is the same as [imath]\frac{11}{20}[/imath]?

A) [imath]\frac{3}{4}[/imath]
B) [imath]45\%[/imath]
C) [imath]\frac{4}{7}[/imath]
D) [imath]55\%[/imath]



Step-by-step Explanation

Step 1: Convert the fraction to a decimal or percent

To convert [imath]\frac{11}{20}[/imath] to a percent:

[imath]\frac{11}{20} = 0.55 =...[/imath]
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If [imath]x = 2[/imath], what is the value of [imath]8x - x[/imath]?

A) [imath]8[/imath]
B) [imath]10[/imath]
C) [imath]14[/imath]
D) [imath]18[/imath]



Step-by-step Explanation

Step 1: Substitute the value of [imath]x[/imath]

We are given [imath]x = 2[/imath], so substitute that into the expression:

[imath]8x - x = 8(2) - 2[/imath]



Step...
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Which of the following is an expression for "the sum of three times a number and -7 is equal to 9"?

A) [imath]3x + (-7) = 9[/imath]
B) [imath]3x + 7 = 9[/imath]
C) [imath]x + 3 + (-7) = 9[/imath]
D) [imath]7x - 3 = 9[/imath]


Step-by-step Explanation

Step 1: Translate the sentence into math

The sentence says:
"The...
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Two cars leave a rest stop at the same time. One travels north at [imath]55 \text{ mph}[/imath], and the other travels south at [imath]45 \text{ mph}[/imath]. In how many hours will they be [imath]200[/imath] miles apart?

A) [imath]1 \frac{1}{5}[/imath] hours
B) [imath]2[/imath] hours
C) [imath]2 \frac{1}{4}[/imath] hours
D) [imath]4[/imath] hours...
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A
1747244462909.png

Two tanks are partially filled with 80 gallons of water each.
  • Tank A is [imath]\frac{3}{4}[/imath] full
  • Tank B is [imath]\frac{5}{8}[/imath] full
What is the maximum total capacity (in gallons) of both tanks together?

A. 200 gallons
B. 240 gallons
C. 256...
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30
0 Votes
A
A structure in a 1 : 25 scale drawing has a height of 30 cm.
If the ratio of the height to the width is 3 : 1, what is the actual width, in meters, rounded to the nearest tenth?

A. 2.0
B. 2.5
C. 3.2
D. 3.6


So the story is, there is a real building, and a toy model (aka...
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0 Votes
If [imath]0.02 \div x = 1[/imath], then [imath]x =[/imath]

[imath]\text{(A) } 0.02 \quad \text{(B) } 50 \quad \text{(C) } 5.0 \quad \text{(D) } 0.5[/imath]


We are given:
[imath]0.02 \div x = 1[/imath]


Step 1: Multiply both sides by [imath]x[/imath]
Rewrite division to fraction (since they are the same thing)...
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0 Votes
A
A tennis court is 78 feet long.
  • Singles court: 27 feet wide
  • Doubles court: 4.5 feet added to each long side, so width becomes:
    [imath]27 + 4.5 + 4.5 = 36[/imath] feet
How much larger is the area of the doubles court than the singles court?


A. 2,808 sq. ft.
B...
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Anonymous (e8ab)
A
0 Votes
What is [imath](600 \times 3) \div 4[/imath]?
[imath]\text{(A) } 450 \quad \text{(B) } 200 \quad \text{(C) } 600 \quad \text{(D) } 300[/imath]



Step 1: Multiply:
[imath]600 \times 3 = 1800[/imath]

Step 2: Divide:
[imath]1800 \div 4 = 450[/imath]


Final answer: (A) [imath]450[/imath]
Remember PEMDAS

PEMDAS...
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Anonymous (3ccc)
A
1 Vote
Convert 24% to a fraction.
[imath]\text{(A) } \frac{6}{25} \quad \text{(B) } \frac{1}{25} \quad \text{(C) } \frac{6}{24} \quad \text{(D) } \frac{1}{24}[/imath]

Answer: A


Step 1: Write 24% as a fraction:
[imath]24\% = \frac{24}{100}[/imath]

Step 2: Simplify:
Find GCF of 24 and 100 → GCF = 4...
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Anonymous (80cd)
A
0 Votes
A
1745947434038.png

Answer: B

1746251450281.png
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Anonymous (db6f)
A
0 Votes
A
Julia earns [imath]68{,}000[/imath] per year and wants to begin investing her money. She figures she can afford to invest [imath]40%[/imath] of her annual salary. Of that, [imath]60%[/imath] will be invested in corporate bonds, while [imath]40%[/imath] will be invested in securities. If the corporate bonds and securities yield...
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1
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Anonymous (f385)
A
0 Votes
The reciprocal of [imath]\frac{1}{8}[/imath] is:
[imath]\text{(A) } 8 \quad \text{(B) } 1 \quad \text{(C) } \frac{1}{8} \quad \text{(D) } \frac{1}{4}[/imath]

Answer: A


The reciprocal of a fraction is found by flipping the numerator and denominator:

[imath]\text{Reciprocal of } \frac{1}{8} =...[/imath]
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Anonymous (a53a)
A
0 Votes
A
Among the Smithsonian’s most admired treasures is the 45.52-carat Hope Diamond, the world’s largest blue diamond. This famous gem was originally purchased in India and sold to King Louis XIV of France in 1668. It later became part of the French crown jewels.

When King Louis XVI and Queen Marie...
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0
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16
Anonymous (2c2b)
A
0 Votes
A
Honeybee stings, while briefly painful, are typically not dangerous. The most important first step is to remove the stinger immediately. Doing this helps minimize symptoms like pain, itching, and swelling. Many people panic after being stung, which can worsen symptoms instead of...
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0
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14
Anonymous (1fcb)
A
0 Votes
A
To prepare pancake batter, start by separating two eggs—place the egg whites into a medium bowl and the yolks into a larger bowl. Beat the egg whites using a mixer set to high until they form stiff peaks. Meanwhile, add 1½ cups of milk and 2 tablespoons of...
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0
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14
Anonymous (a697)
A
0 Votes
A
In 2015, the city of Houston, a sprawling urban area heavily reliant on cars, introduced an advanced traffic coordination network. Embedded sensors beneath major intersections transmitted real-time data on vehicle volume to a central operations hub. Engineers used this data to...
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0
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22
Anonymous (ef0d)
A
0 Votes
A
In the 20th century, the futurist and inventor Dr. Elaine Porter often speculated on upcoming advancements in technology. While wireless charging didn’t become commonplace until the 2010s, Porter outlined the concept in a 1962 journal article. In her 1971 book Future Currents, she...
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0
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14
Anonymous (adb8)
A
0 Votes
A
Australia has a unique political setup. Like the United Kingdom, it is a parliamentary democracy operating within the framework of a constitutional monarchy. In fact, both countries recognize the same monarch. How does this work? The key lies in understanding the difference between managing the...
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0
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Anonymous (d83f)
A
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