ASVAB Arithmetic Reasoning Practice Test 2

Answer: A

Correct answer: 9/20. Percent means per hundred, so 45 percent is $\frac{45}{100}$.

Divide the numerator and denominator by 5:

Check: 9 divided by 20 is 0.45.

• A (correct): 45 percent is 45 over 100, and dividing top and bottom by 5 gives 9/20.
• B: This reads the digits 4 and 5 as a fraction; 4/5 is 80 percent.
• C: This reduces 45 over 100 incorrectly; 9/10 is 90 percent.
• D: This divides by 1,000 instead of 100, treating 45 percent as 4.5 percent; 9/200 equals 0.045.

Answer: B

Correct answer: 168 muffins. Equal groups call for multiplication:

muffins.

• A: This adds 24 and 7, but the story describes equal groups, which calls for multiplication.
• B (correct): Seven equal groups of 24 is 24 x 7 = 168.
• C: This subtracts 7 from 24, which does not match anything happening in the story.
• D: This is 24 x 6, one tray short of the 7 trays filled.

Answer: B

Correct answer: twelve and forty-five thousandths. Read the whole number (twelve), say "and" for the decimal point, then read the decimal digits 045 as forty-five and name the place of the last digit. The 5 is in the thousandths place, so it is twelve and forty-five thousandths.

• A: Forty-five hundredths would be 12.45; the 5 here is three places past the point, which is thousandths.
• B (correct): The last digit, 5, sits in the thousandths place, so the decimal part 045 is read as forty-five thousandths.
• C: Four hundred fifty thousandths is 12.450, which places the 4 in the tenths place instead of the hundredths place.
• D: Ten-thousandths would need four decimal places; 12.045 has only three.

Answer: C

Correct answer: $0.45. Divide the total cost by the number of bars:

per bar. Check:

• A: This swaps the digits of the correct unit price, a common slip when dividing.
• B: This divides 24 by 10.80, which gives bars per dollar, not dollars per bar.
• C (correct): Unit price is total cost divided by units: 10.80 ÷ 24 = $0.45.
• D: This is a division error; 24 × 0.43 is only $10.32.

Answer: A

Correct answer: 24 percent. Pure amount:

Water adds none, and the total volume becomes 15 liters.

Concentration:

or 24 percent.

• A (correct): The 3.6 liters of disinfectant are now spread through 15 liters, and 3.6 divided by 15 is 24 percent.
• B: This averages 40 percent and 0 percent as if the volumes were equal, but there is more of the 40 percent solution.
• C: Adding water does not change the amount of disinfectant, but it does increase the volume, so the strength drops.
• D: This weights 40 percent by the 6 liters of water instead of by the 9 liters of solution.

Answer: B

Correct answer: $3.40. Total cost:

for 20 gallons.

Average price: $68.00 divided by 20 is $3.40 per gallon.

• A: $3.45 averages the two prices, but more gallons were bought at the lower price.
• B (correct): The total cost is $38.40 + $29.60 = $68.00 for 20 gallons, which is $3.40 per gallon.
• C: This multiplies 12 gallons by the higher price, matching the amounts with the wrong prices.
• D: $68.00 is the total cost of the gas, not the price per gallon.

Answer: B

Correct answer: 8.5 cm. Going from real distance to map distance, divide by the real length each centimeter stands for:

• A: This multiplies by the scale, which converts map length to real length, the wrong direction.
• B (correct): Dividing the real distance by kilometers per centimeter gives 340 ÷ 40 = 8.5 cm.
• C: This divides 40 by 340, turning the scale upside down.
• D: This subtracts 40 from 340 instead of dividing.

Answer: B

Correct answer: 45 minutes. Rate:

tank per hour.

Time for 1 tank:

• A: This multiplies 2/3 by 1/2 (1/3 hour), which gives less time than the 30 minutes already spent on part of the tank.
• B (correct): The pump fills 2/3 divided by 1/2 = 4/3 tanks per hour, so one tank takes 3/4 hour, or 45 minutes.
• C: This treats the rate of 4/3 tanks per hour as if it were 4/3 hours.
• D: This assumes the remaining 1/3 of the tank takes another full half hour, but 1/3 is only half of 2/3.

Answer: A

Correct answer: 3 hours. Time = amount divided by rate:

The rate was per minute, so the answer is in minutes; convert:

• A (correct): 8,100 divided by 45 is 180 minutes, and 180 divided by 60 is 3 hours.
• B: 180 is the time in minutes; it still has to be divided by 60 to give hours.
• C: This treats 180 minutes as 1.80 hours; minutes convert to hours by dividing by 60, not 100.
• D: The decimal is misplaced; 180 minutes divided by 60 is 3, not 30.

Answer: D

Correct answer: 7%. Tax amount:

Rate:

which is 7%. Check:

• A: This divides the $4.48 tax by the $68.48 total; the tax rate is based on the price before tax.
• B: This treats the dollar amount of tax as the percent without dividing by the price.
• C: This misplaces the decimal; 0.07 as a percent is 7%, not 0.7%.
• D (correct): The tax is 68.48 − 64 = $4.48, and 4.48 ÷ 64 = 0.07 = 7%.

Answer: A

Correct answer: $9. First find the cost:

Then find the change:

• A (correct): The purchase costs 5 x $3 + 2 x $28 = $15 + $56 = $71, and $80 - $71 = $9.
• B: This is the cost of the purchase, an in-between number, not the change asked for.
• C: This counts only one roll of wire: $15 + $28 = $43, and $80 - $43 = $37.
• D: This adds one of each price ($3 + $28 = $31) instead of multiplying by the quantities.

Answer: C

Correct answer: 14 hours. Alone for 5 hours she finishes

leaving $\frac{3}{4}$.

Team rate:

per hour, so the rest takes

Total:

• A: This is only the time after the coworker joins; the question asks for total elapsed time, so the first 5 hours must be added.
• B: This is how long the two would need for the entire job if they started together, ignoring the solo stage.
• C (correct): She finishes 1/4 alone, the pair then needs 9 hours for the remaining 3/4, and 5 + 9 = 14 hours.
• D: This adds the solo 5 hours to a full 12-hour team job, forgetting that 1/4 of the work was already done.

Answer: C

Correct answer: 11:30 a.m. In the first 2 hours they close

leaving 8.5 miles. During the 30-minute rest only the slower hiker moves, closing

and leaving 7 miles. Walking together again they close 7 mph, so they need 1 more hour. Total time is

so they meet at 11:30 a.m.

• A: This ignores the rest and divides the whole 22.5 miles by 7 mph.
• B: This treats the rest as stopping both hikers, so no distance is closed during those 30 minutes.
• C (correct): The meeting comes 3.5 hours after the start once the rest and the slower hiker's progress during it are counted.
• D: This ignores the rest and also reads 3.21 hours as 3 hours 21 minutes.

Answer: C

Correct answer: 10 liters. Parts:

so one part is

Antifreeze: 15 liters; water: 25 liters.

Only antifreeze is added, so the water stays at 25 liters. For a 1:1 ratio, antifreeze must also be 25 liters:

• A: This adds half the difference; the antifreeze must increase by the full 10-liter difference to match the water.
• B: This is the amount of antifreeze already in the mix, not the amount to add.
• C (correct): The mix has 15 liters of antifreeze and 25 of water; adding 10 liters makes 25 liters of each.
• D: This is the amount of water, which stays the same; it is not the amount to add.

Answer: A

Correct answer: 53. Parentheses first:

Exponent next: 2² = 4.

Then divide and multiply from left to right:

Finally,

• A (correct): Parentheses give 8, the exponent gives 4, then 96 ÷ 8 = 12, 12 × 4 = 48, and 48 + 5 = 53.
• B: This multiplies 8 × 4 before dividing, giving 96 ÷ 32 = 3, which breaks the left-to-right rule.
• C: This ignores the parentheses, computing 96 ÷ 2 + 6 × 4 + 5.
• D: This squares 12 × 2 instead of squaring only the 2.