ASVAB Arithmetic Reasoning Test 4

Answer: A

Correct answer: 1.5. Move the decimal point two places to the left: 150 percent becomes 1.50. A percent over 100 gives a decimal greater than 1.

• A (correct): Moving the decimal point in 150 two places to the left gives 1.50, or 1.5.
• B: This moves the decimal point only one place to the left.
• C: This moves the decimal point three places to the left; 0.15 is 15 percent.
• D: This drops the percent sign without moving the decimal point.

Answer: A

Correct answer: 2:3. Write the quantities in the order named: ambulances to engines is 6:9. The greatest common factor is 3, so the ratio simplifies to 2:3.

• A (correct): Ambulances to engines is 6:9; dividing both terms by 3 gives 2:3.
• B: This is engines to ambulances, the reverse of the order the question names.
• C: This compares ambulances with all 15 vehicles, a part-to-whole ratio.
• D: This compares engines with all 15 vehicles, which is neither the right order nor part-to-part.

Answer: A

Correct answer: $12.48. Find 10% by moving the decimal point one place left: $6.24. Double it for 20%:

• A (correct): 20% is 0.20 × 62.40 = $12.48, or double the 10% amount of $6.24.
• B: This is only 10% of the bill; 20% is twice that amount.
• C: This is the bill plus the tip; the question asks for the tip alone.
• D: This reverses the last two digits of the correct tip.

Answer: D

Correct answer: 15 miles. Convert the time to hours: 25 minutes = 25/60 hour = 5/12 hour.

Distance = rate × time =

• A: This multiplies 36 by 25 without converting minutes to hours.
• B: This divides 36 by 25 instead of multiplying the speed by the time in hours.
• C: This treats 25 minutes as 0.25 hour, which is only 15 minutes.
• D (correct): Twenty-five minutes is 25/60 of an hour, and 36 × 25/60 = 15 miles.

Answer: A

Correct answer: 428. Use the inverse operation: number = quotient × divisor + remainder.

Check: 428 ÷ 9 is 47 with 5 left over.

• A (correct): Multiply the quotient by the divisor and add the remainder: 9 × 47 + 5 = 423 + 5 = 428.
• B: This multiplies 9 × 47 but forgets to add the remainder.
• C: This subtracts the remainder instead of adding it.
• D: This is 9 × 48, which would give a quotient of 48 with no remainder.

Answer: C

Correct answer: 5,742. To multiply by 99, multiply by 100 and subtract the number once.

• A: This adds 58 to 5,800 instead of subtracting it.
• B: This subtracts 158 instead of 58 from 5,800.
• C (correct): 58 × 100 = 5,800, and subtracting one 58 gives 5,742.
• D: This is 1,000 too small, from a borrowing slip in the thousands place.

Answer: C

Correct answer: 50 percent. Pure amounts:

gallon and

for 6 gallons in 12 gallons.

Concentration:

or 50 percent.

• A: 40 percent averages the two concentrations without weighting by volume; there is three times as much of the 60 percent solution.
• B: This gives the larger volume to the 20 percent solution, reversing the amounts.
• C (correct): The pure amounts are 0.6 and 5.4 gallons, giving 6 gallons in 12, which is 50 percent.
• D: This adds the two percentages, but a mixture cannot be stronger than its strongest part.

Answer: A

Correct answer: 23 gallons. Find the rate first:

per gallon.

Then divide the new distance by the rate:

• A (correct): The van gets 378 / 14 = 27 miles per gallon, and 621 / 27 = 23 gallons.
• B: This is the mileage rate in miles per gallon, an in-between step rather than the fuel needed.
• C: This covers only the extra 243 miles beyond the first trip (243 / 27 = 9), not the whole 621-mile trip.
• D: This adds the first trip's 14 gallons to the 23 gallons the new trip needs.

Answer: A

Correct answer: 48 mph. 20 minutes is one-third of an hour, so the time is $\frac{4}{3}$ hours.

• A (correct): 1 hour 20 minutes is 4/3 of an hour, and 64 divided by 4/3 is 48.
• B: This writes 1 hour 20 minutes as 1.2 hours; 20 minutes is one-third of an hour.
• C: This divides by 80 minutes, which gives miles per minute, not miles per hour.
• D: This multiplies the distance by the time instead of dividing.

Answer: D

Correct answer: 7.5 hours. The unknown rate is the team rate minus the known rate:

Invert:

• A: This subtracts the times (5 - 3) instead of the rates.
• B: This adds the two times, which has no meaning for work rates.
• C: This adds the rates instead of subtracting the known worker's rate from the team rate.
• D (correct): Subtracting rates gives 1/3 - 1/5 = 2/15 of the trailer per hour, so the other operator alone needs 15/2 = 7.5 hours.

Answer: C

Correct answer: 3 3/4 cups. Multiply the amount per batch by the number of batches:

Since

remainder 3, this is $3\frac{3}{4}$ cups.

• A: Multiplying both the top and bottom by 5 (15/20) leaves the value unchanged; only the numerator is multiplied by a whole number.
• B: This divides 5 by 3/4, which tells how many batches 5 cups would make.
• C (correct): 5 times 3/4 is 15/4, and 15 divided by 4 is 3 with remainder 3.
• D: This subtracts 3/4 from 5 instead of multiplying for 5 batches.

Answer: B

Correct answer: $60.20. Miles per gallon:

Gallons for the trip:

Cost:

Estimate: about 18 gallons at about 3.5 dollars is about 63 dollars, which is close.

• A: This is the number of gallons needed, not the cost; it still has to be multiplied by $3.44.
• B (correct): The car gets 32 miles per gallon, so 560 miles needs 17.5 gallons, and 17.5 times 3.44 is 60.20.
• C: This is the cost of the 12.9 gallons for the first 412.8 miles, not for the 560-mile trip.
• D: This multiplies the miles by the price per gallon, skipping the miles-per-gallon step.

Answer: C

Correct answer: 11:00 a.m. In the first hour only the bus moves:

remain at 9:00 a.m.

Moving toward each other, add speeds:

Time:

after 9:00 a.m., so they meet at 11:00 a.m.

• A: The 2 hours of closing time are counted from 8:00, but the car does not start until 9:00.
• B: This divides all 245 miles by 100 mph and ignores the 45 miles the bus covered alone.
• C (correct): By 9:00 the bus has gone 45 miles, leaving 200 miles that close at 100 mph, so they meet 2 hours after 9:00.
• D: This ignores the bus's head start and also counts from 8:00 instead of 9:00.

Answer: D

Correct answer: 36 percent. Pure acid:

Total volume: 10 liters. Concentration:

or 36 percent.

• A: 30 percent averages the three concentrations without weighting by volume; most of the mixture is the 50 percent solution.
• B: This pairs the 5 liters with 10 percent and the 2 liters with 50 percent, reversing the volumes.
• C: 3.6 is the number of liters of pure acid; it still has to be divided by the 10-liter total.
• D (correct): The pure amounts are 0.2 + 0.9 + 2.5 = 3.6 liters in 10 liters, which is 36 percent.

Answer: A

Correct answer: 540 miles. The gap closes at

per hour. In the final hour before meeting they close exactly 540 miles, so 1 hour before they meet they are 540 miles apart. Check: they meet after

and at 1.5 hours they have covered 810 miles, leaving 540.

• A (correct): In the last hour they close the gap at their combined speed of 540 mph.
• B: This is how far the two planes have flown together by that time, not the gap still between them.
• C: This uses the difference of the speeds, which applies only when one plane chases the other.
• D: This counts only the faster plane's last hour and forgets that the other plane is also closing the gap.