ASVAB Arithmetic Reasoning Practice Test 6

Answer: B

Correct answer: $21.00. With 40% off, you pay 60% of the price:

• A: This is the amount saved (40% of $35); it must be subtracted from the price.
• B (correct): Paying 60% of the price: 0.60 × 35 = $21.
• C: This adds 40% to the price instead of taking it off.
• D: This takes off only 4% instead of 40%.

Answer: A

Correct answer: 325 gallons. Water used: 35% of

Water left:

(or 65% of 500 = 325).

• A (correct): The crew used 0.35 × 500 = 175 gallons, so 500 − 175 = 325 gallons are left.
• B: This is the amount used, not the amount left.
• C: This subtracts 35 gallons instead of 35% of 500.
• D: This adds 35% to the tank instead of taking it away, giving more water than the tank holds.

Answer: D

Correct answer: $13.00. Find 10 percent by moving the decimal point one place left: $26. Five percent is half of that, so the tax is

• A: This is 20 percent of 260, which comes from dividing by 5 instead of taking 5 percent.
• B: This uses 0.005 for 5 percent; 5 percent is 0.05.
• C: This uses 0.5 for 5 percent, which is 50 percent of the price.
• D (correct): 10 percent of 260 is 26, and 5 percent is half of that, or 13.

Answer: D

Correct answer: 2/3. An hour has 60 minutes, so 40 minutes is $\frac{40}{60}$. Divide the top and bottom by 20 to get $\frac{2}{3}$ hour.

• A: This treats an hour as 100 minutes (40/100); an hour has 60 minutes.
• B: Three-quarters of an hour is 45 minutes, not 40.
• C: Five-sixths of an hour is 50 minutes, not 40.
• D (correct): 40 out of 60 minutes is 40/60, which simplifies to 2/3 by dividing by 20.

Answer: C

Correct answer: 6:00 p.m. By 3:00 p.m. the freight has a lead of

The express gains

each hour, so it needs

Three hours after 3:00 p.m. is 6:00 p.m.

• A: This adds the speeds to get 80 mph, which is the rule for trains moving toward each other.
• B: This finds the 3-hour chase time but counts it from the freight's 1:00 p.m. start.
• C (correct): The 60-mile lead closes at 20 mph in 3 hours, counted from 3:00 p.m.
• D: This divides the 60-mile lead by the express's full speed of 50 mph instead of by the 20 mph it gains.

Answer: D

Correct answer: 17.1 square meters. Area is length times width. Multiply

the factors have one decimal place each, so the product has two: 17.10. The area is 17.1 square meters, close to the estimate

• A: This multiplies 45 by 38 but never places the two decimal places back in the product.
• B: This places three decimal places in the product; the factors have only two in total.
• C: This multiplies the whole parts (4 times 3) and the decimal parts (0.5 times 0.8) separately and adds them, which skips the cross products.
• D (correct): 45 times 38 is 1,710, and two decimal places in all give 17.10, or 17.1.

Answer: C

Correct answer: 5. A number is divisible by 9 when its digits add to a multiple of 9. The known digits add to

The next multiple of 9 is 18, so the missing digit is

giving

• A: The digit sum would be 17, which is not a multiple of 9.
• B: The digit sum would be 16, which is not a multiple of 9.
• C (correct): The digits then add to 4 + 7 + 5 + 2 = 18, a multiple of 9.
• D: The digit sum would be 13, which is not a multiple of 9.

Answer: B

Correct answer: $0.05. Unit prices:

per battery, and

per battery.

Difference:

per battery.

• A: This is the difference between the two pack prices, not the difference per battery.
• B (correct): The 12-pack costs $0.75 per battery and the 20-pack costs $0.70, a difference of $0.05.
• C: This is the price per battery of the 20-pack, an intermediate value.
• D: This is the price per battery of the 12-pack, an intermediate value.

Answer: B

Correct answer: 180. Add the ratio terms:

parts. One part is

rounds.

The 3-part share is

rounds.

• A: This is the share of the squad with 2 parts, 2 × 60.
• B (correct): There are 2 + 3 + 4 = 9 parts, each 540 ÷ 9 = 60 rounds, so 3 parts is 180.
• C: This is the share of the squad with 4 parts, 4 × 60.
• D: This is the value of one part, not the 3-part share.

Answer: B

Correct answer: 2:5. The fraction 2/7 is part-to-whole: 2 of every 7 vehicles are trucks. The other

are jeeps, so trucks to jeeps is 2:5.

• A: This is trucks to all vehicles, a part-to-whole ratio, not trucks to jeeps.
• B (correct): If trucks are 2 parts out of 7, jeeps are 7 - 2 = 5 parts, so trucks to jeeps is 2:5.
• C: This is jeeps to trucks, the reverse of the order asked.
• D: This is jeeps to all vehicles, not trucks to jeeps.

Answer: B

Correct answer: 3 hours. Toward each other, add speeds:

• A: This subtracts the speeds; approaching objects close the gap at the sum of their speeds.
• B (correct): Walking toward each other they close the gap at 6.5 mph, and 19.5 divided by 6.5 is 3.
• C: This uses the average speed of 3.25 mph instead of the combined speed.
• D: This uses only the slower hiker's speed, as if the other hiker stood still.

Answer: B

Correct answer: 420 cases. After the first issue $\frac{4}{7}$ remains; after the second, half of that, $\frac{2}{7}$, remains.

• A: This subtracts 3/7 and 1/2 from 1 as if both were fractions of the starting amount, giving 1/14.
• B (correct): The 120 cases are 1/2 of 4/7, or 2/7, of the starting amount, and 120 divided by 2/7 is 420.
• C: This undoes only the second issue; 240 is the number of cases after the first issue.
• D: This divides 120 by 3/7, the fraction issued first, instead of by the fraction left.

Answer: A

Correct answer: 3 gallons. Area:

which is 4 sections of 1,000 square feet.

Fertilizer:

Convert:

• A (correct): The lawn is 4,000 square feet, which needs 4 x 3 = 12 quarts, and 12 / 4 = 3 gallons.
• B: This is the amount in quarts; the units were never converted to gallons.
• C: This multiplies 12 quarts by 4 instead of dividing when changing to the larger unit.
• D: This converts 3 quarts for a single 1,000-square-foot section and ignores the lawn's size.

Answer: D

Correct answer: 3 3/8 feet. Total used:

Then borrow:

• A: This subtracts the two shelves but ignores the wood lost in the saw cuts.
• B: This counts the sawdust for only one cut; there are two cuts at 1/8 foot each.
• C: The fraction was found by borrowing 1 from the 12, but the whole number was not lowered to 11 before subtracting.
• D (correct): The shelves and two saw cuts use 3 5/8 + 4 6/8 + 2/8 = 8 5/8 feet, and 12 - 8 5/8 = 3 3/8 feet.

Answer: D

Correct answer: 4 hours. With a common denominator of 24, the three rates are

per hour, so in 2 hours they finish $\frac{1}{2}$.

The two slower pumps drain

per hour, so the remaining half takes

• A: This is the total time for the whole job; the question asks only for the time after the breakdown.
• B: This assumes the pumps keep working at the full three-pump rate after the fastest one stops.
• C: This is how long the two remaining pumps would need for the entire job, ignoring the half already done.
• D (correct): All three drain 1/4 per hour, so 1/2 is done after 2 hours; the remaining two drain 1/8 per hour, so the last half takes 4 hours.