Arithmetic Reasoning Practice Test 5 (ASVAB)

Answer: C

Correct answer: 20 feet. Add the ratio terms:

parts. One part is

The shorter piece is 4 parts:

• A: This is the longer piece, 5 parts of 5 feet.
• B: This divides 45 by 5, using one ratio term instead of the 9 total parts.
• C (correct): There are 4 + 5 = 9 parts of 45 ÷ 9 = 5 feet, so the shorter piece is 4 × 5 = 20 feet.
• D: This multiplies 45 by 4/5, using a part-to-part ratio as if it were a fraction of the whole.

Answer: C

Correct answer: $2,200. Round to friendly numbers:

The exact value,

confirms the estimate.

• A: This is ten times too small; 200 tickets at about $10 each is about $2,000.
• B: This is ten times too large, likely from a misplaced zero.
• C (correct): Rounding 198 to 200 gives 200 x $11 = $2,200, very close to the exact $2,178.
• D: This adds 198 and 11 instead of multiplying tickets by price.

Answer: B

Correct answer: 18 quarts. Convert to one unit before adding: 3 gallons × 4 = 12 quarts.

Then

• A: This adds 3 and 6 without converting gallons to quarts first.
• B (correct): Converting 3 gallons gives 12 quarts, and 12 + 6 = 18 quarts.
• C: This uses 8 per gallon, which is the number of pints in a gallon, not quarts.
• D: This converts the 3 gallons but forgets to add the other 6 quarts.

Answer: D

Correct answer: 3/8. Use the common denominator 8:

• A: This subtracts straight across (6/6); denominators are never subtracted.
• B: This renames 1/2 as 2/8, but 1/2 equals 4/8.
• C: This adds the fractions (11/8) instead of subtracting.
• D (correct): Renaming 1/2 as 4/8 gives 7/8 - 4/8 = 3/8.

Answer: A

Correct answer: 50 mph. Distance:

so 250 miles. Time:

because the stop adds time but no distance. Average speed =

• A (correct): The trip covers 250 miles in 5 hours, counting the 0.75-hour stop.
• B: This simply averages 58 and 60 and leaves out the stop entirely.
• C: This divides 250 miles by 4.25 hours of driving and forgets to add the lunch stop.
• D: This writes 45 minutes as 0.45 hour instead of 0.75 hour.

Answer: D

Correct answer: $195.50. Apply each change to the current price. After the increase:

After the decrease:

The base changed, so the price does not return to $200.

• A: This assumes equal percent changes cancel; the 15% decrease is figured on $230, not $200.
• B: This is the price after the increase only; the later 15% decrease was not applied.
• C: This applies the 15% decrease to the original $200 and skips the increase.
• D (correct): 200 × 1.15 = $230, then 230 × 0.85 = $195.50, because the decrease is taken from the larger price.

Answer: A

Correct answer: 24 minutes. Add the rates:

of the batch per minute.

Time:

which is faster than either copier alone, as it should be.

• A (correct): Together they print 1/40 + 1/60 = 1/24 of the batch per minute, so the job takes 24 minutes.
• B: This averages the two times; working together must be faster than either copier alone.
• C: This adds the two times, which would be slower than either copier alone.
• D: This halves the faster copier's time, as if both copiers were as fast as Copier A.

Answer: D

Correct answer: 3 7/24 feet. Rename over 24: $6\frac{3}{24}-2\frac{20}{24}$. Because 3/24 is smaller than 20/24, borrow 1 whole to get $5\frac{27}{24}$.

Then

• A: This subtracts the smaller fraction from the larger one (5/6 minus 1/8) instead of borrowing a whole.
• B: The borrow was made in the fraction part, but the whole number was not reduced from 6 to 5.
• C: This is the sum of the two lengths; a piece cut off must be subtracted.
• D (correct): Rename with denominator 24, borrow 1 from the 6, and subtract: $5\frac{27}{24}-2\frac{20}{24}=3\frac{7}{24}$.

Answer: C

Correct answer: 7.5 cups. Keep cups on top in both ratios:

Cross-multiply:

• A: This is 50 / 20, the scale factor, without multiplying it by the 3 cups in the recipe.
• B: This simply doubles the recipe, which makes 40 pancakes, not 50.
• C (correct): Setting 3/20 = x/50 gives x = 3 x 50 / 20 = 7.5 cups.
• D: This adds the 30 extra pancakes to the 3 cups, mixing pancakes with cups.

Answer: B

Correct answer: 2/5. Combined rate:

per hour.

Work done in 4 hours:

Remaining:

• A: This is the fraction already tiled, not the fraction still untiled.
• B (correct): Together they tile 3/20 per hour, so 4 hours covers 3/5 of the floor and 2/5 remains.
• C: This counts only the tile setter's 4/12 and leaves out the helper's work.
• D: This treats the pair as needing 12 + 15 = 27 hours, adding times instead of rates.

Answer: A

Correct answer: 2,800 grams. Find the total in kilograms:

Convert to grams by moving the decimal point three places right:

grams.

• A (correct): 8 times 0.35 is 2.8 kilograms, and 2.8 times 1,000 is 2,800 grams.
• B: This converts kilograms to grams by multiplying by 100 instead of 1,000.
• C: This is the amount in kilograms; the unit was changed without converting the number.
• D: This moves the decimal point four places instead of three when converting.

Answer: B

Correct answer: $24. Tarps:

Rope:

Total cost:

Change:

so the crew receives $24.

• A: This subtracts only the cost of the tarps and forgets the rope.
• B (correct): Tarps cost $322 and rope costs $54, for $376 in all, so the change is $400 − $376 = $24.
• C: This subtracts the tarps and the price of just one coil of rope.
• D: $376 is the total cost of the purchase, not the change.

Answer: C

Correct answer: $0.12. 64-ounce bottle:

dollar per ounce.

150-ounce bottle with coupon:

dollar per ounce. The lowest price is $0.12 per ounce.

• A: This is the 150-ounce bottle's price per ounce without the coupon.
• B: This is the 64-ounce bottle's price per ounce, which is the highest of the three per-ounce prices.
• C (correct): With the coupon the 150-ounce bottle costs $18.00, and 18.00 divided by 150 is $0.12 per ounce.
• D: This adds the $1.50 to the price instead of subtracting it: 21.00 divided by 150.

Answer: D

Correct answer: 2.8 hours. Call the job 30 units. A, B and C do 5, 3 and 2 units per hour.

Stage 1: A and B do 8 units per hour, so 16 units in 2 hours, leaving 14 units. Stage 2: B and C do 5 units per hour, so

• A: This is the total elapsed time; the question asks only for the time after C joins.
• B: This is the time if all three worked together on the whole attic from the start.
• C: This lets C finish the remaining 7/15 alone and leaves out B's continued work.
• D (correct): A and B finish 8/15 in 2 hours, leaving 7/15; B and C do 1/6 per hour, so the rest takes 2.8 hours.

Answer: C

Correct answer: $65.00. A total with 8 percent tax is 108 percent of the original price.

Original price:

Check: 8 percent of 65 is 5.20, and 65 plus 5.20 is 70.20.

• A: This takes 8 percent off the total, but the tax was figured on the pre-tax price, so you must divide by 1.08.
• B: This subtracts 8 dollars, treating the 8 percent as a dollar amount.
• C (correct): The total is 108 percent of the price, and 70.20 divided by 1.08 is 65.
• D: This adds tax again to the total instead of removing it.