Arithmetic Reasoning Practice Test 3 for the ASVAB

Answer: B

Correct answer: 7/15. Compare each numerator with half of its denominator. Only 7/15 has a numerator (7) smaller than half its denominator (7.5), so it is the only fraction less than 1/2.

• A: Half of 9 is 4.5, and 5 is more than that, so 5/9 is greater than 1/2.
• B (correct): Half of 15 is 7.5, and 7 is less than 7.5, so 7/15 is below 1/2.
• C: Half of 11 is 5.5, and 6 is more than that, so 6/11 is greater than 1/2.
• D: Half of 17 is 8.5, and 9 is more than that, so 9/17 is greater than 1/2.

Answer: C

Correct answer: 0.485 liter. Liters are larger than milliliters, so divide by 1,000 and move the decimal point three places left:

liter.

• A: This moves the decimal point only two places, which divides by 100.
• B: This moves the decimal point only one place, which divides by 10.
• C (correct): Dividing by 1,000 moves the decimal point three places left, so 485 becomes 0.485.
• D: This multiplies by 1,000; changing to a larger unit should give a smaller number.

Answer: B

Correct answer: 18 ounces. Write 25 percent as 0.25, or one fourth, and multiply by the whole:

• A: This is the 75 percent of the jug that is left, not the 25 percent that was used.
• B (correct): 25 percent is one fourth, and 72 divided by 4 is 18.
• C: This writes 25 percent as 0.025 instead of 0.25, moving the decimal point one place too far.
• D: This divides 72 by 3, which finds about 33 percent rather than 25 percent.

Answer: D

Correct answer: 58 words per minute. A unit rate is the first quantity divided by the second:

words per minute.

• A: This divides by 60, as if the typing took a full hour instead of 30 minutes.
• B: The division is right but the decimal point is misplaced; 30 times 5.8 is only 174.
• C: This is the rate per hour (58 times 60), not the rate per minute.
• D (correct): Dividing 1,740 words by 30 minutes gives 58 words for each minute.

Answer: B

Correct answer: 73 remainder 4.

leaving 55, and

fits into 55 with 4 left. So the quotient is 73 remainder 4.

Check: multiply the quotient by the divisor and add the remainder:

• A: A remainder of 21 is larger than the divisor 17, so one more 17 fits; the quotient is too small.
• B (correct): 73 × 17 = 1,241, and 1,241 + 4 = 1,245, so the check returns the original number.
• C: 74 × 17 = 1,258, which is already more than 1,245, so 74 is too large.
• D: 73 × 17 + 14 = 1,255, not 1,245, so the remainder is wrong.

Answer: D

Correct answer: 67.5 miles. Keep inches on top in both ratios:

Cross-multiply:

Each inch stands for 7.5 miles, and

• A: This multiplies 9 by 15 as if 1 inch, not 2 inches, stood for 15 miles.
• B: This flips one ratio, putting miles on top in one fraction and inches on top in the other.
• C: This adds 9 and 15, but a map scale is a ratio that calls for multiplying.
• D (correct): Setting 2/15 = 9/x gives 2x = 135, so x = 67.5 miles.

Answer: C

Correct answer: 420. Monday: one-third of 840 is 280, leaving 560 cans.

Tuesday: 25% of 560 is 140, so

cans remain. The 25% applies to what was left, not to the starting 840.

• A: This is the number given away on Tuesday, an intermediate value rather than the cans remaining.
• B: This is the count after Monday only; the Tuesday step was skipped.
• C (correct): After Monday 560 cans are left, Tuesday removes 25% of 560 (140), and 560 − 140 = 420 cans remain.
• D: This applies the 25% to the original 840 cans instead of to the 560 cans left after Monday.

Answer: B

Correct answer: 21. Translate in order: three times a number is $3x$, and subtracting 15 from it gives

Add 15:

Divide by 3:

• A: This comes from 3x + 15 = 48, which adds 15 instead of subtracting it.
• B (correct): The sentence is 3x - 15 = 48, so 3x = 63 and x = 21.
• C: This comes from 3(x - 15) = 48, which subtracts before multiplying.
• D: This divides 48 by 3 and ignores the 15 that was subtracted.

Answer: D

Correct answer: $180. Convert time to years:

year. Then

so the interest is $180.

• A: This uses 8 as the number of years; the months must be converted to years first.
• B: This is a full year of interest; 8 months is only two-thirds of a year.
• C: This treats 8 months as 0.8 year; 8 months is 8 ÷ 12 ≈ 0.67 year.
• D (correct): Eight months is 8/12 of a year, so 6,000 × 0.045 × 8/12 = $180.

Answer: D

Correct answer: 11/16 inch. Convert the fraction first:

Pad all values to four places: 0.7000, 0.6875, 0.6900, 0.6950. The smallest is 0.6875, so the 11/16-inch strip is thinnest.

• A: 0.6900 is larger than 11/16, which converts to 0.6875.
• B: This looks small because of its extra digit, but 0.6950 is larger than both 0.6875 and 0.6900.
• C: 0.7 has the fewest digits, but padded to 0.7000 it is actually the thickest of the four.
• D (correct): 11/16 equals 0.6875, which is less than 0.6900, 0.6950, and 0.7000.

Answer: D

Correct answer: 165. Needed total:

Current total:

Fifth game:

• A: Scoring the target average would only work if the first four games already averaged 160, but they average 158.75.
• B: 158.75 is the average of the first four games, not the score needed in the fifth.
• C: This uses a total of 4 times 160 instead of 5 times 160, forgetting to count the new game.
• D (correct): Five games averaging 160 must total 800, and 800 minus the 635 already bowled leaves 165.

Answer: A

Correct answer: 208. 36 goes into 74 twice (72), leaving 2. Bring down the 8: 36 does not go into 28, so write 0 in the tens place. Bring down the last 8: 36 goes into 288 exactly 8 times.

The quotient is 208. Check:

An estimate,

rules out 28 and 2,080.

• A (correct): 36 × 200 = 7,200, the remaining 288 is 36 × 8, so the quotient is 208.
• B: This skips the zero in the tens place; 36 × 28 = 1,008, far less than 7,488.
• C: This puts an extra zero in the quotient; 36 × 2,080 is about 75,000.
• D: 36 × 218 = 7,848, which is more than 7,488, so a digit is wrong.

Answer: C

Correct answer: 6 hours. Stage 1:

per hour, so 4 hours finishes $\frac{1}{2}$.

Stage 2:

per hour, so the remaining half takes

Total:

• A: This is only the time after the third volunteer joins; the first 4 hours must be added.
• B: This is the time if all three had worked together from the start.
• C (correct): The first two finish 1/2 in 4 hours; all three pack 1/4 per hour, so the second half takes 2 hours, for 6 hours in all.
• D: This is how long the first two volunteers would need for the whole job without the third.

Answer: C

Correct answer: 40 minutes. Find each unit rate: Machine A makes

bottles per minute, and Machine B makes

bottles per minute.

Together they fill

bottles per minute, so 680 bottles take

• A: This divides 680 by the average rate of 8.5 per minute, which is the rate of one machine, not both together.
• B: This uses only Machine A's rate, 680 ÷ 9.
• C (correct): The rates are 9 and 8 bottles per minute, 17 together, and 680 ÷ 17 = 40 minutes.
• D: This uses only Machine B's rate, 680 ÷ 8.

Answer: D

Correct answer: 15 mph. Find each section's time:

(40 minutes) and

(20 minutes). The total time is 2 hours, so the average speed is

Averaging the three speeds fails because she spends far more time on the slow section.

• A: This is the simple mean of 10, 15 and 30, which ignores that the slow section takes the most time.
• B: This comes from writing 40 minutes as 0.4 hour and 20 minutes as 0.2 hour, which makes the total time look like 1.6 hours.
• C: This averages only the slowest and fastest speeds and still ignores how long each section takes.
• D (correct): Total distance 30 miles divided by total time 2 hours gives 15 mph.