Arithmetic Reasoning Practice Test 1

Answer: B

Correct answer: 18 mph. Write the time as a decimal: 1 hour 30 minutes = 1.5 hours. Speed = distance ÷ time =

• A: This multiplies the distance by the time instead of dividing.
• B (correct): Dividing 27 miles by 1.5 hours gives 18 mph.
• C: This writes 1 hour 30 minutes as 1.3 hours instead of 1.5 hours.
• D: This rounds the time up to 2 hours before dividing.

Answer: D

Correct answer: 5 3/4 cups. Divide the numerator by the denominator:

remainder 3. The quotient is the whole number and the remainder stays over 4, giving $5\frac{3}{4}$ cups.

• A: 4 3/4 equals 19/4; the quotient of 23 by 4 is 5, not 4.
• B: The whole part is right, but the remainder is 3, not 1.
• C: 6 3/4 equals 27/4, which is 4 quarters more than the measured amount.
• D (correct): 23 divided by 4 is 5 with remainder 3, so the amount is 5 3/4 cups.

Answer: C

Correct answer: 37 inches. Required total:

Known boards:

Third board:

• A: The third board does not have to equal the average; the known boards do not balance around 40.
• B: 41.5 is the average of the two known boards, not the length of the missing one.
• C (correct): The three boards must total 120 inches, and 120 minus 83 leaves 37.
• D: 83 inches is the sum of the two known boards; it still has to be subtracted from the 120-inch total.

Answer: D

Correct answer: 0.004. To change a percent to a decimal, move the decimal point two places to the left. 0.4 becomes 0.04 after one place and 0.004 after two, so 0.4 percent is 0.004.

• A: This moves the decimal point only one place left; 0.04 equals 4 percent.
• B: This drops the percent sign without moving the decimal point; 0.4 equals 40 percent.
• C: This moves the decimal point to the right, which changes a decimal into a percent, not the reverse.
• D (correct): Moving the decimal point in 0.4 two places to the left gives 0.004.

Answer: A

Correct answer: $362.52. Subtotal:

After discount:

With tax:

• A (correct): Subtotal $380, discounted to $342, then $342 × 1.06 = $362.52.
• B: This is the price after the discount, before the sales tax is added.
• C: This nets the percents to a 4% discount; the tax is figured on the discounted amount, so the steps cannot simply be combined that way.
• D: This adds the tax to the full $380 and skips the 10% discount.

Answer: B

Correct answer: 14 hours. Unit rate:

per hour.

Time:

Gallons divided by gallons per hour leaves hours.

• A: This multiplies 21 gallons by 1.5 gallons per hour; the units show this is not a time.
• B (correct): The heater burns 1.5 gallons per hour, and 21 divided by 1.5 is 14.
• C: This divides 21 by 4 hours, skipping the step of finding the burn rate.
• D: This divides 21 by 6 and forgets that the 6 gallons last 4 hours, not 1 hour.

Answer: C

Correct answer: 0.83. Divide the numerator by the denominator:

The hundredths digit is 3 and the next digit is 3, which is less than 5, so the gauge shows 0.83.

• A: This rounds up even though the digit after the hundredths place is 3, which is less than 5.
• B: This writes the digits 5 and 6 after a decimal point instead of dividing 5 by 6.
• C (correct): 5 divided by 6 is 0.8333..., and the digit after the hundredths place is 3, so it rounds to 0.83.
• D: This divides 6 by 5, which turns the fraction upside down and gives more than a full tank.

Answer: B

Correct answer: 15.25 miles. The total is known, so the third day is a missing part:

Combine:

• A: This is the total for the first two days, an in-between number.
• B (correct): The first two days total 31.75 miles, and 47 - 31.75 = 15.25 miles.
• C: This adds all three numbers, but 47 is already the total.
• D: This subtracts only the first day's distance from the total.

Answer: C

Correct answer: 7.00 mm. The hundredths digit is 9 and the next digit is 7, so round up. Raising 6.99 by one hundredth carries all the way:

Keep the zeros to show the value is to the nearest hundredth: 7.00 mm.

• A: This simply drops the last digit instead of rounding; the 7 after the hundredths place means round up.
• B: This turns the hundredths 9 into 0 but forgets to carry the 1 through the tenths and into the ones place.
• C (correct): The digit after the hundredths place is 7, so the hundredths digit 9 goes up by one, which carries into the tenths and ones.
• D: This adds one to the tenths place instead of to the hundredths place, then carries.

Answer: C

Correct answer: 5.25 cups. Set up cups over people on both sides:

Cross-multiply: 4x = 21, so x = 5.25 cups.

• A: This adds the 10 extra people as 10 extra cups instead of scaling.
• B: This is only the scale factor 14 ÷ 4, not multiplied by the 1.5 cups.
• C (correct): Each person needs 1.5 ÷ 4 = 0.375 cup, and 0.375 × 14 = 5.25 cups.
• D: This multiplies 1.5 cups by 14, as if 1.5 cups served one person.

Answer: A

Correct answer: (330 ÷ 55) × 60. Let the units guide the setup: miles ÷ (miles per hour) = hours, so

To express hours in minutes, multiply by 60:

• A (correct): Miles divided by miles per hour leaves hours, and multiplying hours by 60 gives minutes.
• B: This gives the time in hours, not minutes; it still needs to be multiplied by 60.
• C: Multiplying miles by miles per hour leaves miles squared per hour, which is not a time.
• D: Dividing the speed by the distance gives a rate in reciprocal hours, the inverse of the time.

Answer: C

Correct answer: 66. Bruised: 4% of

Good apples:

Crates:

with 24 apples left over. Only full crates count, so 66 crates are shipped.

• A: This rounds 66.67 up, but the last crate would hold only 24 apples and is not full.
• B: This packs all 2,500 apples and forgets to remove the bruised ones first.
• C (correct): After discarding 100 bruised apples, 2,400 remain; 2,400 ÷ 36 = 66 full crates with 24 apples left over.
• D: This treats 4% as 0.4 and discards 1,000 apples instead of 100.

Answer: C

Correct answer: $1,010.00. Rent:

Savings:

Other bills:

Remaining:

• A: This subtracts rent and savings but forgets the $1,150 of other bills.
• B: This subtracts only the $1,150 of bills and leaves out rent and savings.
• C (correct): Rent $1,008 + savings $432 + bills $1,150 = $2,590, and 3,600 − 2,590 = $1,010.
• D: This figures the 12% savings on the pay left after rent; the stem says both percents are of take-home pay.

Answer: D

Correct answer: 18 hours. Here one job means one roof. Crew A works at $\frac{2}{9}$ roof per hour and crew B at $\frac{3}{9}$, so together $\frac{5}{9}$ roof per hour.

Time = work / rate:

• A: This multiplies 10 roofs by the rate of 5/9 roof per hour instead of dividing by it.
• B: This is crew B's time working alone; crew A's help is left out.
• C: This averages the two crews' solo times (45 and 30 hours) instead of adding their rates.
• D (correct): Together the crews shingle 5 roofs every 9 hours, or 5/9 roof per hour, so 10 roofs take 10 / (5/9) = 18 hours.

Answer: B

Correct answer: 2 vans. Divide by the bus size:

so 9 buses are full and 16 soldiers are left over.

Those 16 soldiers need vans: 16 ÷ 12 is 1 remainder 4, so 2 vans are needed.

• A: One van seats only 12, so 4 of the 16 leftover soldiers would have no seat.
• B (correct): 9 full buses carry 396, leaving 16 soldiers, and 16 soldiers need 2 vans of 12.
• C: 16 is the number of leftover soldiers, not the number of vans.
• D: 10 is the number of buses that would be needed for everyone, not the number of vans.