25 Arithmetic Practice Questions & Answers

1. 1. A warehouse received 3,487 cartons on Monday and 2,965 cartons on Tuesday. How many cartons did it receive in all?

   • A.5,342
   • B.6,352
   • C.6,442
   • D.6,452✓ Answer

   Add column by column from the right and carry each ten: 7+5=12 (write 2, carry 1); 8+6+1=15 (write 5, carry 1); 4+9+1=14 (write 4, carry 1); 3+2+1=6, giving 6,452. 5,342 comes from never carrying, 6,352 from dropping the carry into the hundreds column, and 6,442 from dropping the carry into the tens column.

   Ref QB-ST89SSSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Whole number operations (addition with regrouping)Report a problem with this question

2. 2. What is 47 × 36?

   • A.1,692✓ Answer
   • B.1,652
   • C.1,492
   • D.423

   Multiply by each digit and keep the place value: 47 × 6 = 282 and 47 × 30 = 1,410 (the 3 is in the tens place, so the second partial product needs a placeholder zero); 282 + 1,410 = 1,692. 423 comes from forgetting the placeholder zero (282 + 141), 1,652 from dropping the carry in 47 × 6, and 1,492 from dropping the carry in 47 × 3.

   Ref QB-8BQRZQSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Whole number operations (multi-digit multiplication)Report a problem with this question

3. 3. A print shop packs 1,543 brochures into boxes that each hold exactly 7 brochures, filling every box it can completely. How many brochures are left over?

   • A.3✓ Answer
   • B.4
   • C.7
   • D.220

   Divide: 7 × 220 = 1,540, and 1,543 − 1,540 = 3, so 1,543 ÷ 7 = 220 remainder 3. The leftover brochures are the remainder. 220 is the number of full boxes (the quotient), 7 is the box size (the divisor), and 4 is how many more brochures would be needed to fill another box.

   Ref QB-RTVWKRSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Whole number operations (division with a remainder)Report a problem with this question

4. 4. A training center has 250 sheets of card stock. Each workbook cover uses 6 sheets. How many complete workbook covers can be made?

   • A.41✓ Answer
   • B.4
   • C.40
   • D.42

   250 ÷ 6 = 41 remainder 4 (6 × 41 = 246). Only complete covers count, so round the quotient down to 41; the 4 leftover sheets are not enough for another cover. 42 rounds up as if a partial cover counted, 4 is the remainder, and 40 comes from estimating 240 ÷ 6 instead of dividing exactly.

   Ref QB-BBSRHUSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Whole number operations (division in real-life contexts)Report a problem with this question

5. 5. Evaluate: 48 − 6 × (5 − 2) + 10 ÷ 2

   • A.21
   • B.25
   • C.68
   • D.35✓ Answer

   Order of operations: parentheses first (5 − 2 = 3), then multiplication and division (6 × 3 = 18 and 10 ÷ 2 = 5), then addition and subtraction from left to right: 48 − 18 + 5 = 35. 68 comes from working strictly left to right, 25 from adding 18 + 5 before subtracting, and 21 from skipping the parentheses (48 − 30 − 2 + 5).

   Ref QB-UTXW4VSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Whole number operations (order of operations)Report a problem with this question

6. 6. What is 2/5 + 3/8?

   • A.5/40
   • B.5/13
   • C.31/40✓ Answer
   • D.5/8

   Fractions can only be added over a common denominator. The least common denominator of 5 and 8 is 40: 2/5 = 16/40 and 3/8 = 15/40, so the sum is 31/40, which is already in lowest terms. 5/13 adds numerators and denominators straight across, 5/40 adds the numerators without converting them, and 5/8 adds the numerators and keeps one of the original denominators.

   Ref QB-ABEECTSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Fraction operations (adding with a common denominator)Report a problem with this question

7. 7. A carpenter cuts a piece 2 2/3 feet long from a board that is 6 1/4 feet long. How long is the remaining piece?

   • A.4 5/12 feet
   • B.3 7/12 feet✓ Answer
   • C.3 5/12 feet
   • D.4 7/12 feet

   Rewrite with denominator 12: 6 3/12 − 2 8/12. Because 3/12 is less than 8/12, borrow one whole as 12/12: 5 15/12 − 2 8/12 = 3 7/12. 4 5/12 subtracts the smaller fraction from the larger instead of borrowing, 4 7/12 borrows but forgets to reduce the whole number, and 3 5/12 borrows the whole as 10/12, as if it were base ten.

   Ref QB-TTKKXTSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Fraction operations (subtracting mixed numbers with borrowing)Report a problem with this question

8. 8. A spool holds 2 1/4 yards of ribbon. Each bow uses 3/8 yard. How many bows can be made from the spool?

   • A.2 2/3
   • B.1/6
   • C.6✓ Answer
   • D.27/32

   Convert to an improper fraction and multiply by the reciprocal of the divisor: 2 1/4 ÷ 3/8 = 9/4 × 8/3 = 72/12 = 6. 27/32 multiplies without flipping the divisor, 1/6 flips the dividend instead of the divisor, and 2 2/3 keeps the whole number 2 aside and divides only 1/4 by 3/8.

   Ref QB-5BNRGMSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Fraction operations (dividing by multiplying by the reciprocal)Report a problem with this question

9. 9. The value of 4 2/3 × 1 4/5 is between which two whole numbers?

   • A.4 and 5
   • B.8 and 9✓ Answer
   • C.6 and 7
   • D.9 and 10

   Convert to improper fractions: 14/3 × 9/5 = 126/15 = 8 2/5, which lies between 8 and 9. 4 and 5 comes from multiplying the whole parts and the fraction parts separately (4 × 1 + 2/3 × 4/5), 6 and 7 from adding the numbers instead of multiplying, and 9 and 10 from rounding both factors up (5 × 2 = 10).

   Ref QB-NTTW3NSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Fraction operations (multiplying mixed numbers; estimation)Report a problem with this question

10. 10. A student club raises $360. It spends 1/3 of the money on supplies and 1/4 of the money on travel. How much money is left?

    • A.$180
    • B.$210
    • C.$30
    • D.$150✓ Answer

    Both fractions are of the full $360: 1/3 × 360 = $120 and 1/4 × 360 = $90, so $360 − $120 − $90 = $150 is left (equivalently, 5/12 of $360). $180 takes 1/4 of the remaining $240 instead of the total, $210 is the amount spent rather than the amount left, and $30 multiplies $360 by 1/3 − 1/4.

    Ref QB-WXWURRSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Fraction operations (fractions of a whole in real-life contexts)Report a problem with this question

11. 11. A machinist stacks three spacers with thicknesses of 14.6 mm, 0.075 mm, and 3.18 mm. What is the total thickness of the stack?

    • A.53.9 mm
    • B.17.855 mm✓ Answer
    • C.17.755 mm
    • D.0.539 mm

    Line up the decimal points and pad with zeros: 14.600 + 0.075 + 3.180. The hundredths column is 0 + 7 + 8 = 15, so write 5 and carry 1 into the tenths, giving 17.855. 17.755 drops that carry across the column, while 0.539 and 53.9 add the digits as whole numbers (146 + 75 + 318 = 539) and then guess where the decimal point goes.

    Ref QB-DFRP6RSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Decimal operations (adding decimals by aligning decimal points)Report a problem with this question

12. 12. What is 3.6 × 0.48?

    • A.0.432
    • B.1.728✓ Answer
    • C.17.28
    • D.0.1728

    Multiply as whole numbers: 36 × 48 = 1,728. The factors have 1 + 2 = 3 decimal places in total, so the product has 3 decimal places: 1.728. 17.28 and 0.1728 miscount the decimal places, and 0.432 comes from forgetting the placeholder zero in the second partial product (288 + 144 = 432).

    Ref QB-XX97XSSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Decimal operations (multiplying decimals; counting decimal places)Report a problem with this question

13. 13. A technician cuts a 9.12-meter length of cable into pieces that are each 0.24 meter long. How many pieces does the technician get?

    • A.3.8
    • B.38✓ Answer
    • C.380
    • D.0.38

    To divide by a decimal, move the decimal point in the divisor and the dividend the same number of places: 9.12 ÷ 0.24 becomes 912 ÷ 24 = 38 (check: 24 × 38 = 912). 3.8 moves the point in the dividend one place fewer than in the divisor, 380 moves it one place more, and 0.38 does not move the point in the dividend at all.

    Ref QB-EF42CSSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Decimal operations (dividing by a decimal)Report a problem with this question

14. 14. A lab balance displays a mass of 5.2968 grams. What is this mass rounded to the nearest thousandth of a gram?

    • A.5.30 g
    • B.5.29 g
    • C.5.297 g✓ Answer
    • D.5.296 g

    The thousandths digit is 6, and the digit to its right is 8. Because 8 is 5 or more, round the 6 up to 7: 5.297. 5.296 truncates (chops off the 8) instead of rounding, 5.30 rounds to the nearest hundredth instead, and 5.29 truncates at the hundredths place.

    Ref QB-YXMH4USource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Decimal operations (rounding to a place value)Report a problem with this question

15. 15. A metal part was 4.06 cm thick. After machining, it is 3.875 cm thick. How much thickness was removed?

    • A.0.185 cm✓ Answer
    • B.1.185 cm
    • C.0.285 cm
    • D.1.815 cm

    Pad and align: 4.060 − 3.875, borrowing across each column, gives 0.185 (check: 3.875 + 0.185 = 4.060). 1.815 subtracts the smaller digit from the larger in every column instead of borrowing, 1.185 borrows but forgets to reduce the ones digit, and 0.285 forgets to reduce the tenths digit after lending to the hundredths.

    Ref QB-FFFCHTSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Decimal operations (subtracting decimals in a measurement context)Report a problem with this question

16. 16. A jacket regularly priced at $240 is on sale for 35% off. What is the sale price?

    • A.$231.60
    • B.$156✓ Answer
    • C.$84
    • D.$205

    Convert the percent to a decimal by moving the point two places left: 35% = 0.35. The discount is 0.35 × 240 = $84, so the sale price is 240 − 84 = $156 (or 0.65 × 240). $84 is only the discount, $205 subtracts 35 dollars instead of 35 percent, and $231.60 uses 3.5% (0.035) by misplacing the decimal point.

    Ref QB-ZXYU9VSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Percent (percent of a number; discounts)Report a problem with this question

17. 17. A store had 160 units of a product in stock and has sold 56 of them. What percent of the stock has been sold?

    • A.35%✓ Answer
    • B.56%
    • C.0.35%
    • D.65%

    Percent = part ÷ whole × 100 = 56 ÷ 160 × 100 = 0.35 × 100 = 35%. 65% is the complement (the percent still unsold), 56% treats the number sold as the percent, and 0.35% forgets to multiply the decimal by 100.

    Ref QB-GFTPPUSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Percent (finding what percent one number is of another)Report a problem with this question

18. 18. After a 20% discount, a power drill costs $64. What was the original price?

    • A.$80✓ Answer
    • B.$84
    • C.$76.80
    • D.$51.20

    After a 20% discount, the sale price is 80% of the original, so original = part ÷ percent = 64 ÷ 0.80 = $80 (check: 80 − 16 = 64). $76.80 adds 20% of the sale price instead of the original, $84 adds 20 dollars, and $51.20 takes another 20% off the sale price.

    Ref QB-2YB7FWSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Percent (finding the whole from a part and a percent)Report a problem with this question

19. 19. A factory reduced its weekly scrap from 250 pounds to 200 pounds. What was the percent decrease?

    • A.20%✓ Answer
    • B.50%
    • C.25%
    • D.80%

    Percent change = (old − new) ÷ ORIGINAL × 100 = (250 − 200) ÷ 250 × 100 = 50 ÷ 250 × 100 = 20%. 25% divides the change by the new amount (50 ÷ 200), 50% reads the 50-pound change as a percent, and 80% is the new amount as a percent of the old one (200 ÷ 250).

    Ref QB-HF62VVSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Percent (percent decrease)Report a problem with this question

20. 20. A store raises the price of a $150 printer stand by 20%. Later, it lowers the new price by 20%. What is the final price?

    • A.$150
    • B.$180
    • C.$120
    • D.$144✓ Answer

    Apply each change to the price at that moment: 150 × 1.20 = $180, then 180 × 0.80 = $144. The 20% decrease is taken from the larger $180 price ($36), so it removes more than the $30 that was added. $150 assumes the two changes cancel, $180 applies only the increase, and $120 applies only the decrease to the original price.

    Ref QB-3QVBXKSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Percent (successive percent increase and decrease)Report a problem with this question

21. 21. Order these values from least to greatest: 0.35, 3/8, 36%, 1/3.

    • A.0.35, 36%, 1/3, 3/8
    • B.1/3, 3/8, 0.35, 36%
    • C.3/8, 1/3, 0.35, 36%
    • D.1/3, 0.35, 36%, 3/8✓ Answer

    Convert everything to decimals: 1/3 ≈ 0.333, 0.35, 36% = 0.36, and 3/8 = 0.375, so the order is 1/3, 0.35, 36%, 3/8. Putting 3/8 below 1/3 assumes a larger denominator always means a smaller fraction, listing the fractions first groups the values by format instead of size, and starting with 0.35 compares the digits without converting.

    Ref QB-K73HHMSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Number comparisons and equivalents (ordering differently formatted values)Report a problem with this question

22. 22. Which percent is equal to the fraction 3/400?

    • A.7.5%
    • B.75%
    • C.0.75%✓ Answer
    • D.0.075%

    3/400 = 0.0075, and moving the decimal point two places right turns a decimal into a percent: 0.0075 = 0.75%. Check: 0.75% means 0.75/100 = 0.0075. 7.5% and 75% move the point too far, and 0.075% moves it only one place.

    Ref QB-4Q8P4NSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Number comparisons and equivalents (fraction, decimal and percent equivalents)Report a problem with this question

23. 23. Which inequality is true?

    • A.5/9 > 4/7
    • B.2/3 < 3/5
    • C.3/5 < 5/8✓ Answer
    • D.7/9 < 7/10

    Compare with a common denominator: 3/5 = 24/40 and 5/8 = 25/40, so 3/5 < 5/8 is true. The others are false: 5/9 = 35/63 is less than 4/7 = 36/63 (bigger numbers do not mean a bigger fraction); 2/3 ≈ 0.667 is greater than 3/5 = 0.6; and with equal numerators, the larger denominator gives the smaller fraction, so 7/9 > 7/10.

    Ref QB-M7EUPNSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Number comparisons and equivalents (inequality symbol notation)Report a problem with this question

24. 24. On a number line, point P lies exactly halfway between 1/4 and 1/2. What number is at point P?

    • A.1/3
    • B.1/8
    • C.3/4
    • D.3/8✓ Answer

    Rename with eighths: 1/4 = 2/8 and 1/2 = 4/8, and the number halfway between them is 3/8 (0.375). 1/3 averages the denominators 4 and 2 instead of the values, 3/4 adds the two fractions without dividing by 2, and 1/8 finds half the distance but forgets to add it to the starting point 1/4.

    Ref QB-5QKZ9PSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Number comparisons and equivalents (using the number line)Report a problem with this question

25. 25. Which expression has the same value as 36 × 25?

    • A.36 × 100 ÷ 2
    • B.36 × 4 × 100
    • C.9 × 100✓ Answer
    • D.30 × 20 + 6 × 5

    Regroup the factors: 36 = 9 × 4, so 36 × 25 = 9 × (4 × 25) = 9 × 100 = 900. 36 × 100 ÷ 2 treats 25 as half of 100 (it is a quarter), 30 × 20 + 6 × 5 keeps only two of the four partial products, and 36 × 4 × 100 multiplies by 4 where it should divide by 4, since 25 = 100 ÷ 4.

    Ref QB-N7S6VPSource: College Board Next-Generation ACCUPLACER Test Specifications — Arithmetic: Number comparisons and equivalents (equivalent number statements and mental math)Report a problem with this question

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