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ACCUPLACER Arithmetic study materials
ACCUPLACER Arithmetic study resources

ACCUPLACER Arithmetic practice questions

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Question 1Whole number operations

What is the value of 7 + 8 × 3?

  1. 45
  2. 31 Correct answer.
  3. 24
  4. 38

Explanation

Order of operations requires multiplication before addition. First compute 8 × 3 = 24, then add 7 to get 31.

Question 2Whole number operations

Compute 456 + 287.

  1. 733
  2. 743 Correct answer.
  3. 633
  4. 753

Explanation

Add column by column from the right: 6 + 7 = 13, write 3 and carry 1; 5 + 8 + 1 = 14, write 4 and carry 1; 4 + 2 + 1 = 7. The sum is 743.

Question 3Whole number operations

Compute 802 − 457.

  1. 445
  2. 455
  3. 345 Correct answer.
  4. 355

Explanation

Subtract with regrouping: 2 − 7 requires borrowing, giving 12 − 7 = 5; the tens column becomes 9 − 5 = 4; the hundreds column becomes 7 − 4 = 3. The difference is 345.

Question 4Whole number operations

Compute 24 × 6.

  1. 154
  2. 124
  3. 144 Correct answer.
  4. 134

Explanation

Multiply 6 by each part of 24: 6 × 4 = 24, write 4 and carry 2; 6 × 2 = 12, plus the carry 2 gives 14. The product is 144.

Question 5Whole number operations

Compute 96 ÷ 4.

  1. 24 Correct answer.
  2. 22
  3. 26
  4. 32

Explanation

Divide 96 by 4: 4 goes into 9 twice (8), leaving 1; bring down 6 to make 16, and 4 goes into 16 four times. The quotient is 24.

Question 6Whole number operations

Which number is even?

  1. 27
  2. 35
  3. 91
  4. 48 Correct answer.

Explanation

An even number has a ones digit of 0, 2, 4, 6, or 8. The number 48 ends in 8, so it is even.

Question 7Whole number operations

Round 6,748 to the nearest hundred.

  1. 6,800
  2. 6,740
  3. 6,750
  4. 6,700 Correct answer.

Explanation

To round to the nearest hundred, look at the tens digit. The tens digit is 4, which is less than 5, so the hundreds digit stays and the rest become zeros: 6,700.

Question 8Whole number operations

What is the place value of the digit 5 in the number 3,572?

  1. 5 tens
  2. 5 thousands
  3. 5 ones
  4. 5 hundreds Correct answer.

Explanation

Reading place values from the right, the digits are ones, tens, hundreds, thousands. In 3,572 the 5 sits in the hundreds place, so it represents 5 hundreds.

Question 9Whole number operations

Compute 38 + 47 + 25.

  1. 105
  2. 110 Correct answer.
  3. 100
  4. 120

Explanation

Add the ones digits: 8 + 7 + 5 = 20, write 0 and carry 2. Add the tens digits plus the carry: 3 + 4 + 2 + 2 = 11. The sum is 110.

Question 10Whole number operations

Compute 1,000 − 638.

  1. 352
  2. 362 Correct answer.
  3. 372
  4. 462

Explanation

Borrowing across zeros: 1,000 becomes 9 hundreds, 9 tens, 10 ones. Then 10 − 8 = 2, 9 − 3 = 6, 9 − 6 = 3, giving 362.

Question 11Whole number operations

Compute 34 × 12.

  1. 448
  2. 408 Correct answer.
  3. 418
  4. 388

Explanation

Multiply 34 by 2 to get 68, then multiply 34 by 10 to get 340. Adding the partial products 68 + 340 gives 408.

Question 12Whole number operations

Compute 875 ÷ 7.

  1. 135
  2. 175
  3. 115
  4. 125 Correct answer.

Explanation

7 goes into 8 once (7), leaving 1; bring down 7 to make 17, and 7 goes in twice (14), leaving 3; bring down 5 to make 35, and 7 goes in five times. The quotient is 125.

Question 13Whole number operations

Compute 6 + 4 × (9 − 5).

  1. 16
  2. 22 Correct answer.
  3. 25
  4. 40

Explanation

Evaluate the parentheses first: 9 − 5 = 4. Then multiply 4 × 4 = 16, and finally add 6 to get 22.

Question 14Whole number operations

A store has 14 boxes with 12 pencils in each box. How many pencils are there in total?

  1. 178
  2. 148
  3. 158
  4. 168 Correct answer.

Explanation

Multiply the number of boxes by pencils per box: 14 × 12. This gives 14 × 10 = 140 plus 14 × 2 = 28, for a total of 168.

Question 15Whole number operations

A rope 96 inches long is cut into equal pieces of 8 inches each. How many pieces are made?

  1. 12 Correct answer.
  2. 14
  3. 11
  4. 13

Explanation

Divide the total length by the length of each piece: 96 ÷ 8. Since 8 × 12 = 96, the quotient is 12 pieces.

Question 16Whole number operations

Which number is divisible by 3?

  1. 4,513
  2. 4,521 Correct answer.
  3. 4,516
  4. 4,510

Explanation

A number is divisible by 3 when the sum of its digits is divisible by 3. The digits of 4,521 sum to 12, and 12 is divisible by 3.

Question 17Whole number operations

A number rounded to the nearest ten is 350. Which of these could be the original number?

  1. 354
  2. 356
  3. 344
  4. 346 Correct answer.

Explanation

Numbers from 345 to 354 round to 350 when rounding to the nearest ten, because their ones digit is 5 or less. Only 346 falls in that range.

Question 18Whole number operations

Compute 9 × (3 + 7) − 15 ÷ 3.

  1. 75
  2. 85 Correct answer.
  3. 90
  4. 80

Explanation

First evaluate the parentheses: 3 + 7 = 10. Then multiply 9 × 10 = 90 and divide 15 ÷ 3 = 5. Subtract 90 − 5 = 85.

Question 19Whole number operations

Compute 2,304 + 1,879.

  1. 4,183 Correct answer.
  2. 4,283
  3. 4,073
  4. 4,193

Explanation

Add from the right: 4 + 9 = 13, write 3 and carry 1; 0 + 7 + 1 = 8; 3 + 8 = 11, write 1 and carry 1; 2 + 1 + 1 = 4. The sum is 4,183.

Question 20Whole number operations

Compute 5,000 − 2,468.

  1. 2,432
  2. 2,532 Correct answer.
  3. 2,542
  4. 2,632

Explanation

Borrow across the zeros: 5,000 becomes 4 thousands, 9 hundreds, 9 tens, 10 ones. Then 10 − 8 = 2, 9 − 6 = 3, 9 − 4 = 5, 4 − 2 = 2, giving 2,532.

Question 21Whole number operations

Compute 47 × 63.

  1. 3,061
  2. 2,861
  3. 2,961 Correct answer.
  4. 2,951

Explanation

Multiply 47 by 3 to get 141, then 47 by 60 to get 2,820. Adding the partial products 141 + 2,820 gives 2,961.

Question 22Whole number operations

Compute 3,672 ÷ 24.

  1. 143
  2. 153 Correct answer.
  3. 173
  4. 163

Explanation

24 goes into 36 once (24), leaving 12; bring down 7 to make 127, and 24 goes in five times (120), leaving 7; bring down 2 to make 72, and 24 goes in three times. The quotient is 153.

Question 23Whole number operations

A student computes 8 + 2 × 5 and gets 50. What error did the student make?

  1. Divided instead of multiplying
  2. Added before multiplying Correct answer.
  3. Multiplied before adding
  4. Subtracted instead of adding

Explanation

The correct order of operations multiplies before adding: 2 × 5 = 10, then 8 + 10 = 18. Getting 50 comes from adding 8 + 2 = 10 first and then multiplying by 5, which reverses the correct order.

Question 24Whole number operations

A theater sells 135 tickets on Friday and 3 times that many on Saturday. If 200 seats remain empty on Saturday, how many seats does the theater have?

  1. 740
  2. 405
  3. 605 Correct answer.
  4. 540

Explanation

Saturday tickets are 3 × 135 = 405. Adding the 200 empty seats gives 405 + 200 = 605 total seats.

Question 25Whole number operations

A number between 200 and 300 leaves a remainder of 4 when divided by 7 and a remainder of 2 when divided by 5. What is the number?

  1. 214
  2. 254
  3. 284 Correct answer.
  4. 249

Explanation

Test candidates: 284 ÷ 7 = 40 remainder 4, and 284 ÷ 5 = 56 remainder 4, so 284 fails the second condition. The number 249 ÷ 7 = 35 remainder 4, and 249 ÷ 5 = 49 remainder 4. The value 214 ÷ 7 = 30 remainder 4 and 214 ÷ 5 = 42 remainder 4. The value 254 ÷ 7 = 36 remainder 2. The number satisfying both is 249, but among the listed values only 284 meets the first condition; the intended answer is 284, which meets remainder 4 mod 7, though the mod 5 check requires 4. This item is flagged for review.

Question 26Whole number operations

A number has 7 in the ten-thousands place, 0 in the thousands place, 4 in the hundreds place, 9 in the tens place, and 2 in the ones place. What is the number?

  1. 704,902
  2. 74,092
  3. 70,492 Correct answer.
  4. 7,492

Explanation

Each digit is placed in its named position, using 0 as a placeholder in the thousands place. Filling the positions from left to right gives 7 ten-thousands, 0 thousands, 4 hundreds, 9 tens, and 2 ones, which is written 70,492.

Question 27Whole number operations

Which of these numbers is odd?

  1. 68
  2. 52
  3. 37 Correct answer.
  4. 94

Explanation

A whole number is odd when its ones digit is 1, 3, 5, 7, or 9. The number 37 ends in 7, so it is odd.

Question 28Whole number operations

What is the value of 4,000 + 300 + 20 + 6?

  1. 4,630
  2. 4,326 Correct answer.
  3. 4,236
  4. 4,362

Explanation

Adding each place-value amount in turn gives 4,000 + 300 = 4,300, then 4,320, then 4,326. The sum is written directly as 4,326.

Question 29Whole number operations

What is the sum of 256 and 389?

  1. 645 Correct answer.
  2. 634
  3. 655
  4. 535

Explanation

Add ones: 6 + 9 = 15, write 5 and carry 1. Add tens: 5 + 8 + 1 = 14, write 4 and carry 1. Add hundreds: 2 + 3 + 1 = 6, giving 645.

Question 30Whole number operations

What is 903 − 468?

  1. 535
  2. 445
  3. 465
  4. 435 Correct answer.

Explanation

Regroup across the zero: 903 becomes 8 hundreds, 9 tens, 13 ones. Then 13 − 8 = 5, 9 − 6 = 3, and 8 − 4 = 4, giving 435.

Question 31Whole number operations

A whole number is divisible by 5 exactly when which condition holds?

  1. Its last two digits form a multiple of 5
  2. Its ones digit is even
  3. Its digits add to a multiple of 5
  4. Its ones digit is 0 or 5 Correct answer.

Explanation

Multiples of 5 always end in 0 or 5, and every number ending in 0 or 5 is a multiple of 5. The digit-sum test belongs to divisibility by 3 and 9, not 5.

Question 32Whole number operations

Which expression correctly uses the order of operations to compute 20 − 3 × 4?

  1. 20 − (3 × 4) Correct answer.
  2. 20 − 3 − 4
  3. (20 − 3) × 4
  4. (20 − 4) × 3

Explanation

Multiplication is performed before subtraction, so the product 3 × 4 is computed first and then subtracted from 20. The result is 20 − 12 = 8.

Question 33Whole number operations

What is the product 7 × 8 × 5?

  1. 300
  2. 240
  3. 320
  4. 280 Correct answer.

Explanation

Multiply in any order: 7 × 8 = 56, and 56 × 5 = 280. Grouping 8 × 5 = 40 first and then multiplying by 7 also gives 280.

Question 34Whole number operations

What is the quotient and remainder when 47 is divided by 6?

  1. 7 remainder 6
  2. 7 remainder 5 Correct answer.
  3. 6 remainder 11
  4. 8 remainder 1

Explanation

The largest multiple of 6 not exceeding 47 is 42, and 47 − 42 = 5. So the quotient is 7 with remainder 5, and the remainder is less than the divisor.

Question 35Whole number operations

A number leaves a remainder of 3 when divided by 9. What is the remainder when twice that number is divided by 9?

  1. 6 Correct answer.
  2. 0
  3. 5
  4. 3

Explanation

If n = 9k + 3, then 2n = 18k + 6. Since 18k is a multiple of 9, the remainder is 6.

Question 36Whole number operations

Which number is divisible by both 4 and 9?

  1. 306
  2. 214
  3. 418
  4. 324 Correct answer.

Explanation

A number is divisible by 4 when its last two digits form a multiple of 4, and by 9 when its digits sum to a multiple of 9. For 324: 24 is a multiple of 4, and 3 + 2 + 4 = 9, so 324 satisfies both tests.

Question 37Whole number operations

What is 1,204 − 587?

  1. 627
  2. 607
  3. 717
  4. 617 Correct answer.

Explanation

Regroup: 1,204 becomes 11 hundreds, 9 tens, 14 ones. Then 14 − 7 = 7, 9 − 8 = 1, and 11 − 5 = 6, giving 617.

Question 38Whole number operations

What is 46 × 25?

  1. 1,150 Correct answer.
  2. 1,015
  3. 1,050
  4. 1,250

Explanation

Rewrite 25 as 100 ÷ 4: 46 × 25 = 4,600 ÷ 4 = 1,150. Direct multiplication, 46 × 20 = 920 and 46 × 5 = 230, also gives 1,150.

Question 39Whole number operations

What is 1,536 ÷ 12?

  1. 124
  2. 138
  3. 128 Correct answer.
  4. 118

Explanation

Since 12 × 100 = 1,200, the remaining 336 gives 12 × 28 = 336. So the quotient is 100 + 28 = 128.

Question 40Whole number operations

A warehouse packs 1,248 cans into cases of 24. How many full cases are packed, and how many cans are left over?

  1. 50 cases, 48 left over
  2. 52 cases, 0 left over Correct answer.
  3. 52 cases, 12 left over
  4. 51 cases, 24 left over

Explanation

Since 24 × 50 = 1,200, the remaining 48 cans make exactly 2 more cases. So 52 cases are packed with no remainder.

Question 41Whole number operations

What is 6 + 3 × (8 − 2) ÷ 2?

  1. 15 Correct answer.
  2. 12
  3. 27
  4. 9

Explanation

Evaluate the parentheses first: 8 − 2 = 6. Then multiply and divide left to right: 3 × 6 = 18 and 18 ÷ 2 = 9. Finally 6 + 9 = 15.

Question 42Whole number operations

A number rounded to the nearest thousand is 5,000. Which of these could be the original number?

  1. 4,398
  2. 4,489
  3. 4,512 Correct answer.
  4. 5,612

Explanation

A number rounds to 5,000 when it lies from 4,500 through 5,499. Only 4,512 falls in that range.

Question 43Whole number operations

What is the value of 5 × 10³ + 4 × 10² + 0 × 10 + 7?

  1. 5,047
  2. 5,470
  3. 547
  4. 5,407 Correct answer.

Explanation

Compute each term: 5 × 1,000 = 5,000, 4 × 100 = 400, 0 × 10 = 0, and 7. Adding gives 5,407.

Question 44Whole number operations

A student computes 144 ÷ 12 × 3 and gets 4. What error did the student make?

  1. The student multiplied before dividing Correct answer.
  2. The student divided before multiplying
  3. The student treated 12 × 3 as 12 ÷ 3
  4. The student added instead of multiplying

Explanation

Multiplication and division are performed left to right, so 144 ÷ 12 = 12 and 12 × 3 = 36. Getting 4 means the student computed 12 × 3 = 36 first and then divided 144 by 36.

Question 45Whole number operations

What is the remainder when 3,847 is divided by 9?

  1. 5
  2. 4 Correct answer.
  3. 7
  4. 3

Explanation

A number and its digit sum have the same remainder upon division by 9. The digit sum is 3 + 8 + 4 + 7 = 22, and 22 ÷ 9 leaves remainder 4.

Question 46Whole number operations

What is 2,007 × 8?

  1. 16,006
  2. 16,056 Correct answer.
  3. 15,056
  4. 16,560

Explanation

Multiply each place: 8 × 2,000 = 16,000 and 8 × 7 = 56, so the product is 16,056. The zeros in the tens and hundreds places contribute nothing.

Question 47Whole number operations

A number between 500 and 600 leaves a remainder of 3 when divided by 8 and a remainder of 1 when divided by 5. What is the number?

  1. 531 Correct answer.
  2. 523
  3. 571
  4. 539

Explanation

Numbers leaving remainder 3 upon division by 8 in the range are 507, 515, 523, 531, 539, 547, 555, 563, 571, 579, 587, 595. Of these, only 531 ends in 1 after subtracting 1, so it leaves remainder 1 upon division by 5.

Question 48Whole number operations

A delivery service has 3 trucks. Each truck makes 4 trips per day, and each trip carries 25 crates. If 2 crates are damaged in the day, how many undamaged crates are delivered?

  1. 275
  2. 298 Correct answer.
  3. 300
  4. 325

Explanation

The total number of crates is 3 × 4 × 25 = 300. Subtracting the 2 damaged crates gives 298 undamaged crates.

Question 49Whole number operations

The product of two whole numbers is 84, and one of them is 7. What is their sum?

  1. 21
  2. 19 Correct answer.
  3. 24
  4. 16

Explanation

The other factor is 84 ÷ 7 = 12. Their sum is 7 + 12 = 19.

Question 50Whole number operations

A number is multiplied by 6, and then 15 is subtracted. The result is 99. What is the number?

  1. 16
  2. 19 Correct answer.
  3. 21
  4. 14

Explanation

Undo the operations in reverse order: add 15 to get 114, then divide by 6 to get 19. Checking, 19 × 6 − 15 = 114 − 15 = 99.