40 Word Problems & Reasoning Practice Questions & Answers

1. 1. Maya has 4 packs of stickers. Each pack has 6 stickers. She also has 5 loose stickers. How many stickers does Maya have in all?

   • A.15 stickers
   • B.24 stickers
   • C.44 stickers
   • D.29 stickers✓ Answer

   First multiply to find the stickers in the packs, then add the loose ones. 4 × 6 = 24, and 24 + 5 = 29. The answer 24 comes from stopping after the first step, and 44 comes from multiplying 4 by both 6 and 5.

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2. 2. Diego buys 5 boxes of crayons. Each box has 8 crayons. He gives 9 crayons to his sister. Which equation can be used to find n, the number of crayons Diego has left?

   • A.5 + 8 - 9 = n
   • B.5 × 8 + 9 = n
   • C.5 × 9 - 8 = n
   • D.5 × 8 - 9 = n✓ Answer

   Equal boxes mean multiply, and giving crayons away means subtract. So 5 × 8 = 40 crayons, then 40 - 9 = 31, which is 5 × 8 - 9 = n. Adding the 9 is the most common slip, because the word "gives" can sound like "gets".

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3. 3. Aiko has 30 cards. She puts 6 cards in each of 4 rows. The rest of the cards stay in her hand. Which equation can be used to find n, the number of cards in her hand?

   • A.30 + 4 × 6 = n
   • B.4 + 6 + n = 30
   • C.n - 4 × 6 = 30
   • D.4 × 6 + n = 30✓ Answer

   The cards in the rows plus the cards in her hand make all 30 cards. The rows hold 4 × 6 = 24 cards, so 4 × 6 + n = 30 and n = 6. Writing 4 + 6 forgets that there are 4 rows of 6, not 4 cards and 6 cards.

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4. 4. Priya bakes 40 muffins. She puts them into 4 boxes with the same number in each box. Then she adds 3 more muffins to one box. How many muffins are in that box now?

   • A.10 muffins
   • B.7 muffins
   • C.13 muffins✓ Answer
   • D.43 muffins

   First share the muffins equally by dividing, then add the extra ones to that box. 40 ÷ 4 = 10, and 10 + 3 = 13. The answer 43 adds the 3 to all 40 muffins instead of to just one box.

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5. 5. Coach Amara has 42 balls. She puts 7 balls in each bag. Then she gives 2 of the bags to another team. How many bags does Coach Amara keep?

   • A.40 bags
   • B.5 bags
   • C.6 bags
   • D.4 bags✓ Answer

   First divide to find how many bags she fills, then subtract the bags she gives away. 42 ÷ 7 = 6 bags, and 6 - 2 = 4 bags. The answer 40 subtracts 2 from the 42 balls, but the 2 counts bags, not balls.

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6. 6. A school library has 456 books. It gets 128 new books. Then students check out 75 books. How many books are still in the library?

   • A.509 books✓ Answer
   • B.511 books
   • C.659 books
   • D.584 books

   Add the new books first, then subtract the books that leave. 456 + 128 = 584, and 584 - 75 = 509, regrouping a ten and a hundred. The answer 511 comes from subtracting the smaller digit from the bigger one in each place instead of regrouping.

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7. 7. Sofia's school collected 289 cans on Monday and 412 cans on Tuesday. Round each number to the nearest hundred. Then add to estimate the total. What is the estimate?

   • A.800 cans
   • B.701 cans
   • C.700 cans✓ Answer
   • D.600 cans

   Round each number first, then add the rounded numbers. 289 rounds up to 300 because 8 tens is 5 or more, and 412 rounds down to 400, so 300 + 400 = 700. The answer 701 is the exact sum, but the question asks for the rounded estimate.

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8. 8. A farm stand sold 47 apples in the morning and 38 apples in the afternoon. Round each number to the nearest ten. Then subtract to estimate how many more apples were sold in the morning. What is the estimate?

   • A.90 more apples
   • B.10 more apples✓ Answer
   • C.20 more apples
   • D.9 more apples

   Round each number to the nearest ten, then subtract. 47 rounds to 50 and 38 rounds to 40, so 50 - 40 = 10. The answer 9 is the exact difference, and 20 comes from rounding 38 down to 30.

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9. 9. Ana's soccer practice starts at 3:45. It lasts 50 minutes. Then she walks home, which takes 15 minutes. What time does Ana get home?

   • A.4:35
   • B.4:10
   • C.4:50✓ Answer
   • D.5:00

   Add the two times one at a time, and remember an hour has 60 minutes, not 100. 3:45 plus 15 minutes is 4:00, plus 35 more minutes is 4:35, then 15 minutes more is 4:50. The answer 4:10 comes from adding the minutes as if an hour had 100 minutes.

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10. 10. A field trip bus leaves school at 9:35 and gets to the museum at 10:10. The ride home takes 15 minutes longer than the ride there. How many minutes is the ride home?

    • A.90 minutes
    • B.75 minutes
    • C.35 minutes
    • D.50 minutes✓ Answer

    First find how long the ride there took, then add 15 minutes. From 9:35 to 10:00 is 25 minutes and from 10:00 to 10:10 is 10 more, so the ride there is 35 minutes and the ride home is 35 + 15 = 50 minutes. The answer 75 comes from subtracting 935 from 1010 like ordinary numbers, but time does not count by hundreds.

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11. 11. A cooler holds 24 liters of water. Mr. Okafor pours all of it into 3 jugs so each jug has the same amount. Then he adds 5 more liters to one jug. How many liters are in that jug now?

    • A.8 liters
    • B.13 liters✓ Answer
    • C.29 liters
    • D.19 liters

    First divide to find how much water goes in each jug, then add the extra water to that jug. 24 ÷ 3 = 8 liters, and 8 + 5 = 13 liters. The answer 29 adds the 5 liters to the whole cooler instead of to one jug.

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12. 12. Each bag of flour has a mass of 5 kilograms. Kai buys 6 bags. He uses 9 kilograms of flour to bake bread. How many kilograms of flour are left?

    • A.39 kilograms
    • B.2 kilograms
    • C.21 kilograms✓ Answer
    • D.30 kilograms

    First multiply to find all the flour Kai bought, then subtract what he used. 6 × 5 = 30 kilograms, and 30 - 9 = 21 kilograms. The answer 2 comes from adding 5 + 6 = 11 instead of multiplying and then taking away 9, and 30 stops after the first step.

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13. 13. A picture graph shows how many books two classes read. Each star stands for 5 books. Room 1 has 7 stars. Room 2 has 4 stars. How many more books did Room 1 read than Room 2?

    • A.20 more books
    • B.15 more books✓ Answer
    • C.3 more books
    • D.55 more books

    Use the key to turn stars into books, then subtract. Room 1 read 7 × 5 = 35 books and Room 2 read 4 × 5 = 20 books, so 35 - 20 = 15 more books. The answer 3 counts the extra stars but forgets that each star means 5 books.

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14. 14. A bar graph shows the favorite pets of a class: dogs, 18 students; cats, 7 students; fish, 5 students. How many more students chose dogs than chose cats and fish together?

    • A.30 more students
    • B.6 more students✓ Answer
    • C.13 more students
    • D.11 more students

    First add cats and fish to make one group, then compare that group with dogs. 7 + 5 = 12, and 18 - 12 = 6 more students. The answer 11 compares dogs with cats only and forgets to include the fish.

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15. 15. In a picture graph, each circle stands for 4 students, and half a circle stands for 2 students. Soccer has 5 whole circles and half a circle. Basketball has 3 whole circles. How many students chose soccer or basketball in all?

    • A.36 students
    • B.34 students✓ Answer
    • C.32 students
    • D.10 students

    Find each sport's total using the key, then add the two totals. Soccer is 5 × 4 + 2 = 22 students and basketball is 3 × 4 = 12 students, so 22 + 12 = 34. The answer 32 skips the half circle, and 36 counts the half circle as a whole one.

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16. 16. Lena's garden bed is a rectangle 6 feet long and 4 feet wide. She wants a fence all the way around it. She already has 8 feet of fence. How many more feet of fence does she need?

    • A.12 feet✓ Answer
    • B.2 feet
    • C.16 feet
    • D.20 feet

    A fence goes around the edge, so find the perimeter, then subtract the fence she has. The perimeter is 6 + 4 + 6 + 4 = 20 feet, and 20 - 8 = 12 feet. The answer 16 uses the area, 6 × 4 = 24, which measures the inside of the bed and not the edge.

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17. 17. Omar's bedroom has two rectangle rugs. One rug is 7 feet long and 3 feet wide. The other rug is 5 feet long and 4 feet wide. What is the total area of both rugs?

    • A.19 square feet
    • B.41 square feet✓ Answer
    • C.38 square feet
    • D.35 square feet

    Find each rug's area by multiplying length times width, then add the two areas. 7 × 3 = 21 and 5 × 4 = 20, so 21 + 20 = 41 square feet. The answer 38 adds the two perimeters, 20 + 18, which measure the edges instead of the floor covered.

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18. 18. Ravi has exactly 18 meters of fence. He wants to make a rectangle garden that uses all 18 meters. Which garden size gives him the most area for planting?

    • A.5 meters by 4 meters✓ Answer
    • B.6 meters by 3 meters
    • C.7 meters by 2 meters
    • D.8 meters by 1 meter

    Every choice uses 18 meters of fence, so find the area of each one and pick the biggest. The areas are 6 × 3 = 18, 5 × 4 = 20, 7 × 2 = 14 and 8 × 1 = 8 square meters, so 5 meters by 4 meters is largest. Many children think the longest garden has the most room, but the long, thin one has the least.

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19. 19. Ms. Rivera's class has $40 for a party. Each pizza costs $8, and each juice pack costs $4. The class buys 3 pizzas. How many juice packs can they buy with the money that is left?

    • A.4 juice packs✓ Answer
    • B.10 juice packs
    • C.6 juice packs
    • D.2 juice packs

    First find what the pizzas cost and subtract it from the budget, then divide the money left by the juice price. 3 × 8 = 24 dollars, 40 - 24 = 16 dollars, and 16 ÷ 4 = 4 juice packs. The answer 10 divides all $40 by 4 and forgets that the pizzas were already bought.

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20. 20. Mia has $30 to spend on art supplies. A paint set costs $8. A pack of brushes costs $3. Which plan costs $30 or less?

    • A.2 paint sets and 6 brush packs
    • B.2 paint sets and 5 brush packs
    • C.3 paint sets and 2 brush packs✓ Answer
    • D.3 paint sets and 3 brush packs

    For each plan, multiply to find the cost of the paint and of the brushes, then add and compare with $30. Three paint sets and two brush packs cost 24 + 6 = 30 dollars, which fits. The other plans cost 16 + 15 = 31, 24 + 9 = 33 and 16 + 18 = 34 dollars, so each one goes over by a few dollars.

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21. 21. The school play has two acts. Act 1 ends at 7:15. Then there is a 10-minute break. Act 2 starts right after the break and lasts 40 minutes. What time does the play end?

    • A.7:55
    • B.8:05✓ Answer
    • C.8:15
    • D.7:25

    Add the break first, then add the length of Act 2, crossing the hour carefully. 7:15 plus 10 minutes is 7:25, and 7:25 plus 35 minutes is 8:00, plus 5 more minutes is 8:05. The answer 7:55 forgets to add the 10-minute break.

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22. 22. The gym has 7 rows of chairs with 8 chairs in each row. For the concert, the custodian sets up 60 more chairs. How many chairs are in the gym now?

    • A.56 chairs
    • B.68 chairs
    • C.116 chairs✓ Answer
    • D.75 chairs

    Rows with the same number of chairs mean multiply, then add the new chairs. 7 × 8 = 56 chairs, and 56 + 60 = 116 chairs. The answer 75 adds 7 + 8 + 60 instead of multiplying the rows, and 56 stops before adding the new chairs.

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23. 23. Which statement is ALWAYS true for every whole number?

    • A.Any whole number times 3 gives an odd product.
    • B.Any whole number plus 2 gives an even sum.
    • C.Any whole number times 4 gives an even product.✓ Answer
    • D.Any whole number plus 3 gives an odd sum.

    Test each claim with a few examples and look for one that breaks it. Times 4 means 2 groups of (2 x the number), so the product always splits into two equal halves and is even. The others break: 3 × 2 = 6 is even, 1 + 3 = 4 is even, and 1 + 2 = 3 is odd.

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24. 24. Leo says, "When you add two odd numbers, the sum is always odd." Which example shows that Leo is wrong?

    • A.2 + 4 = 6
    • B.3 + 5 = 8✓ Answer
    • C.5 + 6 = 11
    • D.3 + 4 = 7

    A counterexample must follow the rule's condition (two odd numbers) and still break the claim. Only 3 + 5 adds two odd numbers, and its sum, 8, is even. The other examples do not add two odd numbers, so they cannot test Leo's claim at all.

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25. 25. Mia says 1/8 is bigger than 1/4 because 8 is bigger than 4. Is Mia correct? Which statement explains why?

    • A.Yes, because 1/8 cuts the whole into more pieces, so it is more.
    • B.No, because eighths are smaller pieces than fourths of the same whole.✓ Answer
    • C.No, because 1/8 and 1/4 are equal since both have a 1 on top.
    • D.Yes, because a bigger bottom number always makes a bigger fraction.

    When the top numbers are the same, compare the size of the pieces. Cutting the same whole into 8 equal parts makes smaller pieces than cutting it into 4, so 1/8 < 1/4. A bigger bottom number means more pieces, and each piece is smaller.

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26. 26. Sam ate 1/2 of a small pizza. Kim ate 1/4 of a very large pizza. Sam says, "I ate more pizza, because 1/2 is more than 1/4." Is Sam's reasoning correct? Which statement explains why?

    • A.No, because 1/4 is always more than 1/2, since 4 is bigger than 2.
    • B.Yes, because Sam's pizza was cut into fewer slices, so each slice was more.
    • C.No, because 1/2 and 1/4 can only be compared when the pizzas are the same size.✓ Answer
    • D.Yes, because 1/2 is always more than 1/4, no matter how big the pizzas are.

    Comparing fractions only works when both fractions are of the same whole. Half of a small pizza can be less than a fourth of a very large pizza, so Sam cannot decide from 1/2 > 1/4 alone. The rule 1/2 > 1/4 is true only when the two pizzas are the same size.

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27. 27. Two fraction strips are the same size. Strip A is cut into 4 equal parts, and 2 parts are shaded. Strip B is cut into 2 equal parts, and 1 part is shaded. Which reason shows that 2/4 = 1/2?

    • A.The shaded parts of both strips cover the same length.✓ Answer
    • B.Strip B has bigger parts, so 1/2 must be the larger one.
    • C.Strip A has more shaded parts, so 2/4 must be larger.
    • D.Both strips have exactly two parts that are shaded in.

    Two fractions are equal when they cover the same amount of the same-size whole. Two fourths of strip A line up exactly with one half of strip B, so 2/4 = 1/2. Counting shaded parts is not enough, because the parts are different sizes.

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28. 28. Why is 6 × 7 = 6 × 5 + 6 × 2 a true equation?

    • A.The 6 is split into 5 + 1, and each part is multiplied by 7.
    • B.The 7 is split into 5 + 2, but only the 5 is multiplied by 6.
    • C.The 6 and the 7 are added first, and that sum is split up.
    • D.The 7 is split into 5 + 2, and each part is multiplied by 6.✓ Answer

    This is the distributive property: you can break one factor into parts and multiply each part by the other factor. Here 7 = 5 + 2, so 6 × 7 = 6 × 5 + 6 × 2 = 30 + 12 = 42. Both parts must be multiplied by 6, or the total comes out too small.

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29. 29. Raj wrote 8 × 7 = 8 × 5 + 7 × 2. Which statement explains Raj's work?

    • A.It is wrong, because both the 5 and the 2 must be times 8.✓ Answer
    • B.It is wrong, because he should multiply 5 × 2, not add them.
    • C.It is wrong, because he should split the 8 instead of the 7.
    • D.It is right, because 5 + 2 = 7, so the parts match the 7.

    When you split 7 into 5 + 2, each part must be multiplied by the same factor, 8. The correct equation is 8 × 7 = 8 × 5 + 8 × 2 = 40 + 16 = 56. Raj's version gives 40 + 14 = 54, so splitting 7 correctly is not enough when one part is multiplied by the wrong number.

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30. 30. Nora knows that 3 × 4 = 4 × 3. She says, "So 12 ÷ 3 is the same as 3 ÷ 12." Which statement about Nora's idea is true?

    • A.Switching the numbers is fine when both numbers are even.
    • B.Switching the numbers works in division just as in multiplication.
    • C.Switching the numbers is fine when the bigger number is first.
    • D.Switching the numbers in division changes the problem.✓ Answer

    The order of factors does not matter in multiplication, but the order matters in division. 12 ÷ 3 means sharing 12 into 3 equal groups, which gives 4 in each group, while 3 ÷ 12 means sharing only 3 among 12 groups, which is a different problem. So the switching rule for multiplication does not carry over to division.

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31. 31. Lucy says 32 ÷ 8 = 4. Which fact proves that Lucy is right?

    • A.8 × 4 = 32✓ Answer
    • B.8 - 4 = 4
    • C.8 + 24 = 32
    • D.32 - 8 = 24

    Division is an unknown-factor problem: 32 ÷ 8 asks what number times 8 makes 32. Since 8 × 4 = 32, the missing factor is 4, so Lucy is right. A subtraction fact like 8 - 4 = 4 also ends in 4, but it does not show anything about 32 ÷ 8.

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32. 32. Omar adds 298 + 405 and gets 603. Round each number to the nearest hundred. Which statement shows whether Omar's answer is reasonable?

    • A.Rounding gives 300 + 500 = 800, so 603 is too small.
    • B.Rounding gives 300 + 400 = 700, so 603 is too far off.✓ Answer
    • C.Rounding gives 200 + 400 = 600, so 603 is about right.
    • D.Rounding gives 290 + 400 = 690, so 603 is about right.

    Round each number to the nearest hundred by looking at the tens digit: 298 rounds up to 300, and 405 rounds down to 400. The estimate 300 + 400 = 700 is far from 603, so Omar made a mistake (the exact sum is 703). Rounding 298 down to 200 is the most tempting slip, but 298 is much closer to 300.

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33. 33. Ethan solved 503 - 168 and got 465. Which statement explains Ethan's mistake?

    • A.He made no mistake, since 465 + 168 is equal to 503.
    • B.He forgot to regroup, but only in the hundreds place.
    • C.He added the two numbers instead of subtracting them.
    • D.He took the smaller digit from the larger one in each place.✓ Answer

    Check each place: 3 - 8 cannot be done without regrouping, so Ethan did 8 - 3 = 5, then 6 - 0 = 6, then 5 - 1 = 4, giving 465. He should regroup from the hundreds, which gives 503 - 168 = 335. Adding back proves it: 465 + 168 = 633, not 503, while 335 + 168 = 503.

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34. 34. Zara says, "Rectangles with the same perimeter always have the same area." Which pair of rectangles shows that Zara is wrong? Side lengths are in units.

    • A.A 2 by 4 rectangle and a 4 by 2 rectangle
    • B.A 1 by 5 rectangle and a 2 by 5 rectangle
    • C.A 1 by 5 rectangle and a 2 by 4 rectangle✓ Answer
    • D.A 2 by 3 rectangle and a 1 by 6 rectangle

    A counterexample needs two rectangles with the SAME perimeter but DIFFERENT areas. A 1 by 5 rectangle and a 2 by 4 rectangle both have perimeter 12 units, but their areas are 5 and 8 square units. The 2 by 3 and 1 by 6 pair is tempting, but it has the same area (6) and different perimeters (10 and 14), so it does not test Zara's claim.

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35. 35. Tom says a rectangle that is 2 units by 6 units has a bigger area than a rectangle that is 3 units by 4 units, because its perimeter is bigger. Is Tom correct? Which statement explains why?

    • A.No, because the 3 by 4 rectangle is wider, so its area is bigger.
    • B.Yes, because the 2 by 6 rectangle is longer, so it covers more.
    • C.No, because both rectangles have an area of 12 square units.✓ Answer
    • D.Yes, because a bigger perimeter always means a bigger area.

    Area counts the unit squares inside, and perimeter measures the distance around, so they must be found separately. Both areas are 12 square units (2 × 6 = 12 and 3 × 4 = 12), while the perimeters are 16 and 14 units. A bigger perimeter does not have to mean a bigger area.

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36. 36. Which model shows why 4 × 7 = 4 × 5 + 4 × 2?

    • A.A 4 by 7 rectangle cut into a 4 by 5 part and a 7 by 2 part
    • B.A 4 by 7 rectangle cut into a 4 by 5 part and a 2 by 2 part
    • C.A 4 by 7 rectangle cut into a 2 by 7 part and a 2 by 7 part
    • D.A 4 by 7 rectangle cut into a 4 by 5 part and a 4 by 2 part✓ Answer

    Cutting the 7-unit side into 5 and 2 keeps the 4-unit side the same for both parts. So the area 4 × 7 = 28 equals 4 × 5 + 4 × 2 = 20 + 8 = 28. The 2 by 7 halves are a real way to split the rectangle, but they show 2 × 7 + 2 × 7 instead.

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37. 37. Kai makes an array with 3 rows of 6 counters. Then he turns it so it has 6 rows of 3 counters. No counters are added or taken away. What does this show?

    • A.3 × 6 and 6 × 3 have the same product.✓ Answer
    • B.3 + 6 and 3 × 6 have the same answer.
    • C.6 × 3 is bigger, since it has more rows.
    • D.3 × 6 and 6 × 3 have different products.

    Turning an array does not change how many counters it has, so 3 rows of 6 and 6 rows of 3 are the same 18 counters. This is the commutative property: 3 × 6 = 6 × 3 = 18. Having more rows does not mean more counters, because each row also got shorter.

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38. 38. Ana and Ben each cut their own ribbon into 2 equal parts. Ana's half is longer than Ben's half. Which statement must be true?

    • A.Ben's whole ribbon is longer than Ana's whole ribbon.
    • B.Ana cut her ribbon into more pieces than Ben did.
    • C.Ana's half is a bigger fraction than Ben's half.
    • D.Ana's whole ribbon is longer than Ben's whole ribbon.✓ Answer

    Both pieces are 1/2, so the fractions are the same; the only way one half can be longer is if it comes from a longer whole. That means Ana's whole ribbon must be longer than Ben's. This is why fractions can only be compared fairly when they refer to the same whole.

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39. 39. Kim says 5 × 7 = 36. Which reason shows that her answer cannot be right?

    • A.Every product of 5 ends in 0 or 5, and 36 ends in a 6.✓ Answer
    • B.Every product of 5 is less than 30, and 36 is too big.
    • C.Every product of 5 is an odd number, and 36 is even.
    • D.Every product of 5 ends in a 5, and 36 does not end in 5.

    Look at the pattern in the 5s row of the multiplication table: 5, 10, 15, 20, 25, 30, 35, ... Every product of 5 ends in 0 or 5, so 36 cannot be 5 × 7 (it is 35). The other rules break: 5 × 2 = 10 is even and does not end in 5, and 5 × 8 = 40 is more than 30.

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40. 40. Lena says, "4 times any whole number is always even." Which reason explains why Lena is right?

    • A.Because 4 equal groups can be split into 2 equal halves.✓ Answer
    • B.Because 4 is even, and any product with 4 in it ends in 4.
    • C.Because a product is even when it has two digits in it.
    • D.Because a product is even when a factor is bigger than 3.

    4 equal groups can always be put into 2 teams of 2 groups each, so the total splits into two equal halves, which is what even means. For example, 4 × 7 = 7 + 7 + 7 + 7 = 14 + 14 = 28. The other reasons break: 5 × 3 = 15 is odd, and 4 × 3 = 12 ends in 2, not 4.

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