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Grade 5 Challenge: Logic & Reasoning Problems Worksheet with Answers

Grade 5 (US) · Year 6 (UK) · Class 5 (India) · Math

Unit 7: Going FurtherChallenge PuzzlesChallenge

Classic reasoning puzzles — ages, heads and legs, consecutive numbers — that reward careful thinking. This free upper elementary worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Logic & Reasoning Problems

Grade 5 · Math

Score___ / 12

Name

Class

Date

Learning goal: Challenge Puzzles

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Three consecutive whole numbers add up to 18. What is the smallest number?

Answer: 5

  1. 1

    Ines is 5 years older than Amara. Together their ages add up to 19. How old is Amara?

    Show your work
    Answer
  2. 2

    Diego is 8 years older than Maria. Together their ages add up to 30. How old is Maria?

    Show your work
    Answer
  3. 3

    7 people each shake hands once with every other person. How many handshakes are there?

    Show your work
    Answer
  4. 4

    Amara is 4 years older than Jayden. Together their ages add up to 30. How old is Jayden?

    Show your work
    Answer
  5. 5

    Three consecutive whole numbers add up to 63. What is the smallest number?

    Show your work
    Answer
  6. 6

    A pen and a notebook cost $16 together. The notebook costs $6 more than the pen. How much does the pen cost?

    Show your work
    Answer
  7. 7

    A snail climbs 8 feet up a wall each day and slides back 1 foot each night. The wall is 25 feet tall. On which day does it reach the top?

    Show your work
    Answer
  8. 8

    Three consecutive whole numbers add up to 57. What is the smallest number?

    Show your work
    Answer
  9. 9

    A pen and a notebook cost $13 together. The notebook costs $3 more than the pen. How much does the pen cost?

    Show your work
    Answer
  10. 10

    A farm has chickens and cows. There are 9 heads and 24 legs. How many cows are there?

    Show your work
    Answer
  11. 11

    Three consecutive whole numbers add up to 54. What is the smallest number?

    Show your work
    Answer
  12. 12

    Three consecutive whole numbers add up to 60. What is the smallest number?

    Show your work
    Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/5/challenge_logic

Answer key (click to show)
  1. 1.7
  2. 2.11
  3. 3.21
  4. 4.13
  5. 5.20
  6. 6.$5
  7. 7.day 4
  8. 8.18
  9. 9.$5
  10. 10.3
  11. 11.17
  12. 12.19

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How to use this worksheet

  • Use it as a 10–15 minute warm-up or homework task rather than a long drill.
  • Ask students to show their working so you can see where a mistake started, not just that it happened.
  • Mark it with the answer key together, then print a fresh version of the same topic to practise the questions they missed.

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More Grade 5 Math worksheets

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Guides for teaching Challenge: Logic & Reasoning Problems

Long Division Step by Step: An Easy Method (With Remainders)Divide, multiply, subtract, bring down — the four-step routine that makes long division manageable, with worked examples, remainders, zeros and two-digit divisors.Order of Operations (PEMDAS / BODMAS): Rules, Examples and Common MistakesWhy multiplication doesn't always come before division, how exponents and negatives trip students up, and worked examples you can check.Adding and Subtracting Fractions: A Step-by-Step Guide for Grades 5–6Like and unlike denominators, mixed numbers, and the three mistakes that cause most wrong answers — with worked examples.

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