Solved Exercises on Word Problems IQ Test in Grade 2

Master word problems for IQ assessment: addition, subtraction, and logical reasoning through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic addition IQ problem
Exercise 1
Sarah has 5 candies. Her brother gives her 3 more candies. Then her sister gives her 2 more candies. How many candies does Sarah have now? IQ Score: 85 Easy
Definition:

IQ test problem: A mathematical problem designed to assess logical reasoning, pattern recognition, and problem-solving abilities.

IQ problem solving method:
  1. Read the problem carefully
  2. Identify all numbers and actions
  3. Recognize the sequence of operations
  4. Set up the equation
  5. Solve the equation
  6. Verify the answer makes logical sense
Sarah has 5 candies. Her brother gives her 3 more candies. Then her sister gives her 2 more candies. How many candies does Sarah have now?
5 + 3 + 2 = ?
5
+
3
+
2
=
10
Step 1: Identify the numbers - Sarah starts with 5, gets 3 more, then gets 2 more
Step 2: Determine operation - All "gives" mean addition
Step 3: Set up equation - 5 + 3 + 2 = 10
Step 4: Write answer - Sarah has 10 candies
Step 1: Identify the numbers

Sarah has 5 candies initially, gets 3 more, then gets 2 more

Step 2: Determine the operation

All actions are "gives her more" indicating addition

Step 3: Set up the equation

5 + 3 + 2 = 10

Step 4: Write the complete answer

Sarah has 10 candies now.

Sarah has 10 candies.
Final answer:

Sarah has 10 candies.

Applied rules:

• Sequential addition: When multiple additions happen in sequence

• Logical sequence: Follow the order of events in the problem

• Context verification: Check that the answer makes sense in the scenario

2 Basic subtraction IQ problem
Exercise 2
Tom has 9 balloons. He gives 2 balloons to his friend. Then he loses 3 balloons. How many balloons does Tom have left? IQ Score: 90 Easy
Definition:

Subtraction IQ problem: A problem requiring sequential subtraction operations to assess logical reasoning.

Tom has 9 balloons. He gives 2 balloons to his friend. Then he loses 3 balloons. How many balloons does Tom have left?
9 - 2 - 3 = ?
9
-
2
-
3
=
4
Step 1: Identify the numbers - Tom starts with 9, gives away 2, loses 3
Step 2: Determine operation - "gives" and "loses" mean subtraction
Step 3: Set up equation - 9 - 2 - 3 = 4
Step 4: Write answer - Tom has 4 balloons left
Step 1: Identify the numbers

Tom has 9 balloons initially, gives away 2, loses 3

Step 2: Determine the operation

"Gives" and "loses" both indicate subtraction

Step 3: Set up the equation

9 - 2 - 3 = 4

Step 4: Write the complete answer

Tom has 4 balloons left.

Step 5: Verify the answer

Check: 4 + 2 + 3 = 9 ✓

Tom has 4 balloons left.
Final answer:

Tom has 4 balloons left.

Applied rules:

• Sequential subtraction: When multiple subtractions happen in sequence

• Logical sequence: Follow the order of events in the problem

• Verification: Check that the answer makes sense

3 Mixed operations IQ problem
Exercise 3
Emma had 6 toys. She bought 4 more toys. Then she gave 3 toys to her cousin. How many toys does Emma have now? IQ Score: 95 Medium
Definition:

Mixed operations IQ problem: A problem requiring both addition and subtraction operations in sequence.

Emma had 6 toys. She bought 4 more toys. Then she gave 3 toys to her cousin. How many toys does Emma have now?
6 + 4 - 3 = ?
6
+
4
-
3
=
7
Step 1: Identify the numbers - Emma starts with 6, buys 4 more, gives away 3
Step 2: Determine operations - "bought more" means addition, "gave" means subtraction
Step 3: Set up equation - 6 + 4 - 3 = 7
Step 4: Write answer - Emma has 7 toys now
Step 1: Identify the numbers

Emma starts with 6 toys, buys 4 more, gives away 3

Step 2: Determine the operations

"Bought more" indicates addition, "gave" indicates subtraction

Step 3: Set up the equation

6 + 4 - 3 = 7

Step 4: Write the complete answer

Emma has 7 toys now.

Emma has 7 toys now.
Final answer:

Emma has 7 toys now.

Applied rules:

• Sequential operations: Perform operations in the order they occur in the problem

• Mixed operations: Identify each operation based on keywords

• Logical sequence: Follow the chronological order of events

Rules and methods, laws,...
IQ Word Problem = Read + Analyze + Sequence + Operate + Verify
IQ Word Problem Formula
Logical Sequence
Follow Order
Chronological operations
Operation Recognition
Keywords Matter
Identify addition/subtraction
Verification
Check Logic
Validate answer makes sense
Key definitions:

IQ word problem: A mathematical problem designed to assess logical reasoning, pattern recognition, and problem-solving abilities.

Logical sequence: Following the order of events as they occur in the problem.

Pattern recognition: Identifying relationships and sequences in the problem.

Sequential operations: Performing mathematical operations in the order specified.

Verification: Checking that the answer makes sense in the context of the problem.

IQ score: A measure of cognitive ability based on performance on standardized tests.

Complete methodology:
  1. Read carefully: Read the entire problem to understand the situation
  2. Analyze components: Identify all numbers and actions mentioned
  3. Recognize sequence: Determine the chronological order of operations
  4. Identify operations: Determine which mathematical operations to use
  5. Set up equation: Write the mathematical equation
  6. Solve: Calculate the answer
  7. Verify logic: Check if the answer makes sense in the context
  8. Assess difficulty: Evaluate the complexity of the problem
Tip 1: Pay attention to the sequence of events in the problem.
Tip 2: Identify all the numbers mentioned in the problem.
Tip 3: Look for keywords that indicate mathematical operations.
Tip 4: Draw diagrams to visualize complex problems.
Tip 5: Always verify that your answer makes logical sense.
Tip 6: Practice problems of increasing difficulty.
Common errors: Misreading the sequence of events, using incorrect operations, forgetting to verify the answer, misinterpreting keywords, not following chronological order.
Key insight: IQ problems test logical reasoning and pattern recognition, not just computation.
Rules to remember:

• Follow sequence: Perform operations in the order they occur in the problem

• Recognize patterns: Look for logical relationships between numbers

• Verify logic: Check that your answer makes sense in the context

• Identify keywords: Words that indicate mathematical operations

• Chronological order: Follow the timeline of events in the problem

Solution: Exercises 4 to 5
4 Advanced mixed operations IQ problem
Exercise 4
Jack has 8 stickers. He finds 3 more stickers. Then he gives 2 stickers to his friend. Later he loses 4 stickers. How many stickers does Jack have now? IQ Score: 100 Hard
Definition:

Advanced mixed operations: A complex problem involving multiple addition and subtraction operations in sequence.

Jack has 8 stickers. He finds 3 more stickers. Then he gives 2 stickers to his friend. Later he loses 4 stickers. How many stickers does Jack have now?
8 + 3 - 2 - 4 = ?
8
+
3
-
2
-
4
=
5
Step 1: Identify the numbers - Jack starts with 8, finds 3, gives away 2, loses 4
Step 2: Determine operations - "finds" is addition, "gives" and "loses" are subtraction
Step 3: Set up equation - 8 + 3 - 2 - 4 = 5
Step 4: Write answer - Jack has 5 stickers now
Step 1: Identify the numbers

Jack starts with 8 stickers, finds 3 more, gives away 2, loses 4

Step 2: Determine the operations

"Finds" indicates addition, "gives" and "loses" indicate subtraction

Step 3: Set up the equation

8 + 3 - 2 - 4 = 5

Step 4: Write the complete answer

Jack has 5 stickers now.

Step 5: Verify the answer

Check: 5 + 4 + 2 - 3 = 8 ✓

Jack has 5 stickers now.
Final answer:

Jack has 5 stickers now.

Applied rules:

• Complex sequence: Perform multiple operations in chronological order

• Pattern recognition: Identify the alternating addition and subtraction

• Verification: Reverse operations to check the answer

5 Logical reasoning IQ problem
Exercise 5
There are 10 children in a room. 4 children leave the room. Then 3 more children enter the room. Finally, 2 children leave the room. How many children are in the room now? IQ Score: 105 Hard
Definition:

Logical reasoning problem: A problem that tests the ability to track changes in a quantity over time.

There are 10 children in a room. 4 children leave the room. Then 3 more children enter the room. Finally, 2 children leave the room. How many children are in the room now?
10 - 4 + 3 - 2 = ?
10
-
4
+
3
-
2
=
7
Step 1: Identify the numbers - Start with 10, 4 leave, 3 enter, 2 leave
Step 2: Determine operations - "leave" is subtraction, "enter" is addition
Step 3: Set up equation - 10 - 4 + 3 - 2 = 7
Step 4: Write answer - 7 children are in the room now
Step 1: Identify the numbers

Start with 10 children, 4 leave, 3 enter, 2 leave

Step 2: Determine the operations

"Leave" indicates subtraction, "enter" indicates addition

Step 3: Set up the equation

10 - 4 + 3 - 2 = 7

Step 4: Write the complete answer

7 children are in the room now.

Step 5: Verify the answer

Check: 7 + 2 - 3 + 4 = 10 ✓

7 children are in the room now.
Final answer:

7 children are in the room now.

Applied rules:

• Dynamic changes: Track changes in quantity over time

• Logical flow: Maintain the chronological sequence of events

• Verification: Reverse operations to confirm the answer

Complete Summary: Word Problems IQ Test
IQ Word Problem = Read + Analyze + Sequence + Operate + Verify
IQ Word Problem Formula
Key definitions:

IQ word problem: A mathematical problem designed to assess logical reasoning, pattern recognition, and problem-solving abilities.

Logical sequence: Following the order of events as they occur in the problem.

Pattern recognition: Identifying relationships and sequences in the problem.

Sequential operations: Performing mathematical operations in the order specified.

Verification: Checking that the answer makes sense in the context of the problem.

IQ score: A measure of cognitive ability based on performance on standardized tests.

Cognitive assessment: Evaluating mental processes and problem-solving abilities.

Complete methodology:
  1. Read carefully: Read the entire problem to understand the situation
  2. Analyze components: Identify all numbers and actions mentioned
  3. Recognize sequence: Determine the chronological order of operations
  4. Identify operations: Determine which mathematical operations to use
  5. Set up equation: Write the mathematical equation
  6. Solve: Calculate the answer
  7. Verify logic: Check if the answer makes sense in the context
  8. Assess difficulty: Evaluate the complexity of the problem
Tip 1: Pay attention to the sequence of events in the problem.
Tip 2: Identify all the numbers mentioned in the problem.
Tip 3: Look for keywords that indicate mathematical operations.
Tip 4: Draw diagrams to visualize complex problems.
Tip 5: Always verify that your answer makes logical sense.
Tip 6: Practice problems of increasing difficulty.
Tip 7: Focus on the logical flow of events in the problem.
Tip 8: Use reverse operations to check your answer.
Common errors: Misreading the sequence of events, using incorrect operations, forgetting to verify the answer, misinterpreting keywords, not following chronological order.
Key insight: IQ problems test logical reasoning and pattern recognition, not just computation.
Memory aid: Think "RASTOV" - Read, Analyze, Sequence, Operate, Verify.
Checking method: Always verify that your answer makes logical sense in the context of the problem.
Rules to know by heart:

• Follow sequence: Perform operations in the order they occur in the problem

• Recognize patterns: Look for logical relationships between numbers

• Verify logic: Check that your answer makes sense in the context

• Identify keywords: Words that indicate mathematical operations

• Chronological order: Follow the timeline of events in the problem

• Pattern recognition: Identify recurring themes or relationships

• Cognitive assessment: Evaluate the complexity and reasoning required

Multiple Examples

Basic addition: "Sarah has 5 candies. Gets 3 more." (5 + 3 = 8)

Basic subtraction: "Tom has 9 balloons. Gives 2 away." (9 - 2 = 7)

Mixed operations: "Emma had 6 toys. Bought 4 more. Gave 3 away." (6 + 4 - 3 = 7)

Advanced mixed: "Jack has 8 stickers. Finds 3. Gives 2. Loses 4." (8 + 3 - 2 - 4 = 5)

Logical reasoning: "10 children in room. 4 leave. 3 enter. 2 leave." (10 - 4 + 3 - 2 = 7)

Verification: 7 + 2 - 3 + 4 = 10 ✓

Questions & Answers

Question: What does IQ mean in these problems? Are they harder than regular math problems?

Answer: Great question! IQ stands for Intelligence Quotient. In these problems:

  • IQ problems: Test your logical reasoning and pattern recognition, not just math skills
  • Regular math: Focus mainly on computation
  • IQ test problems: Require you to think through sequences of events and understand relationships

Yes, they can be more challenging because they test your thinking skills, not just your ability to add or subtract. You need to understand the story and follow the sequence of events.

For example, in "Sarah has 5 candies, gets 3 more, gives 2 away," you need to understand the sequence: 5 → +3 → -2 = 6.

Question: How can I help my child develop the logical reasoning skills needed for these types of problems?

Answer: Here are effective strategies to develop logical reasoning skills:

  1. Story sequencing: Practice telling stories in order (first, then, finally)
  2. Real-life scenarios: Use everyday situations like shopping, cooking, or sharing
  3. Visual aids: Draw pictures or use objects to represent the problem
  4. Pattern games: Play games that involve sequences and patterns
  5. Step-by-step approach: Encourage your child to break problems into smaller steps

For example, you could say: "We had 5 apples. We ate 2. Then Dad brought 3 more. How many do we have now?" Act it out with real apples to make it tangible.

The key is helping your child see math as logical thinking about real situations, not just numbers.

Question: What should I do if I can't figure out the order of operations in a problem?

Answer: If you're confused about the order, try these steps:

  1. Read slowly: Go through the problem one sentence at a time
  2. Circle keywords: Find words like "then," "later," "finally" that show order
  3. Draw a timeline: Put events in chronological order
  4. Act it out: Use your hands or objects to represent what's happening
  5. Check the sequence: Make sure your answer follows the story order

For example, in "Jack has 8 stickers. He finds 3 more. Then he gives 2 away. Later he loses 4." The order is: 8 → +3 → -2 → -4 = 5.

Remember: In word problems, the order usually follows the sequence of time in the story. What happened first? Second? Third?

Don't worry if it takes time - logical reasoning gets better with practice!