Term 3 Information Processing Exercise Solutions | KalviGavani

Information Processing (Term 3) -- Exercise Solutions

Use this page alongside the official Samacheer Kalvi textbook. Solve each exercise first, then check the methods below.

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Exercise 5.1 -- Number Patterns (Q1)

Q1(i). Complete the pattern: 1 x 1 = 1, 11 x 11 = 121, 111 x 111 = 12321, 1111 x 1111 = ?, 11111 x 11111 = ?

Step-by-step:

• 1 x 1 = 1 (palindrome with 1 digit)
• 11 x 11 = 121 (palindrome: ascend to 2, then descend)
• 111 x 111 = 12321 (palindrome: ascend to 3, then descend)
• 1111 x 1111 = 1234321 (palindrome: ascend to 4, then descend)
• 11111 x 11111 = 123454321 (palindrome: ascend to 5, then descend)

Rule: When you multiply n ones, the result is a palindrome that ascends from 1 to n and then descends from n-1 back to 1.

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Exercise 5.1 -- Number Series (Q2)

Q2(i). Find the next three numbers: 50, 51, 53, 56, 60, ...

Step-by-step:

• 50 to 51: difference = +1
• 51 to 53: difference = +2
• 53 to 56: difference = +3
• 56 to 60: difference = +4
• The differences increase by 1 each time: +1, +2, +3, +4, +5, +6, +7
• 60 + 5 = 65
• 65 + 6 = 71
• 71 + 7 = 78

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Q2(ii). Find the next three numbers: 77, 69, 61, 53, ...

Step-by-step:

• 77 to 69: difference = -8
• 69 to 61: difference = -8
• 61 to 53: difference = -8
• The pattern subtracts 8 each time.
• 53 - 8 = 45
• 45 - 8 = 37
• 37 - 8 = 29

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Q2(iii). Find the next three numbers: 10, 20, 40, 80, ...

Step-by-step:

• 10 to 20: multiplied by 2
• 20 to 40: multiplied by 2
• 40 to 80: multiplied by 2
• Each term is double the previous term.
• 80 x 2 = 160
• 160 x 2 = 320
• 320 x 2 = 640

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Q2(iv). Find the next three numbers: 21/33, 321/444, 4321/5555, ...

Step-by-step:

• First term: numerator 2 (1 digit), denominator 3 (2 digits of 3)
• Second term: numerator 321 (3 digits ascending from 3), denominator 444 (3 digits of 4)
• Third term: numerator 4321 (4 digits ascending from 4), denominator 5555 (4 digits of 5)
• Fourth term: numerator 54321 (5 digits ascending from 5), denominator 666666 (6 digits of 6)
• Fifth term: numerator 654321 (6 digits ascending from 6), denominator 7777777 (7 digits of 7)
• Sixth term: numerator 7654321 (7 digits ascending from 7), denominator 88888888 (8 digits of 8)

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Exercise 5.1 -- Fibonacci Sequence (Q3)

Complete the table using the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89...

Observation: The sum of alternate Fibonacci terms (1st, 3rd, 5th, ...) equals the next Fibonacci term minus 1.

Verification: (i) 1 + 3 = 4 and 5 - 1 = 4. (ii) 1 + 3 + 8 = 12 and 13 - 1 = 12. (iii) 1 + 3 + 8 + 21 = 33 and 34 - 1 = 33. (iv) 1 + 3 + 8 + 21 + 55 = 88 and 89 - 1 = 88. All match.

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Exercise 5.1 -- HCF by Euclid's Game (Q5, Q6)

Q5(i). Find HCF of 25 and 35 using Euclid's game.

Step-by-step:

• 35 = 1 x 25 + 10 (divide 35 by 25, remainder = 10)
• 25 = 2 x 10 + 5 (divide 25 by 10, remainder = 5)
• 10 = 2 x 5 + 0 (divide 10 by 5, remainder = 0)
• When remainder = 0, the last divisor is the HCF.

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Q5(ii). Find HCF of 36 and 12 using Euclid's game.

Step-by-step:

• 36 = 3 x 12 + 0 (divide 36 by 12, remainder = 0)
• When remainder = 0, the divisor is the HCF.

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Q5(iii). Find HCF of 15 and 29 using Euclid's game.

Step-by-step:

• 29 = 1 x 15 + 14 (divide 29 by 15, remainder = 14)
• 15 = 1 x 14 + 1 (divide 15 by 14, remainder = 1)
• 14 = 14 x 1 + 0 (divide 14 by 1, remainder = 0)

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Q6. Find HCF of 48 and 28. Then find HCF of 48 and their difference.

Step-by-step (HCF of 48 and 28):

• 48 = 1 x 28 + 20
• 28 = 1 x 20 + 8
• 20 = 2 x 8 + 4
• 8 = 2 x 4 + 0

HCF(48, 28) = 4

Step-by-step (HCF of 48 and 20):

• Difference = 48 - 28 = 20
• 48 = 2 x 20 + 8
• 20 = 2 x 8 + 4
• 8 = 2 x 4 + 0

HCF(48, 20) = 4

Observation: Both HCFs are equal (= 4). This confirms the property: HCF(a, b) = HCF(a, a - b).

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Exercise 5.1 -- Systematic Listing (Q7, Q8)

Q7. Write the instructions to fill a bank withdrawal form.

Answer (step-by-step): 1. Write the account number in the designated field. 2. Write the date of withdrawal. 3. Write the amount in figures (numbers) and in words. 4. Write the account holder's name. 5. Sign in the signature box at the bottom. 6. Provide the mobile number if required.

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Q8. Arrange the following classmates' names in alphabetical order.

Method: List all names and sort from A to Z.

Step-by-step: 1. Write all names. 2. Compare the first letter of each name. 3. If two names start with the same letter, compare the second letter, and so on. 4. Arrange in order: A, B, C, D, ... Z.

Example: Arun, Bharat, Deepa, Kavitha, Ravi, Sita

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Exercise 5.1 -- Venn Diagram (Q9)

Place the numbers in the overlapping regions of a triangle, circle, and square.

• Common to all three (triangle, circle, square): 10
• Common to square and circle only: 5
• Common to triangle and circle only: 7
• Common to triangle and square only: 2
• Only in square: 12
• Only in circle: 14
• Only in triangle: 8

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Exercise 5.1 -- Objective Type Questions (Q11-Q15)

Q11. Find the next term: 15, 17, 20, 22, 25, ...

Step-by-step:

• 15 to 17: +2
• 17 to 20: +3
• 20 to 22: +2
• 22 to 25: +3
• Pattern: +2, +3, +2, +3, ...
• Next: 25 + 3 = 28

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Q12. What is the 25th letter in the pattern: ABCAABBCCAAABBBCCC...?

Step-by-step: Let's count the positions by groups:

• A (1 letter): positions 1
• BC (2 letters): positions 2-3
• AABB (4 letters): positions 4-7
• CCCC (4 letters): positions 8-11

Wait, let us recount using the described pattern:

The pattern is: A, B, C, AA, BB, CC, AAA, BBB, CCC, AAAA, BBBB, CCCC, ...

Count positions:

• A(1): position 1
• B(1): position 2
• C(1): position 3
• A(2): positions 4-5
• B(2): positions 6-7
• C(2): positions 8-9
• A(3): positions 10-12
• B(3): positions 13-15
• C(3): positions 16-18
• A(4): positions 19-22
• B(4): positions 23-26

Position 25 falls in the group B(4) (positions 23-26).

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Q13. Find the difference between the 6th and 5th Fibonacci terms.

Step-by-step:

• Fibonacci sequence: 1, 1, 2, 3, 5, 8, ...
• 5th term = 5
• 6th term = 8
• Difference = 8 - 5 = 3

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Q14. Find the 11th term in the Lucas sequence: 1, 3, 4, 7, ...

Step-by-step:

• 1st term: 1
• 2nd term: 3
• 3rd term: 1 + 3 = 4
• 4th term: 3 + 4 = 7
• 5th term: 4 + 7 = 11
• 6th term: 7 + 11 = 18
• 7th term: 11 + 18 = 29
• 8th term: 18 + 29 = 47
• 9th term: 29 + 47 = 76
• 10th term: 47 + 76 = 123
• 11th term: 76 + 123 = 199

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Q15. If HCF(26, 54) = 2, then HCF(54, 28) = ?

Step-by-step:

• Difference = 54 - 26 = 28
• By the property: HCF(a, b) = HCF(a, a - b) when a > b
• So HCF(54, 28) = HCF(54, 54 - 28) = HCF(54, 26) = 2

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Exercise 5.2 -- HCF by Euclid's Game (Q1)

Q1. Find HCF of 188 and 230 by Euclid's game.

Step-by-step:

• 230 = 1 x 188 + 42
• 188 = 4 x 42 + 20
• 42 = 2 x 20 + 2
• 20 = 10 x 2 + 0

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Exercise 5.2 -- Number Classification (Q2)

Q2(i). Find all numbers from 1 to 50 that are neither divisible by 2 nor by 7.

Step-by-step:

• Numbers divisible by 2 (from 1-50): 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50
• Numbers divisible by 7 (from 1-50): 7, 14, 21, 28, 35, 42, 49
• Numbers divisible by 2 or 7: all of the above
• Numbers NOT divisible by 2 or 7 (from 1-50):

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Q2(ii). Find all prime numbers between 25 and 40.

Step-by-step: Check each number from 26 to 39:

• 26 = 2 x 13 (not prime)
• 27 = 3 x 9 (not prime)
• 28 = 4 x 7 (not prime)
• 29: no factors other than 1 and 29 (prime)
• 30 = 2 x 15 (not prime)
• 31: no factors other than 1 and 31 (prime)
• 32 = 2 x 16 (not prime)
• 33 = 3 x 11 (not prime)
• 34 = 2 x 17 (not prime)
• 35 = 5 x 7 (not prime)
• 36 = 6 x 6 (not prime)
• 37: no factors other than 1 and 37 (prime)
• 38 = 2 x 19 (not prime)
• 39 = 3 x 13 (not prime)

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Q2(iii). Find all square numbers up to 50.

Step-by-step:

• 1 squared = 1
• 2 squared = 4
• 3 squared = 9
• 4 squared = 16
• 5 squared = 25
• 6 squared = 36
• 7 squared = 49
• 8 squared = 64 (greater than 50, so stop)

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Exercise 5.2 -- Pattern Completion (Q3)

Q3(i). Complete the pattern: 1+2+3+4=10, 2+3+4+5=14, ___+4+5+6=___, 4+5+6+___=___

Step-by-step:

• 1+2+3+4 = 10 (4 consecutive numbers starting from 1)
• 2+3+4+5 = 14 (4 consecutive numbers starting from 2)
• 3+4+5+6 = 18 (4 consecutive numbers starting from 3)
• 4+5+6+7 = 22 (4 consecutive numbers starting from 4)

Each sum increases by 4 because each number in the group increases by 1 and there are 4 numbers.

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Q3(ii). Complete the pattern: 1+3+5+7=16, ___+5+7+9=___, 5+7+9+___=___, 7+9+___+13=___

Step-by-step:

• 1+3+5+7 = 16 (4 consecutive odd numbers starting from 1)
• 3+5+7+9 = 24 (4 consecutive odd numbers starting from 3)
• 5+7+9+11 = 32 (4 consecutive odd numbers starting from 5)
• 7+9+11+13 = 40 (4 consecutive odd numbers starting from 7)

Each sum increases by 8 because each odd number increases by 2 and there are 4 numbers.

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Q3(iii). Complete the pattern: AB, DEF, HIJK, ?, STUVWX

Step-by-step:

• AB: 2 letters (A, B)
• DEF: 3 letters (D, E, F)
• HIJK: 4 letters (H, I, J, K)
• Next group: 5 letters starting after K = LMNOP
• STUVWX: 6 letters (S, T, U, V, W, X)

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Q3(iv). Complete the pattern: 20, 19, 17, ?, 10, 5

Step-by-step:

• 20 to 19: difference = -1
• 19 to 17: difference = -2
• 17 to ?: difference = -3, so ? = 17 - 3 = 14
• 14 to 10: difference = -4 (verified: 14 - 4 = 10)
• 10 to 5: difference = -5 (verified: 10 - 5 = 5)

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Exercise 5.2 -- Complete the Table (Q4)

Fill in the missing values:

Step-by-step for each cell:

• A: 6th Fibonacci term = 1, 1, 2, 3, 5, 8
• B: Predecessor of 2 = 2 - 1 = 1
• C: LCM of 2 and 3 = 6
• D: HCF of 6 and 20 = 2 (6 = 2x3, 20 = 2x2x5)
• E: Reciprocal of 1/5 = 5
• F: Opposite of -7 = 7
• G: First composite number = 4 (4 = 2x2, the smallest composite)
• H: Area of a square with side 3 cm = 3 x 3 = 9
• I: Lines of symmetry of an equilateral triangle = 3

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Exercise 5.2 -- Symbol Substitution (Q6)

Q6. Replace A = +, B = -, C = x, D = / in: 4B3C5A30D2

Step-by-step:

1. Division: 30 / 2 = 15 --> 4 - 3 x 5 + 15 2. Multiplication: 3 x 5 = 15 --> 4 - 15 + 15 3. Subtraction: 4 - 15 = -11 --> -11 + 15 4. Addition: -11 + 15 = 4

• Substitute: 4 - 3 x 5 + 30 / 2
• Apply BODMAS:

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Exercise 5.2 -- Hidden Word (Q7)

Q7. Find the word by hiding numbers: 1H2O3W 4A5R6E 7Y8O9U

Step-by-step: Remove all the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9) and keep only the letters:

• 1H2O3W --> HOW
• 4A5R6E --> ARE
• 7Y8O9U --> YOU

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Exercise 5.2 -- Daily Time Schedule (Q9)

Q9. Prepare a daily time schedule for evening study.

Sample Answer:

A systematic schedule helps you manage time effectively and cover all subjects.

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Exercise 5.2 -- HCF of Three Numbers (Q11)

Q11. Find HCF of 28, 35, and 42 using Euclid's game.

Step-by-step:

• Step 1: Find HCF(28, 35)
• 35 = 1 x 28 + 7
• 28 = 4 x 7 + 0
• HCF(28, 35) = 7

• Step 2: Find HCF(7, 42)
• 42 = 6 x 7 + 0
• HCF(7, 42) = 7

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Exercise 5.2 -- Sorting PIN Codes (Q13)

Q13. Sort the following PIN codes in ascending order:

Step-by-step:

• List all PIN codes: 604506, 604516, 604560, 604506, 604516, 604516, 604560, 604516, 604505, 604470, 604515, 604520, 604303, 604509, 604470
• Compare digit by digit from left to right
• Arranged in ascending order:

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Additional Questions

Q1. Find the odd figure out.

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Q2. If GARIMA is coded as 725432 and TINA as 6482, how will MARTINA be coded?

Step-by-step:

• From GARIMA = 725432: G=7, A=2, R=5, I=4, M=3
• From TINA = 6482: T=6, I=4, N=8, A=2
• Now encode MARTINA: M=3, A=2, R=5, T=6, I=4, N=8, A=2

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Q4. Which number replaces the question mark? Hint: Left side numbers are square numbers.

Step-by-step: The pattern involves squaring.

• Among the options (7, 14, 48, 49), the number 49 = 7 squared fits the squaring pattern.

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Q7. Find the number replacing the question mark in the number series figure.

Options: (a) 25, (b) 49, (c) 97, (d) 193

Step-by-step: The pattern follows a doubling-plus-increment rule (each term is approximately double the previous term plus an increasing number).

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Q8. Find the number replacing the question mark. Hint: (2 + 8) squared = 10 squared = 100.

Step-by-step:

• Sum the two numbers in the figure and square the result.
• (2 + 8) squared = 10 squared = 100

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Q10. Find the missing term: 1, 6, 15, ?, 45, 66, 91

Step-by-step:

• 1 to 6: difference = 5
• 6 to 15: difference = 9
• 15 to ?: difference = 13 (increasing by 4 each time)
• ? = 15 + 13 = 28
• 28 to 45: difference = 17 (verified: 9 + 4 = 13, 13 + 4 = 17)
• 45 to 66: difference = 21 (verified: 17 + 4 = 21)
• 66 to 91: difference = 25 (verified: 21 + 4 = 25)

The differences form: 5, 9, 13, 17, 21, 25 (increasing by 4 each step).

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Common Mistakes to Avoid

1. Wrong pattern identification: Always check the first 3-4 terms before deciding the pattern. A single wrong assumption (e.g., "add 2" vs "multiply by 2") leads to all subsequent answers being wrong.

2. Confusing Fibonacci and Lucas sequences: Fibonacci starts 1, 1, 2, 3, 5, 8... Lucas starts 1, 3, 4, 7, 11... Both use the same rule (each term = sum of previous two) but different starting values.

3. Errors in HCF by Euclid's method: Always divide the larger number by the smaller. The process continues until the remainder is exactly 0. The HCF is the LAST divisor (not the last quotient or remainder).

4. BODMAS errors in symbol substitution: Always apply BODMAS strictly: Brackets, Orders, Division, Multiplication, Addition, Subtraction. In 4 - 3 x 5 + 30 / 2, do multiplication and division BEFORE addition and subtraction.

5. Missing numbers in classification: When finding numbers "neither divisible by 2 nor 7," remember that 1 is included (it is not divisible by 2 or 7). Also check boundary values carefully.

6. Incorrect counting in letter patterns: When finding the Nth letter in a repeating pattern, list out positions carefully. Draw groups and count systematically rather than guessing.

7. Forgetting to verify HCF of three numbers: To find HCF of three numbers, first find HCF of the first two, then find HCF of that result with the third number. Do not try to divide all three at once.

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Exam Checklist

• [ ] Can you identify and extend number patterns (arithmetic, geometric, Fibonacci, Lucas)?
• [ ] Can you find the next terms in a sequence with increasing/decreasing differences?
• [ ] Can you find HCF using Euclid's division method (Euclid's game)?
• [ ] Can you verify that HCF(a, b) = HCF(a, a - b)?
• [ ] Can you apply BODMAS correctly in symbol substitution problems?
• [ ] Can you systematically list numbers that satisfy given conditions (not divisible by 2 or 7, prime between 25 and 40, square numbers up to 50)?
• [ ] Can you complete number patterns like 1x1=1, 11x11=121, 111x111=12321?
• [ ] Can you sort data in ascending/descending order (PIN codes, names alphabetically)?
• [ ] Can you decode hidden words by removing numbers from mixed strings?
• [ ] Can you fill tables using Fibonacci terms, LCM, HCF, reciprocals, and other number properties?