Samacheer Kalvi Class 6 Maths Solutions Term 3 Chapter 5 Information Processing Exercise 5.2

Miscellaneous Practice Questions

 

Question 1. Find HCF of 188 and 230 by Euclid's game.
Answer: We use Euclid's game to find the HCF. This rule says that HCF of two numbers `(a, b)` is the same as HCF of `(a, a - b)` if `a > b`. We apply this rule repeatedly to simplify the numbers.
HCF (188, 230)
\( \implies \) HCF (230, 230 – 188) (because 230 > 188)
\( \implies \) HCF (188, 42) (Here, we take the smaller number from the pair and the difference)
\( \implies \) HCF (146, 42) (188 - 42 = 146)
\( \implies \) HCF (104, 42) (146 - 42 = 104)
\( \implies \) HCF (62, 42) (104 - 42 = 62)
\( \implies \) HCF (42, 20) (62 - 42 = 20)
\( \implies \) HCF (22, 20) (42 - 20 = 22)
\( \implies \) HCF (20, 2) (22 - 20 = 2)
\( \implies \) HCF (18, 2) (20 - 2 = 18)
\( \implies \) 2 (18 is divisible by 2, so 2 is the HCF)
Therefore, the HCF of 230 and 188 is 2.
In simple words: To find the highest common factor (HCF) of 188 and 230, we keep subtracting the smaller number from the larger one. We do this until we get a number that divides evenly into the other. This process leads us to the answer 2.

🎯 Exam Tip: When using Euclid's game, always ensure the larger number comes first in the pair before performing the subtraction. The process continues until one number divides the other without a remainder.

 

Question 2. Write the numbers from 1 to 50. From that find the following.
(i) The numbers which are neither divisible by 2 nor 7.
(ii) The prime numbers between 25 and 40
(iii) All square numbers upto 50.
Answer: First, let's list all numbers from 1 to 50:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50.

(i) The numbers that cannot be divided evenly by 2 or 7 are: 9, 11, 13, 15, 17, 19, 23, 25, 27, 29, 31, 33, 37, 39, 41, 43, 45, 47. These numbers don't have 2 or 7 as their factors.
(ii) The prime numbers (numbers only divisible by 1 and themselves) between 25 and 40 are: 29, 31, 37. Prime numbers are the building blocks of all other numbers.
(iii) The square numbers (numbers you get by multiplying a whole number by itself) up to 50 are: 1, 4, 9, 16, 25, 36, 49.
In simple words: We list numbers from 1 to 50. Then we find numbers that 2 or 7 don't divide into, prime numbers between 25 and 40 (only 1 and themselves can divide them), and square numbers (like 1x1, 2x2, etc.) up to 50.

🎯 Exam Tip: To find numbers not divisible by 2 or 7, first list all numbers, then cross out all even numbers (divisible by 2), and then cross out all multiples of 7. The remaining numbers are your answer.

 

Question 3. Complete the following pattern.
(i) 1 + 2 + 3 + 4 = 10
2+ 3+ 4+ 5 = 14
___ + 4 + 5 + 6 = ___
4 + 5 + 6 + ___ = ___
(ii) 1 + 3 + 5 + 7 = 16
___ + 5 + 7 + 9 = 24
5 + 7 + 9 + ___ = ___
7 + 9 + ___ + 13 = ___
(iii) AB, DEF, HIJK, ___, STUVWX
(vi) 20, 19, 17, ___, 10, 5
Answer: We need to complete each pattern by finding the missing numbers or letters.
(i) This pattern adds four consecutive numbers, and the sum increases by 4 each time.
1 + 2 + 3 + 4 = 10
2 + 3 + 4 + 5 = 14
**3** + 4 + 5 + 6 = **18**
4 + 5 + 6 + **7** = **22**
The missing numbers are 3 and 18, and 7 and 22.

(ii) This pattern adds four consecutive odd numbers, and the sum increases by 8 each time.
1 + 3 + 5 + 7 = 16
**3** + 5 + 7 + 9 = 24
5 + 7 + 9 + **11** = **32**
7 + 9 + **11** + 13 = **40**
The missing numbers are 3, 11 and 32, and 11 and 40.

(iii) This is a letter pattern where each group of letters increases by one letter, starting from A. The letters are consecutive.
AB (2 letters)
DEF (3 letters)
HIJK (4 letters)
Following this, the next group should have 5 letters and start after K.
HIJK, **MNOPQ**, STUVWX
The missing part is MNOPQ.

(iv) (Based on source's (vi) label and solution's (iv) value) This is a number pattern where the difference between numbers increases. The differences are -1, -2, -3, -4.
20, 19 (difference of -1)
19, 17 (difference of -2)
17, **14** (difference of -3)
14, 10 (difference of -4)
10, 5 (difference of -5)
The missing number is 14.
In simple words: For the number sums, we look at how the starting number and the total change. For letters, we see how many letters are in each group and what letters come next in the alphabet. For the last number pattern, we check the difference between each number to find the rule.

🎯 Exam Tip: For numerical patterns, look for constant differences, common ratios, or sums that follow a sequence. For letter patterns, count the letters in each group and observe if they are consecutive or follow a skip pattern.

 

Question 4. Complete the table by using the following instructions.

A : It is the 6th term in the Fibonacci sequence.
B: The predecessor of 2.
C: LCM of 2 and 3.
D: HCF of 6 and 20.
E : The reciprocal of 1/5.
F: The opposite number of -7.
G: The first composite number.
H : Area of a square of side 3 cm.
I: The number of lines of symmetry of an equilateral triangle.
Answer: Let's find the value for each instruction to complete the table.
A: The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, ... The 6th term (starting count from 1) is 5. If starting count from 0, it's 8. Based on the solution `A-8`, it refers to the 7th term (0-indexed) or 6th term (1-indexed, but usually 0-indexed is implied for programming, but in math context 1st, 2nd, etc usually implies 1-indexed. Let's assume the solution implies the sequence starts 1,1,2,3,5,8... making 8 the 6th term, or 0,1,1,2,3,5,8... making 8 the 7th term for the "6th term" instruction to resolve to 8.) Let's use 8, which is \( F_6 \) if \( F_0=0, F_1=1 \).
B: The predecessor of 2 is the number that comes just before it, which is 1.
C: The Least Common Multiple (LCM) of 2 and 3 is the smallest number that both 2 and 3 can divide into, which is 6.
D: The Highest Common Factor (HCF) of 6 and 20 is the largest number that divides both 6 and 20. The factors of 6 are 1, 2, 3, 6. The factors of 20 are 1, 2, 4, 5, 10, 20. The HCF is 2.
E: The reciprocal of 1/5 means flipping the fraction, so it's 5/1 or 5.
F: The opposite number of -7 is its positive counterpart, which is 7.
G: The first composite number is the smallest whole number greater than 1 that is not prime. This is 4.
H: The area of a square with a side of 3 cm is \( 3 \text{ cm} \times 3 \text{ cm} = 9 \text{ cm}^2 \).
I: An equilateral triangle has three equal sides and three equal angles, meaning it has 3 lines of symmetry.

Now, let's fill the table and discuss observations:

After completing the table, we observe the following mapping:
A – 8, B – 1, C – 6, D – 2, E – 5, F – 7, G – 4, H – 9, I – 3.
In simple words: We calculate each value based on the given instructions for A through I. Then, we place these values into the table. For instance, A is the 6th Fibonacci number (8), B is the number before 2 (1), and so on. After filling, we see which letter matches which number.

🎯 Exam Tip: Carefully read each instruction and perform the correct mathematical or logical operation. Double-check your calculations for HCF, LCM, and areas to avoid errors.

 

Question 5. Assign the number for English alphabets as 1 for A, 2 for B upto 26 for Z. Find the meaning of

Answer: We need to convert each number back to its corresponding letter in the English alphabet, where A=1, B=2, and so on.
7 corresponds to G
15 corresponds to O
15 corresponds to O
4 corresponds to D
13 corresponds to M
15 corresponds to O
18 corresponds to R
14 corresponds to N
9 corresponds to I
14 corresponds to N
7 corresponds to G
Putting these letters together, we get "GOOD MORNING". This is a common greeting used to wish someone a pleasant start to their day.
In simple words: We change each number into its matching letter from the alphabet (A=1, B=2, etc.). When we put all the letters together, they spell "GOOD MORNING".

🎯 Exam Tip: To avoid mistakes in letter-to-number conversions, quickly write out the alphabet and its corresponding numbers (A=1, B=2, etc.) as a reference.

 

Question 6. Replace the letter with symbols as + for A, – for B, × for C, and ÷ for D. Find the answer for the pattern 4B3C5A30D2 by doing the given operations.
Answer: First, we replace the letters in the pattern with their assigned mathematical symbols:
Given symbols: + for A, – for B, × for C, + for D. (Note: The instruction says + for D initially, then the solution proceeds as if D is division. Following the common convention and the actual calculation, D will be division.)
The pattern is 4B3C5A30D2.
Replacing the letters, this becomes: \( 4 - 3 \times 5 + 30 \div 2 \).
Now, we solve this expression using the BIDMAS (Brackets, Indices, Division, Multiplication, Addition, Subtraction) rule, which tells us the order of operations:
\( 4 - 3 \times 5 + 30 \div 2 \)
First, perform Division and Multiplication from left to right:
\( 3 \times 5 = 15 \)
\( 30 \div 2 = 15 \)
So, the expression becomes: \( 4 - 15 + 15 \).
Next, perform Addition and Subtraction from left to right:
\( 4 - 15 = -11 \)
Then, \( -11 + 15 = 4 \).
The final answer is 4. This showcases how a sequence of operations can be simplified step-by-step.
In simple words: We change letters in the number sentence into math signs (like B becomes minus, C becomes multiply). Then, we solve the math problem using the correct order: first divide and multiply, then add and subtract. The answer we get is 4.

🎯 Exam Tip: Always follow the BIDMAS/PEMDAS rule strictly (Brackets/Parentheses, Indices/Exponents, Division, Multiplication, Addition, Subtraction). Mistakes often occur when operations are performed out of order.

 

Question 7. Observe the pattern and find the word by hiding the Numbers 1 H 2 0 3 W, 4 A 5 R 6 E, 7 Y 8 0 9 U.
Answer: In this pattern, numbers and letters are mixed. We need to hide all the numbers to reveal the hidden word.
The given string is: 1 H 2 0 3 W, 4 A 5 R 6 E, 7 Y 8 0 9 U.
Let's remove all the numbers:
From "1 H 2 0 3 W", we get H O W.
From "4 A 5 R 6 E", we get A R E.
From "7 Y 8 0 9 U", we get Y O U.
Putting the remaining letters together, we get "HOW ARE YOU". This is a common way to ask someone about their well-being.
In simple words: In the jumbled line of numbers and letters, we take out all the numbers. The letters that are left behind then spell out the question "HOW ARE YOU".

🎯 Exam Tip: When given a mixed pattern of numbers and letters, carefully identify the instructions. If the instruction is to "hide numbers", simply remove all digits and arrange the remaining letters in order.

 

Question 8. Arrange the following from the eldest to the youngest. What do you get?

Answer: We need to arrange the family members from the oldest to the youngest and then see what word the letters spell.
Let's list the family members and their typical age order:
1. Grandparents (F) - generally the eldest generation.
2. Parents (A) - the next generation.
3. Uncle (M) - usually of the same generation as parents.
4. Elder sister (I) - older than 'you'.
5. You (L) - the reference point.
6. Younger brother (Y) - the youngest sibling.

Arranging the letters from eldest to youngest gives us:
F – refers to grandparents
A – refers to parents
M – refers to an uncle
I – refers to elder sister
L – refers to me (you)
Y – refers to the younger brother

So, when we put the letters in order, we get FAMILY. This sequence represents the generational structure within a family.
In simple words: We list the family members from oldest to youngest: grandparents, then parents, then uncle, then elder sister, then you, then younger brother. Taking the first letter of each of these family members in that order spells out the word "FAMILY".

🎯 Exam Tip: For arrangement questions, first identify the clear order (e.g., eldest to youngest, smallest to largest). Then, map the given labels to that order to form the final sequence or word.

 

Question 9. Prepare a daily time schedule for evening study at home.
Answer: A good evening study schedule helps manage time effectively and ensures all subjects are covered. Here's a sample schedule:
5:00 pm to 6:00 pm – Mathematics (Focus on problem-solving, which often requires a fresh mind.)
6:00 pm to 7:00 pm – Science (Review concepts, diagrams, and experiments.)
7:00 pm to 8:00 pm – Social Science (Read history, geography, and civics, making notes.)
8:00 pm to 9:00 pm – Dinner & Recreation (Take a necessary break to relax and recharge.)
9:00 pm to 10:00 pm – Tamil and English (Practice language skills, reading, and writing.)
This schedule provides a balanced approach to academic learning and personal well-being.
In simple words: This is a plan for studying in the evening. It sets times for different subjects like Math, Science, and Languages, with a break for dinner and fun in between.

🎯 Exam Tip: When creating a schedule, remember to include short breaks between study sessions to maintain focus. Allocate more time to subjects you find challenging.

 

Question 10. Observe the geometrical pattern and answer the following questions.
(i) Write down the number of sticks used in each iterative pattern,
(ii) Draw the next figure in the pattern also find the total number of sticks used in it.
Answer: The pattern shows triangles made of sticks, growing in size with each iteration. We need to observe how the number of sticks changes.
(i) Let's count the sticks for each figure shown:
The first figure (a single small triangle) uses 3 sticks.
The second figure (a larger triangle made of 4 small triangles) uses 9 sticks.
The third figure (an even larger triangle made of 9 small triangles) uses 18 sticks.
So, the number of sticks used in each pattern is 3, 9, 18. This shows a non-linear growth.

(ii) To find the next figure and its sticks, we look at the pattern of differences. The difference between 9 and 3 is 6. The difference between 18 and 9 is 9. It seems the differences are increasing by 3 each time (6, then 9). So, the next difference should be 12. Therefore, the number of sticks in the next figure would be \( 18 + 12 = 30 \).
The next figure would be a triangle that is even larger, typically made by stacking the previous pattern. Visually, it would be a large triangle divided into 16 smaller equilateral triangles, formed by an arrangement of 4 rows of small triangles. This type of pattern is common in fractals and geometric progressions.
The total number of sticks used in the next figure is 30.
In simple words: We count the sticks in each triangle drawing. The first has 3, the second has 9, and the third has 18. To find the next one, we notice the number of new sticks added grows by 3 each time (6, then 9). So, we add 12 sticks to 18, making the next figure use 30 sticks.

🎯 Exam Tip: For geometric patterns, first count the elements (like sticks or dots) in each step. Then, look for a numerical relationship or rule (arithmetic, geometric, or based on differences) to predict the next terms.

 

Question 11. Find the HCF of 28, 35, 42 by Euclid's game.
Answer: To find the HCF of three numbers (28, 35, 42) using Euclid's game, we can find the HCF of two numbers first, and then find the HCF of the result with the third number. Let's start with 28 and 35.
HCF (28, 35):
HCF (35, 28)
\( \implies \) HCF (28, 35 - 28) = HCF (28, 7)
Since 28 is divisible by 7 ( \( 28 = 4 \times 7 \) ), the HCF of 28 and 35 is 7.

Now, we find the HCF of this result (7) and the third number (42).
HCF (7, 42):
Since 42 is divisible by 7 ( \( 42 = 6 \times 7 \) ), the HCF of 7 and 42 is 7.

Therefore, the HCF of 28, 35, and 42 is 7. This method systematically reduces the problem to smaller parts.
In simple words: To find the highest common factor (HCF) of 28, 35, and 42, we first find the HCF of two numbers, say 28 and 35. We keep subtracting the smaller number from the larger one until we find the HCF, which is 7. Then, we find the HCF of 7 and the last number, 42. Since 42 can be divided by 7, the final HCF for all three numbers is 7.

🎯 Exam Tip: When finding the HCF of three or more numbers, find the HCF of any two numbers first, then find the HCF of the result with the next number, and so on. This simplifies the process.

 

Question 12. Follow the given instructions to fill your name in the OMR sheet.
1. The name should be written in capital letters from left to right.
2. One alphabet is to be entered in each box.
3. If any empty boxes are there at the end they should be left blank.
4. Ballpoint pen is to be used for shading the bubbles for the corresponding alphabets.
Answer: The instructions provide a clear guide on how to correctly fill out an OMR (Optical Mark Recognition) sheet for a name. OMR sheets are used for automated data collection.
1. Write your name using only CAPITAL LETTERS. This helps in clear reading and processing.
2. Each letter of your name should go into a separate box. Do not combine letters in one box.
3. If your name is shorter than the number of boxes, leave the extra boxes at the end completely empty. Do not fill them with spaces or other marks.
4. Use a ballpoint pen to darken the circle (bubble) that matches each letter you have written above. Ensure the shading is dark and complete so the machine can read it accurately.
**Solution:** Do your self. (This implies the student needs to practice filling out the OMR sheet with their own name following these rules.)
In simple words: These rules tell you how to write your name on a special answer sheet. You must use big letters, put one letter in each box, leave empty boxes blank, and use a pen to color in the correct letter circles.

🎯 Exam Tip: Always practice filling OMR sheets beforehand to avoid common mistakes like light shading, multiple markings, or writing outside the boxes, which can lead to your answers not being read correctly.

 

Question 13. Consider the Postal index number (PIN) written on the letters as follows: 604506; 604516; 604560; 604506; 604516; 604516; 604560; 604516; 604505; 604470; 604515; 604520; 604303; 604509; 604470. How the letters can be sorted as per Postal Index Numbers?
Answer: To sort the letters by their Postal Index Numbers (PIN), we first list all the given PIN codes:
604506, 604516, 604560, 604506, 604516, 604516, 604560, 604516, 604505, 604470, 604515, 604520, 604303, 604509, 604470.

We notice that "604" is common for all these postal index numbers. This means all these PINs belong to the same geographical region or postal circle. To sort them, we need to compare the remaining 3 digits after '604'.
Let's extract and list the last three digits for each PIN:
506, 516, 560, 506, 516, 516, 560, 516, 505, 470, 515, 520, 303, 509, 470.

Now, we arrange these last three-digit numbers in ascending order (from smallest to largest):
303, 470, 470, 505, 506, 506, 509, 515, 516, 516, 516, 516, 520, 560, 560.

So, the letters can be sorted by their full Postal Index Numbers as follows, by combining "604" with these sorted last three digits:
604303, 604470, 604470, 604505, 604506, 604506, 604509, 604515, 604516, 604516, 604516, 604516, 604520, 604560, 604560.
This systematic sorting helps in organizing mail efficiently for delivery.
In simple words: To sort the letters by their PIN codes, we first see that all the codes start with "604". So, we only need to look at the last three numbers. We write down these last three numbers from all the PINs, put them in order from smallest to largest, and then combine them back with "604" to get the full sorted list of PIN codes.

🎯 Exam Tip: For large sets of numbers with common prefixes, simplify the sorting process by only comparing the differing digits. This saves time and reduces the chance of errors.