Number Play Class 7 Worksheet with Answers Maths Chapter 6 - #NCSOLVE 📚

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Class 7 Maths Chapter 6 Number Play Worksheet with Answers Pdf

Number Play Class 7 Maths Worksheet

Class 7 Maths Chapter 6 Worksheet with Answers – Class 7 Number Play Worksheet

Multiple Choice Questions

Choose the correct option.

Question 1.
What will be the number sequence in the given arrangement of a group of children, if each child calls out the number of children in front of them who are taller than them?

(a) 0, 1, 1, 2, 4, 1, 5
(b) 0, 0, 1, 3, 1, 3, 1
(c) 0, 1, 2, 3, 4, 5, 6
(d) 0, 1, 2, 1, 3, 1, 5
Answer:
(b) 0, 0, 1, 3, 1, 3, 1

Question 2.
The 10th number in the Virahanka-Fibonacci number sequence ‘1, 2, 3, 5, 8, 13, 21, is
(a) 55
(b) 89
(c) 144
(d) 233
Answer:
(b) 89

Question 3.
The parity of which of the following is an odd number.
(a) Sum of 4 even numbers
(b) Sum of 3 even numbers
(c) Sum of 3 odd and 2 even numbers
(d) Sum of 2 odd and 3 even numbers
Answer:
(c) Sum of 3 odd and 2 even numbers

Question 4.
An expression which have always an odd parity, is
(a) 2n + 1
(b) n + 2
(c) 10n
(d) 3n + 4
Answer:
(a) 2n + 1

Question 5.
In a 3 x 3 square grid for consecutive numbers 1 to 0, the smallest and the largest possible sum for any column or row is
(a) 5, 21
(b) 6, 24
(c) 7, 32
(d) 13, 45
Answer:
(b) 6, 24

Question 6.
Which term of the Virahanka-Fibonacci sequence is the number 4181?
(a) 18
(b) 19
(c) 17
(d) 16
Answer:
(a) 18

Question 7.
The sum and parity of the sum of numbers from 1 to 50 is
(a) 1035, odd
(b) 1100, even
(c) 1275, odd
(d) 1350, even
Answer:
(c) 1275, odd

Question 8.
Some of the flowers like Lili-3 petals, Buttercups-5 petals, Delphinium-8 petals, show Virahanka-Fibonacci sequence. The next flower in the sequence would be
(a) Corn marigold – 13 petals
(b) Aster – 21 petals
(c) Daisy – 34 petals
(d) Sunflower – 55 petals
Answer:
(a) Corn marigold – 13 petals

Assertion and Reason-based Questions.

Directions. In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option as:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
(c) Assertion (A) is true but Reason (R) is false.
(d) Assertion (A) is false but Reason (R) is true.

Question 1.
Assertion: Even + even = even, and odd + odd = odd.
Reason: The parity of the sum of any two consecutive numbers is odd and the parity of the sum of any two odd numbers is even.
Answer:
(d) Assertion (A) is false but Reason (R) is true.

Question 2.
Assertion: A 3 x 3 magic square can be made using the numbers 2-10.
Reason: If we add 1 to each number of the magic square for 1-9, we will get a 3 x 3 magic square for 2-10.
Answer:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Fill in the blanks.

1. The parity of the sum of 5 even and 7 odd numbers is ________.
Answer:
odd

2. The parity of the number of small squares in a 25 x 12 grid is ________.
Answer:
even

3. The nth even number or nth term for multiples of 2 is ________.
Answer:
2n

4. In the Virahanka-Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21, 34, 55, …, the next number after 55 is ________.
Answer:
89

5. The values of A, B and C in cryptarithm sum

Answer:
A = 1, B = 2, C = 3 (Answer may vary)

True or False

State whether the following statements are ‘always true’, ‘sometimes true’ or ‘never true’.

1. If a person says T and he is second in the line then he is shorter than the first person.
Answer:
Always true

2. The largest possible number in a group of 6 people is 4.
Answer:
Sometimes True

3. The first person will always call ‘0’.
Answer:
Always true

4. If a person is neither first nor last in line (i.e., if they are standing somewhere in between), then they cannot say ‘0’.
Answer:
Sometimes True

5. The shortest person at the end of the queue wiLt have the Largest number.
Answer:
Always true

Solve the following.

Question 1.
If an expression 4k + 2 evaluates to 6, 10, 14, … for (k = 1, 2, 3, …), you will find that many numbers are missing. What expression should be used if you want to have complete even numbers.
Answer:
2k

Question 2.
If you have some odd numbers 1, 3, 5, 7, 9, 11 and 13, and you have to choose any 5 of them to make a sum of 30. Is it possible? Explain why?
Answer:
Not possible

Question 3.
What happens if five odd numbers are added? Can their sum be arranged into pairs? Investigate the outcome, when adding:
(a) 7 odd numbers
(b) 8 odd numbers
Answer:
No, (a) odd number (b) even number

Question 4.
Complete the square grid with numbers 1 to 9 such that the magic sum is 15.

Answer:

Question 5.
In a one-day match, each of the opening batsmen scored more than a half century but their scores differ by 1 run. One of them exclaims that their total score is 112. Is this possible? Why or why not?
Answer:
Not possible

Question 6.
Vidya has an even number of ?1 coins, an odd number of ?2 coins, and an odd number of ?5 coins in her piggy bank. After calculating, she found the total to be ?50:
Did Vidya make an error in her calculation? If yes, explain the error. If no, provide possible counts of each type of coin she might have.
Answer:
Yes, made an error

Question 7.
Here is a possible 2 × 3 grid filled with 3 odd numbers and 3 even numbers that satisfy the parity odd (o) or even (e) sums of the rows and columns. The numbers are arranged so that the parity of each row and column matches the given conditions:
Answer:

Question 8.
Take a magic square: (a) increase each number by 2; (b) double each number.
In each case, are the resulting grids also magic squares? How does the magic sum change in each case?
Answer:
(a) Yes
(b) Yes

Question 9.
Solve the following cryptarithms.

Answer:
(a) A = 8
(b) A = 5, B = 1
(c) A = 2, B = 9

NUMBERS TELL US THINGS

Green Valley School is organizing an Annual Day junction. Students who want to participate have prepared various activities to showcase their talents. For this, some students of Class VII are standing in a queue, and each one states a number as follows.

After sometime, students shuffled their positions and the numbers were changed as follows.

Here, the rule is each student states a number that reflects the count of the taller students in front of them.
Check if the numbers each student stated match the rule in both the arrangements.

Question 1.
Write down the number each child should say based on this rule for the arrangement shown below.

Answer:
Neha – 0, Ram – 1, Priya – 2, Ankur – 0, Ria – 4, Leena – 3, Rohit – 5, Mansi -1

Question 2.
Re-arrange the above children so that the sequence is organized as follows. (Write the name of the child in the order).
(a) 0, 0, 1, 1, 3, 4, 1, 5
(b) 0, 1, 0, 3, 0, 1, 0, 1
(c) 0, 0, 0, 1, 2, 3, 4, 5
(d) 0, 0, 1, 1, 1, 1, 1, 1
Answer:
(a) Ria, Ankur, Ram, Neha, Leena, Rohit, Mansi, Priya
(b) Priya, Rohit, Leena, Ria, Neha, Ram, Ankur, Mansi
(c) Ria, Rohit, Ankur, Mansi, Neha, Ram, Leena, Priya
(d) Ria, Ankur, Rohit, Priya, Leena, Ram, Neha, Mansi

Question 3.
For each statement given below, decide if it is always true, sometimes true, or never true, and explain your reasoning.
(a) The number stated by the first person will be ‘0’.
(b) The highest number in a sequence of arrangement of a group of persons represents the shortest person.
(c) If an individual states ‘0’, they are considered the tallest in the group.
(d) A person standing in the middle (not on either end) cannot be assigned the number ‘0’.
Answer:
(a) Always true
(b) Sometimes true
(c) Sometimes true
(d) Sometimes true

PICKING PARITY

Question 4.
Sunaina has some cherries and a puzzle to solve. She has three baskets, and each basket needs to hold exactly one bunch oj cherries as given below. The total number oj cherries in all the bowls should add up to 20.

Can you figure out which 3 bunches oj cherries make the total 20? Is it possible or not?
Answer:
Not possible

Question 5.
During a class, the teacher explained the concept of even and odd numbers to the students:

Based on this information answer the questions given below.
(a) What happens if three odd numbers are added? Can their sum be arranged into pairs?
Answer:
Their sum will be an odd number, No

(b) Investigate the outcome when you add:
(i) 5 odd numbers
(ii) 6 odd numbers
(iii) 7 odd numbers
Answer:
(i) Odd number
(ii) Even number
(iii) Odd number

Question 6.
Based on your understanding of how odd and even numbers are visually represented, determine whether the result is odd or even in the following cases:
(a) The sum of three even numbers.
(b) The sum of six odd numbers.
(c) The sum of three odd numbers and two even numbers.
(d) The sum of two even numbers and two odd numbers.
Answer:
(a) Even number
(b) Even number
(c) Odd number
(d) Even number

Question 7.
Raman has an odd number of ₹ 1 coins, an odd number of coins, and an even number of ₹ 10 coins in his piggy bank. After calculating, he found the total to be ₹ 200.
Did Raman make an error in his calculation? If yes, explain it. If no, provide possible counts of each type of coins he might have.
Answer:
No; 5 ₹ 1 coins, 11 ₹ 5 coins, 14 ₹ 10 coins (Answer may vary)

Question 8.
We know that even + even = even and even + odd = odd. Using a similar approach, determine the parity in the following cases:
(a) even – odd
(b) odd – even
(c) odd – odd
(d) even – even
Answer:
(a) odd
(b) odd
(c) even
(d) even

Question 9.
State true or false:
(a) Adding an odd count of even numbers yields an odd result.
(b) Adding an even count of odd numbers yields an even result.
(c) Adding an even count of even numbers yields an odd result.
(d) Adding an odd count of odd numbers yields an even result.
Answer:
(a) False
(b) True
(c) False
(d) False

Question 10.
Two friends, John and Joseph, have joined the company exactly one year apart. Today, they are celebrating their work anniversaries. Joseph exclaims that the sum of their work anniversary years is 36. Can their combined years of service be 36? If yes, calculate the total years of their service.
Answer:
No

Small Squares in. Grids

Question 11.
There are two grids: Grid 1 and Grid 2. Grid 1 is 2×3 grid, there are 6 squares (an even number). Grid 2 is a 3 x 3 grid, there are 9 squares (an odd number). By observing the product of the dimensions, we can determine whether the total number of squares is odd or even.

Determine the parity of the number of small squares in the following grids:
(a) 17 × 23
(b) 32 × 56
(c) 235 × 376
Answer:
(a) Odd
(b) Even
(c) Even

Parity of Expressions

Question 12.
While explaining the concept of parity, Sunita told Gunita that, we take the expression 4k + 2, it evaluates to 6,10,14,… (for k = 1, 2, 3, …), but many even numbers are missing. So, we use the expression 2k, where k is any number (1, 2, 3, …). This generates all even numbers. That is when k = 1, 2, 3, …, the result is 2, 4, 6, 8, and so on, covering all even numbers.
Can you now find an expression to create a list of all odd numbers? Write the expression for different values of k.
Answer:
2n + 1, where n = 1, 2, 3,…

Question 13.
What is the parity of the sum of numbers from 1 to 50?
Answer:
Odd

Question 14.
Here, is a 2 × 3 grid. Fill the 6 boxes with 3 odd numbers and 3 even numbers to satisfy the parity of the row and coLumn sum. For. each row and column the parity of the sum is written in the circle; (e) for even and (o)for odd.

Answer:

2	3	6
1	4	5

SOME EXPLORATIONS IN GRIDS

Question 15.
Use nunbers 1 to q without repeating and flit in the blank grids so that the numbers given in the coloured circles are the sums of corresponding rows and columns.

Answer:

Question 16.
While explaining the concept of magic square a teacher told that, 4A square grid is called a magic square when the numbers in each row, column, arid diagonal add up to the same total. This total is called the magic sum.
(a) Create a 3 × 3 magic square whose magic sum is:
(i) 18
(ii) 42
Answer:

(b) Fill in the missing numbers in the magic square, ensuring that the sum of each row, column, and diagonal equals 72.

Answer:

Question 17.
Can a magic square be formed using nine non-consecutive numbers? If so, then make it.
Answer:
Yes,

Question 18.
Explore methods for constructing magic squares using the following sets of q consecutive numbers:
(a) 8 to 16
(b) 5 to 13
(c) 65 to 73
Answer:
Do it Yourself

Question 19.
Observe the magic square given alongside. Find the value of x and complete the magic square given below.

Answer:
x = 6,

Question 20.
How many different magic squares can be created using the numbers 1 to 9? One example is shown here.

Answer:
Only one. (By changing the orientation and reflection, it can be created 8, but in each case the magic sum will be the same)

Question 21.
Take a magic square: (a) increase each number by 2; (b) double each number.
In each case, are the resulting grids also magic squares? How does the magic sum change in each case?

Answer:
Do it yourself

Question 22.
Make a 3 × 3 magic square where the sum of all rows, columns, and diagonals is 0. Use negative numbers if needed, but all numbers cannot be zero.

Answer:

Question 23.
Sujoy is filling a magic box where the sum of all rows, columns, and diagonals must be 18. He filled up the numbers in the 3 × 3 grid but made same mistakes.

Find the mistake Sujoy made while filling the magic box and correct it. Give a reason for your correction.
Answer:

NATURE, FAVORITE SEQUENCE: THE VIRAHANKA-FIBONACCI NUMBERS!

Kavya is a Class VII student. The day the teacher explained the concept of Virahanka-Fibonacci numbers, she was absent. So, she took help from her friend Prerna.
Prerna explained, ‘A series of numbers, starting from 1 where every number is the sum of its two preceding numbers, is known as Virahanka-Fibonacci numbers. Example: 1, 2, 3, 5, 8, 13, 21, 34, 55,

Question 24.
After this, Prerna asked Kavya to find the three missing terms in these Fibonacci-type sequences to check her understanding.
(a) 2, 2, 4, 6, 10, ________, ________, ________
(b) 10, 12, 22, 34, ________, ________, ________
Answer:
(a) 16, 26, 42
(b) 56, 90, 146

Question 25.
Find the spirals in different fruits or in petals of flowers that follow the Virahanka sequence.
Answer:
Do it yourself

Question 26.
Two consecutive numbers in the Virahanka-Fibonacci sequence are 2584 and 4181. What are the next 3 terms in the sequence?
Answer:
6765, 10946, 17711

Question 27.
What is the parity of 17th term oj the Virahanka-Fibonacci sequence?
Answer:
Even

Question 28.
The Maths lab in XXX Public School is on the just floor. To reach it, one must use a 9 steps staircase. Students usually climb the stairs by taking either 1 step at a time or 2 steps at a time.
In how many different ways can the students reach the first floor?
Answer:
55

DIGITS IN DISGUISE

Question 29.
Replace the letters by using suitable numerals to solve the Jollowing Cryptarithmetic puzzle:

Answer:
(a) A = 5, B = 1
(b) A = 9, B = 2, C = 1
(c) A = 2, B = 1, C = 4 (Answer may vary)
(d) T = 1, D = 9, O = 0

Fun time
Some children are standing in a row:

• Rohit is 11th from the left
• Aman is 21st from the right.
• When they interchange their positions, Rohit becomes 14th from the left.

The post Number Play Class 7 Worksheet with Answers Maths Chapter 6 appeared first on Learn CBSE.

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