Construct a 3 × 3 magic square to get a magic sum of 93 .

Given, Construct a 3 × 3 magic square Magic sum or magic number = 93 Middle number of the magic square = 93 3 = 31 Now let us select numbers greater than and numbers less than 31 with equal difference between them, and fill the table as per the construction steps of magic square. Let the numbers be 23 , 25 , 27 , 29 , 31 , 33 , 35 , 37 , a n d 39 (The common difference being 2 ). Then fill the numbers diagonally in ascending order, in the " 3 × 3 table with the middle row and column extended" as shown below.: Now we have to fill the internal blocks by transposing the numbers to the opposite block. Thus we get one of the many possible magic squares with magic sum 93 .

Look at the given grid Add the numbers in the middle column. We get _____

It is given to add the numbers in the number grid. We need to add the numbers in the middle column of the number grid. So, in the middle column, we have the numbers → 1 , 5 , 9 Here, 1 + 5 + 9 = 15 , when we change the position of the numbers still the answer remains the same → 9 + 5 + 1 = 15 Hence, the required answer is given above.

Fill this magic square using all the numbers from 21 to 29 . Rule: The total of each side is 75 .

Given: To fill the squares using all the numbers from 21 to 29 . The total of each side is 75 . For each side to be 75 if we add: 22 + 28 + 25 = 75 28 + 22 + 25 = 75 25 + 22 + 28 = 75 Thus, Therefore, the magic square is completed.

Fill this magic square using all the numbers from 46 to 54 . Rule: The total of each line is 150 .

Given: To fill the squares using all the numbers from 46 to 54 . The total of each line is 150 . For each line to be 150 if we add: 53 + 48 + 49 = 150 46 + 50 + 54 = 150 51 + 52 + 47 = 150 Thus, Therefore, the magic square is completed.

Look at the given grid Add the numbers on the diagonal. We get 6 + 5 + 4 = 15

It is given to add the numbers in the number grid. We know that, We need to add the numbers on the diagonal of the number grid. So, on the one diagonal, we have the numbers → 6 + 5 + 4 = 15 and other we have the numbers → 8 , 5 , 2 Here, 8 + 5 + 2 = 15 , when we change the position of the numbers still the answer remains the same → 2 + 5 + 8 = 15 Hence, the required answer is 15 .

Complete the magic square: 14 0 8 6 11 4 7 2 1 12

We know that the sum of numbers along the horizontal line, the vertical line and the diagonal of a magic square are equal. Here, sum of last column = 0 + 11 + 7 + 12 = 30 Solving for the last row, x + 2 + 1 + 12 = 30 ⇒ x + 15 = 30 ⇒ x = 15 14 0 8 6 11 4 7 15 2 1 12 Solving for first column, x + 8 + 4 + 15 = 30 ⇒ x + 27 = 30 ⇒ x = 3 3 14 0 8 6 11 4 7 15 2 1 12 Solving for first row, x + 3 + 14 + 0 = 30 ⇒ x + 17 = 30 ⇒ x = 13 3 14 13 0 8 6 11 4 7 15 2 1 12 Solving for second row, 8 + x + 6 + 11 = 30 ⇒ x + 25 = 30 ⇒ x = 5 3 14 13 0 8 5 6 11 4 7 15 2 1 12 Solving for second column, 14 + 5 + x + 2 = 30 ⇒ x + 21 = 30 ⇒ x = 9 3 14 13 0 8 5 6 11 4 9 7 15 2 1 12 Solving for third column, 13 + 6 + x + 1 = 30 ⇒ x + 20 = 30 ⇒ x = 10 3 14 13 0 8 5 6 11 4 9 10 7 15 2 1 12

EASY

Earn 100

Here is a calendar. Ask your friend to choose a $3 \times 3$ square in this and tell you the smallest number in that square. In your mind, add $8$ to that number and multiply it by $9$ . Give him/her this answer as the sum of the number in his/her square. He/She will be surprised by how you did it. Can you explain how you can work out this problem by forming an equation and solving it.

SUN MON TUES WED THURS FRI SAT

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

Important Questions on Equations and Inequations

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Look at the given grid.

Question Image

Add the numbers in the first row. We get $8 + 1 + 6 =$

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Construct a

3 \times 3

magic square to get a magic sum of

93

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Fill in the numbers from $1$ to $6$ without repetition, so that each side of the triangle adds up to $12$ .

Question Image

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Look at the given grid

Question Image

Add the numbers in the middle column. We get _____

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the following magic square by supplying the missing numbers:

$2$	$15$	$16$
$9$	$12$
		$7$	$10$
$14$			$17$

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Fill this magic square using all the numbers from $21$ to $29 .$

Question Image

Rule: The total of each side is $75 .$

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Find the values of X and Y respectively, if each number is the sum of the two numbers directly below it.

Question Image

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the following magic square by supplying the missing numbers:

	$9$	$2$
	$5$
$8$

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the following magic square by supplying the missing numbers:

	$18$	$17$	$4$
		$14$	$11$
	$9$	$10$
$19$			$16$

HARD

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Now you fill these stars. Use numbers

1 - 9

and the rule that the numbers on each line add up to

15

https://img-nm.mnimgs.com/img/study_content/content_ck_images/images/105825_q.png

HARD

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Use the given numbers. Fill the boxes so that if you add in any direction the answer should be same.

$10$
	$20$
		$30$

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the following magic square by supplying the missing numbers:

$16$	$2$
	$10$
		$4$

HARD

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Fill this magic square using all the numbers from $46$ to $54$ .

Question Image

Rule: The total of each line is $150$ .

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Look at the given grid

Question Image

Add the numbers on the diagonal. We get $6 + 5 + 4 = 15$

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the magic square given below, so that the sum of the numbers in each row or in each column or along each diagonal is $15$ .

$6$	$1$
	$5$

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square

1	–10	0
–4	–3	–2
–6	4	–7

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

In a magic square each row, column and diagonal have the same sum. Check which of the following is a magic square.

5	–1	–4
–5	–2	7
0	3	–3

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the magic square:

	$14$		$0$
$8$		$6$	$11$
$4$			$7$
	$2$	$1$	$12$

MEDIUM

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

What number should be put in the empty box at the centre so that the total is the same in all directions?

$7$	$2$	$3$
$0$		$8$
$5$	$6$	$1$

EASY

Mathematics>Algebra>Equations and Inequations>Solving Linear Equations in One Variable

Complete the following magic square by supplying the missing numbers.

	$9$	$2$
	$5$
$8$

SUN	MON	TUES	WED	THURS	FRI	SAT
		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

Important Questions on Equations and Inequations

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