Applying Algebra in Calendars

Q. Find four consecutive odd numbers with a sum of 80. How do you do that?

Q. Find the value of A, B, C, D, E, F, G, H and I for which (ABC)×(DEF)=GHI
(A) (6, 5, 7, 8, 2, 6, 1, 8, 4)
(B) (7, 9, 5, 2, 6, 4, 8, 4, 0)
(C) (4, 6, 7, 8, 5, 7, 0, 8, 9)
(D) (1, 0, 3, 7, 8, 4, 2, 1, 0)
(E) None of these

Q.

Leah has $28$ more marbles than Dan. $\frac{1}{3}$ of Leah’s marbles is equal to $\frac{4}{5}$ of Dan’s marbles. Find the number of marbles that Leah has.

Q.

Take nine numbers forming a square in a calendar and mark the four numbers at the corners. Then the difference between the product of the diagonal pairs is always ____.

1. 21

2. 28

3. 15

4. 14

Q.

Consider this calendar. Select the numbers 4, 5, 6, 11, 12, 13, 18, 19, 20 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.

1. 3

2. 7

3. 9

4. 8

Q.

Consider this calendar. Select the numbers 1, 2, 3, 8, 9, 10, 15, 16, 17 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.

1. 8

2. 5

3. 3

4. 9

Q.

Take nine numbers forming a square in a calendar and mark the four numbers at the corners. Then the difference between the squares of the diagonal pairs is always ____.

1. 24

2. 28

3. 56

4. 12

Q. The sum of two consecutive odd numbers is 68. Find the numbers.

Q.

Below is a copy of a calendar for July 2015 .

Statement: The sum of any three dates in a row is always a multiple of 3.

(Do it algebraically and check if the given statement is true or false)

1. True

2. False

Q.

Below is a copy of a calendar for July 2015.

Statement: The sum of any two adjacent dates is always an even number. (Example of adjacent dates: 1 and 8, 22 and 29 etc)

(Do it algebraically and check if the given statement is true or false)

1. False

2. True

Q.

Below is a copy of a calendar of July 2015

Then the sum of three dates in a diagonal is always a multiple of ____.

(Do it algebraically and choose the right answer)

1. 7

2. 5

3. 3

4. 2

Q.

Write the sum of two consecutive even numbers, the greater of which is equal to $2n$.

Q.

Nine numbers are taken from calender as shown

14 15 16

21 22 23

28 29 30

If the sum of all given numbers is S, then the value of $\frac{S}{9}$ equals to ____.

1. 22
2. 23
3. 29
4. 21

Q.

Question Given:

{x:x belongs to N, x is greater than (>) 29} _ Infinite Set

{x:x belongs to N, x is lesser than (<) 16}_ Finite Set

Draw a Venn Diagram using this information.

Query:

How can we draw a Venn Diagram with an Infinite Set?

Q.

The sum of $3$ consecutive numbers is $27$. Find all the numbers.

Q. 20. Solve for x, y and z. x + xy + xz = -12 y + yz + xy = 30 z + xz + yz = 18

Q.

Below is a copy of a calendar of July 2015

Then the products of the diagonals of any 2 $\times$ 2 square are always ____ apart.

(Do it algebraically and choose the right answer)

1. 4

2. 7

3. 9

4. 11

Q. Consider this calendar. Select the numbers 1, 2, 3, 8, 9, 10, 15, 16, 17 such that they form a square. The sum of the selected numbers of the square, is ____ times the middle number of the square.

1. 9

Q.

Below is a copy of a calendar for July 2015 .

Statement: The sum of any three dates in a row is always a multiple of 3.

(Do it algebraically and check if the given statement is true or false)

Q. If two adjacent sides of a square are represented by the vectors $x\overline{i}+\overline{j}+4\overline{k}$ and $3\overline{i}+y\overline{j}$ then $xy=$

1. $1$
2. $2$
3. $3$
4. $-3$

Q.

An unchanging relation is given by the following star

If using the same unchanging relation, new star is formed an shown, then the value of a & b is equal to

1. 11, 2

2. 2, 11

3. 9, 3

4. 3, 9

Q.

Below is a copy of a calendar for July 2015.

Statement: The sum of any two adjacent dates is always an even number. (Example of adjacent dates: 1 and 8, 22 and 29 etc)

Do it algebraically and check if the given statement is true or false.

Q. Consider the dates of a week as

1

2

3

4

5

6

7

If the sum of these dates is S, then the value of $\frac{S}{7}$ is .

1. 28
2. 7
3. 4
4. 14

Q. The home is 13.5 miles away and you are left with $\$26$. If a cab ride costs $\$1.25$ for the first mile, and $\$2.25$ per mile after the first one, then how much distance will you have to walk for ?

1. 1 mile
2. 1.5 mile
3. 2 mile
4. 2.5 mile

Q.

why does t valu of pie is 22/7 or 3.14

Q.

x-(x-y) - y-(y-x) =?

Q. Draw and explain the polynomial identity: $(x+4{)}^2=x^2+4^2+8x$