NCERT Solutions Class 5 Mathematics Chapter 7 Can you see the pattern

3. Magic Squares
____Do you remember magic triangles? Cone now, let’s make some magic squares.
Q. Fill this square using all the numbers from 46 to 54.
Ans. In this magic square, the sum of each of the row of numbers (across down and diagonally) is always the same. We have to complete the magic squares, remembering that the numbers in each line are equal to 150.
Clearly:
In 3 rd row: The required number = 150 - 52 - 47 = 150 - 99 = 51
In 3 rd column: The required number = 150 - 49 - 47 = 150 - 96 = 54
In 2 nd row: The required number = 150 - 46 - 54 = 150 - 100 = 50
In 2 nd column: The required number = 150 - 50 - 52 = 150 - 102 = 188
In 1 st row: The required number = 150 - 18 - 49 = 150 - 97 = 53
Therefore, the complete magic square is

Q. Fill this square suing all the numbers from 21 to 29.
Rule: The total of each side is 75.
Ans. Let us fix 26 on the top most left hand side box.
Taking the diagonal of the square, we have
26 + 25 = 51 and 75 - 51 = 24
Therefore, put 24 at the end of this diagonal.
Fix 22 on the top most - right side box.
Taking the diagonal in which 22 lies, we have
22 + 25 = 47 and 75 - 47 = 28
Therefore, put 28 at the end of this diagonal.
Clearly,
In 1 st row: The required number = 75 - (26 + 22) = 75 - 48 = 27
In 1 st column: The required number = 75 - (26 + 28) = 75 - 54 = 21
In 2 nd row: The required number = 75 - (21 + 25) = 75 - 46 = 29
In 2 nd column: The required number = 75 - (28 + 24) = 75 - 52 = 27
Therefore, the complete magic square is as shown below:

3. Fill in the blank spaces in the same way.
(a) 14 +…..+……= 34 + 24 + 20
(b) ……+ 42 + ……= 65 +…. + 80
(c) 200 + 300 + ….. = ….. + 400 + …….
(d) ….. + ….. + ….. = ….. + ….. + …….
Ans.
(a) 14 + 20 + 34 = 34 + 14 +20
(b) 80 + 42 + 65 = 65 + 42 + 80
(c) 200 + 300 + 400 = 300 + 400 + 200
(d) 34 + 29 +47 = 47 + 34 +29

4. Now you try and change these numbers into special numbers:
(a) 28 (b) 132 (c) 273
Ans. (a)

5. Choose any 3 x 3 box from a calendar and find the total in the same way.
Play this game with your family.
Ans. Let us mark a 3 3 box (9 dates) on the calendar and see some magic.

Take the smallest number: 2
Add 8 to it: +8
10
Multiply it by 9 x 9
Total 90

6. Take any number. Now multiply it by 2, 3, …… at every step. Also add 3 to it at each step. Look at the difference in the answer. Is it the same at every step?
12 2 + 3 = 27
12 3 + 3 = 39
12 4 + 3 = 51
12 5 + 3 = 63

Ans. Filling in the blank boxes, we have
12 6 + 3 = 75
12 7 + 3 = 87
12 8 + 3 = 99
12 9 + 3 = 111

7. Look at the numbers below. Look for the pattern. Can you take it forward?
(9 – 1) ÷ 8 = 1
(98 – 2) ÷ 8 = 12
(987 – 3) ÷ 8 = 123
(9876 – 4) ÷ 8 = ____
(98765 – 5) ÷ 8 = ____
( ____–__ ) ÷ 8 = ____
( ____–__ ) ÷ 8 = ____
Ans. Yes, the given pattern can be taken forward as under:
(9 – 1) ÷ 8 = 1
(98 – 2) ÷ 8 = 12
(987 – 3) ÷ 8 = 123
(9876 – 4) ÷ 8 = 1234
(98765 – 5) ÷ 8 = 12345
(987654 – 6) ÷ 8 = 123456
(9876543 – 7) ÷8 = 1234567

8. Smart Adding
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + .. + .. + .. + .. + .. + .. + .. + 20 = 155
21 + .. + .. + .. + .. + .. + .. + .. + .. + 30 = …
31 + .. + .. + .. + .. + .. + .. + .. + .. + 40 = …
41 + .. + .. + .. + .. + .. + .. + .. + .. + 50 = …
51 + .. + .. + .. + .. + .. + .. + .. + .. + 60 = 555
61 + .. + .. + .. + .. + .. + .. + .. + .. + 70 = …
Ans. 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55
11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 155
21 + 22 + 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = 255
31 + 32 + 33 + 34 + 35 + 36 + 37 + 38 + 39 + 40 = 355
41 + 42 + 43 + 44 + 45 + 46 + 47 + 48 + 49 + 50 = 455
51 + 52 + 53 + 54 + 55 + 56 + 57 + 58 + 59 + 60 = 555
61 + 62 + 63 + 64 + 65 + 66 + 67 + 68 + 69 + 70 = 655

9. Take the first two odd numbers, now add the, see what you get.
Now, at every step, add the next odd number.
1 + 3 = 4 = 2 x 2
1 + 3 + 5 = 9 = 3 x 3
1 + 3 + 5 + 7 = 16 = 4 x 4

How far can you go on?
Ans. Let us complete it.
1 + 3 + 5 + 7 +9 = 25 = 5 5
1 + 3 + 5 + 7 + 9 + 11 = 36 = 6 6
1 + 3 + 5 + 7 + 9 + 11 + 13 = 49 = 7 7

10. Secret Numbers
Banno and binod were playing a guessing game by writing clues about a secret number. Each tried by writing clues about a secret number. Each tried to guess the other’s secret number from the clues. Can you guess their secret numbers?

(a) It is larger than half of 100.
Ans. (a) It is larger than half of 100 means > 50.

(b) It is more than 6 tens and less than 7 tens.
Ans. (b) It is more than 6 tens and less than 7 tens it lies between 60 and 70.

(c) The tens digit is one more than he one’s digit.
Ans. (c) The tens digit is one more than one’s digit is 6-5 =5.

(d) Together the digits have a sum of 11.
Ans. (d) Together the digits have the sum of 11, so the number is 65.

11. Write a set of clues for a secret number of your own. Then give it to a friend to guess your secret answer.
Ans. A set of clues to find secret numbers are:
____ It is larger than half of 100.
It is more than 7 tens and less than 8 tens.
The tens digit is one less than the one’s digit.
Together the digits have a sum of 15.

12. (a) Ask your friend-Write down his age. Add 5 to it. Multiply the sum by 2.
Subtract 10 from it. Next divide it by 2. What do you get?
Ans. (a) Age: 7
Add 5 to it: 7 + 5 = 12
Multiply the sum by 2 = 12 x 2 = 24
Subtract 10 from it = 24 - 10 = 14
Divide it by 2 =14/2 = 7

Ans.
(b) Take a number as 5(say)
Double it 5 x 2 = 10
Multiply by 5 = 10 x 5 = 50
Divide your answer by 10 = 50 ÷ 10 = 5
Thus, we got the supposed answer.

(c) Look at this pattern of number and take it forward.
1 = 1 x 1
121 = 11 x 11
12321 = 111 x 111
1234321 = ?
Ans. (c) Taking the pattern forward, we have
1234321 = 1111 x 1111.

 

Question. Look at the pattern of numbers on this caterpillar. Which of the following numbers will be in this pattern?

(a) 1800
(b) 1660
(c) 1760
(d) 1640

Answer : B

Question. How many times would I be writing the digit 2 if I wrote down ALL THE ODD NUMBERS from 300 to 900 once?
(a) 70
(b) 30
(c) 0
(d) 10

Answer : B

Question. The three balloons shown here have to be coloured in such a way that each balloon is of a DIFFERENT colour. In how many different ways can you colour the 3 balloons if you have only 3 colours - blue, red and yellow?

(a) 6
(b) 3
(c) 2
(d) 1

Answer : A

Question. See the pattern of shapes below: What are the next three figures in the pattern?   

Answer : A

Question. Starting with 48, I keep subtracting 3 till I get 3. How many times did I subtract?
(a) 12
(b) 13
(c) 15
(d) 16

Answer : C

Question. According to the pattern followed by the numbers in the first 3 boxes below, what number should come in the empty box?  

(a) 30
(b) 35
(c) 36
(d) 42

Answer : D

Question. When people hold hands to form 'human chains', their arms form 'V's like this:   How many people would be needed to form a human chain like this so that 23 'V's are formed?

(a) 46
(b) 24
(c) 23
(d) 22

Answer : B

Question. Hema was born on 29th February, 1984. In which of these years could she have celebrated her birthday on the correct date?
(a) 1990
(b) 1992
(c) 1994
(d) All

Answer : B

Question. The three T-shirts hanging on the line below belong to Keya, Lata and Meera - but not in that order. The letter on a T-shirt does  NOT match the first letter of the name of the girl who owns it. Also, the T-shirt hanging in the middle is Meera's . Which T-shirt belongs  to whom?

(a) K- Keya's, L - Lata's, M- Meera's
(b) K- Lata's, L - Meera's, M- Keya's
(c) K- Meera's, L - Keya's, M- Lata's
(d) K- Keya's, L - Meera's, M- Lata's

Answer : B

Question. Shireen starts from 100 and writes a series of numbers in which EACH NUMBER IS 4 MORE THAN THE NUMBER AFTER IT.
Shireen's series will be
(a) 100, 104, 108,112, .......
(b) 100, 104,100, 104, .......
(c) 100, 96, 92,88, ........
(d) 100, 400, 800, 1200, .......

Answer : C

Question. The 'cells' in the given  figure  are numbered from 1 onwards in the order shown. If the same order is continued until all cells are filled, the number that will come in place of X is: 

(a) 24
(b) 25
(c) 26
(d) 27

Answer : B

Question. Which is the smallest number of four digits in which EACH DIGIT IS SMALLER THAN the digit immediately to its right?
(a) 1000
(b) 1023
(c) 1234
(d) 4321

Answer : C

Question. Nancy and Radha are playing noughts and crosses. Given figure shows where the game stands right now. (The crosses are Radha's.)
In how many different ways could Radha place the next cross in one of the five empty spaces to MAKE SURE that she is the winner?

(a) 1
(b) 2
(c) 3
(d) 0, no matter where she puts it, she cannot be sure of winning

Answer : B

Question. Bulbul thinks of a 3-digit number, decreases it by 50 and then increases it by 35. The resulting number will be
(a) 15 less than Bulbul's original number.
(b) 85 more than Bulbul's original number.
(c) 25 more than Bulbul's original number.
(d) 25 less than Bulbul's original number.

Answer : A

Question. The given pattern of triangles and circles is growing in a certain way. Observe it carefully. What will the TENTH figure in the pattern look like?

Answer : A

Question. You start from 45 on this number line, and jump back 3 steps, 2 steps, 3 steps, 2 steps and so on. In how many jumps will you reach 0?

(a) 5
(b) 18
(c) 25
(d) 235

Answer : B

Question. 3 STRAIGHT roads can form a maximum of 3 crossings as shown in this figure: What is the maximum number of crossings that can be formed by 4 STRAIGHT roads, given that only two roads meet at a crossing?

(a) 4
(b) 5
(c) 6
(d) 8

Answer : C

Question. Bulbul thinks of a 3-digit number, decreases it by 50 and then increases it by 35. The resulting number will be
(a) 15 less than Bulbul's original number.
(b) 85 more than Bulbul's original number.
(c) 25 more than Bulbul's original number.
(d) 25 less than Bulbul's original number.

Answer : A

Question. Aman and Aliya are playing a game in which they have to form words by placing letters on a board that has white and shaded squares. Read how points are scored in this game to answer the question. 
Aliya has to place the word  on this line:How should she place it to score the maximum possible points?

Answer : D

Question. Which number should come in place of ............. ?
1/7 + 2/7 + ........... /7 = 1(3/7)
(a) 1
(b) 2
(c) 3
(d) 7

Answer : D

Question. See the given pattern ; The number that should come in the empty box is

(a) 2000
(b) 2500
(c) 2520
(d) 2200

Answer : D

Question. See the paper wheel shown in the given image. Which of the pieces below is a part cut out from this paper wheel?

Answer : D

Question. If we start from 1000 and count in thirties, which of the following numbers will be in the resulting series?
(a) 1300
(b) 1200
(c) 1100
(d) 1050

Answer : A

Question. If October 1 of some year is a Sunday, then August 1 of that year would have been a
(a) Sunday
(b) Monday
(c) Tuesday
(d) Wednesday.

Answer : C

Question. Ajita makes a pattern as shown below by drawing dots in rows of boxes. Study the pattern and answer the question
What would the next row look like if this pattern is continued?

Answer : A

Question. What time is this clock showing?

(a) 7:55
(b) 8:05
(c) 8:55
(d) 11:40

Answer : A

Question. How many triangles of any size are there in the figure?

(a) 4
(b) 5
(c) 8
(d) 10

Answer : D

Question. Three regular dice with 1 to 6 dots on their faces are arranged as shown:
What is the sum of the number of dots on all the HIDDEN faces of the dice in this arrangement?

(a) 24
(b) 39
(c) 44
(d) 63

Answer : B

Question. See the given pattern of shapes :
What are the next three figures in the pattern?

Answer : A

Question. Which of the following pairs of shapes when joined together (by placing them edge to edge) can form a SQUARE? (The shapes can be turned if required)

Answer : B

Question. Look at the game below. You have to enter the maze at the place marked 'IN' and go through the boxes collecting as many points as possible before coming out at the place marked 'OUT'. You CANNOT enter the same box twice .What is the greatest possible total that your points could add up to in this game?

(a) 14
(b) 22
(c) 36
(d) 45

Answer : C

Question. Ajita makes a pattern as shown below by drawing dots in rows of boxes. Study the pattern and answer the question

(a) 10
(b) 5
(c) 2
(d) 1

Answer : B

Question. Abbas went for drama class every Thursday during his summer holidays which started on 15 April, Sunday and ended on 30 June.  How many drama classes did he go for?
(a) 15
(b) 11
(c) 10
(d) 6

Answer : B

Question. Dinu's teacher gives him the following number cards:  She asks him to pick any two cards from these and put them next to each other to form a number between 30 and 50.  Which two cards should he choose?
6        2        1        5
(a) 2 and 5
(b) 5 and 1
(c) 2 and 6
(d) It is not possible to make such a number.

Answer : D

A desk calendar consists of  6 sheets , with a different month  on EACH  side  of the sheet. The first 6 months appear in order as the sheets are turned over one by one. The months in the second half of the year are printed on the flip side of these sheets in order, but starting from BACK to FRONT. That is, December appears on the flip side of the first month, January. Which month will be on the flip side of the page showing April?

 

(a) May
(b) September
(c) October
(d) August

Answer : B

Question. What is 19 - 18 + 17 - 16 + 15 - 14 +13 - 12?
(a) 124
(b) 48
(c) 4
(d) 1

Answer : C