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Practice each question, then open the answer or worked solution.
Smart Adding
Solution:-
(ii) Did you notice some pattern in the answers?
Solution:-
Yes, I found that the difference in the answer is the same, i.e., 100 at every step.
Fun with Odd Numbers
Take the first two odd numbers. Now, add them, and see what you get. Now, at every step, add the next odd number. How far can you go on?
Solution:-
We can’t predict because there are infinite numbers.
Secret Numbers
Banno and Binod were playing a guessing game 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?
(i) It is larger than half of 100
It is more than 6 tens and less than 7 tens
The tens digit is one more than the ones digit
Together, the digits have a sum of 11
Solution:-
It is larger than half of 100, i.e. number > 100
It is more than 6 tens and less than 7 tens, so the number lies between 70 and 60
The tens digit is one more than the ones digit = 6 – 1 = 5
Together, the digits have a sum of 11 = 6 + 5 = 11
Therefore, the number is 65
(ii) It is smaller than half of 100
It is more than 4 tens and less than 5 tens
The tens digit is two more than the ones digit
Together, the digits have a sum of 6
Solution:-
It is smaller than half of 100 = number > 100
It is more than 4 tens and less than 5 tens = number lies between 40 and 50
The tens digit is two more than the ones digit = 4 – 2 = 2
Together, the digits have a sum of 6 = 4 + 2 = 6
Therefore, the number is 42
Number Surprises
a) Ask your friend to write — W down your age. Add 5 to it. Multiply the sum by 2. Subtract 10 from it. Next, divide it by 2. What do you get? Is your friend surprised?
Solution:-
Let us assume the age is 11.
Then, adding 5 to it, we get = 16
Multiply by 2, we get = 32
Subtract from 10, we get = 22
Divided by 2, we get = 11
Yes, my friend was really surprised.
Solution:-
Solution:-
Solution:-
1 = 1 × 1
121 = 11 × 11
12321 = 111 × 111
1234321 = 1111 × 1111
123454321 = 11111 × 11111
12345654321 = 111111 × 111111
1234567654321 = 1111111 × 1111111
1234567654321 = 1111111 × 1111111
1234567654321 = 1111111 × 1111111