Q31Written answer
If A × 3 = 1A, then A = ______.
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Worked solution
Solution: 5
Explanation:
Using the place values of the numbers, we can write it as:
10 + A = 3A
10 = 2A
A = 5
NCERT Exemplar · Class 8 · Maths
Chapter 13: Playing with Numbers
Practice each question, then open the answer or worked solution.
Questions
45 questionsQ32Written answer
If B × B = AB, then either A = 2, B = 5 or A = ______, B = ______.
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Worked solution
Solution: A= 1 and B= 6
Explanation:
From the given equations, B can take the values between 4 and 9
When you take B = 4, 4×4 = 16
Then, A=1 and B = 6
Q33Written answer
If the digit 1 is placed after a 2-digit number whose tens is t and one’s digit is u, the new number is ______.
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Worked solution
Solution: tu1
Explanation:
Assume that, the number is initially 10t+u or tu, but after adding 1 to the unit place, tu gets shifted to the one unit higher. It means that 100t+10u+1 or tu1.
State whether the statements given in questions 34 to 44 are true (T) or false (F):
Q34Written answer
A two-digit number ab is always divisible by 2 if b is an even number.
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Worked solution
Solution: True
Explanation:
If a number with two digits and the number in the unit place is even, then the number is said to be an even number and it is divisible by 2 (using the divisibility test of 2)
Q35Written answer
A three-digit number abc is divisible by 5 if c is an even number.
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Worked solution
Solution: False
Explanation:
If a number with three digits and if the unit digit is an even number, then the number is said to be an even number. A number is divisible by 5, only if the unit digit is either 0 or 5 (divisibility test of 5)
Q36Written answer
A four-digit number abcd is divisible by 4 if ab is divisible by 4.
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Worked solution
Solution: False
Explanation:
Assume that 2463 is a four-digit number which is equal to abcd.
We know that 24 is divisible by 4, but 2463 is not divisible by 4.
Q37Written answer
A three-digit number abc is divisible by 6 if c is an even number and
a + b + c is a multiple of 3.
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Worked solution
Solution: True
Explanation:
In case, if a number is divisible by 6, it is also divisible by 2 and 3.
If c is an even number, then the sum of digits is divisible by 3.
Q38Written answer
Number of the form 3N + 2 will leave remainder 2 when divided by 3.
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Worked solution
Solution: True
Explanation:
The given number is of the form 3N+2
It can be written as (multiples of 3) + 2
When the given number 3N+2 is divided by 3, we will get the remainder 2. For example, take 11.
11 can be written as (3×3) + 2
Q39Written answer
Number 7N + 1 will leave remainder 1, when divided by 7.
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Worked solution
Solution: True
Explanation:
The given number is of the form 7N+1
It can be written as (multiples of 7) + 1
When the given number 7N+1 is divided by 7, we will get the remainder 1. For example, take 22.
22 can be written as (7×3) + 1
Q40Written answer
If a number a is divisible by b, then it must be divisible by each factor of b.
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Worked solution
Solution: True
Explanation:
Let a= 27, and b = 9
Here, when 27 is divisible by 9, we will get 3
Now, consider the factor of 9 = 1, 3 and 9
In this case, 27 is divisible by the factors such as 1 and 3. Hence the given statement is true.