Answer:
1. Answer: (a) 10 × 5 + 2
Explanation: 52 = 50+2
=(10×5)+(2×1)
=10×5+2
2. Answer: (a) 10 × 3 + 9
Explanation: 39 = 30+9
=(10×3)+(9×1)
=10×3+9
3. Answer: (b) 333
Explanation: The general form of any three-digit number is, abc =a×100+b×10+c
Here, 3×100+3×10+3
=300+30+3
=333
4. Answer: (a) 718
Explanation:100 x 7 + 10 x 1 + 8
= 700 + 10 + 8
= 718
5. Answer: (d) 50
Explanation: In 19, 27, 99, one’s digit is not divisible by 2.
6. Answer: (c) 500
Explanation: In 500, one’s digit is divisible by 2.
7. Answer: (b) 37
Explanation: In 37, one’s digit is not divisible by 2.
8. Answer: (a) 0 or 3 or 6 or 9
Explanation: 1 + 0 + 8 = 9
1 + 3 + 8 = 12;
9, 12, 15, 18 each is divisible by 3
9. Answer: (b) 3
Explanation: 9 + 2 + 7 = 18
9 + 5 + 7 = 21;
9 + 8 + 7 = 24.
each of 18, 21 and 24 is divisible by 3
10. Answer: (a) 1
Explanation: Since the number 21y5 is a multiple of 9.
So, the sum of its digits 2+1+y+5=8+y is a multiple of 9.
∴(8+y) is either 0 or 9 or 18 or ...
Since y is a digit, so (8+y) must be equal to 9.
i.e., 8+y=9
⇒ y=9−8
=1
11. Answer: (d) 457
Explanation: 4 + 5 + 7 = 16 is not divisible by 3.
12. Answer: (b) 237
Explanation: 2 + 3 + 7 = 12 is divisible by 3.
13. Answer: (a) 234
Explanation: 2 + 3 + 4 = 9 is divisible by 9.
14. Answer: (c) 122
Explanation: To be completely divisible by 5, the number should have 0 or 5 at its one’s digit place.
15. Answer: (c) 110
Explanation: If any number has 0 at its one’s digit place, then it is divisible by 10.
Hence, 110/10 = 11
16. Answer: (b) 3
Explanation: A number is divisible by 9 if the sum of the digits of the number is divisible by 9.
Sum of digits of given number =2+4+x
= 6+x
Let us say that (x+6) is a multiple of 9,
⟹ x + 6 = 9
x=3
17. Answer: (b) 3
Explanation: 2146587 = 2 + 1 + 4 + 6 + 5 + 8 + 7 = 33
Since 33 is divisible by 3, hence 2146587 is divisible by 3
18. Answer: (b) 90
Explanation: At the unit place of 90 we have 0. Hence, as per the divisibility rule for 5, 90 is divisible by 5.
19. Answer: (a) 1
Explanation: Given, 80x is divisible by 9.
Thus, sum of digits of 80x will also be divisible by 9.
8 + 0 + x is divisible by 9 only if, x = 1
8 + 0 + 1
= 9
20. Answer: (b) Either 3 or 8
Explanation: N divided by 5 leaves a remainder of 3
→ We know, A number divisible by 5 has Unit Digit 0 or 5.
⇒ Unit Digit of N=0+3=3 or 5+3=8
21. Answer: (b) 79968
Explanation: Divisibility rule of 12: Number divisible by both 3 and 4.
⇒ Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3.
⇒ Divisibility rule of 4: A number is divisible by 4 if the last two digits are a multiple of 4.
⇒ 123452=1+2+3+4+5+2=17
⇒ 78968=7+8+9+6+8=28
⇒ 123452 and 78968 are not divisible by 3 so it's not divisible by 12
⇒ 79998=7+9+9+9+8=42, it is divisible by 3.
⇒ Last two digits 98 is not divisible by 4
∴ 79998 is not divisible by 12.
⇒ 79968=7+9+9+6+8=39, it is divisible by 3
⇒ Last two digits 68 are divisible by 4.
∴ 79968 is divisible by 12.
22. Answer: (c) 6
Explanation: Factors of 477=1,3,9,53,159,477
The number 477 is divisible by each of the following numbers except 6.
23. Answer: (b) 3
Explanation: If N/5 gives remainder 3, then N = 5a+3 for a natural number a.For a being even, 5a has unit place 0 and 3 added gives unit place 3 For a being odd, 5a has unit place 5 and 3 added gives unit place 8. So, it's either 3 or 8.
24. Answer: (a) True
Explanation: A number divisible by 8 will be divisible by 4 as 4 is a factor of 8 (Example: 24 is divisible by both 4 and 8), but vice versa may not be true (Example: 20 is divisible by 4 but not by 8). So, the answer is True.
25. Answer: (d) 91
Explanation: 91 is divisible by 7 and 13. So, it is not a prime number.
Rest all the given numbers are prime numbers since they don't have any factors other than 1 and themselves.
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