Question Review – Number System
Detailed breakdown of your past mock questions with AI feedback.
Question 1
What is the smallest number which when divided by 12, 15 and 20 leaves a remainder 5 in each case?
60
65
70
75
Correct Answer & Solution
To find the smallest number, we first need to find the Least Common Multiple (LCM) of 12, 15, and 20. 12 = 2² x 3 15 = 3 x 5 20 = 2² x 5 LCM(12, 15, 20) = 2² x 3 x 5 = 60. Since the number leaves a remainder of 5 in each case, the required number is LCM + remainder. Required number = 60 + 5 = 65.
Question 2
Which one of the following is divisible by 3?
241
612
445
1001
Correct Answer & Solution
A number is divisible by 3 if the sum of its digits is divisible by 3. A) 2 + 4 + 1 = 7 (not divisible by 3) B) 6 + 1 + 2 = 9 (divisible by 3) C) 4 + 4 + 5 = 13 (not divisible by 3) D) 1 + 0 + 0 + 1 = 2 (not divisible by 3) Thus, 612 is divisible by 3.
Question 3
What is the unit digit of 7⁴⁵?
3
5
7
9
Correct Answer & Solution
The cyclicity of the unit digit of 7 is 4. The pattern is 7¹, 7², 7³, 7⁴ → 7, 9, 3, 1. To find the unit digit of 7⁴⁵, we need to find the remainder when 45 is divided by 4. 45 ÷ 4 gives a remainder of 1. So, the unit digit will be the first in the cycle, which is 7.
Question 4
If a number is divided by 5, it leaves a remainder 4. What will be the remainder if the square of the number is divided by 5?
1
2
4
3
Correct Answer & Solution
Let the number be N. According to the question, N = 5k + 4 for some integer k. We need to find the remainder for N² / 5. N² = (5k + 4)² = (5k)² + 2*(5k)*(4) + 4² = 25k² + 40k + 16. Now, divide N² by 5: (25k² + 40k + 16) / 5. 25k² is divisible by 5. 40k is divisible by 5. The remainder is determined by 16 / 5, which is 1.
Question 5
What is the sum of first 10 odd numbers?
100
99
121
81
Correct Answer & Solution
The sum of the first n odd numbers is given by the formula n². Here, n = 10. So, the sum is 10² = 100.