Govt. Exams
Entrance Exams
Prime numbers less than 20: 2, 3, 5, 7, 11, 13, 17, 19. Sum = 2+3+5+7+11+13+17+19 = 77.
2^5 = 2×2×2×2×2 = 32. Therefore, x = 5.
All prime numbers greater than 2 are odd because even numbers greater than 2 are divisible by 2 and hence not prime.
Let the three consecutive odd numbers be (x-2), x, and (x+2). Their sum: (x-2) + x + (x+2) = 51, so 3x = 51, x = 17.
Let the number be x. According to problem: 3x - 4 = 17. Therefore, 3x = 21, x = 7.
Using the formula: HCF × LCM = Product of two numbers. Therefore, 13 × LCM = 2028. LCM = 2028 ÷ 13 = 156.
For divisibility by both 6 and 8, the number must be divisible by LCM(6,8) = 24. Check: 48 ÷ 24 = 2 ✓. Option A is correct.
Using formula for sum of first n natural numbers: S = n(n+1)/2 where n=99. S = 99(100)/2 = 9900/2 = 4950.
Let the integers be x and x+1. Sum = x + (x+1) = 51. 2x + 1 = 51. 2x = 50. x = 25. The larger integer = 26.
Even numbers from 1 to 100: 2, 4, 6, ..., 100. This is an AP with first term 2, last term 100, common difference 2. Number of terms = (100-2)/2 + 1 = 50.
