The product of two consecutive odd numbers is 483. What is the sum of these two numbers?
A43
B44
C45
D46
Correct Answer:
B. 44
Explanation:
Let the two consecutive odd numbers be (2n-1) and (2n+1). Their product: (2n-1)(2n+1) = 483. This gives 4n² - 1 = 483, so 4n² = 484, n² = 121, n = 11. The numbers are 21 and 23. Sum = 21 + 23 = 44.
The sum of three consecutive integers is 54. If the smallest of these integers is multiplied by 3 and then 5 is added, what is the result?
A56
B58
C59
D61
Correct Answer:
A. 56
Explanation:
Let three consecutive integers be n, n+1, n+2. Sum: n + (n+1) + (n+2) = 54, so 3n + 3 = 54, 3n = 51, n = 17. The smallest number is 17. Required result: 3(17) + 5 = 51 + 5 = 56.
A four-digit number is formed by repeating a two-digit number (e.g., if the two-digit number is 23, the four-digit number is 2323). This four-digit number is always divisible by which of the following?
A7 only
B11 and 101
C13 only
D17 and 19
Correct Answer:
B. 11 and 101
Explanation:
Let the two-digit number be AB (value = 10A + B). The four-digit number ABAB = 1000A + 100B + 10A + B = 1010A + 101B = 101(10A + B) = 101 × AB. Also, ABAB = 1100A + 11B = 11(100A + B). So it's always divisible by both 11 and 101.
