Three consecutive integers add up to 51. What are these integers?

Solution: Let the two consecutive odd positive integers be x and x + 2. x < 10, x + 2 < 10, x + (x + 2) > 11 x + 2 <...

Solution: Let the two consecutive even positive integers be x and x + 2. x > 5, x + 2 > 5, x + (x + 2) < 23 x > 5, x...

Solution: True. Justification: At least one out of every three consecutive positive integers is divisible by 2. Therefore, The product of three consecutive positive integers is divisible by 2. At least one out of every...

Solution: Let the three consecutive positive integers be n, n + 1 and n + 2, where n is any integer. By Euclid’s division lemma, we have a = bq + r; 0 ≤...

Let the three consecutive integers be x, x+1and x+2. According to the question, 2x+3(x+1)+4(x+2)=74 => 2x+3x+3+4x+8=74 => 9x+11=74 =>9x+11-11=74-11 [Subtracting 11fromboth sides] => 9x=63 => 9x/9=63/9 [Dividing both sides by9] => x=7 Hence first integer = 7, second integer=7...

True, because n(n+1)(n+2) will always be divisible by 6, as least one of the factors will be divisible by 2 and at one of the factors will be divisible by...

(b) A + A + 2 + A + 4 + A + 6 = 180 4A + 12 = 180 A = 42. Next four consecutive even numbers are 50 + 52 +...

(e) Let the three consecutive integers be x, x + 1 and x + 2  According to the question,  x + x + 1 + x + 2 = 39  or, 3x +...

 (a) According to the question,  x + x + 2 + x + 4 + x + 6 + x + 8 = 140  or, 5x + 20 = 140  or, 5x =...

(d) Lowest number of set A = 280/5 – 4 = 52  Lowest number of other set = 52 × 2 – 71 = 33   Required sum = 33 + 34...