Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74.

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 ≤...

Correct answer is option (C) 0 ≤ r < b

Let the three consecutive integers bex, x+1and x+2. According to the question, x+x+1+x+2 = 51 => 3x+3=51 => 3x+3-3=51-3 [Subtracting 3 from both sides] => 3x=48 => 3x/3 = 48/3 [Dividing both sides by 3] X=16 Hence, first...

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...

Let x be the smaller of the two consecutive odd positive integers. Then, the other integer is x + 2. Since both the integers are smaller than 10, x + 2 <...

Let x be the smaller of the two consecutive even positive integers. Then, the other integer is x + 2.  Since both the integers are larger than 5,  x > 5 ..........................

(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 +...