Find all pairs of consecutive even positive integers, both of which are larger than 5 such that their sum is less than 23,

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: Since x and y are odd positive integers, we have x = 2m + 1 and y = 2n + 1 => x2 + y2 = (2m + 1)2 + (2n +...

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...

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 <...

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

(b) Quicker Approach: The unit's digit of the number 16128 is 8, From the given answer choices, 126 × 128 = 16128 Required larger number = 128

 (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...