The sum of four consecutive even numbers. A, B, C, and D is 180. What is the sum of the set of next four consecutive even numbers ?

R: set of real numbers Q: set of rational numbers Therefore, R – Q is a set of irrational numbers.

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 ..........................

Let the four consecutive numbers in AP be (a - 3d), (a - d), (a + d) and (a + 3d) So, according to the question. a-3d + a - d +...

(b) According to the question, x + x + 2 + x + 4 + x + 6 = 228 4x + 12 = 228 4x = 228 – 12 = 216 x =...

(c) From the given alternatives, 112 × 114 = 12768 Larger number = 114

(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) Let the smaller number be x  x (x + 2) = 5358  x2 + 2x – 5328 = 0 (x + 74) (x – 42) = 0  x = 72 

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

(d) Let the two numbers be x and (x + 2).  Then, x2 + (x + 2)2 = 6500  x2 + x2 + 4x + 4 = 6500  2x2 + 4x – 6496...