You can solve the question in this way also: Call the space furthest to the left space I; the
space adjacent to the space furthest to the left space II; the space in the center space III; the
space adjacent to the space furthest to the right space IV; and the space furthest to the right
space V. You can place any of the 12 letters in space I. For each of these 12 letters in space I,
you can place 12 − 1 = 11 letters in space II. For any pair of letters in spaces I and II, you can
place 12 − 2 = 10 letters in space III. For any triplet of letters in spaces I, II, and III, you can
place 9 letters in space IV. For any set of 4 letters in spaces I, II, III, and IV, you can place 8
letters in space V. The number of possible five-letter codes is (12)(11)(10)(9)(8).This can be
rewritten as which equals matching (C).48 . C
Consider option I. The sum of two negative integers is a negative integer. So option I will be
part of the correct answer; eliminate (A) and (D).Consider option II. The sum of two rational numbers is a rational number; eliminate (B).Consider option III. The sum of two irrational numbers is not necessarily an irrational
number. For example, the sum of the irrational number and the irrational number
is 3, which is a rational number. Option III will not be part of the correct answer. (C) is
correct.49 . D
Begin by writing the equation in the form . Dividing both sides of the equation
5 x^2 + 24y^2 = 40 by 40 will leave 1 on the right side of the equation, and you have
so Now our equation is in the form Thus, a^2 = 8
and and the two axes will have lengths and . Therefore, the
sum of the axes is