Point B is above the line x = y, so for that point y > x. When x and y are
both negative, will be greater than 1 if x is less than y. Point D is below
the line x = y, so for that point y < x. Point E, however, is above the line x =
y, so for that point y > x, and > 1.27 . D
If the average of the 5 original scores was 83, then the sum of those 5
scores was 5 × 83 = 415. When each score is increased by 2, the sum goes
up to 425, one-fifth of which is 85. So the new average is 85 and
statement I is true. Statement II, however, is not true because if both the
lowest and highest scores go up by the same amount, the difference
between those scores remains the same. So I is true and II is not, and the
answer is either (A) or (D). What about III? To find the lowest score that
one of the 5 students can get, imagine that after the increase the other 4
students all get perfect 100s. Four 100s add up to 400, which leaves 425 –
400 = 25 for the fifth and lowest possible score for the 5 students. III is
true.
28 . C
You could do this one by picking numbers, but for any set of numbers
you might pick, more than one of the answer choices will be true. You
will therefore have to pick at least two sets of numbers to find the correct
answer. The statement that must be true is the one that holds for all a, b,
c, and d that fit the given conditions. (A) is tempting: You might think that
the product of the larger a and c will be greater than the product of the
smaller b and d, and it is if all you pick are positive integers. (A) doesn’t
hold when you consider negatives, however. But (C) holds for all possible
values of a, b, c, and d. The sum of two larger quantities is greater than
the sum of two smaller quantities.