Example 3: Is p
p/3
-p + x -q + x
Multiplying both sides of p/3
Hence, is sufficient. As to , subtract x from both sides of -p + x
-q + x, which yields -p -q.
Multiplying both sides of this inequality by -1, and recalling that multiplying both sides of an inequality by a negative number reverses the inequality, yields p Hence, is also sufficient. The answer is D.
Example 4: If x is both the cube of an integer and between 2 and 200, what is the value of x?
x is odd.
x is the square of an integer.
Since x is both a cube and between 2 and 200, we are looking at the integers:
which reduce to
8, 27, 64, 125
Since there are two odd integers in this set, is not sufficient to uniquely determine the value of x. This eliminates choices A and D.
Next, there is only one perfect square, 64, in the set. Hence, is suffi
ABC is the base word.
If C immediately follows B, then C can be moved to the front of the codeword to generate another word.
From , we cannot determine whether CAB is a code word since gives no rule for generating another word from the base word. This eliminates A and D
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