1. D
Try x = y = 2. Then Column A = yx
= 2² = 4. Column B = yx + 1 = 2³ = 8,
making Column B greater. But if x = 2 and y = 1/2;,
Column A = (1/2)² = 1/4 and Column B = (1/2)³ = 1/8. In this
case, Column A is greater than Column B, so the answer is D.
2. A
The variable m can be any integer that ends in either a 2
or a 7; n can be any integer that ends in either a 1 or a
6. Plugging in will show that in any case, m + n
will leave a remainder of 3 when divided by 5, and mn will
leave a remainder of 2 when divided by 5, so Column A is
greater.
3. A
You can solve for b using the second equation: b -
3 = 2, so b = 5. Plug in 5 for b in the first
equation and solve for a: 2a + 5 = 17, 2a =
12, a = 6. So Column A is greater than Column B, and
choice (A) is correct.
4. B
First figure out what the simplified form of Column B is. Since
x³ is squared, you must multiply the exponents, leaving
you with x6. Since x is greater than 1,
the number gets larger as it is raised to higher powers. Since
x6 has a larger exponent than
x5, and since x is greater than 1,
Column B must be greater.
5. C
This is a sequence consisting of a cycle of 4 numbers that
repeats forever. The first term is 1, the second term is 2, the
third term is -3, and the fourth term is -4. When it repeats the
first time, the fifth term is 1, the sixth term is 2, the seventh
term is -3, and the eighth term is -4. It will repeat again, and
the ninth term will be 1, the tenth term will be 2, the eleventh
term will be -3, and the twelfth term will be -4. Notice that the
number -4 is so far the fourth, eighth, and twelfth term. Since
it is the fourth term in a repeating cycle of 4 numbers, its
position will always be a multiple of 4. So -4 will be the
fourth, eighth, twelfth, sixteenth, twentieth, etc., terms in the
sequence. This means that -4 will be the 48th term in the
sequence, since 48 is a multiple of 4. If -4 is the 48th term,
then the 49th term is 1, the 50th term is 2, the 51st term is -3,
and the 52nd term is -4. So the sum of the 49th and 51st terms is
the sum of 1 and -3, or 1-3, or -2. The sum of the 50th and 52nd
terms is the sum of 2 and -4, or 2-4, or -2, so the 2 columns are
the same, and the correct answer is C.
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