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Insect predators usually keep the number of aphids in crop fields low. However, sometimes the aphid population explodes in size, causing major damage. Much explosions happen when unusually cold weather keeps the number of aphids low in the spring. One possible explanation is that, with fewer aphids to feed on, the predator population also drop, and in summer when the aphid population starts to grow there are not enough predators to keep it in check.
Which of the following, if true, would most strengthen the explanations given for aphid population explosions?
Although traditionally artists have rightly been seen as the most _____ audience for the work of their colleagues, today taste is also created by critics and curators and occasionally by collectors.

Quantity A

$$(-87)^{8}$$

Quantity B

$$(\frac{1}{87})^{-8}$$


Which of the following could be the value of x to make sure that $$x^{3}$$-x is divisible by 10?

Indicate all such values.
The lengths of the two sides of the triangle are 1 and $$\sqrt{2}$$ respectively. What is the range of the length of the third side?
If a=$$(-\frac{1}{37})^{12}$$, which of the following equals to $$37^{-12}$$?

Quantity A

$$\frac{111}{1,111}$$

Quantity B

$$\frac{1,111}{11,111}$$


Three coins-two 10-cent coins and one 5-cent coin--are to be flipped simultaneously. For each of the three coins, the probability that the coin will land heads up is $$\frac{1}{2}$$. What is the probability that the total value of the coins that will land heads up is 15 cents?
Give your answer as a decimal.
Which of the following could be a factor of $$\frac{9!}{(6!*3!)}$$?

Indicate all such numbers.
What`s the units digit of the positive difference between $$32^{19}$$ and 32?
If a, b, and c are positive integers such that $$\frac{a}{c}$$=0.075, and $$\frac{b}{c}$$=0.09, What is the least possible value of c?
The speed of light is 3*$$10^{8}$$ meters per second, rounded to the nearest $$10^{8}$$ meters per second. A "light-hour" is the distance that light travels in an hour.

Quantity A

The number of kilometers in a light-hour

Quantity B

$$10^{10}$$




Of the following, which graph best represents a shaded region in which every point (x, y) satisfies the inequality y ≤ |x|?


The table shows the means and ranges of two data sets, X and Y, each containing the same number of measurements.

Quantity A

The standard deviation of data set X

Quantity B

The standard deviation of data set Y


Quantity A

$$\frac{(5!+6!)}{(6!+7!)}$$

Quantity B

$$\frac{1}{6}$$


Three numbers are to be selected at random and without replacement from the five numbers 4, 5, 7, 8 and 11. What is the probability that the three numbers selected could be the lengths of the sides of a triangle?

Quantity A

x

Quantity B

112


$$l_{1}$$∥$$l_{2}$$



Quantity A

m

Quantity B

130


Let x and y be positive integers such that when y is divided by x, the remainder is 4, and when y+10 is divided by x, the remainder is 2. Which of the following must be an integer?

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