If students are fans of both football and basketball, how many students are fans of football but not fans of basketball?

(1) students are basketball fans.

(2) students are football fans.

Is x − 2 an odd number?

(1) x is a prime number

(2) x is two times a positive integer K

What is the sum of x, y, and z?

(1) $x:y:z=3:8:9$

(2) $y-x=20$

In a certain store, the price of a pen is and the price of a notebook is . If pens and notebooks are bought, what is the average price per item of the items purchased?

(1)

(2)

A country's population increased in 2011 and then by in 2012. By what percent did the population increase over those two years?

(1)

(2)

At a city council meeting, one attendee is to be selected at random to be a tiebreaker. What is the probability that the person chosen is retired?

1. One-third of the attendees are retired.
2. Twenty-four of the attendees are not retired.

If  and  are integers, is  an even integer?

1.  is an even integer.
2. 

Each of three plants, $P_{\mathrm{<font\; color="\#FE8080">1</font>}}$, $P_2$, and $P_3$, photosynthesizes glucose at a constant, characteristic rate measured in molecules per minute. If $p_{\mathrm{<font\; color="\#FE8080">1</font>}}$ is the ratio of $P_{\mathrm{<font\; color="\#FE8080">1</font>}}$'s rate to $P_2$'s rate and $p_2$ is the ratio of $P_2$'s rate to $P_3$'s rate, is $P_3$'s rate the greatest of the three?

1. $p_{\mathrm{<font\; color="\#FE8080">1</font>}}<p_2$
2. $p_2<\mathrm{<font\; color="\#FE8080">1</font>}$

$m=\frac{\frac{3}{n}}{\frac{2}{y}+\frac{\mathrm{<font\; color="\#FE8080">1</font>}}{2y}}$ In the expression above, if $yn\ne 0$ , what is the value of m?

1. $y=\frac{3n}{2}$
2. $n=\frac{3}{2}$

If x and y are positive integers, is $\sqrt{x+y+\mathrm{<font\; color="\#FE8080">1</font>}}>3\sqrt{x+\mathrm{<font\; color="\#FE8080">1</font>}}$?

1. $y>8x+8$
2. $x+y>8x+8$

If $d_{\mathrm{<font\; color="\#FE8080">1</font>}}$ and $d_2$ are the numbers of defective items in production runs yielding $r_{\mathrm{<font\; color="\#FE8080">1</font>}}$ and $r_2$ total items, respectively, the ratio of defects per run is greater for which of the two production runs?

1. $d_{\mathrm{<font\; color="\#FE8080">1</font>}}>d_2$
2. $r_2>r_{\mathrm{<font\; color="\#FE8080">1</font>}}$

If 1,200 employees, males and females, requested a raise, how many requests were granted?

1. $\frac{5}{12}$ of the males and $\frac{7}{12}$ of the females had their request granted.
2. 200 of the requests made by males were granted.

The ratio of the number of girls to the number of boys in Group A is twice  what it is in Group B. What is the ratio of the total number of boys and girls in Group A to the total number of boys and girls in Group B?

1. There are 30 more boys and girls in Group A than in Group B.
2. The ratio of the number of girls to the number of boys in Group A is 6 to 5.

A stack of colored cards is sorted such that x blue cards, y red cards, and z green cards are placed on top of each of a number of yellow cards, and there are no cards left over. How many yellow cards are there?

1. The numbers of blue, red, and green cards placed on a given yellow card are in the ratio 3:4:7, respectively.
2. A total of 90 blue cards, 120 red cards, and 210 green cards are placed.

Is $abc=\mathrm{<font\; color="\#FE8080">1</font>}$?

1. $ab=\mathrm{<font\; color="\#FE8080">1</font>}$
2. $bc=\mathrm{<font\; color="\#FE8080">1</font>}$

If k is an integer, is k even?

1. $\frac{k}{2}$ is not an even integer.
2. $5-k$ is an even integer.

The average (arithmetic mean) price of three items sold by a store to a particular customer, before discounts, was $90. If a discount of 20% was applied at the point of purchase to all items of at least $100, what was the total discount saved by the customer?

1. The pre-discount price of the most expensive item that the customer purchased from the store was $180.
2. The pre-discount price of the least expensive item that the customer purchased from the store was $10.

The table above shows the lexical similarities, measured as a percentage of words that are similar, between any two of the four languages A, B, C, and D. For example, the lexical similarity between Language A and Language D is 70. What is the value of $a΄$?

1. The lexical similarity between B and C is 10 percent greater than that between B and A.
2. The lexical similarity between C and D is 105% that of the lexical similarity between A and C.

If $a+n=b$, what is the value of n?

1. $b=5$
2. $b+5=a$