Five persons sat next to each other around a circular table to play cards. Did Grace sit next to Bill?
(1) Dora sat next to Ethyl and Carl.
(2) Grace sat next to Carl.
Each of the coins in a collection is distinct and is either silver or gold. In how many different ways could all of the coins be displayed in a row, if no 2 coins of the same color could be adjacent?
(1) The display contains an equal number of gold and silver coins.
(2) If only the silver coins were displayed, 5,040 different arrangements of the silver coins would be possible.
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If 3 members are to be selected from a group of x members then what is the value of x?
1) If team of 3 members is selected from the group of x members then 30 different combinations of 3 members can be formed with 2 specific members never being together on the team
2) There are a total of 35 ways to make team of 3 members out of team of x members.
How many students aged between 21 and 23 scored between 70 and 90?
(1) 17 students are aged between 21 and 23.
(2) 17 students scored between 70 and 90.
How many different subcommittees can be formed among the six members of the housing committee?
(1) All subcommittees must have at least two members.
(2) Any combination of members is acceptable except those with 1 member.
How many employees are in company C?
1) There are 120 ways to form a team of 3 out of all the employees in company C
2) All the employees in company C can be divided into two teams of equal employees in 126 ways
Scott grew 100 plants from black and white seeds. Only one plant grows from one seed. She may get red or blue flowers from the black seed. She may get red or white flowers from the white seeds. How many black seeds does she have?
I. The number of plants with white flowers = 10.
II. The number of plants with red flowers = 70.
In how many ways can a coach select a university team from a pool of eligible candidates?
(1) The number of eligible candidates is three times greater than the number of slots on the team.
(2) 60% of the 20 athletes are eligible to play on the four-person university team.
A certain number of marbles are to be removed from a box containing only solid-colored red, yellow, and blue marbles. How many more yellow marbles than red marbles are in the box before any are removed?
(1) To guarantee that a red marble is removed, the smallest number of marbles that must be removed from the box is 14.
(2) To guarantee that a yellow marble is removed, the smallest number of marbles that must be removed from the box is 8.
A certain panel is to be composed of exactly three women and exactly two men, chosen from x women and y men. How many different panels can be formed with these constraints?
(1) If two more women were available for selection, exactly 56 different groups of three women could be selected.
(2) x = y + 1