Last year 26 members of a certain club traveled to England, 26 members traveled to France, and 32 members traveled to Italy. Last year no members of the club traveled to both England and France, 6 members traveled to both England and Italy, and 11 members traveled to both France and Italy. How many members of the club traveled to at least one of these three countries last year?
A) 52
B) 67
C) 71
D) 73
E) 79

What is the smallest integer n for which 25^n > 5^12 ?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

What number is 108 more than two-thirds of itself?
A. 72
B. 144
C. 162
D. 216
E. 324

No nation can long survive unless its people are united by a common tongue. For proof, we need only consider Canada, which is being torn asunder by conflicts between French-speaking Quebec and the other provinces, which are dominated by English speakers.

Which of the following, if true, most effectively challenges the author’s conclusion?

(A) Conflicts over language have led to violent clashes between the Basque-speaking minority in Spain and the Spanish-speaking majority.

(B) Proposals to declare English the official language of the United States have met with resistance from members of Hispanic and other minority groups.

(C) Economic and political differences, along with linguistic ones, have contributed to the provincial conflicts in Canada.

(D) The public of India, in existence sine 1948, has a population that speaks hundreds of different, though related, languages.

(E) Switzerland has survived for nearly a thousand years as a home for speakers of three different languages.

In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
A. 144
B. 119
C. 113
D. 88
E. 31

How many integers are there between 1 and 1000, inclusive, that are not divisible by either 11 or 35?
A. 884
B. 890
C. 892
D. 910

How many positive three-digit integers are multiples of 7?
A. 105
B. 106
C. 127
D. 128
E. 142

Set S consists of all prime integers less than 10. If two different numbers are chosen from set S at random, what is the probability that the product of these numbers will be greater than the product of the numbers that were not chosen?

A. 1/3

B. 2/3
C. 1/2
D. 7/10
E. 4/5

On a 2022 World Cup De Bruyne, Ronaldo, Mbappe and Messi together scored x goals. Out of these, 27 goals were not scored by De Bruyne, 22 goals were not scored by Ronaldo, 20 goals were not scored by Mbappe and 18 goals were not scored by Messi. How many goals did Messi score ?
A.7

B. 9
C. 11
D. 13
E. 29

Employees of a discount appliance store receive an additional 20% off of the lowest price on an item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally
cost $450?
1. $280.90
2. $287.00
3. $292.50
4. $306.00
5. $333.89