1. Set \(\)S\(\) consists of all positive integers less than \(\)81\(\) that are not equal to the square of an integer.
| Quantity A | Quantity B |
| The number of integers in set \(\)S\(\) | \(\)72\(\) |
2. Which of the following numbers is farthest from the number \(\)1\(\) on the number line?
(A) \(\)-10\(\)
(B) \(\)-5\(\)
(C) \(\)0\(\)
(D) \(\)5\(\)
(E) \(\)10\(\)
3. For a given two-digit positive integer, the tens digit is \(\)5\(\) more than the units digit. The sum of the digits is \(\)11\(\). Find the integer.
4. \(\)k\(\) is a digit in the decimal \(\)1.3k5\(\), and \(\)1.3k5\(\) is less than \(\)1.33\(\).
| Quantity A | Quantity B |
| \(\)k\(\) | \(\)1\(\) |
5. If \(\)-\frac{ m }{ 9 }\(\) is an even integer, which of the following must be true?
(A) \(\)m\(\) is a negative number.
(B) \(\)m\(\) is a positive number.
(C) \(\)m\(\) is a prime number.
(D) \(\)m\(\) is an odd integer.
(E) \(\)m\(\) is an even integer.
6. Which one of the following choices does not equal any of the other choices?
(A) \(\)5.43 + 4.63-3.24-2.32\(\)
(B) \(\)5.53 + 4.73-3.34-2.42\(\)
(C) \(\)5.53 + 4.53-3.34-2.22\(\)
(D) \(\)5.43 + 4.73-3.24-2.42\(\)
(E) \(\)5.43 + 4.73-3.14-2.22\(\)
7. \(\)X\(\) is a \(\)3\(\)-digit number and \(\)Y\(\) is a 4digit number. All the digits of \(\)X\(\) are greater than \(\)4\(\), and all the digits of \(\)Y\(\) are less than \(\)5\(\).
| Quantity A | Quantity B |
| The sum of the digits of \(\)X\(\) | The sum of the digits of \(\)Y\(\) |
8. \(\)x\(\) is a two-digit number. The digits of the number differ by \(\)6\(\), and the squares of the digits differ by \(\)60\(\).
| Quantity A | Quantity B |
| \(\)x\(\) | \(\)60\(\) |
9. Which one of the following is the minimum value of the sum of two integers whose product is \(\)36\(\)?
(A) \(\)37\(\)
(B) \(\)20\(\)
(C) \(\)15\(\)
(D) \(\)13\(\)
(E) \(\)12\(\)
10. \(\)n\(\) is a positive integer
| Quantity A | Quantity B |
| \(\)n\(\) | The sum of two integers whose product is \(\)n\(\) |
11. \(\)k\(\) is a digit in the decimal \(\)12.15k9\(\), which, if rounded to the nearest hundredth, would equal \(\)12.16\(\).
| Quantity A | Quantity B |
| \(\)k\(\) | \(\)4\(\) |
12. To the nearest integer, the non-negative fourth root of integer \(\)n\(\) rounds to \(\)3\(\). Inclusive, \(\)n\(\) is between
(A) \(\)0and1\(\)
(B) \(\)2 and 3\(\)
(C) \(\)4 and 9\(\)
(D) \(\)10 and 39\(\)
(E) \(\)40 and 150\(\)
13. Positive integers \(\)a\(\) and \(\)b\(\) each have exactly four factors. If \(\)a\(\) is a one-digit number and \(\)b= a + 9\(\), what is the value of \(\)a\(\)?
14. If \(\)a\(\) and \(\)c\(\) are positive integers and \(\)4a + 3 = b\(\) and \(\)4c + 1 = d\(\), which of the following could be the value of \(\)b + d\(\)?
(A) \(\)46\(\)
(B) \(\)58\(\)
(C) \(\)68\(\)
(D) \(\)74\(\)
(E) \(\)82\(\)
15. If \(\)a + b + c + d + e\(\) is odd, and \(\)a, b, c, d\(\), and \(\)e\(\) are integers, which of the following could be the number of integers among \(\)a, b, c, d\(\), and \(\)e\(\) that are even?
Indicate all such numbers.
(A) \(\)0\(\)
(B) \(\)1\(\)
(C) \(\)2\(\)
(D) \(\)3\(\)
(E) \(\)4\(\)
(F) \(\)5\(\)
Answer:
1 C
2 A
3 83
4 D
5 E
6 E
7 D
8 D
9 E
10 B
11 A
12 E
13 6
14 C
15 A,C,E
