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