1. [latex]r, s[latex], and [latex]t[latex] are three consecutive odd integers such that [latex]r<s<t[latex].
| Quantity A | Quantity B |
| [latex]r+s+1[latex] | [latex]s+t-1[latex] |
2. By how much is the greatest of five consecutive even integers greater than the smallest among them?
(A) [latex]1[latex]
(B) [latex]2[latex]
(C) [latex]4[latex]
(D) [latex]8[latex]
(E) [latex]10[latex]
3. Which one of the following could be an integer?
(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of [latex]6[latex] and [latex]9[latex]
4. Three consecutive integers have a sum of [latex]-84[latex].
| Quantity A | Quantity B |
| The least of the three integers | [latex]-28[latex] |
5. (The average of five consecutive integers starting from [latex]m[latex]) – (the average of six consecutive integers starting from [latex]m[latex]) =
(A) [latex]-1/4[latex]
(B) [latex]-1/2[latex]
(C) [latex]0[latex]
(D) [latex]1/2[latex]
(E) [latex]1/4[latex]
6. [latex]a, b, c, d[latex], and [latex]e[latex] are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by [latex]20[latex]%. Which one of the following numbers was deleted?
(A) [latex]a[latex]
(B) [latex]b[latex]
(C) [latex]c[latex]
(D) [latex]d[latex]
(E) [latex]e[latex]
7. [latex]a, b[latex], and [latex]c[latex] are consecutive integers in increasing order of size.
| Quantity A | Quantity B |
| [latex]a/5-b/6[latex] | [latex]b/5-c/6[latex] |
8. [latex]a, b, c, d[latex], and [latex]e[latex] are five consecutive integers in increasing order of size. Which one of the following expressions is not odd?
(A) [latex]a + b + c[latex]
(B) [latex]ab + c[latex]
(C) [latex]ab + d[latex]
(D) [latex]ac + d [latex]
(E) [latex]ac + e[latex]
9. A set has exactly five consecutive positive integers starting with [latex]1[latex]. What is the percentage decrease in the average of the numbers when the greatest one of the numbers is removed from the set?
(A) [latex]5[latex]
(B) [latex]8.5[latex]
(C) [latex]12.5[latex]
(D) [latex]15.2[latex]
(E) [latex]16.66[latex]
10. If [latex]n[latex] is the smallest of three consecutive positive integers, which of the following must be true?
(A) [latex]n[latex] is divisible by [latex]3[latex]
(B) [latex]n[latex] is even
(C) [latex]n[latex] is odd
(D) [latex](n)(n + 2)[latex] is even
(E) [latex]n(n + 1)(n + 2)[latex] is divisible by [latex]3[latex]
11. What is the sum of all the integers from [latex]1[latex] to [latex]80[latex], inclusive?
(A) [latex]3,200[latex]
(B) [latex]3,210[latex]
(C) [latex]3,230[latex]
(D) [latex]3,240[latex]
(E) [latex]3,450[latex]
12. [latex]a, b[latex], and [latex]c[latex] are consecutive integers such that [latex]a < b < c < 4[latex]
| Quantity A | Quantity B |
| The range of [latex]a,b[latex] and [latex]c[latex] | The average of [latex]a,b[latex] and [latex]c[latex] |
13. The average of a set of [latex]18[latex] consecutive integers is [latex]22.5[latex]. What is the smallest integer in the set?
14. [latex]p[latex] is the sum of all the integers from [latex]1[latex] to [latex]150[latex], inclusive. [latex]q[latex] is the sum of all the integers from [latex]1[latex] to [latex]148[latex], inclusive. What is the value of [latex]p-q[latex]?
Answer:
1 B
2 D
3 B
4 B
5 B
6 C
7 B
8 E
9 E
10 E
11 D
12 D
13 14
14 299
