Numbers & Operations
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Set 1: Multiple Choice
1.    The number 48 consists of how many distinct prime factors?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
2.    Which of the following fractions is in its simplest reduced form?
(A)
(B)
(C)
(D)
(E)
3.    The number 210 is divisible by all of the following integers EXCEPT
(A) 6
(B) 8
(C) 10
(D) 21
(E) 35
4.    In the arithmetic sequence (5, 9, 13, 17, . . .), where n1 = 5, what is the value of n8?
(A) 29
(B) 33
(C) 37
(D) 41
(E) 45
5.    If , what is the value of x?
(A) 22 + 1
(B) 32 – 3
(C) 22 + 3
(D) 23
(E) 32
6.    A master of the secretarial arts types at a rate of 55 words per minute. If there are 330 words per page, how many pages could a master be expected to type in four and a half hours?
(A) 6
(B) 12
(C) 37.5
(D) 45
(E) 247.5
7.    In the correctly worked addition problem above, which digit could represent X?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 0
8.    If b is a positive integer, which of the following equals 3b4?
(A)
(B)
(C)
(D)
(E)
9.    If set S consists of all positive prime integers greater than 5 and set T consists of all positive odd integers less than 21, which of the following must be true?
  I. Set T contains more numbers than set S.
 II. There are no even numbers in either set S or set T.
III. All numbers in set S are in set T.
(A) I
(B) II
(C) I and III
(D) II and III
(E) I, II, III
10.    In the geometric sequence (4, 12, 36, 108, 324, . . .), where n1 = 4, what is the value of n9?
(A)
(B)
(C) 236
(D) 69
(E)
11.    When s is divided by 6, the remainder is 5. What is the remainder when 2s is divided by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
12.    288 is divisible by 2n. What is the greatest possible value for n?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
13.    z is a multiple of 3, and y is a multiple of 5. a is an even integer divisible by both z and y. Therefore, a could equal which of the following?
(A) 45
(B) 62
(C) 75
(D) 80
(E) 90
14.    If , then which of the following MUST be true?
(A)
(B)
(C)
(D)
(E)
15.    When 8263 is expanded out, what digit will be in the units (1’s) space?
(A) 8
(B) 4
(C) 2
(D) 6
(E) 5
16.    There are six numbers in a certain arithmetic sequence, the sum of which is 297. If the last number in the sequence is 67, by what constant amount is each number increased in the sequence?
(A) 3
(B) 7
(C) 14
(D) 30
(E) 32
17.    The first two terms of set A are 2 and 3. The rest of the terms are obtained either by adding the two previous terms together, when the last term is odd, or by subtracting the previous term from the term before it, when the last term is even. What is the mode of set A?
(A) –3
(B) –2
(C) 0
(D) 2
(E) 3
18.    If sm = 64 and s and m are both integers, what is the LEAST possible value of s – m?
(A) 4
(B) –4
(C) –6
(D) –8
(E) –12
19.    If 4x = 6412, what is the value of ?
(A) 236
(B) 224
(C) 216
(D) 212
(E) 26
20.    A geometric sequence consists of five terms, the sum of which is 1023. If the common ratio of the sequence is 4, what is the first term of the sequence?
(A) –9
(B) –6
(C) 3
(D) 6
(E) 9


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