[单项选择]If n is a positive integer and n2 is divisible by 72, then the largest positive integer that must divide n is ？（）
A. 6
B. 12
C. 24
D. 36
E. 48

[单项选择]

For any positive integer n, n＞1, the "length" of n is the number of positive primes (not necessarily distinct) whose product is n. For example, the length of 50 is 3 since 50=(2)(5)(5)
Which of the following integers has length 3 ？（）

A. 3
B. 15
C. 60
D. 64
E. 105

[单项选择]When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ？（）
A. 3
B. 4
C. 7
D. 8
E. 12

[单项选择]If n is a positive integer, then n(n+1)(n+2) is （）.
A. even only when n is even
B. even only when n is odd
C. odd whenever n is odd
D. divisible by 3 only when n is odd
E. divisible by 4 whenever n is even

[单项选择]

If n is a positive integer, is the value of b-a at least twice the value of 3ⁿ-2ⁿ ？（）
(1)a=2ⁿ+1 and b=3ⁿ+1
(2)n=3

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]If n is a positive integer and k+2=3ⁿ, which of the following could NOT be a value of K ？（）
A. 1
B. 4
C. 7
D. 25
E. 79

[单项选择]If n is a positive integer and k=5.1×10ⁿ, what is the value of k ？（）
(1)6,000＜k＜500,000
(2)k²=2.601×10⁹

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]If an integer n is divisible by both 6 and 8, then it must also be divisible by which of the following ？（）
A. 10
B. 12
C. 14
D. 16
E. 18

[单项选择]

What is the remainder when the positive integer x is divided by 2 ？（）
(1)x is an odd integer.
(2)x is a multiple of 3.

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]

What is the least positive integer that is divisible by each of the integers 1 through 7, inclusive ？（）

A. 420
B. 840
C. 1，260
D. 2，520
E. 5，040

[单项选择]Can the positive integer p be expressed as the product of two integers, each of which is greater than 1 ？（）
(1)31＜p＜37
(2)p is odd

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]

If a is a positive integer, and if the units’ digit of a² is 9 and the units’ digit of (a+1)² is 4, what is the units’ digit of (a+2)² ？（）

A. 1
B. 3
C. 5
D. 7
E. 9

[单项选择]Is the positive integer x an even number ？（）
(1)If z is divided by 3, the remainder is 2.
(2)If x is divided by 5, the remainder is 2.

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]What is the tens digit of positive integer x ？（）
(1)x divided by 100 has a remainder of 30.
(2)x divided by 110 has a remainder of 30.

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]Is the integer n a multiple of 140 ？（）
(1) n is a multiple of 10.
(2) n is a multiple of 14.

A. 条件（1）充分，但条件（2）不充分.
B. 条件（2）充分，但条件（1）不充分.
C. 条件（1）和（2）单独都不充分，但条件（1）和条件（2）联合起来充分.
D. 条件（1）充分，条件（2）也充分.
E. 条件（1）和条件（2）单独都不充分，条件（1）和条件（2）联合起来也不充分.

[单项选择]When the integer n is divided by 6, the remainder is 3. Which of the following is NOT a multiple of 6 ？（）
A. n-3
B. T+3
C. 2n
D. 3n
E. 4n

[单项选择]The integer n is a multiple of both 5 and 3. Which of the following is (are) true
I. n is odd.
II. n=30.
III. n is a multiple of 15.
A. III only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III

[填空题]下列程序是判断一个整数(＞=3)是否为素数，请补充完整。
Dim n As Integer
n=InputBox("请输入一个整数(＞=3)")
k=Int(Sqr(n))
i：2
swit=0
While i<=k And swit=0
If n Mod i=0 Then
[7]
E1se
[8]
End If
Wend
If swit=0 Then
Print n；"是一个素数。"
E1se
Print n；"不是一个素数。"
End If

[单项选择]阅读下列FORTRAN77程序：
PARAMETER(L=3)
INTEGER N(L)
DATA N/3*0/
DO 20 I=1，L
DO 20 J=1，L
N(J)=N(I)+1
20 CONTINUE
WRITE(*，*)N(L)
END
上述程序运行后，输出的值为（）。
A. 3
B. 5
C. 7
D. 9