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发布时间:2023-09-29 14:10:45

[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.

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[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 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]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]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 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. (E) 48
[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
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[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]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]If n is a positive integer and k+2=3n, which of the following could NOT be a value of K ?()
A. 1
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[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 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]An even number x divided by 7 give some quotient plus a remainder of 6. Which of the following, when added to x, gives a sum which must be divisible by 14 ?()
A. 1
B. 3
C. 7
D. 8
E. 13
[单项选择]I had to take a step, even though I understand that that step was in the direction of ______ rather than success.
A. prestige
B. coefficient
C. catastrophe
D. compliment
[单项选择]Even if I had met him,I wouldn't have told him about our plan.


A. 如果我见过他,我也不会告诉他我们的计划。
B. 如果我再见到他,我就不会告诉他我们的计划。
C. 即使我见过他,我也不会告诉他我们的计划。
D. 即使我再见到他,我也不会告诉他我们的计划。

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