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Q36 If a and b are positive integers such that a – b and are both even integers, which of the following must be an odd integer?

If 2 different representatives are to be selected at random from a group of 10 employees and if p is the probability that both representatives selected will be women, is p > 1/2?

(2) The probability that both representatives selected will be men is less than 1/10.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Of all the students in a certain dormitory, 1/2are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?

以下是引用bolodong在2006-12-7 0:17:00的发言：

Q36 If a and b are positive integers such that a – b and a/b are both even integers, which of the following must be an odd integer?

a: a/2.

b:b/2

ca+b/2)

d(a+2)/2

eb+2)/2

answer:d

According to a-b and a/b being both even integers, we can have a=4m, b=2n ==> (a+2)/2 = (4m+2)/2=2m+1, Hence D must stand.

Q5:

If k, m, and t are positive integers and k/6 + m/4 = t/12, do t and 12 have a common factor greater than 1 ?

(1) k is a multiple of 3.

(2) m is a multiple of 3.

. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

answer:a

k/6 + m/4 = t/12 ==> (2k+ 3m)/12 = t/12 ==> 2k + 3m = t ==> 1) the common factor can be at least 3 . for 2), we don't know. Hence, the answer is A

Q5: 这题啥意思啊？

If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 5-letter code words to the number of 4-letter code words?

A. 5 to 4

B. 3 to 2

C. 2 to 1

D. 5 to 1

E. 6 to 1

answer:e P(5,10)/P(4,10) = 6, hence, the answer is E.

Due to time concern, I answer only 3 of you questions, let the other xdjm do the rest.

Next time, please pose your question one at a time so that others to help you better.

Q22:

A. 5

B. 6

C. 7

D. 8

E. 9

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

A. 2

B. 5

C. 6

D. 7

E. 14