请教几道数学题

lasiaberyl

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.

                  

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.

D. EACH statement ALONE is sufficient.

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

Q10:

If x² + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1)     a = 1

(2)     b = 2

                  

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.

D. EACH statement ALONE is sufficient.

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

Q17:

How many prime numbers between 1 and 100 are factors of 7,150 ?

 

A.     One

B.     Two

C.     Three

D.     Four

E.      Five                             answer:d

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?

 

A.     a/2

B.     b/2

C.     (a+b)/2

D.     (a+2)/2

E.      (b+2)/2                                  answer:d

我觉得答案也许错了，不过也许是我错了，谢谢大家帮忙

 

xuewen

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.

Q5:（1）因为K是3的倍数，设K=3x（x=1,2.3....),带入化简提取公因数得到3*(2x+m)=t所以t至少有因子3，所以t和12有3这个common factor，而且3>1,符合要求；

  （2）同理设m=3y（y=1,2,3....),带入化简。。。得到2k+9x=t，这样t的因子是不确定的，所以(1)就可以解答问题了，选A

Q10:

If x² + 3x + c = (x + a)(x + b) for all x, what is the value of c ?

(1)     a = 1

(2)     b = 2

原方程两边打开，化简得到x^2+3x+c=x^2+(a+b)x+ab

由于对于所有x都成立，所以方程两边对应可以得到a+b=3， ab=c

这样，如果知道a=1，那么可以得到b=2，c就等于ab=2

同理，（2）也符合要求。  选D

Q17:

How many prime numbers between 1 and 100 are factors of 7,150 ?

 

A.     One

B.     Two

C.     Three

D.     Four

E.      Five                             answer:d

7150=2*5*5*13*11，所以1~100之间有2、5、11、13这四个质数因子，选D。

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?

 

A.     a/2

B.     b/2

C.     (a+b)/2

D.     (a+2)/2

E.      (b+2)/2                                  answer:d

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?

 

A.     a/2

B.     b/2

C.     (a+b)/2

D.     (a+2)/2

E.      (b+2)/2                                  answer:d

我觉得LZ好像题目不完整啊，“a-b and ？？？？are both......"这样没有办法做啊~~

lasiaberyl

是a-b和a/b

呵呵，不好意思

lasiaberyl

还有，谢谢啦~~~

xuewen

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

C.     (a+b)/2

D.     (a+2)/2

E.      (b+2)/2

因为a/b为偶数，设a/b=2k(k=1,2,3....),则a=2bk, 即a为偶数，因为a-b为偶数，所以b也为偶数。

将a=2bk代入D选项中，得到（2bk+2）/2=bk+1, 因为b为偶数（已证），所以bk也为偶数，那么bk+1就一定是奇数。

LZ什么时候考捏~加油哦~不用谢啊  ~

lasiaberyl

21号就考了，现在还总是粗心大意，

xuewen

呵呵~我28考~加油！！

baibaiyueyue

我也是21~~

lasiaberyl

3q