28-Q26

duluxstar

Q26:

If positive integer x is a multiple of 6 and positive integer y is a multiple of 14, is xy a multiple of 105?

(1) x is a multiple of 9.

(2)     y is a multiple of 25.

              

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:

这题应该很简单的，但却越算越糊涂，请教如何做的

aurora2008

Let me try it..............

(1) x is a multiple of 6 & 9;

i.e., x is a multiple of 18;

i.e., x = 18m & y = 14n (since y is a multiple of 14)

i.e., xy = 252mn or 252k (m,n,k are any positive integers)

For k =1, 2, 3, 4 etc; xy is not a multiple of 105

Whereas for k=5, xy is a multiple of 105 ---> INSUFF

(2) y is a multiple of 14 & 25;

i.e., y is a multiple of 350; [14×25]

i.e., x = 6m & y = 350n (since x is a multiple of 6)

i.e., xy = 2100mn or 2100k (m,n,k are any positive integers)

2100 is divisible by 105 ... hence xy is a multiple of 105 ...

SUFFICIENT

Answer is B.

yubyuber

X是6倍数，包含因子2，3；Y是14的倍数，包含因子2，7

105=3x7x5,所以要xy是105的倍数，则需要xy包含因子3，7，5.

3和7已经有了，则只需要找出一个因子5就可以，条件2刚好满足，

所以答案应该是B

duluxstar

can you explain how to get 350, I'm not sure the answer, someone please answer it.

AJingJing

C. Right??

18*350 is definitely the multiple of 3*35.