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  If m, r, x, and y are positive, is theratio of m to r equal to the ratio of x to y ?

  (1) The ratio of m to y is equal tothe ratio of x to r.

  (2) The ratio of m + r to x + y isequal to the ratio of x to y.

  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 TOGETHERare sufficient, but NEITHER statementALONE is sufficient.

  D. EACH statement ALONE issufficient.

  E. Statement (1) and statement (2) TOGETHER are NOT sufficient.

  参考答案:E

  题目翻译:m,r,x都是整数,m和r的比值跟x和y的比值相等吗?

  题目全解:(1)m/y=x/r,推不出,IN;

  (2)(m+r)/(x+y)=x/y,推不出,IN;

  (1)+(2),推不出,IN.

  For any positive integer n, the lengthof n is defined as the number of prime factors whose product is n. For example, the length of 75 is 3, since 75= 3*5*5. How many two-digit positiveintegers have length 4 ?

  (A) 9

  (B) 11

  (C) 12

  (D) 14

  (E) 15

  参考答案:B

  题目翻译:正数n的长度被定义为它质数因子的个数。多少两位数长度是4?

  题目全解:

  4个2:2*2*2*2=16; (1个)

  3个2:2*2*2*3=24;2*2*2*5=40;2*2*2*7=56; 2*2*2*11=88; (4个)

  2个2:2*2*3*3=36;2*2*3*5=60;2*2*3*7=84;(3个)

  1个2:2*3*3*3=54;2*3*3*5=90;(2个)

  0个2:3*3*3*3=81。(1个)

  共11个。

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