[求助]PREP1 DS问题求解

 3。 How many different prime numbers are factors of the positive integer n?

(1) four different prime numbers are factors of 2n

(2) four different prime numbers are factors of n^2

Ans: (B)

23.  At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japenese, do more students at the school study French than Japanese?

(1) 16 students at the school study both French and Japanese.

(2) 10 percent of the students at the school who study Japanese also study French.

Ans: (B) 

34. 2927-!-item-!-187;#058&003024

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

Ans: (A)

39.3582-!-item-!-187;#058&003470 For the students in class A, the range of their heights is r centimeters and the greatest height is g centimeters. For the students in class B, the range of their heights is s centimeters and the greatest height is h centimeters. Is the least height of the students in class A greater than the least height of the students in class B ?

(1) r < s

(2) g > h

Ans: (C)

70. 6067-!-item-!-187;#058&004849 Is the integer x divisible by 6 ?

(1) x + 3 is divisible by 3.

(2) x + 3 is an odd number.

Ans: (C)

84. 7517-!-item-!-187;#058&005572 If p is a prime number greater than 2, what is the value of p ?

(1) There are a total of 100 prime numbers between 1 and p + 1.

(2) There are a total of p prime numbers between 1 and 3,912.

Ans: (D)

114. 11816-!-item-!-187;#058&007868 Henry purchased 3 items during a sale. He received a 20 percent discount off the regular price of the most expensive item and a 10 percent discount off the regular price of each of the other 2 items. Was the total amount of the 3 discounts greater than 15 percent of the sum of the regular prices of the 3 items?

(1) The regular price of the most expensive item was $50, and the regular price of the next most expensive item was $20.

(2) The regular price of the least expensive item was $15.

Ans: (A)

125. 12932-!-item-!-187;#058&009020 The sequence a1, a2, a3, . . . , an of n integers is such that ak = k if k is odd and ak = -ak - 1 if k is even. Is the sum of the terms in the sequence positive?

(1) n is odd.

(2) an is positive.

Ans: (D)

131. 13306-!-item-!-187;#058&009213
The positive integer k has exactly two positive prime factors, 3 and 7. If k has a total of 6 positive factors, including 1 and k,what is the value of k ?

(1) 32 is a factor of k.

(2) 72 is not a factor of k.

Ans: (D)

167. 16626-!-item-!-187;#058&010859 If x, y, and z are integers and xy + z is an odd integer, is x an even integer?

(1) xy + xz is an even integer.

(2) y + xz is an odd integer.

Ans: (A)

169. 16735-!-item-!-187;#058&010875 If the integers a and n are greater than 1 and the product of the first 8 positive integers is a multiple of an, what is the value of a ?

(1) an = 64

(2) n = 6

Ans: (B)

176. 17491-!-item-!-187;#058&011140 If x and y are positive integers, is the product xy even?

(1) 5x - 4y is even.

 (2) 6x + 7y is even.

Ans: (D)

202. 19528-!-item-!-187;#058&012279 Each employee of Company Z is an employee of either Division X or Division Y, but not both. If each division has some part-time employees, is the ratio of the number of full-time employees to the number of part-time employees greater for Division X than for Company Z ?

(1) The ratio of the number of full-time employees to the number of part-time employees is less for Division Y than for Company Z.

(2) More than half of the full-time employees of Company Z are employees of Division X, and more than half of the part-time employees of Company Z are employees of Division Y.

Ans: (D)

一下发了这么多题目希望板上的N人帮忙解答下啊，我一直找不出合理的解释。谢谢了！

(1) four different prime numbers are factors of 2n 不充分，此四个质因子包含2和不含2是两种情况

(2) four different prime numbers are factors of n^2  充分，因为n^2有四个质因子，只可能是他们的平方。因此n也只有4个质因子（其他不是平方数的因子无法开方成新的质因子）

23.  At least 100 students at a certain high school study Japanese. If 4 percent of the students at the school who study French also study Japenese, do more students at the school study French than Japanese?

(1) 16 students at the school study both French and Japanese.不充分  算出French 400人，注意题干是at least 100人，因此不能确定是否比Japanese大小，ETS太变态了！

(2) 10 percent of the students at the school who study Japanese also study French.充分。由比率大小推的French》Japanese

34. 2927-!-item-!-187;#058&003024

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.  充分，最后的standard deviation 同比例减小

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons 不充分，无法得知每个倒出的多少，无法确定方差

39.3582-!-item-!-187;#058&003470 For the students in class A, the range of their heights is r centimeters and the greatest height is g centimeters. For the students in class B, the range of their heights is s centimeters and the greatest height is h centimeters. Is the least height of the students in class A greater than the least height of the students in class B ?

题干意思等同于 is g-r > h-s?

(1) r < s 

(2) g > h

分别都不充分，合解不等式，充分。

Ans: (C)

70. 6067-!-item-!-187;#058&004849 Is the integer x divisible by 6 ?

(1) x + 3 is divisible by 3.  不充分，是3的倍数，未必是6的倍数

(2) x + 3 is an odd number.    不充分，只能说明x是偶数

合解，x既是偶数又是3的倍数，因此是6的倍数.

好多啊！抛砖引玉一下，我复习阅读去了，阅读差的要死！lz着急可短我！

谢谢楼上的啊一下好多解释，慢慢消化。后面一半的几道题目有哪个热心人能帮忙指点迷津下啊。急啊～8月考呢！