# 《毕出21套》解析：数学第2套

## 数学第 2 套DS

1.The cardinality of a finite set is the number of elements in the set. What is the cardinality of set A?

(1) 2 is the cardinality of exactly 6 subsets of set A.

(2) Set A has a total of 16 subsets, including the empty set and set A itself.

(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.

### 解：

（1）集合A中恰好有6个子集的元素个数为2

（2）集合A共有16个子集，包括空集和它本身

2. X,81,73,71,98,73,64

What is the value of X in the above list of 7 numbers?

(1) The average (arithmetic mean) of these 7 numbers is 80.

(2) The range of these 7 numbers is 36.

(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.

### 解：

3.If 1 < d <2, is the tenths digit of the decimal representation of d equal to 9?

(1)d+0.01<2

(2)d+0.05>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.

### 解：

4.If b is the product of three consecutive positive integers c, c+ 1, and c+2, is b a multiple of 24?

(1)b is a multiple of 8.

(2)c is odd.

(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.

### 解：

3个连续的正整数的乘积一定是3的倍数，因为每3个连续的正整数中必有一个是3的倍数。因此，根据条件1，若b是8的倍数，则b同时是3和8的倍数，自然也是24的倍数。条件2说c是奇数，则只有c+1是偶数，无法保证其中有8，所以单独2不行，答案为A。

5.If x and z are integers, is x+z2odd?

(1)x is odd and z is even.

(2)x-z is odd.

(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.

### 解：

6.If x an integer?

(1) x2is an integer.

(2) x/2 is not an integer.

(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.

### 解：

7.If m and n are positive integers, what is the value of 3/m + n/4?

(1) mn=12

(2) 3/m is in lowest terms and n/4 is in lowest terms.

(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.

### 解：

3/m + n/4 = (12+mn)/4m。根据条件1可得24/(4m)，因为无法确定m的值，所以单独1是不充分的。单独根据条件2显然更不充分。把两个条件相加，如果3/m和4/n都是最简式，则m不能是3的倍数，n不能是2的倍数。m*n = 12，则m = 4，n= 3。显然可以求得题干中算式的答案，答案为C。

8.If x, y, and d are integers and d is odd are both x and y divisible by d?

(1) x+y is divisible by d.

(2) x-y is divisible by d.

(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.

### 解：

9.If K is a positive integer less than 10 and N=4321+K, what is the value of K?

(1) N is divisible by 3.

(2) N is divisible by 7.

(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.

### 解：

10.If m and n are positive integers, is n even?

(1) m(m+2)+1=mn

(2) m(m+n) is odd.

(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.

### 解：

11.If @ denotes a mathematical operation, does x@y=y@x for all x and y?

(1) For all x and y, x@y=2(x2+y2).

(2) For all y, 0@y=2y2.

(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.

### 解：

12.The 9 participants in a race were divided into 3 teams with 3 runners on each team. A team was awarded 6-n points if one of its runners finished in nth place, where 1≤n≤5. If all of the runners finished the race and if there were no ties was each team awarded at least 1 point?

(1) No team was awarded more than a total of 6 points.

(2) No pair of teammates finished in consecutive places among the top five places.

(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.

### 解：

13. If x and y are integers, is xy+1 divisible by 3?

(1)When x is divided by 3, the remainder is 1.

(2)When y is divided by 9, the remainder is 8.

(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.

### 解：

x=3m+1，y=9n+8，其中m，n是整数。

xy+1=(3m+1)(9n+8)+1

=27mn+24m+9n+84-1

=3(9mn4-8m+3n+3)

14.If x is a positive integer, how many positive integers less than x are divisors of x?

(1)x^2 is divisible by exactly 4 positive integers less than x^2.

(2)2x is divisible by exactly 3 positive integers less than 2x.

(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.

### 解：

15.Sprinklers are being installed to water a lawn. Each sprinkler waters in a circle. Can the lawn be watered completely by 4 installed sprinklers?

(1) The lawn is rectangular and its area is 32 square yards.

(2) Each sprinkler can completely water a circular area of lawn with a maximum radius of 2 yards.

(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.

### 解：

16.In quadrilateral ABCD, is angle BCD a right angle?

(1) Angle ABC is a right angle.

(2) Angle ADC is a right angle.

(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.

### 解：

17.

In rectangular region PQRS above, T is a point on side PS. If PS =4, what is the area of region PQRS?

(1)ΔQTR is equilateral.

(2) Segments PT and TS have equal length.

(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.

### 解：

18.The top surface area of a square table top was changed so that one of the dimensions was reduced by 1 inch and the other dimension was increased by 2 inches. What was the surface area before these changes were made?

(1) After the changes were made, the surface area was 70 square inches.

(2) There was a 25 percent increase in one of the dimensions.

(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.

### 解：

19.Is the perimeter of a certain rectangular garden greater than 50 meters?

(1) The two shorter sides of the garden are each 15 meters long.

(2) The length of the gardens 5 meters greater than the width of the garden.

(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.

### 解：

20.

In the figure above, points A, B, C, and D are collinear and AB, BC, and CD are semicircles with diameters d1cm, d2cm, and d3cm, respectively. What is the sum of the lengths of AB, BC and CD in centimeters?

(1) d1: d2: d3 is 3:2:1

(2) The length of AD is 48 cm.

(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.

### 解：

21.In the rectangular coordinate system, line k passes through the point(n,-1). Is the slope of line k greater than zero?

(1) Line k passes through the origin.

(2) Line k passes through the point(1, n+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.

### 解：

22.What is the length of the hypotenuse of △ABC?

(1) The lengths of the three sides of △ABC are consecutive even integers .

(2) The hypotenuse of △ABC is 4 units longer than the shorter leg.

(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.

### 解：

23.In the standard (x, y) coordinate plane, what is the slope of the line containing the distinct points P and Q?

(1) Both P and Q lie on the graph of |x|+|y| =1

(2) Both P and Q lie on the graph of |x+y|=1

(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.

### 解：

24.Alan and Sue have each been saving one dollar a day and will continue to do so for the next month. If Sue began saving several days before Alan, in how many days from today will Alan have saved one-half as much as Sue?

(1) As of today, Alan has saved 7 dollars and Sue has saved 27 dollars.

(2) Three days from today, Alan will have saved one-third as much as Sue.

(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.

### 解：

25.What is the value of x/yz?

(1) x=y/2 and z=2x/5

(2) x/z=5/2 and 1/y=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.

(D) EACH statement ALONE is sufficient.

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

### 解：

26.Of the numbers q, r, s, and t, which is greatest?

(1)The average(arithmetic mean) of q and r is s.

(2)The sum of q and r is t.

(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.

### 解：

27. A box of light bulbs contains exactly 3 light bulbs that are defective. What is the probability that a sample of light bulbs picked at random from this box will contain at least 1 defective light bulb?

(1) The light bulbs in the sample will be picked 1 at a time without replacement.

(2) The sample will contain exactly 20 light bulbs.

(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.

28. Is xy<6?

(1)x<3 and y<2

(2)1/2 < x < 2/3 and y2<64

(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.

29. What is the median of the data set S that consists of the integers 17, 29, 10, 26, 15, and x?

(1) The average (arithmetic mean) of S is 17.

(2) The range of S is 24.

(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.

30. If x≠1，is y equal to x+1?

(1)(y−2)/(x−1)=1

(2)y2=(x+1)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.

31. Three dice, each with faces numbered 1 through 6, were tossed onto a game board. If one of the dice turned up 4, what was the sum of the numbers that turned up on all three dice?

(1)The sum of two of the numbers that turned up was 10.

(2)The sum of two of the numbers that turned up was 11.

(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.

32. Is x2-y2 a positive number?

(1) x-y is a positive number.

(2) x+y is a positive number.

(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.

33. An investment has been growing at a fixed annual rate of 20% since it was first made;no portion of the investment has been withdrawn, and all interest has been reinvested. How much is the investment now worth?

(1) The value of the investment has increased by 44% since it was first made.

(2) If one year ago $600 had been withdrawn, today the investment would be worth 12% less than it is actually now worth. (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. 解： 条件1：只给出百分比，没有任何一个实际值是不可能得到现在价值多少的。 条件2： 假设现在是x，则一年以前是x/1.2，1年以前拿掉了600，则有(x/1.2-600)*1.2=(1-0.12)x，可以求出x，充分。 答案为B。 34. If x+y+z>0, is z>1? (1) z>x+y+1 (2) x+y+1<0 (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. 解： 条件1：z>x+y+1且x+y+z>0，得出x+y+x+y>-1，即，x+y>-1/2. 由z>x+y+1可知，z要大于1则必须x+y>0，无法得知，不充分。 条件2：由x+y+1<0得出，一个小于-1的数+z>0，因此z必须大于1，充分。 答案为B。 35. In the first 2 hours after Meadow's self-service laundry opens, m large washing machines and n small washing machines are in continual use. Including the time for filling and emptying the washing machines, each load of laundry takes 30 minutes in a large washing machine and 20 minutes in a small washing machine. What is the total number of loads of laundry done at Meadow's self-service laundry during this 2-hour period? (1) n=3m (2) 2m+3n=55 (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. 解： 题干的意思为，2小时用m个大洗衣机和n个小洗衣机工作。大洗衣机30分钟处理1 load，小洗衣机20分钟处理1 load，问2小时内一共处理了多少load。 显然，依题意可以直接列方程，则有： 总量 = 4m + 6n 显然，条件2可以，因为直接等式两侧同乘以2，即可得知4m + 6n = 110，答案为B。 36. Let S be a set of outcomes and let A and B be events with outcomes in S. Let ~B denote the set of all outcomes in S that are not in B and let P(A) denote the probability that event A occurs. What is the value of P(A)? (1) P(A∪B)=0.7 (2) P(A∪~B)=0.9 (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. 解： 条件1：P(A∪B) = P(A) + P(B) - P(AB) = 0.7，显然单独无法判断P(A)，不充分。 条件2：P(A∪~B) = 1 - P(B) + P(AB) = 0.9，显然单独无法判断P(A)，不充分。 条件1+条件2：两个等式相加，即可得出P(A) = 0.6，充分。 因此，答案为C。 37. How many people in Town X read neither the Word newspaper nor the Globe newspaper? (1) Of the 2500 people in Town X, 1000 read no newspaper. (2) Of the people in Town X, 700 read the globe only and 600 read the World only. (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. 解： 条件1：我们知道1000人不读报纸，但我们不知道是否这个城镇只有2种报纸，所以不充分。 条件2并没有告诉我们一共有多少人，有没有人什么也不读等等，所以单独不充分。 条件1+条件2：依然不充分，还是不知道有没有其它的报纸。 答案为E。 38. What is the sum of 3 consecutive integers? (1) The sum of the 3 integers is less than the greatest of the 3 integers. (2) Of the 3 integers, the ratio of the least to the greatest is 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. 解： 条件1：三个数的加和小于三个数中的最大的数。这只能表明这三个数不都是正数，但不能确定它们的加和。 条件2：三个整数中，最小和最大的比值是3。之后-3，-2，-1这三个连续的整数是符合条件的，充分。 因此，答案为B。 39. What is the number of integers that are common to both set S and set T? (1) The number of integers in S is 7, and the number of integers in T is 6. (2) U is the set of integers that are in S only or in T only or in both, and the number of integers in U is 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. (D) EACH statement ALONE is sufficient. (E) Statements (1) and (2) TOGETHER are NOT sufficient. 解： 条件1：只知道S和T各自的元素数量，完全无法知道交集的情况。 条件2：知道U=（S+T+交集）= 10，还是不知道交集的元素数量。 条件1+条件2：可以知道S，T，以及交集的数量，充分。 答案为C。 40. A country's per capita national debt is its national debt divided by its population. Is the per capita national debt of Country G within$5 of $500? (1) Country G's national debt to the nearest$1,000,000,000 is \$43,000,000,000

(2) Country G's population to the nearest 1, 000,000 is 86,000,000

(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.