DS-OG20：第201-220题 练习册详情

1

Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?

(1)The price of Tom's house was $110,000.

(2)The price of Jane's house was $120,000.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

10000人做过此题 平均耗时为2min2s 平均正确率为 70%

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2

What is the value of x if $$x^{3} < x^{2}$$?

(1) -2 < x < 2

(2) x is an integer greater than -2.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

776人做过此题 平均耗时为4min54s 平均正确率为 60%

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3

For any integers x and y, min(x, y) and max(x, y) denote the minimum and the maximum of x and y, respectively. For example, min(5, 2) = 2 and max(5, 2) = 5. For the integer w, what is the value of min(10, w) ?

(1)w = max(20, z) for some integer z.

(2)w = max(10, w)

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

6988人做过此题 平均耗时为22min29s 平均正确率为 48%

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4

A certain bookcase has 2 shelves of books. On the upper shelf, the book with the greatest number of pages has 400 pages. On the lower shelf, the book with the least number of pages has 475 pages. What is the median number of pages for all of the books on the 2 shelves?

(1)There are 25 books on the upper shelf.

(2)There are 24 books on the lower shelf.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9931人做过此题 平均耗时为12min38s 平均正确率为 41%

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5

In the figure, points A, B, C, D, and E lie on a line. A is on both circles, B is the center of the smaller circle, C is the center of the larger circle, D is on the smaller circle, and E is on the larger circle. What is the area of the region inside the larger circle and outside the smaller circle?

(1)AB = 3 and BC =2

(2)CD =1 and DE = 4

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

10000人做过此题 平均耗时为2min3s 平均正确率为 62%

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6

In planning for a trip, Joan estimated both the distance of the trip, in miles, and her average speed, in miles per hour. She accurately divided her estimated distance by her estimated average speed to obtain an estimate for the time, in hours, that the trip would take. Was her estimate within 0.5 hour of the actual time that the trip took?

(1) Joan's estimate for the distance was within 5 miles of the actual distance.

(2) Joan's estimate for her average speed was within 10 miles per hour of her actual average speed.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9968人做过此题 平均耗时为8min51s 平均正确率为 70%

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7

A certain list consists of 3 different numbers. Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

(1)The range of the 3 numbers is equal to twice the difference between the greatest number and the median.

(2)The sum of the 3 numbers is equal to 3 times one of the numbers.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9969人做过此题 平均耗时为15min52s 平均正确率为 57%

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8

Line $$\ell$$ lies in the xy-plane and does not pass through the origin. What is the slope of line $$\ell$$ ?

(1) The x - intercept of line $$\ell$$ is twice the y-intercept of line $$\ell$$。

(2) The x-and y-intercepts of line $$\ell$$ are both positive.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

657人做过此题 平均耗时为4min5s 平均正确率为 47%

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9

y = ax - 5

y = x + 6

y = 3x + b

In the xy-plane, the straight-line graphs of the three equations above each contain the point (p,r). If a and b are constants, what is the value of b?

(1) a = 2

(2) r = 17

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

1029人做过此题 平均耗时为8min1s 平均正确率为 54%

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10

In the figure above, PQR and STU are identical equilateral triangles, and PQ = 6. What is the perimeter of polygon PQWTUVR?

(1) Triangle SWV has perimeter 9.

(2) VW has length 3.5.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

393人做过此题 平均耗时为5min7s 平均正确率为 62%

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11

The range of the numbers in set S is x, and the range of the numbers in set Tis y. If all of the numbers in set Tare also in set S, is x greater than y ?

(1) Set S consists of 7 numbers

(2) Set T consists of 6 numbers

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

7445人做过此题 平均耗时为29min48s 平均正确率为 44%

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12

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1)The area of the triangle is 25 square centimeters.

(2)The 2 legs of the triangle are of equal length.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

10000人做过此题 平均耗时为2min40s 平均正确率为 68%

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13

Six shipments of machine parts were shipped from a factory on two trucks, with each shipment entirely on one of the trucks. Each shipment was labeled either S1, S2, S3, S4, S5 or S6. The table shows the value of each shipment as a fraction of the total value of the six shipments. If the shipments on the first truck had a value greater than 1/2 of the total value of the six shipments, was S3 shipped on the first truck?

(1) S2 and S4 were shipped on the first truck.

(2) S1 and S6 were shipped on the second truck

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9988人做过此题 平均耗时为9min59s 平均正确率为 56%

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14

lf x, y, and z are three-digit positive integers and if x = y+ z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

(1) The tens digit of x is equal to the sum of the tens digits of y and z.

(2) The units digit of x is equal to the sum of the units digits of y and z.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9998人做过此题 平均耗时为9min49s 平均正确率为 53%

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15

The table above shows the results of a survey of 100 voters who each responded "Favorable" or "Unfavorable" or "Not Sure" when asked about their impressions of Candidate M and of Candidate N. What was the number of voters who responded "Favorable" for both candidates?

(1)The number of voters who did not respond "Favorable" for either candidate was 40.

(2)The number of voters who responded "Unfavorable" for both candidates was 10.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9974人做过此题 平均耗时为17min4s 平均正确率为 63%

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16

A school administrator will assign each student in a group of n students to one of m classrooms. If 3 < m < 13 < n, is it possible to assign each of the n students to one of the m classrooms so that each classroom has the same number of students assigned to it?

(1)It is possible to assign each of 3n students to one of m classrooms so that each classroom has the same number of students assigned to it.

(2)It is possible to assign each of 13n students to one of m classrooms so that each classroom has the same number of students assigned to it.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

10000人做过此题 平均耗时为7min15s 平均正确率为 48%

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17

If q, s, and t are all different numbers, is q < s < t?

(1) t - q = |t - s| + |s - q|

(2) t > q

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

321人做过此题 平均耗时为3min23s 平均正确率为 48%

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18

What is the median number of employees assigned per project for the projects at Company Z?

(1)25 percent of the projects at Company Z have 4 or more employees assigned to each project.

(2)35 percent of the projects at Company Z have 2 or fewer employees assigned to each project.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9980人做过此题 平均耗时为7min34s 平均正确率为 60%

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19

Last year, a certain company began manufacturing product X and sold every unit of product X that it produced. Last year the company's total expenses for manufacturing product X were equal to $100,000 plus 5 percent of the company's total revenue from all units of product X sold. If the company made a profit on product X last year, did the company sell more than 21,000 units of product X last year?

(1) The company's total revenue from the sale of product X last year was greater than $110,000

(2) For each unit of product X sold last year, the company's revenue was $5.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9997人做过此题 平均耗时为16min21s 平均正确率为 49%

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20

Beginning in January of last year, Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months of last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2,600, what was the range of the monthly closing balances of Carl's account last year?

(1)Last year the closing balance of Carl's account for April was less than $2,625.

(2)Last year the closing balance of Carl's account for June was less than $2,675.

• Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
• BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

5062人做过此题 平均耗时为16min36s 平均正确率为 49%

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