DS-OG22: 第463-482题 练习册详情

1

If r and s are the roots of the equation $${x}^{2}+{b}{x}+{c}={0}$$, where b and c are constants, is rs < 0 ?

(1) b < 0

(2) c < 0

• 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.

5717人做过此题 平均耗时为27min16s 平均正确率为 46%

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2

The figure above represents an L-shaped garden. What is the value of k?

(1) The area of the garden is 189 square feet.

(2) The perimeter of the garden is 60 feet

• 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.

228人做过此题 平均耗时为3min6s 平均正确率为 93%

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3

The only articles of clothing in a certain closet are shirts, dresses, and jacket. The ratio of the number of shirts to the number of dresses to jackets in the closet is 9:4:5, respectively. If there are more than 7 dresses in the closet, what is the total number of articles of clothing in the closet?

(1) The total number of shirts and jackets inthe closet is less than 30.

(2) The total number of shirts and dresses in the closet is 26.

• 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.

0人做过此题 平均耗时为0 平均正确率为 0%

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4

The figure above represents a circle graph of Company H's total expenses broken down by the expenses for each of its five divisions. If O is the center of the circle and if Company H's total expenses are $5,400,000, what are the expenses for Division R ?

(1)x = 94

(2)The total expenses for Divisions S and T are twice as much as the expenses for Division R.

• 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.

9947人做过此题 平均耗时为12min47s 平均正确率为 54%

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5

If x is negative, is $$x < -3$$?

(1)$${x}^{2} >{9}$$

(2)$${x}^{3}<-{9}$$

• 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.

9991人做过此题 平均耗时为5min7s 平均正确率为 66%

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6

What is the number of cans that can be packed in a certain carton?

(1) The interior volume of this carton is 2,304 cubic inches.

(2) The exterior of each can is 6 inches high and has a diameter of 4 inches.

• 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.

9478人做过此题 平均耗时为21min11s 平均正确率为 69%

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7

Each of the letters in the table above represents one of the numbers 1, 2, or 3, and each of these numbers occurs exactly once in each row and exactly once in each column. What is the value of r?

(1)v + z = 6

(2)s + t + u + x = 6

• 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8min28s 平均正确率为 48%

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8

Material A costs $3 per kilogram, and material B costs $5 per kilogram. If 10 kilograms of material K consists of x kilograms of material A and y kilograms of material B, is x > y?

(1)y > 4

(2)The cost of the 10 kilograms of material K is less than $40.

• 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.

9956人做过此题 平均耗时为16min20s 平均正确率为 60%

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9

At what speed was a train traveling on a trip when it had completed half of the total distance of the trip?

(1)The trip was 460 miles long and took 4 hours to complete.

(2)The train traveled at an average rate of 115 miles per hour on the trip.

• 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.

2309人做过此题 平均耗时为8min21s 平均正确率为 47%

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10

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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11

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 63%

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12

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 67%

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13

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 53%

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14

In the figure above, points A, B, C, D, E, and F lie on a line perpendicular to the square's sides. If point A lies on the square, point B lies on the circle, point C bisects AF, point D is the center of the circle, point E bisects DF, and point F lies on the circle and on the square, what is the difference in area between the square and the circle?

1. $AB=6$ and $BC=4$.
2. $AB=6$ and $EF=3.5$.

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

0人做过此题 平均耗时为0 平均正确率为 0%

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15

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 40%

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16

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 63%

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17

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 57%

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18

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 51%

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19

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 40%

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20

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 47%

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