平面几何-DS-OG：第1-10题 练习册详情

1

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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2

A certain expressway has Exits J, K, L, and M, in that order. What is the road distance from Exit K to Exit L ?

(1)The road distance from Exit J to Exit L is 21 kilometers.

(2)The road distance from Exit K to Exit M is 26 kilometers.

• 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.

9941人做过此题 平均耗时为5min37s 平均正确率为 49%

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3

In △PQR, if PQ = x, QR = x + 2, and PR = y, which of the three angles of △PQR has the greatest degree measure?

(1)y=x + 3

(2)x = 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 statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

9906人做过此题 平均耗时为6min56s 平均正确率为 56%

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4

A circular tub has a band painted around its circumference, as shown above. What is the surface area of this painted band?

(1)x = 0.5

(2)The height of the tub is 1 meter.

• 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6min36s 平均正确率为 68%

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5

The inside of a rectangular carton is 48 centimeters long, 32 centimeters wide, and 15 centimeters high. The carton is filled to capacity with k identical cylindrical cans of fruit that stand upright in rows and columns, as indicated in the figure above. If the cans are 15 centimeters high, what is the value of k ?

(1)Each of the cans has a radius of 4 centimeters.

(2)Six of the cans fit exactly along the length of the carton.

• 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.

3237人做过此题 平均耗时为1min34s 平均正确率为 75%

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6

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 64%

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7

The length of the edging that surrounds circular garden K is $$\frac12$$ the length of the edging that surrounds circular garden G. What is the area of garden K ? (Assume that the edging has negligible width.)

(1)The area of G is 25π square meters.

(2)The edging around G is l0π meters long.

• 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.

1424人做过此题 平均耗时为1min49s 平均正确率为 74%

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8

Quadrilateral RSTU shown above is a site plan for a parking lot in which side RU is parallel to side ST and RU is longer than ST. What is the area of the parking lot?

(1)$$RU = 80$$ meters

(2)$$TU = 20\sqrt{10}$$ meters

• 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.

6635人做过此题 平均耗时为1min13s 平均正确率为 82%

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9

In the figure above, what is the value of x + y ?

(1)x = 70

(2)△ABC and △ADC are both isosceles triangles.

• 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.

8715人做过此题 平均耗时为17min45s 平均正确率为 47%

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10

In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A ?

(1)The area of square region B is 9.

(2)The area of square region C is $$\frac{64}{9}$$

• 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.

2723人做过此题 平均耗时为8min58s 平均正确率为 50%

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