DS-OG：第255-275题 练习册详情

1

If a is a 3-digit integer and b is a 3-digit integer, is the units digit of the product of a and b greater than 5?

(1) The units digit of a is 4

(2) The units digit of b is 7.

• 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.

1552人做过此题 平均耗时为8min59s 平均正确率为 63%

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2

In a certain group of 50 people, how many are doctors who have a law degree?

(1) In a certain group, 36 people are doctors.

(2) In a group, 18 people have a law degree.

• 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.

1367人做过此题 平均耗时为5min35s 平均正确率为 69%

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3

If a and b are integers, is a+b+3 an odd integer?

(1) ab is an odd integer.

(2) a-b is an even integer.

• 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.

1223人做过此题 平均耗时为7min58s 平均正确率为 58%

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4

The people in a line waiting to buy tickets to a show are standing one behind the other. Adam and Beth are among the people in the line, and Beth is standing behind Adam with a number of people between them. If the number of people in front of Adam plus the number of people behind Beth is 18, how many people in the line are behind Beth?

(1) There are a total of 32 people in the line .

(2) 23 people in the line are behind Adam.

• 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.

1498人做过此题 平均耗时为14min3s 平均正确率为 52%

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5

In the figure above, what is the value of z?

(1) x=y=1

(2)w=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.

3590人做过此题 平均耗时为8min48s 平均正确率为 40%

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6

Every object in a box is either a sphere or a cube,and every object in the box is either red or green. How many objects are in the box?

(1) There are six cubes and five green objects in the box.

(2) There are two red spheres in the box.

• 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.

846人做过此题 平均耗时为6min15s 平均正确率为 62%

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7

If x and y are positive integers, is xy even?

(1) $$x^{2} + y^{2} - 1$$ is divisible by 4.

(2) x+y is odd.

• 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.

1316人做过此题 平均耗时为12min0s 平均正确率为 54%

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8

Of a group of 50 households, how many have at least one cat or at least one dog, but not both?

(1) The number of households that have at least one cat and at least one dog is 4.

(2) The number of households that have no cats and no dogs is 14.

• 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.

1184人做过此题 平均耗时为7min24s 平均正确率为 59%

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9

A certain mixture of paint requires blue, yellow, and red paints in ratios of 2:3:1, respectively, and no other ingredients. If there are ample quantities of the blue and red paints available, is there enough of the yellow paint available to make the desired amount of the mixture?

(1) Exactly 20 quarts of the mixture are needed.

(2) Exactly 10 quarts of the yellow paint are available.

• 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.

4221人做过此题 平均耗时为28min37s 平均正确率为 61%

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10

A certain plumber charges $92 for each job completed in 4 hours or less and $23 per hour for each job completed in more than 4 hours. If it took the plumber a total of 7 hours to complete two separate jobs, what was the total amount charged by the plumber for the jobs?

(1) The plumber charges $92 for one of the two jobs.

(2) The plumber charged $138 for one of the two jobs.

• 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.

942人做过此题 平均耗时为9min39s 平均正确率为 62%

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11

Is the area of the triangular region above less than 20?

(1) $$x^{2} +y^{2}\neq z^{2}$$

(2) x+y<13

• 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.

1497人做过此题 平均耗时为12min6s 平均正确率为 44%

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12

If x and y are positive numbers, is $$\frac{x+1}{y+1}>\frac{x}{y}$$?

(1) $$x>1$$

(2) $$x\lt y$$

• 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.

928人做过此题 平均耗时为6min28s 平均正确率为 68%

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13

Jack wants to use a circular rug on his rectangular office floor to cover two small circular stains, each less than $$\frac{π}{100} $$square feet in area and each more than 3 feet from the nearest wall. Can the rug be placed to cover both stains?

(1) Jack's rug covers an area of 9π square feet.

(2) The centers of the stains are less than 4 feet apart.

• 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.

302人做过此题 平均耗时为5min54s 平均正确率为 66%

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14

In the multiplication table above, each letter represents an integer. What is the value of c?

(1) c=f

(2) $$h\neq0$$

• 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.

281人做过此题 平均耗时为4min57s 平均正确率为 45%

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15

Is the product of two positive integers x and y divisible by the sum of x and y?

(1) x=y

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

372人做过此题 平均耗时为2min13s 平均正确率为 66%

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16

For a certain city's library, the average cost of purchasing each new book is $28. The library receives $15,000 from the city each year; the library also receives a bonus of $2,000 if the total number of items checked out over the course of the year exceeds 5,000. Did the library receive the bonus last year?

(1) The library purchased an average of 50 new books each month last year and received enough money from the city to cover this cost.

(2) The lowest number of items checked out in one month was 459.

• 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.

335人做过此题 平均耗时为5min39s 平均正确率为 70%

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17

Is x<5?

(1) $$x^{2}$$>5

(2)$$ x^{2}+x<5$$

• 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.

257人做过此题 平均耗时为2min50s 平均正确率为 43%

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18

Last school year, each of the 200 students at a certain high school attended the school for the entire year. If there were 8 cultural performances at the school during the last school year, what was the average (arithmetic mean) number of students attending each cultural performance?

(1) Last school year, each students attended at least one cultural performance.

(2) Last school year, the average number of cultural performances attended per student was 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

397人做过此题 平均耗时为5min40s 平均正确率为 60%

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19

If x, y, and z are positive numbers, what is the value of the average (arithmetic mean) of x and z?

(1) x-y=y-z

(2) $$x^{2}-y^{2}=z$$

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

258人做过此题 平均耗时为3min29s 平均正确率为 68%

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20

If r and t are three-digit positive integers, is r greater than t?

(1) The tens digit of r is greater than each of the three digits of t.

(2) The tens digit of r is less than either of the other two digits of 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

284人做过此题 平均耗时为2min26s 平均正确率为 48%

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