DS-OG20：第41-60题 练习册详情

1

Square ABCD is inscribed in circle O. What is the area of square region ABCD?

(1) The area of circular region O is 64π.

(2) The circumference of circle O is 16π.

• 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.

9979人做过此题 平均耗时为18min4s 平均正确率为 63%

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2

Lines k and m are parallel to each other. Is the slope of line k positive?

(1)Line k passes through the point (3, 2).

(2)Line m passes through the point (-3, 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.

9998人做过此题 平均耗时为5min58s 平均正确率为 47%

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3

In cross section, a tunnel that carries one lane of one-way traffic is a semicircle with radius 4.2 m. Is the tunnel large enough to accommodate the truck that is approaching the entrance to the tunnel?

(1) The maximum width of the truck is 2.4 m.

(2) The maximum height of the truck is 4 m.

• 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.

599人做过此题 平均耗时为6min6s 平均正确率为 53%

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4

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 51%

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5

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 44%

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6

Robin invested a total of $12,000 in two investments, X and Y, so that the investments earned the same amount of simple annual interest .How many dollars did Robin invest in investment Y ?

(1) Investment X paid 3 percent simple annual interest, and investment Y paid 6 percent simple annual interest.

(2) Robin invested more than $1,000 in investment X.

• 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.

783人做过此题 平均耗时为5min39s 平均正确率为 49%

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7

In a real estate office that employs n salespeople, f of them are females and x of the females are new employees. What is the value of n?

(1)If an employee were randomly selected from the n employees, the probability of selecting a female would be 2/3

(2)If an employee were randomly selected from the f female employees, the probability of selecting a new employee would be 1/2

• 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.

1063人做过此题 平均耗时为8min15s 平均正确率为 64%

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8

Is $\frac{x+1}{y+1}$>$\frac{x}{y}$?

(1)$0 < x < y$

(2)$xy > 0$

• 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• Each statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient. 显示答案

512人做过此题 平均耗时为4min22s 平均正确率为 64%

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9

Do at least 60 percent of the students in Pat's class walk to school?

(1) At least 60 percent of the female students in Pat's class walk to school.

(2) The number of students in Pat's class who walk to school is twice the number of students who do not walk to school.

• 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.

734人做过此题 平均耗时为4min6s 平均正确率为 47%

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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 51%

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11

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 67%

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12

If a and b are positive integers, is $\frac{a}{b} < \frac{9}{11}$ ?



(1)$\frac{ a}{b} < 0.818$



(2)$\frac{ b}{a} > 1.223$

• 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.

603人做过此题 平均耗时为7min29s 平均正确率为 61%

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13

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 64%

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14

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 45%

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15

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 62%

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16

If x and y are positive integers, what is the value of $\sqrt{x}+\sqrt{y}$ ?

(1) x + y = 15

(2) $\sqrt{xy}= 6$

• 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.

706人做过此题 平均耗时为3min46s 平均正确率为 53%

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17

A certain truck uses $\frac{1}{12}$ + ${k}{v}^{2}$ gallons of fuel per mile when its speed is v miles per hour, where k is a constant. At what speed should the truck travel so that it uses $\frac{5}{12}$ gallon of fuel per mile?

(1) The value of k is $\frac{1}{10800}$

(2) When the truck travels at 30 miles per hour, it uses $\frac{1}{6}$ gallon of fuel per mile.

• 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.

990人做过此题 平均耗时为7min25s 平均正确率为 41%

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18

If r and s are positive integers, is r + s even?

1.r is even.

2.s is even.

• 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. This Answer is Incorrect

382人做过此题 平均耗时为1min1s 平均正确率为 64%

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19

In the figure above, ∆PQR has angle measures as shown. Is x < y ?

1.PQ = QR

2.PR > QR

• 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.

409人做过此题 平均耗时为2min19s 平均正确率为 54%

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20

If S is a set of odd integers and 3 and –1 are in S, is –15 in S ?

1.5 is in S.

2.Whenever two numbers are in S, their product is in S.

• 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.

489人做过此题 平均耗时为3min7s 平均正确率为 68%

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