DS-OG：第21-40题 练习册详情

1

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 52%

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2

In a survey of 200 college graduates, 30 percent said they had received student loans during their college careers, and 40 percent said they had received scholarships. What percent of those surveyed said that they had received neither student loans nor scholarships during their college careers?

(1)25 percent of those surveyed said that they had received scholarships but no loans.

(2)50 percent of those surveyed who said that they had received loans also said that they had received scholarships.

• 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.

9999人做过此题 平均耗时为16min57s 平均正确率为 67%

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3

Is the number of members of Club X greater than the number of members of Club Y ?

(1)Of the members of Club X, 20 percent are also members of Club Y.

(2)Of the members of Club Y, 30 percent are also members of Club 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 statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

6340人做过此题 平均耗时为11min23s 平均正确率为 58%

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4

What is the ratio of the average (arithmetic mean) height of students in class X to the average height of students in class Y?

(1)The average height of the students in class X is 120 centimeters.

(2)The average height of the students in class X and class Y combined is 126 centimeters.

• 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1min40s 平均正确率为 74%

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5

In the two-digit integers $$3■$$ and $$ 2▲$$, the symbols $$■$$ and $$▲$$ represent different digits, and the product ( $$3■$$) ($$2▲$$) is equal to 864. What digit does $$■$$ represent?

(1) The sum of $$■$$ and $$▲$$ is 10.

(2) The product of $$■$$ of $$▲$$ is 24.

• 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.

820人做过此题 平均耗时为7min35s 平均正确率为 45%

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6

A total of $60,000 was invested for one year. Part of this amount earned simple annual interest at the rate of x percent per year, and the rest earned simple annual interest at the rate of y percent per year. If the total interest earned by the $60,000 for that year was $4,080, what is the value of x?

(1)$${x}=\frac {3y} {4}$$

(2)The ratio of the amount that earned interest at the rate of x percent per year to the amount that earned interest at the rate of y percent per year was 3 to 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.

5183人做过此题 平均耗时为2min37s 平均正确率为 63%

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7

If the total price of n equally priced shares of a certain stock was $12,000, what was the price per share of the stock?

(1) If the price per share of the stock had been $1 more, the total price of the n shares would have been $300 more.

(2) If the price per share of the stock had been $2 less, the total price of the n shares would have been 5 percent less.

• 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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8

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?

(1)$$x > y$$

(2)$$\frac{xy} {100}<{x}-{y}$$

• 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 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11min1s 平均正确率为 42%

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9

Last year in a group of 30 businesses, 21 reported a net profit and 15 had investments in foreign markets. How many of the businesses did not report a net profit nor invest in foreign markets last year?

(1) last year 12 of the 30 businesses reported a net profit and had investments in foreign markets.

(2) last year 24 of the 30 businesses reported a net profit or invested in foreign markets, or both.

• 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.

9965人做过此题 平均耗时为35min32s 平均正确率为 70%

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10

Are all of the numbers in a certain list of 15 numbers equal?

(1)The sum of all the numbers in the list is 60.

(2)The sum of any 3 numbers in the list is 12.

• 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1min46s 平均正确率为 80%

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11

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 65%

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12

If m and n are positive integers, is m+n divisible by 4?

(1) m and n are each divisible by 2.

(2) Neither m nor n is divisible by 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.

0人做过此题 平均耗时为0 平均正确率为 0%

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13

What is the area of rectangular region R?

(1) Each diagonal of R has length 5.

(2) The perimeter of R 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.

0人做过此题 平均耗时为0 平均正确率为 0%

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14

Stations X and Y are connected by two separate, straight, parallel rail lines that are 250 miles long. Train P and train Q simultaneously left Station X and Station Y, respectively, and each train traveled to the other's point of departure. The two trains passed each other after traveling for 2 hours. When the two trains passed, which train was nearer to its destination?

(1)At the time when the two trains passed, train P had averaged a speed of 70 miles per hour.

(2)Train Q averaged a speed of 55 miles per hour for the entire 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.

10000人做过此题 平均耗时为3min57s 平均正确率为 36%

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15

At a bakery, all donuts are priced equally and all bagels are priced equally. What is the total price of 5 donuts and 3 bagels at the bakery?

(1)At the bakery, the total price of 10 donuts and 6 bagels is $12.90.

(2)At the bakery, the price of a donut is $0.15 less than the price of a bagel.

• 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.

1585人做过此题 平均耗时为3min13s 平均正确率为 42%

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16

If $$x\neq0$$, what is the value of $$(\frac{x^{p}}{x^{q}})^{4}$$？

(1) p = q

(2) x =3

• 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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17

What is the value of x + y in the figure above?

(1)W=95

(2)Z=125

• 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8min21s 平均正确率为 52%

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18

Joanna bought only $0.15 stamps and $0.29 stamps. How many $0.15 stamps did she buy?

(1)She bought $4.40 worth of stamps.

(2)She bought an equal number of $0.15 stamps and $0.29 stamps.

• 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3min2s 平均正确率为 46%

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19

If r, s, and t are nonzero integers, is $$r^{5}s^{3}t^{4}$$ negative ?

(1) rt is negative

(2) s is negative

• 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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20

In the xy-plane,region R consists of all the points (x, y) such that 2x + 3y ≤ 6. Is the point (r, s)in region R ?

(1)3r +2s =6

(2)r ≤ 3 and s ≤ 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.

10000人做过此题 平均耗时为3min42s 平均正确率为 43%

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