DS-OG：第61-80题 练习册详情

1

At a certain picnic, each of the guests was served either a single scoop or a double scoop of ice cream. How many of the guests were served a double scoop of ice cream?

(1)At the picnic, 60 percent of the guests were served a double scoop of ice cream.

(2)A total of 120 scoops of ice cream were served to all the guests at the picnic.

• 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.

221人做过此题 平均耗时为3min11s 平均正确率为 99%

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2

For a convention, a hotel charges a daily room rate of $120 for 1 person and x dollars for each additional person. What is the charge for each additional person?

(1)The daily cost per person for 4 people sharing the cost of a room equally is $45.

(2)The daily cost per person for 2 people sharing the cost of a room equallyis$25 more than the corresponding cost for 4 people.

• 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.

9958人做过此题 平均耗时为15min37s 平均正确率为 42%

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3

Stores L and M each sell a certain product at a different regular price. If both stores discount their regular price of the product, is the discount price at Store M less than the discount price at Store L ?

(1)At Store L the discount price is 10 percent less than the regular price; at Store M the discount price is 15 percent less than the regular price.

(2)At Store L the discount price is $5 less than the regular store price; at Store M the discount price is $6 less than the regular price.

• 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29min9s 平均正确率为 47%

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4

If d denotes a decimal, is $$d \ge 0.5$$?

(1)When d is rounded to the nearest tenth, the result is 0.5.

(2)When d is rounded to the nearest integer, the result is 1.

• 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.

9993人做过此题 平均耗时为8min12s 平均正确率为 43%

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5

How many integers are there between, but not including, integers r and s ?

(1)s-r= 10

(2)There are 9 integers between, but not including, r + 1 and s + 1.

• 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.

4571人做过此题 平均耗时为18min23s 平均正确率为 55%

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6

If n and t are positive integers, is n a factor of t?

(1)$$n=3^{n-2}$$

(2)$$t=3^{n}$$

• 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.

7930人做过此题 平均耗时为26min13s 平均正确率为 48%

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7

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 50%

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8

Three machines, K, M, and P, working simultaneously and independently at their respective constant rates, can complete a certain task in 24 minutes. How long does it take Machine K, working alone at its constant rate, to complete the task?

(1)Machines M and P, working simultaneously and independently at their respective constant rates, can complete the task in 36 minutes.

(2)Machines K and P, working simultaneously and independently at their respective constant rates, can complete the task in 48 minutes.

• 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9min10s 平均正确率为 68%

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9

The table above shows the results of a survey of 100 voters each responded “favorable” or “unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate N. What was the number of voters who responded “favorable” for both candidates?

(1)The number of voters who did not respond “favorable” for either candidate was 40.

(2) The number of voters who responded “unfavorable” for both candidates was 10.

• 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.

9967人做过此题 平均耗时为8min10s 平均正确率为 43%

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10

Mary persuaded n friends to donate $500 each to her election campaign, and then each of these n friends persuaded n more people to donate $500 each to Mary's campaign. If no one donated more than once and if there were no other donations, what was the value of n?

(1)The first n people donated $$\frac1 {16}$$ of the total amount donated.

(2)The total amount donated 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.

9961人做过此题 平均耗时为12min37s 平均正确率为 42%

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11

Carlotta can drive from her home to her office by one of two possible routes. If she must also return by one of these routes, what is the distance of the shorter route?

(1)When she drives from her home to her office by the shorter route and returns by the longer route, she drives a total of 42 kilometers.

(2)When she drives both ways, from her home to her office and back, by the longer route, she drives a total of 46 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.

625人做过此题 平均耗时为1min23s 平均正确率为 92%

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12

Is $$x >{y}$$?

(1)$$x = y + 2$$

(2)$$\frac x 2 = y-1$$

• 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.

5806人做过此题 平均耗时为55s 平均正确率为 84%

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13

If m is an integer, is m odd?

(1)$$\frac m 2$$ is not an even integer.

(2)m - 3 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 statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

1799人做过此题 平均耗时为1min42s 平均正确率为 57%

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14

What is the area of triangular region ABC above?

(1)The product of BD and AC is 20.

(2)x = 45

• 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.

2154人做过此题 平均耗时为5min21s 平均正确率为 53%

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15

In the xy-plane, the line with equation ax + by + c = 0, where $$abc \neq 0$$, has slope$$\frac{2}{3}$$. What is the value of b?

(1) a = 4

(2) c = −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.

10000人做过此题 平均耗时为1min32s 平均正确率为 92%

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16

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

(1)t - p = p - m

(2)t - m = 16

• 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.

9860人做过此题 平均耗时为40min8s 平均正确率为 59%

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17

Each week a certain salesman is paid a fixed amount equal to $300, plus a commission equal to 5 percent of the amount of his sales that week over $1,000. What is the total amount the salesman was paid last week?

(1)The total amount the salesman was paid last week is equal to 10 percent of the amount of his sales last week.

(2)The salesman's sales last week totaled $5,000.

• 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3min55s 平均正确率为 79%

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18

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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19

Leo can buy a certain computer for $${P}_{1}$$ dollars in State A, where the sales tax is $${t}_{1}$$ percent, or he can buy the same computer for $${p}_{2}$$ dollars in State B, where the sales tax is $${t}_{2}$$ percent. Is the total cost of the computer greater in State A than in State B ?

(1)$${t}_{1} >{t}_{2}$$

(2)$${p}_{1}{t}_{1} >{p}_{2}{t}_{2}$$

• 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.

8577人做过此题 平均耗时为27min55s 平均正确率为 67%

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20

If $$r > 0$$ and $$s > 0$$, is$$\frac{r}{s}<\frac{s}{r}$$ ?

(1)$$\frac{r}{3s}=\frac{1}{4}$$

(2)$$s = r + 4$$

• 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.

8075人做过此题 平均耗时为24min5s 平均正确率为 42%

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