DS-OG：第326-345题 练习册详情

1

What is the sum of the first four terms of sequence S?

(1) After the first two terms of S, the value of each term of S is equal to the average (arithmetic mean) of the last two preceding terms.

(2) The average (arithmetic mean) of the first three terms of S is 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

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2

In a certain order, the pretax price of each regular pencil was $0.03, the pretax price of each deluxe pencil was $0.05, and there were 50% more deluxe pencil than regular pencils. All taxes on the order are a fixed percent of the pretax price. The sum of the total pretax price of the order and the tax on the order was $44.10. What was the amount, in dollars, of the tax on the order?

(1) The tax on the order was 5% of the total pretax price of the order.

(2) The order contained exactly 400 regular pencils.

• 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.

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3

If m is an integer greater than 1, is m an even integer?

(1) 32 is a factor of m.

(2) m is a factor of 32.

• 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.

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4

If p, s, and t are positive, is |ps - pt| > p(s - t)?

(1) p < s

(2) s < t

• 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.

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5

If y = $$x^{2} - 6x + 9$$, what is the value of x?

(1) y = 0

(2) x + y = 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.

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6

In the figure shown, quadrilateral ABCD is inscribed in a circle of radius 5. What is the perimeter of quadrilateral ABCD?

(1) The length of AB is 6 and the length of CD is 8.

(2) AC is a diameter of the circle.

• 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.

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7

If $$rs\neq 0$$, is $$ \frac{1}{r} + \frac{1}{s} = 4$$

(1) r + s = 4rs

(2) r = 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.

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8

If a, b, c, and d are numbers on the number line shown and if the tick marks are equally spaced, what is the value of a + c?

(1) a + b =-8

(2) a +d = 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.

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9

Is the median of the five numbers a, b, c, d, and e equal to d?

(1) a < c < e

(2) b < d < c

• 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.

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10

During a certain bicycle ride, was Sherry's average speed faster than 24 kilometers per hour?

( 1 kilometer = 1,000 meters)

(1) Sherry's average speed during the bicycle ride was faster than 7 meters per second.

(2) Sherry's average speed during the bicycle ride was slower than 8 meters per second.

• 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.

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11

Is the integer n a prime number?

(1) $$24 \le n \le 28$$

(2) n is not divisible by 2 or 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.

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12

The total cost of an office dinner was shared equally by k of the n employees who attended the dinner. What was the total cost of the dinner?

(1)Each of the k employees who shared the cost of the dinner paid $19.

(2)If the total cost of the dinner had been shared equally by k + 1 of the n employees who attended the dinner, each of the k + 1 employees would have paid $18.

• 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.

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13

Is x > y?

(1) x + y > x - y

(2) 3x > 2y

• 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.

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14

Which of the positive numbers x or y is greater?

(1) y = 2x

(2) 2x + 5y =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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

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15

What is the volume of the cube above?

(1)The surface area of the cube is 600 square inches.

(2)The length of diagonal AB is $${10}\sqrt3$$ inches.

• 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.

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16

A total of 20 amounts are entered on a spreadsheet that has 5 rows and 4 columns; each of the 20 positions in the spreadsheet contains one amount. The average (arithmetic mean) of the amounts in row i is $${R}_{i}$$ $$(1 \leq i \leq 5)$$. The average of the amounts in column j is Cj $$(1 \leq j \leq 4)$$. What is the average of all 20 amounts on the spreadsheet?

(1) $${R}_{1}+{R}_{2}+{R}_{3}+{R}_{4}+{R}_{5}={550}$$

(2) $${C}_{1}+{C}_{2}+{C}_{3}+{C}_{4}={440}$$

• 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.

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17

If the set S consists of five consecutive positive integers, what is the sum of these five integers?

(1) The integer 11 is in S , but 10 is not in S.

(2) The sum of the even integers in S is 26.

• 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.

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18

What is the value of x?

(1) x + 1 = 2 - 3x

(2) $$\frac{1}{2x} = 2$$

• 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.

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19

Some computers at a certain company are Brand X and the rest are Brand Y. If the ratio of the number of Brand Y computers to the number of Brand X computers at the company is 5 to 6, how many of the computers are Brand Y ?

(1) There are 80 more Brand X computers than Brand Y computers at the company.

(2) There is a total of 880 computers at the company.

• 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.

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20

If a and b are constants, what is the value of a?

(1) a < b

(2) (t - a )(t - b ) = $$t^{2} + t - 12$$, for all values of t

• 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.

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