DS-OG：第306-325题 练习册详情

1

A certain dealership has a number of cars to be sold by its salespeople. How many cars are to be sold?

(1) If each of the salespeople sells 4 of the cars, 23 cars will remain unsold.

(2) If each of the salespeople sells 6 of the cars, 5 cars will remain unsold.

• 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

What is the value of the integer x?

(1) x rounded to the nearest hundred is 7,200.

(2) The hundreds digit of x is 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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3

For all x, the expression $$x^{*}$$ is defined to be ax + a, where a is a constant. What is the value of $$2^{*}?$$

(1) $$3^{*} = 2$$

(2) $$5^{*} = 3$$

• 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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4

If p and q are positive, is $$\frac{q}{p}$$less than 1?

(1) p is less than 4.

(2) q is less than 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.

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5

In the quilting pattern shown above, a small square has its vertices on the side of a larger square. What is the side length, in centimeters, of the larger square?

(1) The side length iof the smaller square is 10 cm.

(2) Each vertex of the small square cuts 1 side of the larger into 2 segments with length in the ratio of 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.

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6

In the rectangular coordinate system above, if $$\bigtriangleup$$ OPQ and $$\bigtriangleup$$ QRS have equal area, what are the coorddinates of point R?

(1) The coordinates of point P are (0,12).

(2) OP = OQ and QS = RS.

• 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 y is greater than 110 percent of x, is y greater than 75?

(1) x > 75

(2) y - x = 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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8

Is xm < ym?

(1) x > y

(2) m < 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

In the figure above, $$\overline{AB}$$, which has length z cm, is tangent to the circle at point A , and $$\overline{BD}$$, which has length y cm, intersects the circle at point C. If BC = x cm and $$z = \sqrt{xy}$$, what is the value of x?

(1) CD = x cm

(2) $$z = 5\sqrt{2}$$

• 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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10

If x, y, and z are three integers, are they consecutive integers?

(1) z - x = 2

(2) x < y < 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.

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11

In the figure shown, lines k and m are parallel to each other, Is x = z?

(1) x = w

(2)y = 180 - 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 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

Was the range of the amounts of money that Company Y budgeted for its project last year equal to the range of the amounts of money that it budgeted for its projects this year?

(1) Both last year and this year, Company Y budgeted money for 12 projects and the least amount of money that it budgeted was $400.

(2) Both last year and this year, the average (arithmetic mean) amount of money that Company Y budgeted per project was $2,000.

• 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 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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13

If x and y are integers, what is the value of x?

(1) xy = 1

(2) $$x\neq - 1$$

• 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 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

What was the amount of money donated to a certain charity?

(1) Of the amount donated, 40 percent came from corporate donations.

(2) Of the amount donated, $1.5 million came from noncorporate donations.

• 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

When the wind speed is 9 miles per hour, the wind-chill factor w is given by

w = -17.366 + 1.19t,

where t is the temperature in degrees Fahrenheit. If at noon yesterday the wind speed was 9 miles per hour, was the wind-chill factor greater than 0 ?

(1) The temperature at noon yesterday was greater than 10 degrees Fahrenheit.

(2) The temperature at noon yesterday was less than 20 degrees Fahrenheit.

• 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 collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1)The units digit of the sum of the numbers on the remaining 35 cards is 6.

(2)The sum of the numbers on the remaining 35 cards is 176.

• 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 x > 0, what is the value of x?

(1) $$x^{3} - x = 0$$

(2) $$ \sqrt[3]{x} - x = 0$$

• 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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18

If x and y are positive integers, what is the remainder when $$10^{x} + y$$ is divided by 3?

(1) x =5

(2) y = 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

Of the 230 single-family homes built in City X last year, how many were occupied at the end of the year?

(1) Of all single- family homes in City X, 90 percent were occupied at the end of last year.

(2) A total of 7,200 single-family homes in City X were occupied at the end of last year.

• 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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20

If x is a positive integer, what is the value of x?

(1) $$x^{2} =\sqrt{x}$$

(2) $$\frac{n}{x}=n$$ and $$n \neq 0$$.

• 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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