DS-OG20：第76-90题 练习册详情

1

In the figure above, RST is a triangle with angle measures as shown and PRTQ is a line segment. What is the value of x + y ?

1.s = 40

2.r = 70

• 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.

258人做过此题 平均耗时为2min5s 平均正确率为 56%

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2

If R, S, and T are points on a line, and if R is 5 meters from T and 2 meters from S, how far is S from T ?

1.R is between S and T.

2.S is to the left of R, and T is to the right of R.

• 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.

169人做过此题 平均耗时为1min46s 平均正确率为 70%

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3

Is n equal to zero?

1.The product of n and some nonzero number is 0.

2.The sum of n and 0 is 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.

170人做过此题 平均耗时为40s 平均正确率为 42%

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4

On a map,$$\frac{1}{2}$$ inch represents 100 miles. According to this map, how many miles is City X from City Y ?

1.City X is 3 inches from City Y on the map.

2.Cities X and Y are each 300 miles from City 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.

167人做过此题 平均耗时为58s 平均正确率为 59%

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5

What is the remainder when the positive integer n is divided by 5 ?

1.When n is divided by 3, the quotient is 4 and the remainder is 1.

2.When n is divided by 4, the remainder 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

173人做过此题 平均耗时为1min35s 平均正确率为 44%

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6

If r and s are positive numbers and θ is one of the operations, +, −, *, or ÷, which operation is θ?

1.If r = s, then r θ s = 0.

2.If r ≠ s, then r θ s ≠ s θ r.

• 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.

384人做过此题 平均耗时为3min19s 平均正确率为 45%

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7

In any sequence of n nonzero numbers, a pair of consecutive terms with opposite signs represents a sign change. For example, the sequence –2, 3, –4, 5 has three sign changes. Does the sequence of nonzero numbers $$s_1$$, $$s_2$$, $$s_3$$, - , $$s_n$$ have an even number of sign changes?

1.$$s_k= (-1)^{k}$$ for all positive integers k from 1 to n.

2.n 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.

397人做过此题 平均耗时为5min35s 平均正确率为 70%

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8

Jack picked 76 apples. Of these, he sold 4y apples to Juanita and 3t apples to Sylvia. If he kept the remaining apples, how many apples did he keep? (t and y are positive integers.)

1.y ≥ 15 and t = 2

2.y = 17

• 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.

363人做过此题 平均耗时为3min58s 平均正确率为 63%

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9

What number is 6 more than x + y ?

1.y is 3 less than x.

2.y is twice 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.

295人做过此题 平均耗时为2min43s 平均正确率为 53%

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10

The total price of 5 pounds of regular coffee and 3 pounds of decaffeinated coffee was $21.50. What was the price of the 5 pounds of regular coffee?

1.If the price of the 5 pounds of regular coffee had been reduced 10 percent and the price of the 3 pounds of decaffeinated coffee had been reduced 20 percent, the total price would have been $18.45.

2.The price of the 5 pounds of regular coffee was $3.50 more than the price of the 3 pounds of decaffeinated coffee.

• 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.

282人做过此题 平均耗时为3min28s 平均正确率为 67%

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11

If a and b are integers, is $$a^{5}$$ < $$4^{b}$$ ?

1.$$a^{3}= –27$$

2.$$b^{2} = 16$$

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

297人做过此题 平均耗时为2min29s 平均正确率为 49%

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12

If each side of parallelogram P has length 1, what is the area of P ?

1.One angle of P measures 45 degrees.
2.The altitude of P is $$\frac{\sqrt{2}}{2}$$

• 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.

198人做过此题 平均耗时为2min57s 平均正确率为 53%

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13

If x is an integer greater than 0, what is the remainder when x is divided by 4 ?

1.The remainder is 3 when x + 1 is divided by 4.

2.The remainder is 0 when 2x is divided 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.

266人做过此题 平均耗时为3min8s 平均正确率为 45%

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14

A certain painting job requires a mixture of yellow, green, and white paint. If 12 quarts of paint are needed for the job, how many quarts of green paint are needed?

1.The ratio of the amount of green paint to the amount of yellow and white paint combined needs to be 1 to 3.

2.The ratio of the amount of yellow paint to the amount of green paint needs to be 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 statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

171人做过此题 平均耗时为1min43s 平均正确率为 54%

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15

Is the average (arithmetic mean) of the numbers x, y, and z greater than z ?

1.z – x < y – z

2.x < z < 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.

163人做过此题 平均耗时为1min54s 平均正确率为 46%

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