DS-Manhattan：第61-80题 练习册详情

1

Is $$x > 0$$?

(1) $$x^2 < 9$$

(2) $$x^3 < -8 $$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

213人做过此题 平均耗时为1min6s 平均正确率为 48%

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2

If $$5^ x = y$$, what is x?

(1) $$y = 25$$

(2) $$y^ 3 = 15,625$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

137人做过此题 平均耗时为52s 平均正确率为 59%

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3

If$$\sqrt{x}=y$$, what is the value of x?

(1) y = 2

(2) 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

136人做过此题 平均耗时为35s 平均正确率为 59%

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4

A circular pizza is cut into eight wedge-shaped slices of equal size. What is the circumference of the pizza?

(1) The area of each slice measures 2 square inches.

(2) The pizza measures 8 inches in diameter.

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

135人做过此题 平均耗时为1min19s 平均正确率为 59%

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5

Is $$ x > 0$$?

(1)$$ x^2 > 0$$

(2) $$x + 2 > 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

133人做过此题 平均耗时为37s 平均正确率为 62%

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6

What is the area of circle O?

(1) The circumference of circle O measures $$24\pi$$ inches.

(2) The diameter of circle O measures 24 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 statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

132人做过此题 平均耗时为28s 平均正确率为 50%

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7

If $ defines a certain operation, is p $ q less than 20?

(1) $$ x $ y = 2x^2 - y$$ for all values of x and y

(2) p = 4, q = 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

137人做过此题 平均耗时为1min5s 平均正确率为 62%

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8

Given the figure to the right, what is $$y_2$$?

(1) $$y_1$$ is 1.5

(2) $$x_1$$ 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

132人做过此题 平均耗时为1min15s 平均正确率为 54%

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9

What is the value of x?

(1) $$x^2 + 5x + 6 = 20$$

(2) $$x \lt 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

134人做过此题 平均耗时为47s 平均正确率为 47%

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10

What is the value of x?

(1)$$\sqrt{4x} = 6$$

(2)$$ x^2 = 81$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

134人做过此题 平均耗时为28s 平均正确率为 42%

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11

If n is a nonzero integer, is $$x^n < 1$$?

(1) $$x \gt 1$$

(2) $$n \gt 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

139人做过此题 平均耗时为1min25s 平均正确率为 89%

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12

Square ABCD pictured to the right has an area of 9 square inches. Sides AD and BC are lengthened to x inches each. By how many inches were sides AD and BC lengthened?

(1) The diagonal of the resulting rectangle measures 5 inches.

(2) The resulting rectangle can be cut into three rectangles of equal size.

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

136人做过此题 平均耗时为2min41s 平均正确率为 83%

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13

Is $$\frac n{14}$$ an integer?

(1) n is divisible by 28.

(2) n is divisible by 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

57人做过此题 平均耗时为30s 平均正确率为 89%

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14

What is the minimal value of function f(x)?

(1) $$f(0) = 16$$

(2) $$f(x) = (x – 4)^2$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

131人做过此题 平均耗时为45s 平均正确率为 53%

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15

If x is a positive integer, is x even?

(1) $$x^4$$ is even

(2) $$4x$$ is even

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

56人做过此题 平均耗时为35s 平均正确率为 91%

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16

If r and q are integers, what is the value of $$（5^r）（3^{q+1})$$?

(1) $$(5^r)(3^q) = 729$$

(2) $$r + q = 6$$

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

131人做过此题 平均耗时为1min0s 平均正确率为 49%

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17

Is $$xy \gt 0$$?

(1) $$x^2 \gt 0$$

(2) $$xy^2 \gt 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

55人做过此题 平均耗时为29s 平均正确率为 89%

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18

What is x?

(1) $$x^2 + 3x + 2 = 0$$

(2) $$x \lt 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

55人做过此题 平均耗时为20s 平均正确率为 71%

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19

If ABCD is a trapezoid, where AB is parallel to CD, what is the area of ABCD?

(1) $$2(AB) + CD = 12$$

(2) The height of the trapezoid is 5 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 statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

130人做过此题 平均耗时为1min31s 平均正确率为 70%

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20

Is x positive?(1) $$(x – 3)^2 > 0$$(2) $$x^3 – 1 > 0$$

• 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

55人做过此题 平均耗时为37s 平均正确率为 85%

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