DS-OG20：第81-100题 练习册详情

1

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 59%

展开题目内容

2

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 61%

展开题目内容

3

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 42%

展开题目内容

4

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 52%

展开题目内容

5

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 52%

展开题目内容

6

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 67%

展开题目内容

7

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 52%

展开题目内容

8

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 69%

展开题目内容

9

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 58%

展开题目内容

10

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 44%

展开题目内容

11

Is the point Q on the circle with center C ?

1.R is a point on the circle and the distance from Q to R is equal to the distance from Q to C.

2.S is a point on the circle and the distance from Q to S is equal to the distance from S to 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.

180人做过此题 平均耗时为2min52s 平均正确率为 98%

展开题目内容

12

In the figure above, if A, B, and C are the areas, respectively, of the three nonoverlapping regions formed by the intersection of two circles of equal area, what is the value of B + C ?

1.$A + 2B + C = 24$

2.$A + C = 18$ and $B = 3$

• 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.

182人做过此题 平均耗时为2min4s 平均正确率为 70%

展开题目内容

13

A company produces a certain toy in only 2 sizes, small or large, and in only 2 colors, red or green. If, for each size, there are equal numbers of red and green toys in a certain production lot, what fraction of the total number of green toys is large?

1.In the production lot, 400 of the small toys are green.

2.In the production lot, $\frac{2}{3}$ of the toys produced are small.

• 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3min21s 平均正确率为 62%

展开题目内容

14

Is quadrilateral PQRS a parallelogram?

1.Adjacent sides PQ and QR have the same length.

2.Adjacent sides RS and SP have the same length.

• 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.

161人做过此题 平均耗时为1min30s 平均正确率为 73%

展开题目内容

15

In the figure above, the vertices of ∆OPQ and ∆QRS have coordinates as indicated. Do ∆OPQ and ∆QRS have equal areas?

1.b = 2a

2.d = 2c

• 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.

80人做过此题 平均耗时为1min0s 平均正确率为 68%

展开题目内容

16

After the first two terms in a sequence of numbers, each term in the sequence is formed by adding all of the preceding terms. Is 12 the fifth term in the sequence?

1.The sum of the first 3 terms in the sequence is 6.

2.The fourth term in the sequence is 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 statement ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

81人做过此题 平均耗时为1min43s 平均正确率为 65%

展开题目内容

17

Jones has worked at Firm X twice as many years as Green, and Green has worked at Firm X four years longer than Smith. How many years has Green worked at Firm X ?

1.Jones has worked at Firm X 9 years longer than Smith.

2.Green has worked at Firm X 5 years less than Jones.

• 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.

74人做过此题 平均耗时为1min21s 平均正确率为 88%

展开题目内容

18

In ∆JKL shown above, what is the length of segment JL ?

1. $JK = 10$

2. $KL = 5$

• 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.

75人做过此题 平均耗时为27s 平均正确率为 87%

展开题目内容

19

br/] A six-sided mosaic contains 24 triangular pieces of tile of the same size and shape, as shown in the figure above. If the sections of tile fit together perfectly, how many square centimeters of tile are in the mosaic?

1.Each side of each triangular piece of tile is 9 centimeters long.

The mosaic can be put inside a rectangular frame that is 40 centimeters wide.

• 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.

81人做过此题 平均耗时为1min35s 平均正确率为 65%

展开题目内容

20

If, in the figure above, ABCD is a rectangular region, what is the value of the ratio $\frac{area of Δ EDA}{area of Δ EBC}$ ?

1.AD = 4

2.AE = 2 and EB = 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.

76人做过此题 平均耗时为46s 平均正确率为 67%

展开题目内容