DS-Manhattan：第21-40题 练习册详情

1

If x and y are positive integers, is (x + y) a prime number?

(1) x = 1

(2) y = 2 * 3 * 5 * 7

• 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.

899人做过此题 平均耗时为4min39s 平均正确率为 44%

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2

On Sunday morning, a printing press printed its newspapers at a constant rate from 1:00 AM to 4:00 AM. How many newspapers did the printing press print on Sunday morning?

(1) The printing rate on Saturday morning was twice that of Sunday morning.

(2) On Saturday morning, the printing press ran at a constant rate from 1:00 AM to 3:00 AM, stopped for a half hour, and then ran at the same constant rate from 3:30 AM to 5:30 AM, printing a total of 4,000 newspapers.

• 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.

702人做过此题 平均耗时为4min56s 平均正确率为 54%

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3

If BD = CD, what is the degree measure of x + y?

(1) v = 74 degrees

(2) w = 32 degrees

• 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.

687人做过此题 平均耗时为3min32s 平均正确率为 53%

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4

If none of the students are ambidextrous, what percentage of the 20 students in Mr. Henderson's class are left-handed?

(1) Of the 12 girls in the class, 25% are left-handed.

(2) 5 of the boys in the class are right-handed.

• 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.

674人做过此题 平均耗时为4min19s 平均正确率为 60%

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5

If X is the average of Y numbers, what is Y?

(1) X = 54.5

(2) The sum of the Y numbers for which X is the average is 2,616.

• 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. Statements (1) and (2) TOGETHER are NOT sufficient.

667人做过此题 平均耗时为4min16s 平均正确率为 49%

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6

A cake recipe uses a constant ratio of 2 teaspoons vanilla extract to 1 ounce chocolate. If the original recipe, which serves four people, is altered proportionally to yield a cake that serves six people, how many ounces of chocolate will be used in the larger cake?

(1) The original recipe calls for exactly five teaspoons of vanilla extract.

(2) If the original recipe were altered proportionally to yield a cake that serves eight people, ten teaspoons of vanilla extract would be used.

• 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.

662人做过此题 平均耗时为8min14s 平均正确率为 61%

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7

If a kennel houses only cats and dogs, what percent of the animals in the kennel are dogs?

(1) The ratio of cats to dogs in the kennel is 2:3.

(2) The ratio of dogs to the total number of animals is 3:5.

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

640人做过此题 平均耗时为2min49s 平均正确率为 69%

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8

Is Hector taller than Charley?

(1) Hector is 5 feet 7 inches tall.

(2) When Hector stands on a 3-inch thick book, he is one inch taller than Charley.

• 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.

649人做过此题 平均耗时为2min48s 平均正确率为 66%

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9

In Greenville last July, what was the average (arithmetic mean) home sale price?

(1) In Greenville last July, there were 100 homes sold for a total of $51 million.

(2) In Greenville last July, condominiums accounted for 60% of the home sales, and the average condominium price was $450,000.

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

637人做过此题 平均耗时为5min1s 平均正确率为 53%

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10

If 3x – 3y = 12z, what is the value of x?

(1) 4z = 2 + y

(2) 4z = 6 – 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 one ALONE is sufficient.
• EACH statement ALONE is sufficient.
• Statements (1) and (2) TOGETHER are NOT sufficient.

648人做过此题 平均耗时为4min3s 平均正确率为 66%

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11

If x and y each represent a single digit, does the number 8.3xy round to 8.3 when it is rounded to the nearest tenth?

(1) x = 5

(2) y = 9

• 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.

634人做过此题 平均耗时为4min38s 平均正确率为 57%

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12

If Sarah was 21 years old exactly 5 years ago, how old was Larry exactly 9 years ago?

(1) Larry is now twice Sarah's age.

(2) Twelve years ago, Jill was 6 years older than Sarah and 20 years younger than Larry.

• 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.

532人做过此题 平均耗时为4min31s 平均正确率为 55%

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13

If x and y are integers, is 5x + y divisible by 5?

(1) x is divisible by 5.

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

535人做过此题 平均耗时为1min54s 平均正确率为 59%

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14

If$$ xy \neq 0$$, what is the ratio of y to x?

(1) y = 3x

(2) x = 11

• 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.

447人做过此题 平均耗时为54s 平均正确率为 63%

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15

If Bob, working alone, can paint a certain room in 3 hours, how long does it take Bob and Richard working together to paint the room?

(1) Richard, working alone, can paint the room in 2 hours.

(2) Richard paints at a constant rate that is 50% greater than the rate at which Bob paints.

• 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.

450人做过此题 平均耗时为2min9s 平均正确率为 42%

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16

If z is an integer, is z even?

(1) $$\frac{z}{2}$$ is even.

(2) 3z 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.

498人做过此题 平均耗时为2min15s 平均正确率为 60%

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17

What is the value of y?

(1) 2 x + 2 y = 14

(2) 2 y + 2 z = 14

• 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.

444人做过此题 平均耗时为1min29s 平均正确率为 53%

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18

At what point does the line ax + y + b = 0 intersect the y-axis?

(1) b = 5

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

540人做过此题 平均耗时为3min17s 平均正确率为 67%

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19

At a certain school, 100 students are in the marching band. If 40% of the students in the orchestra are also in the marching band, how many students are members of neither the orchestra nor the marching band?

(1) There are 1000 students in the school.

(2) 50 students are in the orchestra.

• 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.

520人做过此题 平均耗时为6min0s 平均正确率为 67%

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20

The contents of one full cylindrical silo are to be transferred to another, larger cylindrical silo. The contents of the smaller silo will fill what portion of the larger silo?

(1) The larger silo has twice the base radius, and twice the height, of the smaller one.

(2) The smaller silo has a circular base with a radius of 10 feet.

• 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.

454人做过此题 平均耗时为3min21s 平均正确率为 70%

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