S1 - Simulado 1

Por favor, use o cronômetro abaixo para acompanhar seu tempo e completar o simulado em 62 minutos.

A prova é composta por questões fáceis, intermediárias e difíceis.

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Por isso, não perca tempo em questões de assuntos que você não domina e invista seu tempo para acertar a maior quantidade possível das questões de tópicos que você já domina.

Seu objetivo para esse simulado é acertar pelo menos 12 questões, ou seja, cerca de 40% da prova.

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Começar

Questão 1 de 31

(S1-1)

If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter ?

A

1/120

B

1/60

C

1/20

D

20

E

120

Questão 2 de 31

(S1-2)

Of the following, which is the closest to

A

4

B

7

C

9

D

12

E

16

Questão 3 de 31

(S1-3)

In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)

(1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.

(2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 4 de 31

(S1-4)

Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball has a multiple of 42 within it ?

A

1/16

B

5/42

C

1/8

D

3/16

E

1/4

Questão 5 de 31

(S1-5)

If an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average? (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)

A

3.7

B

9.5

C

31.4

D

53.4

E

136.8

Questão 6 de 31

(S1-6)

If x ≠ 1, then

is equivalent to which of the following?

A

2(5x²)

B

5x²

C

0

D

(5x³ - 5x²) / (x + 1)

E

5x² + 5x³

Questão 7 de 31

(S1-7)

Company X has 50 employees and company Y has 60 employees. Both companies have same number of full time employees, but company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have?

A

3

B

7

C

14

D

17

E

20

Questão 8 de 31

(S1-8)

What is the sum of the reciprocals of all the positive factors of the number 28 ?

A

1/4

B

56/27

C

2

D

3

E

4

Questão 9 de 31

(S1-9)

A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?

A

7%

B

8%

C

8.5%

D

10%

E

11%

Questão 10 de 31

(S1-10)

Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests?

(1) Bill's first 3 tests received an average score of 50.

(2) Bill's last 2 tests received an average score of 50.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 11 de 31

(S1-11)

If P, Q, and R are points on the number line, what is the distance between P and R ?

(1) Q is between P and R.

(2) The distance between P and Q is 5.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 12 de 31

(S1-12)

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Triangle FGH has 9 times the area of triangle ABC.

(2) HF = 9

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 13 de 31

(S1-13)

If s and w are integers, is w/5 an integer?

(1) 4s + 2 is divisible by 5

(2) w + 3 = 4s

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 14 de 31

(S1-14)

The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?

A

P(1 − 0.03x + 0.02x²)

B

P(1 − 0.03x + 0.0002x²)

C

P(1 − 0.3x + 0.002x²)

D

P(1 − 2x²)

E

P(1 − 3x + 2x²)

Questão 15 de 31

(S1-15)

What is the average (arithmetic mean) of the terms in set J?

(1) The sum of any three terms in set J is 21.

(2) Set J consists of 12 total terms.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 16 de 31

(S1-16)

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

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 17 de 31

(S1-17)

A

B

C

D

E

Questão 18 de 31

(S1-18)

What is the two-digit positive integer whose tens digit is a and whose units digit is b?

(1) 2a > 3b > 6

(2) a > 2b > 6

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 19 de 31

(S1-19)

The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers ?

A

16

B

18

C

19

D

20

E

22

Questão 20 de 31

(S1-20)

If m and n are the roots of the equation t² + bt + c = 0, where b and c are constants, are both m and n positive?

(1) b < 0

(2) c < 0

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 21 de 31

(S1-21)

A

527

B

546

C

579

D

600

E

625

Questão 22 de 31

(S1-22)

In a circle centered on point O with radius 8, diameter AC and point B on the circle, pictured above, what is the length of line segment (AB)?

(1) ∠AOB = 120°

(2) OB = BC

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 23 de 31

(S1-23)

The symbol # represents one of the four arithmetic operations: addition, subtraction, multiplication, or division. Is (5 # 6) # 2 = 5 # ( 6 # 2)?

(1) 5 # 6 = 6 # 5

(2) 2 # 0 = 2

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 24 de 31

(S1-24)

If m ≠ −7, then

is equivalent to which of the following?

A

1

B

(m + 7)²

C

m + 7

D

m - 7

E

2m(7 + m)

Questão 25 de 31

(S1-25)

A rental car agency purchased fleet vehicles in two sizes: full-size cars cost $10,000, and compact cars cost $9,000. How many compact cars did the agency purchase?

(1) The agency purchased 7 total cars.

(2) The agency paid $66,000 for its cars.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 26 de 31

(S1-26)

The length of the diagonal of a certain rectangle is 8 and its perimeter is 20. What is the area of the rectangle?

A

18

B

36

C

64

D

80

E

It cannot be determined

Questão 27 de 31

(S1-27)

Eunice sold several cakes. If each cake sold for either exactly $17 or exactly $19, how many $19-cakes did Eunice sell?

(1) Eunice sold a total of 8 cakes.

(2) Eunice made $140 in total revenue from her cakes.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 28 de 31

(S1-28)

The figure above shows two lines intersecting at the point O. If the lines are rotated about O at the same rate and in the directions shown until AB⊥CD, through how many degrees must each line move?

A

90 − θ

B

90 − θ/2

C

90 + θ/2

D

(90 + θ)/2

E

(90 + 2θ)/2

Questão 29 de 31

(S1-29)

If (ax + by)² = (bx + ay)², what is the value of a – b ?

(1) x² > y²

(2) a and b are positive integers.

A

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D

EACH statement ALONE is sufficient.

E

Statements (1) and (2) TOGETHER are not sufficient.

Questão 30 de 31

(S1-30)

A sample of x litres from a container having a 60-litres mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x ?

A

6 litres

B

10 litres

C

15 litres

D

20 litres

E

30 litres

Questão 31 de 31

(S1-31)

Working alone at its constant rate, pump x pumped out 1/3 of the water in a pool in 4 hours. Then pump Y started working and the two pumps, working simultaneously at their respective constant rates, pumped out the rest of the water in 6 hours. How many hours would it have taken pump Y, working alone at its constant rate, to pump out all the water that was pumped out of the pool ?

A

18

B

24

C

36

D

48

E

52

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E-mail

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S1 - Simulado 1

Clique no botão abaixo para começar.

(S1-1) If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter ?

(S1-2) Of the following, which is the closest to

(S1-3) In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.) (1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC. (2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

(S1-4) Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball has a multiple of 42 within it ?

(S1-5) If an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average? (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)

(S1-6) If x ≠ 1, then is equivalent to which of the following?

(S1-7) Company X has 50 employees and company Y has 60 employees. Both companies have same number of full time employees, but company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have?

(S1-8) What is the sum of the reciprocals of all the positive factors of the number 28 ?

(S1-9) A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?

(S1-10) Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests? (1) Bill's first 3 tests received an average score of 50. (2) Bill's last 2 tests received an average score of 50.

(S1-11) If P, Q, and R are points on the number line, what is the distance between P and R ? (1) Q is between P and R. (2) The distance between P and Q is 5.

(S1-12) In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG? (1) Triangle FGH has 9 times the area of triangle ABC. (2) HF = 9

(S1-13) If s and w are integers, is w/5 an integer? (1) 4s + 2 is divisible by 5 (2) w + 3 = 4s

(S1-14) The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?

(S1-15) What is the average (arithmetic mean) of the terms in set J? (1) The sum of any three terms in set J is 21. (2) Set J consists of 12 total terms.

(S1-16) If m, x, and y are positive integers, what is the value of x - y?

(S1-17)

(S1-18) What is the two-digit positive integer whose tens digit is a and whose units digit is b? (1) 2a > 3b > 6 (2) a > 2b > 6

(S1-19) The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers ?

(S1-20) If m and n are the roots of the equation t² + bt + c = 0, where b and c are constants, are both m and n positive? (1) b < 0 (2) c < 0

(S1-21)

(S1-22) In a circle centered on point O with radius 8, diameter AC and point B on the circle, pictured above, what is the length of line segment (AB)? (1) ∠AOB = 120° (2) OB = BC

(S1-23) The symbol # represents one of the four arithmetic operations: addition, subtraction, multiplication, or division. Is (5 # 6) # 2 = 5 # ( 6 # 2)? (1) 5 # 6 = 6 # 5 (2) 2 # 0 = 2

(S1-24) If m ≠ −7, then is equivalent to which of the following?

(S1-25) A rental car agency purchased fleet vehicles in two sizes: full-size cars cost $10,000, and compact cars cost $9,000. How many compact cars did the agency purchase? (1) The agency purchased 7 total cars. (2) The agency paid $66,000 for its cars.

(S1-26) The length of the diagonal of a certain rectangle is 8 and its perimeter is 20. What is the area of the rectangle?

(S1-27) Eunice sold several cakes. If each cake sold for either exactly $17 or exactly $19, how many $19-cakes did Eunice sell? (1) Eunice sold a total of 8 cakes. (2) Eunice made $140 in total revenue from her cakes.

(S1-28) The figure above shows two lines intersecting at the point O. If the lines are rotated about O at the same rate and in the directions shown until AB⊥CD, through how many degrees must each line move?

(S1-29) If (ax + by)² = (bx + ay)², what is the value of a – b ? (1) x² > y² (2) a and b are positive integers.

(S1-30) A sample of x litres from a container having a 60-litres mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x ?

Confirme e envie

(S1-1)

If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain snowstorm, how many seconds did it take for snow accumulation to increase by 1 millimeter ?

(S1-2)

Of the following, which is the closest to

(S1-3)

In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)

(1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.

(2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

(S1-4)

Each factor of 210 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball has a multiple of 42 within it ?

(S1-5)

If an automobile averaged 22.5 miles per gallon of gasoline, approximately how many kilometers per liter of gasoline did the automobile average? (1 mile = 1.6 kilometers and 1 gallon = 3.8 liters, both rounded to the nearest tenth.)

(S1-6)

If x ≠ 1, then

is equivalent to which of the following?

(S1-7)

Company X has 50 employees and company Y has 60 employees. Both companies have same number of full time employees, but company Y has 3 more than twice the number of part-time employees that Company X has. How many part-time employees does Company Y have?

(S1-8)

What is the sum of the reciprocals of all the positive factors of the number 28 ?

(S1-9)

A camera lens filter kit containing 5 filters sells for $57.50. If the filters are purchased individually, 2 of them are priced at $10.45 each, 2 at $12.05 each, 1 at $17.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?

(S1-10)

Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests?

(1) Bill's first 3 tests received an average score of 50.

(2) Bill's last 2 tests received an average score of 50.

(S1-11)

If P, Q, and R are points on the number line, what is the distance between P and R ?

(1) Q is between P and R.

(2) The distance between P and Q is 5.

(S1-12)

In the diagram above, ∠A = ∠F = 50°, ∠B = 20°, and ∠H = 110°. What is the length of FG?

(1) Triangle FGH has 9 times the area of triangle ABC.

(2) HF = 9

(S1-13)

If s and w are integers, is w/5 an integer?

(1) 4s + 2 is divisible by 5

(2) w + 3 = 4s

(S1-14)

The original price of a certain TV set is discounted by x percent, and the reduced price is then discounted by 2x percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?

(S1-15)

What is the average (arithmetic mean) of the terms in set J?

(1) The sum of any three terms in set J is 21.

(2) Set J consists of 12 total terms.

(S1-16)

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

(S1-18)

What is the two-digit positive integer whose tens digit is a and whose units digit is b?

(1) 2a > 3b > 6

(2) a > 2b > 6

(S1-19)

The average (arithmetic mean) of the 5 positive integers k, m, r, s, and t is 16, and k < m < r < s < t. If t is 40, what is the greatest possible value of the median of the 5 integers ?

(S1-20)

If m and n are the roots of the equation t² + bt + c = 0, where b and c are constants, are both m and n positive?

(1) b < 0

(2) c < 0

(S1-22)

In a circle centered on point O with radius 8, diameter AC and point B on the circle, pictured above, what is the length of line segment (AB)?

(1) ∠AOB = 120°

(2) OB = BC

(S1-23)

The symbol # represents one of the four arithmetic operations: addition, subtraction, multiplication, or division. Is (5 # 6) # 2 = 5 # ( 6 # 2)?

(1) 5 # 6 = 6 # 5

(2) 2 # 0 = 2

(S1-24)

If m ≠ −7, then

is equivalent to which of the following?

(S1-25)

A rental car agency purchased fleet vehicles in two sizes: full-size cars cost $10,000, and compact cars cost $9,000. How many compact cars did the agency purchase?

(1) The agency purchased 7 total cars.

(2) The agency paid $66,000 for its cars.

(S1-26)

The length of the diagonal of a certain rectangle is 8 and its perimeter is 20. What is the area of the rectangle?

(S1-27)

Eunice sold several cakes. If each cake sold for either exactly $17 or exactly $19, how many $19-cakes did Eunice sell?

(1) Eunice sold a total of 8 cakes.

(2) Eunice made $140 in total revenue from her cakes.

(S1-28)

The figure above shows two lines intersecting at the point O. If the lines are rotated about O at the same rate and in the directions shown until AB⊥CD, through how many degrees must each line move?

(S1-29)

If (ax + by)² = (bx + ay)², what is the value of a – b ?

(1) x² > y²

(2) a and b are positive integers.

(S1-30)

A sample of x litres from a container having a 60-litres mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x ?