GRE Quant Practice Questions

Written Explanation
 

We need to determine the relationship between ac and 10b.
 
a, b, and c are three consecutive odd integers such that a < b < c;
b = a + 2
c = a + 4
 
Quantity A: ac = a(a + 4) = a² + 4a.
Quantity B: 10b = 10(a + 2) = 10a + 20. 
 
Possibility 1: a = 1
Quantity A: (1)² + 4(1) = 5 
Quantity B: 10(1) + 20 = 30
In this case, Quantity A < Quantity B.
 
Possibility 2: a = 25
Quantity A: (25)² + 4(25) = 725 
Quantity B: 10(25) + 20 = 270 
In this case, Quantity A > Quantity B.
 
Hence, the relationship cannot be determined from the information given.
 
D is the correct answer.   

Written Explanation
 

Quadrilateral ABCD is inscribed in a circle.
Circumference of the circle = 14π.
Let the diameter of the circle be d.
We need to determine the relationship between the length of the diagonal AC and 14.
 
Circumference of the circle = πd 
14π = πd
Cancelling π from both sides,
d = 14
 
Possibility 1: If ∠ABC = ∠CDA = 90°, then triangle ABC and triangle CDA would be right triangles. In this case, diagonal AC = diameter of the circle = 14.
Possibility 2: If ∠ABC ≠ 90° or ∠CDA ≠ 90°, then diagonal AC would not be the diameter of the circle. In this case, diagonal AC < 14.
 
Hence, the relationship cannot be determined with the information given.
 
D is the correct answer.   

Written Explanation
 

The production values are provided along the vertical axis in the graph.
The production of rice is indicated by the dashed line in the graph.
 
The graph shows that the amount of rice produced in 2013 = 28 million metric tons.
If 40 percent of the rice produced in 2013 was exported, it implies that 60 percent of rice remained for domestic use.
Thus, the amount of rice that remained for domestic use in 2013 = 60% of 28 million metric tons = 16.8 million metric tons.
 
D is the correct answer choice. 

Written Explanation
 

When x is divided by 20, the remainder is 13.
Therefore, x = 20k + 13, where k is some non-negative integer.
x² = (20k + 13)² = 400k² + 520k + 169  
Since 400 and 520 are divisible by 40, and the remainder when 169 is divided by 40 is 9, the remainder when 400k² + 520k + 169 is divided by 40 is 9.
 
Hence, the remainder when x² is divided by 40 is 9.
 
B is the correct answer choice.

Written Explanation
 

The above graph shows the values of function f(x) along the vertical axis and the values of the inputs x along the horizontal axis.
At x = –4, the corresponding value of y = 7. Thus, f(–4) = 7.
At x = 7, the corresponding value of y = 10. Thus, f(f(–4)) = 10.
 
E is the correct answer choice.

Written Explanation
 

The mean daily rainfall in the tropical city during the monsoon season = 3.0 inches.
The standard deviation of daily rainfall in the tropical city during the monsoon season = 0.8 inches.
We need to determine the relationship between the probability that a randomly selected day receives between 2.2 and 3.8 inches of rain and the probability that it receives between 3.0 and 5.4 inches of rain.
 
Quantity A:
2.2 inches = 3.0 inches – 1 × (0.8 inches). Thus, 2.2 inches is 1 standard deviation below the mean.
3.8 inches = 3.0 inches + 1 × (0.8 inches). Thus, 3.8 inches is 1 standard deviation above the mean.
Therefore, the required probability is given by the area between –1 and 1 in the standard normal curve.
 
Quantity B:
5.4 inches = 3.0 inches + 3 × (0.8 inches). Thus, 5.4 inches is 3 standard deviations above the mean.
Therefore, the required probability is given by the area between 0 and 3 in the standard normal curve.
 
The area between –1 and 1 is greater than the area between 0 and 3 in the standard normal curve.
 
Hence, Quantity A is greater.
 
A is the correct answer.

Written Explanation
 

The postwoman must deliver parcels to 6 locations.
The Mayor’s office must be the first delivery of the day and the corporate offices must be visited one after the other.
We need to determine in how many different orders the postwoman could make these 6 deliveries.
 
Since the Mayor’s office must be the first delivery of the day, we only need to consider the order for the remaining 5 deliveries.
Since corporate offices must be visited one after the other, we will consider the corporate offices as a single corporate office block for easier calculations.
Thus, we need to count the number of ways to order a hospital, corporate office block, and two different private residences.
The number of different orders in which we can choose to make deliveries to 4 places = 4! = 24.
Additionally, since there are 2 offices in the corporate office block and the delivery to the offices can be made in either order, there are 2 possible orders in which deliveries can be made to the two corporate offices.
Thus, the total number of different orders in which the postwoman could make 6 deliveries = 24 × 2 = 48.
 
B is the correct answer choice.

Written Explanation
 

Let the original number be n.
We need to determine the value of n.
 
Shifting the decimal point two places to the left in a positive decimal number is equivalent to dividing the number by 100.
Since shifting the decimal point of n two places to the left results in a number that 2 times the square of n,
n / 100 = 2n²
n = 200n²
Dividing both sides by n, 
1 = 200n
n = 0.005
 
0.005 is the correct answer.

Written Explanation
 

x > 0
We need to determine the relationship between 3 percent of x³ and x² percent of 2x².
 
Quantity A: 3 percent of x³ = ( 3 / 100 ) × (x³) = ( 3x³ / 100 ). 
Quantity B: x² percent of 2x² = (x² / 100) × (2x²) = (2x⁴ / 100).
 
Possibility 1: x = 1
Quantity A: ( 3x³ / 100  ) = [3(1)³ / 100] = 3 / 100
Quantity B: ( 2x⁴ / 100  ) = [2(1)⁴ / 100] = 2 / 100
In this case, Quantity A > Quantity B.
 
Possibility 2: x = 2
Quantity A: ( 3x³ / 100  ) = [3(2)³ / 100] = 24 / 100
Quantity B: ( 2x⁴ / 100  ) = [2(2)⁴ / 100] = 32 / 100
In this case, Quantity A < Quantity B. 

Hence, the relationship cannot be determined from the information given.
 
D is the correct answer.     

Written Explanation
 

One of the vertices of rectangle R is the point (–5, –3), and the opposite vertex is the point (2, 6). 
We need to determine the relationship between the perimeter of R and 32.
 
Quantity A:
The rectangle ABCD shown in the explanation diagram above represents the rectangle with the given information.
The length of the rectangle = x coordinate of vertex C – x coordinate of vertex A = 2 – (–5) = 7.
The width of the rectangle = y coordinate of vertex C – y coordinate of vertex A = 6 – (–3) = 9.
The perimeter of rectangle R = 2 × (Length + Width) = 2 × (7 + 9) = 32.
 
Quantity B:
32
 
Hence, the two quantities are equal.
 
C is the correct answer.   

Written Explanation
 

Number of senior citizens = 4.
Number of adolescents = 24.
Number of toddlers = 9.
Number of infants = 3.
Total number of passengers = 40.
 
 The probability that a randomly selected book is neither a short story anthology nor a collection of poetry
 = (Number of passengers that are either toddlers or infants) / (Total number of passengers)  
= (9 + 3) / (40)
= 0.3
 
B is the correct answer choice.