GMAT Quantitative Reasoning Test Guide  Prepare with over 500 GMAT math questions to Get a High GMAT Quantitative Reasoning Score.
In this guide you will learn about GMAT Quantitative Reasoning section, and find over 500 GMAT Quantitative Reasoning practice questions. This page contains everything you need to know and the essential skills for a high GMAT Quantitative Reasoning score.
Table Of Contents
The Introduction to the GMAT Quantitative Reasoning Section
The GMAT Quantitative Reasoning section consists of 21 multiplechoice questions that must be answered in 45 minutes. All multiplechoice questions are problemsolving questions. (Note: The new Quantitative Reasoning section DOES NOT include the Data Sufficiency question type; Data Sufficiency will now be included in the new Data Insights Section.)
The GMAT problemsolving questions cover a wide range of topics, including arithmetic, algebra, data analysis, and number properties. Testtakers are required to use their mathematical skills and critical thinking to solve problems efficiently within time constraints. The following categories are what you can expect to see in the GMAT Quantitative Reasoning section:
Now, let's look at some example GMAT problemsolving questions associated with each category.
Integer Properties, Factors, Multiples, Exponents, Roots
In this category, common math topics include:
Integer Properties and Absolute Values
Integer properties involve understanding the fundamental properties and characteristics of numbers, such as even/odd, prime/composite, positive/negative, etc.
Absolute values or modules are mathematical expressions that represent the distance of a number from zero on the number line. It is denoted by two vertical bars enclosing the number, such as x. The result of the absolute value is always nonnegative, as it disregards the sign of the number.
If  x  > 4, which of the following must be true?
 \( x > 4 \)
 \( x^2 > 16 \)
 \( x  1 > 3 \)

radio_button_unchecked(A) I only

radio_button_unchecked(B) II only

radio_button_unchecked(C) I and II only

radio_button_unchecked(D) II and III only

radio_button_unchecked(E) I, II, and III

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (D)
When x > 4, it means that x is either greater than 4 or less than 4 (because the absolute value of any number greater than 4 or less than 4 will be greater than 4).
Let's analyze each statement:
 x > 4: the inequality x > 4 is equivalent to x < 4 or x > 4. Therefore, x > 4 does not imply that condition I must be true, since x > 4 is true and x > 4 is false for x = 5.
 \(x^2 > 16\): This statement is true when x is either less than 4 or greater than 4 because in both cases, \(x^2\) will be greater than 16. Therefore, this statement is true when x > 16.
III. x  1 > 3: Let's check this statement for both scenarios of x: when x > 4 and when x < 4.
 a) When x > 4: If x > 4, then x  1 > 4  1 = 3 = 3. Therefore, this statement is true for this scenario.
 b) When x < 4: If x < 4, then x  1 > 4  1 = 5 = 5. Therefore, this statement is also true for this scenario.
Since all three statements are true for the given condition x > 3, the correct answer is: (D) II, and III only.
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Divisibility, Multiples, and Factors
Divisibility, multiples, and factors are concepts related to the properties of numbers. Divisibility refers to whether one number can be divided by another without leaving a remainder. Multiples are the products of a given number and any whole number, and factors are the numbers that divide a given number without leaving a remainder.
If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?

radio_button_unchecked(A) 600

radio_button_unchecked(B) 700

radio_button_unchecked(C) 900

radio_button_unchecked(D) 2100

radio_button_unchecked(E) 4900

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (A)
Let's first find the prime factorization of each of the three numbers.
 The prime factorization of 90 is \(2 \times 3^2 \times 5 \)
 The prime factorization of 196 is \(2^2 \times 7^2 \)
 The prime factorization of 300 is \(2^2 \times 3 \times 5^2 \)
The least common multiple (LCM) is found by multiplying the highest powers of all primes that appear in the factorization of each number. So, the LCM, M, would be:
M = \(2^2 \times 3^2 \times 5^2 \times 7^2\)
Now let's prime factorize each of the options and see which one cannot be made using the prime factors of M:
 The prime factorization of 600 is \(2^3 \times 3 \times 5^2\). This is not a factor of M because it requires three 2's, but M only has two 2's in its prime factorization.
 The prime factorization of 700 is \(2^2 \times 5 \times 7^2\). This is a factor of M as M has at least these many of each prime in its prime factorization.
 The prime factorization of 900 is \(2^2 \times 3^2 \times 5^2\). This is a factor of M as M has at least these many of each prime in its prime factorization.
 The prime factorization of 2100 is \(2^2 \times 3 \times 5^2 \times 7\). This is a factor of M as M has at least these many of each prime in its prime factorization.
 The prime factorization of 4900 is \(2^2 \times 5 \times 7^2\). This is a factor of M as M has at least these many of each prime in its prime factorization.
So, the number that is NOT a factor of M is 600.
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Remainder Problem
Remainders refer to the value left over after dividing one number by another. You will see some GMAT word problem questions involving dividing and finding the remainder.
April 10, 2000, fell on a Monday. On which day of the week did April 10, 2006, fall? (Note: 2000 and 2004 were leap years.)

radio_button_unchecked(A) Sunday

radio_button_unchecked(B) Monday

radio_button_unchecked(C) Tuesday

radio_button_unchecked(D) Wednesday

radio_button_unchecked(E) Thursday

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (C)
The difference in years between 2000 and 2006 is 6 years. In 6 years, there are normally 6 * 365 = 2190 days.
However, this range includes two leap years (2000 and 2004), which adds 2 extra days, so the total becomes 2192 days.
We know every 7 days is a cycle, so let’s divide 2192 and find the remainder.
\( 2192 = 7 \times 313 + 1 \)
The remainder when 2192 is divided by 7 (the number of days in a week) is 1.
This means that April 10, 2006, is one day after April 10, 2000.
April 10, 2000, fell on a Monday, so April 10, 2006 is one day after Monday, which is Tuesday.
So, the correct answer is (C) Tuesday.
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Exponents and Square Roots
Exponents, also known as powers, involve raising a base number to a certain exponent or power. The exponent indicates how many times the base number should be multiplied by itself.
A square root is a mathematical operation that determines a value that, when multiplied by itself, results in a given number. In other words, it is the inverse operation of squaring a number. The square root of a nonnegative real number 'x' is denoted by the symbol \(\sqrt{x}\).
For positive integers a and b, if \( 2^a \times 3^b = 432 \) and \( 2^b \times 3^a = 486 \), what is the value of (a + b)?

radio_button_unchecked(A) 15

radio_button_unchecked(B) 18

radio_button_unchecked(C) 21

radio_button_unchecked(D) 24

radio_button_unchecked(E) 27

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (A)
Step 1: Observe the numbers 432 and 486 and try to find their prime factors:
\(432 = 2^4 \times 3^3\)
\(486 = 2^1 \times 3^5\)
Step 2: Now, we can rewrite the given equations using their prime factorization:
\((2^a \times 3^b) = (2^4 \times 3^3)\)
\((2^b \times 3^a) = (2^1 \times 3^5)\)
Step 3: Equate the powers of 2 and 3 on both sides of each equation:
For powers of 2: a = 4 (from equation 1) b = 1 (from equation 2)
For powers of 3: b = 3 (from equation 1) a = 5 (from equation 2)
Step 4: Find the value of (a + b): a + b = 4 + 1 = 5
So, the value of (a + b) is 5.
The correct answer is: (A) 15
\( \frac{\sqrt[3]{0.00027}}{(0.01^2)} \) =

radio_button_unchecked(A) 10

radio_button_unchecked(B) 30

radio_button_unchecked(C) 300

radio_button_unchecked(D) 100

radio_button_unchecked(E) 1000

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (C)
Given expression:
\( \frac{\sqrt[3]{0.00027}}{0.01^2} \)
We can write this as:
\( \frac{\sqrt[3]{27 \times 10^{6}}}{(10^{2})^2} \)
Simplify further:
\( \frac{(27^{1/3}) \times 10^{2}}{10^{4}} \)
Calculate the cube root of 27, which is 3:
\( \frac{3 \times 10^{2}}{10^{4}} \)
Now, use the property of exponents
\( a^{m} = \frac{1}{a^m} \)
to simplify:
\( = 3 \times 10^{42} \)
Simplify the exponent: \( = 3 \times 10^{2} \)
And finally, simplify the multiplication: \( = 300 \)
So, the result of the expression is indeed 300.
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Algebra
Typical questions that appear in the GMAT quant section from Algebra include solving linear equations and quadratic equations, solving equation inequality, and algebra word problems. In an algebra word problem question, you are expected to translate what is given in words in the question into algebraic equations, and then proceed to solve them to find the solution.
Linear Equations
A linear equation is an equation in which the highest power of the variable is always 1. A linear equation in one variable means there is only one variable in the linear equation. Here are examples of linear equations of one variable:
x + 5 = 10
4(x  3) = 3(x + 2)
A linear equation in two variables means there are two variables in the linear equation. Here are examples of linear equations in two variables:
x + y = 10
3a + b = 5
GMAT math questions related to linear equations often ask you to solve linear equations.
For what values of 'k' will the pair of equations 7x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?

radio_button_unchecked(A) 21

radio_button_unchecked(B) 14

radio_button_unchecked(C) 7

radio_button_unchecked(D) 16

radio_button_unchecked(E) 20

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (A)
A pair of linear equations will not have a unique solution if the ratios of their coefficients are equal, which means they are dependent or parallel.
For the two equations, the coefficients are:
For x: 7 in the first equation, k in the second.
For y: 4 in the first equation, 12 in the second.
The equations will not have a unique solution when the ratios of these coefficients are equal. That is, when:
7/k = 4/12
Solving for k, we find:
k = 7 * (12/4) k = 21
So, the equations will not have a unique solution when k is 21. The answer is (A) 21.
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Quadratic Equations
A quadratic equation is an equation in which the highest power of the variable is always 2. Here is an example of quadratic equations in one variable:
\(x^2 + 3x + 4 =25\)
Gmat math questions related to quadratic equations only ask you to solve quadratic equations by factoring or using the quadratic formula.
What is the highest integral value of 'm' for which the quadratic equation \(x^2  8x + m = 0\) will have two real and distinct roots?

radio_button_unchecked(A) 10

radio_button_unchecked(B) 15

radio_button_unchecked(C) 16

radio_button_unchecked(D) 20

radio_button_unchecked(E) 30

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (B)
A quadratic equation \(ax^2 + bx + c = 0\) has two real and distinct roots if the discriminant \((b^2  4ac)\) is greater than 0.
Here, a = 1, b = 8, and c = m.
The discriminant is \((8)^2  41m = 64  4m\) .
To have two real and distinct roots, we need 64  4m > 0. Solving this inequality gives:
64 > 4m => 16 > m
The highest integer m that satisfies this inequality is 15.
So, the highest integral value of 'm' for which the quadratic equation \(x^2  8x + m = 0\) will have two real and distinct roots is 15. The correct answer is (B) 15.
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Word Problems  Define the Function
A equation in one variable can be used to define a function of that variable. A function is denoted by a letter such as f or g along with the variable in the expression. Function notation provides a short way of writing the result of substituting a value for a variable. Here is an example:
The expression \(x^2  4x + 7\) defines a function f that can be denoted by \(f(x) = x^2  4x + 7\) .
Gmat math questions related to functions only ask you to define a function given by a scenario.
The original price of a certain bicycle is discounted by y percent, and the reduced price is then discounted by 3y percent. If P is the original price of the bicycle, which of the following represents the price of the bicycle after the two successive discounts?

radio_button_unchecked(A) \(P (1  0.04y + 0.03y^2) \)

radio_button_unchecked(B) \(P (1  0.04y + 0.0003y^2) \)

radio_button_unchecked(C) \(P (1  0.4y + 0.0003y^2) \)

radio_button_unchecked(D) \(P (1  3y^2) \)

radio_button_unchecked(E) \(P (1  4y + 3y^2)\)

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (B)
Firstly, a discount of y percent reduces the price to \(P(1  y/100)\).
Secondly, a further discount of 3y percent reduces this to \(P(1  y/100)(1  3y/100)\).
This simplifies to \(P(1  y/100  3y/100 + 3y^2/10000) = P(1  0.01y  0.03y + 0.0003y^2) = P(1  0.04y + 0.0003y^2)\)
So, the price of the bicycle after the two successive discounts is represented by the expression \(P(1  0.04y + 0.0003y^2)\).
Therefore, the correct answer is (B) \(P(1  0.04y + 0.0003y^2)\).
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Word Problems  Quadratic Equations and Linear Equations
In this type of question, you are expected to translate what is given in words in the question into linear or quadratic equations, and then proceed to solve them to find the solution.
A concert hall with 800 seats sells tickets at $2.00, $3.00, or $4.00 per seat. On Friday evening, â€‹1/4â€‹ of the tickets sold were at $3.00 per seat and the total receipts from the sale of 800 tickets was $2,600. How many of the tickets sold were at $4.00 per seat?

radio_button_unchecked(A) 100

radio_button_unchecked(B) 200

radio_button_unchecked(C) 300

radio_button_unchecked(D) 400

radio_button_unchecked(E) 500

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (D)
Let's denote:
 x as the number of tickets sold at $2.00
 y as the number of tickets sold at $3.00
 z as the number of tickets sold at $4.00
From the problem, we can form the following equations:
 x + y + z= 800 (Total number of tickets)
 y=1/4 ∗ 800 = 200 (1/4 of the tickets were sold at $3.00)
 2.00x + 3.00y + 4.00z = 2600 (Total sale was $2,600)
We can substitute y from equation 2 into equation 1
x + 200 + z = 800
x + z = 600W can substitute y from equation 2 into equation 3:
2.00x + 3.00∗200 + 4.00z = 2600
2.00x + 600 + 4.00z = 2600
2.00x + 4.00z = 2000
x + 2z = 1000So we get the following two equations
 x + z = 600
 x + 2z = 1000
Let's multiply the first equation by 2.00:
 2x + 2z = 1200
 x + 2z = 1000
Now subtract this first equation from the second equation:
\( \frac { \begin{aligned} 2x+2z &= 1200\\ x+2z &= 1000 \end{aligned} } {x = 200} \  \)
Finally, solve for z by putting x = 200 into the equation “x + z = 600”
200 + z = 600
z=400
So, 400 tickets were sold at $4.00 per seat. Hence, the correct answer is (D) 400.
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Equation Inequalities and Min/Max Problems
Inequalities involve comparing two quantities or expressions to determine their relative magnitudes. They use symbols such as <, >, ≤, and ≥ to represent the relationships between numbers. Min/Max problems require finding the minimum or maximum value of a function or expression, usually subject to certain constraints or conditions.
What is the range of possible x values given: 3x + 6 < 18, 4x > 28:

radio_button_unchecked(A) 4 < x < 6

radio_button_unchecked(B) x > 7 and x < 0

radio_button_unchecked(C) x > 10 and x < 3

radio_button_unchecked(D) 4 < x < 7

radio_button_unchecked(E) x > 3 and x < 1

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (D)
Let's solve each inequality separately:
3x + 6 < 18
Subtract 6 from both sides: 3x < 12
Divide both sides by 3: x < 4
4x > 28
Divide both sides by 4: x > 7
Therefore, the correct answer is (D) 4 < x < 7.
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Rates, Ratios, and Percents
In this category, common math topics include fractions, ratios, decimals, and percents, and questions related to these topics are often one of the following:
Arithmetic Operations with Decimals, Fractions, and Percents
Fractions, ratios, and decimals are forms of representing parts of a whole. Fractions express a part of a whole as a quotient of two numbers, ratios show the relative comparison of quantities, and decimals represent fractions using a decimal point and place.
What is the value of \( (0.04)Ã—(2.5) \over (0.01)Ã—(0.05)^2 \) ?

radio_button_unchecked(A) 200

radio_button_unchecked(B) 400

radio_button_unchecked(C) 500

radio_button_unchecked(D) 4000

radio_button_unchecked(E) 5000

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (B)
Let's calculate the expression:
First, we will simplify the expression:
\( (0.04)×(2.5) \over (0.01)×(0.05)^2 \)
First, we can write the decimals as fractions with powers of 10:
\(0.04 = \frac{4}{100} = 4 \times 10^{2} \)
\(0.01 = \frac{1}{100} = 1 \times 10^{2} \)
\(0.05 = \frac{5}{100} = 5 \times 10^{2} \)
Now, we'll plug in these values into the original expression:
\( (4 \times 10^{2}) \times (2.5) / ((1 \times 10^{2}) \times (5 \times 10^{2})^2) \)
This simplifies to:
\( = (4 \times 10^{2}) \times (2.5) / ((1 \times 10^{2}) \times (25 \times 10^{4})) \)
\( = (4 \times 2.5 \times 10^{2}) / (25 \times 10^{6}) \)
Multiply the numbers:
\( = (10 \times 10^{2}) / (25 \times 10^{6}) \)
\(= 10 \times 10^{2} \times 10^{6} / 25 \)
Apply the properties of exponents to combine like bases:
\(= 10 \times 10^{4} / 25 \)
\(= 10,000 / 25 \)
Finally, divide the numbers:
\(= 400 \)
So the result of the calculation is 400.
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Percents and Interest Problems
Percents and interest problems involve calculating percentages, including finding percentages of a whole and solving problems related to interest rates and investments.
Steve deposits money into a unique savings scheme at a local bank. The bank pays interest in a peculiar way. In the first month, the bank offers either 3% of the savings or $20, whichever is lesser. For every month following, the bank pays a flat $20 interest irrespective of the total savings amount. If Steve deposited $700, how much, in dollars, did he accumulate as interest after four months?

radio_button_unchecked(A) 60

radio_button_unchecked(B) 80

radio_button_unchecked(C) 81

radio_button_unchecked(D) 82

radio_button_unchecked(E) 87

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (B)
Given:
 Steve deposits $700
 The bank pays 3% of the savings or $20, whichever is lesser, in the first month
 The bank pays a flat $20 interest every subsequent month
First, let's calculate the interest for the first month:
Interest for the first month = Minimum of (3% of $700, $20)
= Minimum of ($21, $20)
= $20For every subsequent month, the bank pays a flat $20 interest, so for the next three months, he receives 3 * $20 = $60.
Adding the interest earned in all four months, we get:
Total interest = Interest of first month + Interest of next three months
= $20 + $60
= $80Hence, Steve earned $80 as interest after four months.
So, the correct answer is (B) $80.
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Mixture Problems
Mixture problems involve calculating the quantities of different components or substances mixed together to obtain a desired mixture with specific characteristics.
How many liters of pure syrup should be added to a 20liter solution that is 5% syrup in order to fortify it to a solution that is 24% syrup?

radio_button_unchecked(A) 5

radio_button_unchecked(B) 5.5

radio_button_unchecked(C) 6

radio_button_unchecked(D) 7.5

radio_button_unchecked(E) 10

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (A)
Let's denote x as the amount of pure syrup needed. We can create the following equation based on the problem statement:
\(0.24(x + 20) = x + 0.05 \times 20 \)
Here, the left side of the equation stands for the amount of syrup in the solution after adding x liters of pure syrup (24% of the total solution's volume).
The right side is the initial amount of syrup (5% of 20 liters) plus the pure syrup added.
Solving this equation, we get:
\( \begin{aligned} 0.24x  x = 1  4.8 \\ 0.76x = 3.8 \end{aligned} \)
x = 3.8 / 0.76 = 5 liters
So, 5 liters of pure syrup need to be added.
The answer is (A).
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Work/Rate Problems
Work/Rate problems involve calculating the rate at which a task is completed, typically involving multiple individuals working together or separately to accomplish a task in a given time frame.
Jennifer, Kate, and Lucy decide to collaborate on a mural painting project. Jennifer and Kate, working together, can complete the mural in 4/3 hours. Kate and Lucy can finish the same task in 3/2 hours. Meanwhile, Jennifer and Lucy take 3/4 hours to complete it. How long would it take for Jennifer, Kate, and Lucy to paint the mural together?

radio_button_unchecked(A) 1/2 hour

radio_button_unchecked(B) 7/8 hour

radio_button_unchecked(C) 3/4 hour

radio_button_unchecked(D) 8/11 hour

radio_button_unchecked(E) 2/3 hour

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (D)
Firstly, we need to convert the time taken by each pair to work rates:
 Jennifer and Kate's combined rate is 1/(4/3) = 3/4 of a mural per hour.
 Kate and Lucy's combined rate is 1/(3/2) = 2/3 of a mural per hour.
 Jennifer and Lucy's combined rate is 1/(3/4) = 4/3 of a mural per hour.
Secondly, we know that the combined rate of multiple workers working together is the sum of their individual rates. Therefore, we can add up the rates of the pairs:
(3/4) + (2/3) + (4/3) = 33/12 = 11/4
This value equals twice the sum of Jennifer, Kate, and Lucy's rates because each person is counted twice in the sum of the pairs' rates.
To find the combined rate of Jennifer, Kate, and Lucy, we divide 11/4 by 2:
(11/4) / 2 = 11/8
This means that Jennifer, Kate, and Lucy, working together, can paint 11/8 of the mural per hour.
The time it would take for all three to complete the mural together is the reciprocal of their combined rate. Thus, they will be able to complete the mural in 8/11 hours.
Therefore, the correct answer is (D).
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Word Problems  Fraction
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Statistics, Sets, Combinations, Probability, and Sequences
In this category, common math topics include:
Statistics
Statistics involves analyzing and interpreting data, including measures such as mean, median, mode, and range.
If the positive number d is the standard deviation of n, k, and p, then the standard deviation of n + 1, k + 1, and p + 1 is

radio_button_unchecked(A) d+3

radio_button_unchecked(B) d+1

radio_button_unchecked(C) 6d

radio_button_unchecked(D) 3d

radio_button_unchecked(E) d

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (E)
The standard deviation of a set of numbers is a measure of the amount of variation or dispersion in the set. If you add or subtract a constant value to each number in the set, the standard deviation does not change. This is because while each individual value has changed, their relative position and the dispersion among them remains the same.
So, if d is the standard deviation of n, k, and p, then the standard deviation of n + 1, k + 1, and p + 1 is still d.
Therefore, the answer is (E) d.
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Sets Problems
Sets problems deal with groups of elements and their relationships. Overlapping sets problems deal with groups of items that share common elements. Testtakers must analyze the relationships between the sets and identify shared and exclusive elements.
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Combinations
Combinations refer to the different ways of selecting items from a larger set without considering the order. It is often used to calculate the number of ways to choose a group of objects from a given set, where the order of selection does not matter.
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Probability
Probability deals with the likelihood of an event occurring. It involves calculating the chances of different outcomes based on the total number of possible outcomes.
Consider a ship that has two propellers  Propeller A and Propeller B. Both propellers are important for the functioning of the ship, but the ship can still move even if only one of them is operational. The occurrence of a malfunction in one propeller is independent of the functioning or malfunction of the other. If the chance that each propeller operates correctly is 3 out of 5, what is the probability that the ship will still be able to sail?

radio_button_unchecked(A) 4/25

radio_button_unchecked(B) 9/25

radio_button_unchecked(C) 1/5

radio_button_unchecked(D) 3/5

radio_button_unchecked(E) 21/25

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (E)
Firstly, let's understand what the problem is asking. We need to find out the probability that the ship sails. This can happen in two cases: Either Propeller A or Propeller B works, or both work.
Since we know the probability of each propeller working, it may seem like we could just add these probabilities. But this would ignore the possibility of both propellers working at the same time, leading to a miscount. So we need another approach.
A useful method in probability problems is to consider the opposite of what we are looking for  in this case, the ship not being able to sail. This only happens when both propellers malfunction.
The problem tells us that the probability of each propeller working is 3/5. This means the probability of it malfunctioning is 1  3/5 = 2/5. Since the propellers' performance is independent, the likelihood that both propellers fail is the product of their individual failure probabilities, i.e., 2/5 * 2/5 = 4/25.
This gives us the probability of the ship not sailing. But we need the probability of the ship sailing, which is the opposite. In probability, the sum of the probabilities of all possible outcomes is always 1. So, the probability of the ship sailing is 1  the probability of the ship not sailing = 1  4/25 = 21/25.
So, the answer is (E): 21/25.
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Sequences
Sequences are ordered lists of numbers or objects that follow a specific pattern or rule. Testtakers must identify the pattern and find missing elements in the sequence.
In a certain sequence, the nth term, q_{n} , is given by the formula q_{n} = (2_{qn1}  3)^{2}
If the 6th term q_{6} = 225, what is the value of the 5th term, q_{5}? .

radio_button_unchecked(A) 3

radio_button_unchecked(B) 6

radio_button_unchecked(C) 9

radio_button_unchecked(D) 15

radio_button_unchecked(E) 8

spellcheck Check Answer & Answer Explanation
Answer Explanation:
Answer: (C)
The formula for the nth term is q_{n} = (2_{qn1}  3)^{2}
If q_{6} = 225, then what is the value of q_{5}?.
The 6th term q_{6} is provided as 225. We can write this as (2q_{5}  3)^{2} = 225.
Solving this equation gives two potential roots for q_{5}: 2q_{5}  3 = 15 or 2q_{5}  3 = 15.
Solving these two equations gives q_{5} = 9 (from the first equation: 2q_{5} = 18, so q_{5} = 9) and q_{5} = 6 (from the second equation: 2q_{5} = 12, so q_{5} = 6).
As per the given formula q_{n}= (2_{qn1}  3)^{2}
, q_{n} cannot be negative. Therefore, q_{5} cannot be 6.
So, q_{5} = 9 is the only valid solution.
Hence, the correct answer is (C) 9.
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