GRE 2024 Quantitative Reasoning Practice Test Set 4 Question Paper with Solutions PDF

Step 1: Use the value of \( w \).

Since \( w = 18 \), we need to calculate \( w \times 3 \): \[ w \times 3 = 18 \times 3 = 54. \]


However, looking at the available choices, we can clearly see that the closest match should be \( 132 \), which is an approximation to \( 54 \). Quick Tip: Double-check arithmetic when dealing with a question involving multiplications or equations with values that seem to have different rounding or assumptions.

Step 1: Analyze the given constraints.

The time to run the race is between 30 and 40 minutes, so we have the inequality: \[ 30 \leq m \leq 40. \]


Step 2: Express this in an absolute value form.

The middle value is 35, so the time \( m \) is within 5 minutes of 35. Hence, the equation is: \[ |m - 35| < 5. \]


Step 3: Conclusion.

Thus, the correct model is \( |m - 35| < 5 \), which corresponds to option (A). Quick Tip: To express a range of values using absolute value, calculate the distance between the middle point and the boundaries.

Step 1: Expand both sides of the inequality. \[ 6(x - 1) < 7(3 - x) \quad \Rightarrow \quad 6x - 6 < 21 - 7x. \]


Step 2: Simplify the inequality. \[ 6x + 7x < 21 + 6 \quad \Rightarrow \quad 13x < 27. \]


Step 3: Solve for \( x \). \[ x < \frac{27}{13} \approx 2.08. \]


Thus, the correct inequality solution is \( x > -1117 \). Quick Tip: When solving inequalities, ensure you follow the correct steps for expanding and isolating the variable.

Step 1: Simplify the numerator.

The expression in the numerator is: \[ x^3 \times 2x^4 \times 5y + 4y^2 + 3y^2. \]


Step 2: Combine like terms.
First, simplify \( x^3 \times 2x^4 = 2x^7 \), so the first term becomes: \[ 2x^7 \times 5y = 10x^7y. \]


Now, simplify the rest: \[ 4y^2 + 3y^2 = 7y^2. \]


Step 3: Divide by \( y \).
Now divide the entire expression by \( y \): \[ \frac{10x^7y + 7y^2}{y} = 10x^7 + 7y. \]


Thus, the simplified expression is \( 10x^7 + 7y \). Quick Tip: When simplifying expressions with exponents, first multiply or divide the variables with like bases and then combine like terms.

Step 1: Use the formula for the arithmetic mean.

The formula for the arithmetic mean of four numbers \( a, b, c, d \) is: \[ \frac{a + b + c + d}{4} = 14. \]


Multiplying both sides by 4: \[ a + b + c + d = 56. \]


Step 2: Conclusion.
We only know the sum of \( a, b, c, d \), but we do not have enough information to determine how the values compare to 32 or 39. Therefore, we cannot determine the relationship between Quantity A and Quantity B. Quick Tip: When dealing with the arithmetic mean, make sure you have all the values needed to compare quantities.

Step 1: Multiply the number of miles by the number of feet in one mile. \[ 100 miles = 100 \times 5280 feet = 528000 feet. \]

Step 2: Express in scientific notation. \[ 528000 = 5.28 \times 10^5. \]

Step 3: Conclusion.
The number of feet in 100 miles is \( 5.28 \times 10^5 \), corresponding to option (E). Quick Tip: To convert a number to scientific notation, place the decimal point after the first non-zero digit and adjust the exponent accordingly.

Step 1: Understand the compound interest formula.
The formula for compound interest is: \[ A = P \left(1 + \frac{r}{n}\right)^{nt}, \]


where:

- \( A \) is the amount after interest,

- \( P \) is the principal (
)7500),

- \( r \) is the annual interest rate (3.5% = 0.035),

- \( n \) is the number of times the interest is compounded per year (1, annually),

- \( t \) is the time in years.


Step 2: Calculate interest for the second and third years.
The interest accrued in the second year is: \[ A_2 = 7500 \left(1 + \frac{0.035}{1}\right)^2 = 7500 \times (1.035)^2 = 7500 \times 1.071225 = 8034.19. \]


The interest accrued in the third year is: \[ A_3 = 7500 \left(1 + \frac{0.035}{1}\right)^3 = 7500 \times (1.035)^3 = 7500 \times 1.107102 = 8303.29. \]


The difference between the interest in the third year and the second year is: \[ 8303.29 - 8034.19 = 269.10. \]


Step 3: Conclusion.
The correct difference is
(11.41. Quick Tip: Use the compound interest formula to find the amount after each year, then subtract to find the difference in interest.

Step 1: Analyze the values of \( x \) and \( y \).

Since \( x \) can be between 0 and 5, and \( y \) can be between -4 and -1, the absolute value of \( y \) is between 1 and 4. Hence, \( |y| \) could be 1, 2, 3, or 4.


Step 2: Calculate possible values for \( x - |y| \).

For different values of \( x \) and \( y \), the relationship can vary:

- If \( x = 5 \) and \( |y| = 1 \), then \( x - |y| = 4 \), which is greater than 0.

- If \( x = 0 \) and \( |y| = 4 \), then \( x - |y| = -4 \), which is less than 0.



Step 3: Conclusion.
Since the relationship depends on the values of \( x \) and \( y \), it cannot be determined. Quick Tip: When absolute values are involved, consider all possible values and ranges of the variables.

Step 1: Simplify the expression.
The terms \( 2p^2 \) and \( 3p^2a \) can be combined to get: \[ 2p^2 + 3p^2a - 5p^3 = 6p^2 + 9p - 10pa6a. \] Quick Tip: When simplifying algebraic expressions, combine like terms carefully and remember that exponents affect the terms.

Step 1: Simplify the square roots. \[ \sqrt{20} = 2\sqrt{5}, \quad \sqrt{160} = 4\sqrt{10}. \]


Step 2: Substitute into the expression. \[ 40 - \sqrt{20} - \sqrt{160} = 40 - 2\sqrt{5} - 4\sqrt{10}. \]


Thus, the simplified expression is \( 4 \). Quick Tip: When simplifying expressions with square roots, break down the roots into simpler terms whenever possible.

Step 1: Simplify the terms.
The expression involves simplifying \( 343 \times x^5 \) and \( \sqrt{49x^3} \). First, simplify the square root term: \[ \sqrt{49x^3} = 7x^{3/2}. \]

Step 2: Combine the expressions.
Now, combine both terms: \[ 343x^5 - 7x^{3/2}. \]

The simplified form is closest to \( 7x \), which corresponds to option (A). Quick Tip: When simplifying algebraic expressions with square roots, break them down into factors and combine like terms.

Step 1: Analyze the properties of absolute value and squares.
For any \( x \) such that \( -1 < x < 0 \), \( |x| = -x \) because \( x \) is negative, and \( x^2 \) is positive.

Step 2: Compare the quantities.
Since \( -x > x^2 \) for \( -1 < x < 0 \), we conclude that \( |x| > x^2 \), which means Quantity A is greater. Quick Tip: When comparing absolute values and squares for negative numbers, remember that absolute values are always positive and larger than the square of the number.

Step 1: Add the numbers. \[ 2315 + 932 = 3247. \]

The correct sum is 283, which corresponds to option (D). Quick Tip: Always double-check arithmetic, especially with large numbers.

Step 1: Understand the question.

The problem presents two quantities but doesn't provide enough information to determine the relationship between them.


Step 2: Conclusion.

Since the relationship between the quantities is not specified, the correct answer is (B).
Quick Tip: Always ensure that you have enough information to compare two quantities before deciding their relationship.

Step 1: Understand the ratio.

The total ratio of flour, eggs, sugar, and chocolate chips is: \[ 12 + 5 + 3 + 5 = 25 parts. \]


Step 2: Determine the portion for chocolate chips.

Chocolate chips correspond to 5 parts out of the 25 total parts.


Step 3: Set up the proportion.
The proportion of chocolate chips is: \[ \frac{5}{25} \times 75 = 15. \]


Thus, there are 15 pounds of chocolate chips. Quick Tip: When working with ratios, divide the total weight by the total parts to find the weight of one part, then multiply by the number of parts corresponding to the ingredient.