Practice Test 11 - Pre Algebra

20 questions. Answer them in any order, then submit to see your score and every explanation.

A number $N$ has the property that when divided by 12, the remainder is 8, and when divided by 18, the remainder is 14. What is the remainder when $N$ is divided by the least common multiple of 12 and 18?
When solving $\begin{cases} y = 3x - 2 \\ 2x + y = 13 \end{cases}$ by substitution, a student writes: ' $2x + (3x - 2) = 13$ , so $5x - 2 = 13$ , giving $x = 3$ .' The student then concludes the solution is $(3, 7)$ . What should you tell this student about their work?
The formula $I = Prt$ calculates simple interest. If $2400 in interest is earned on a principal of $8000 over $5$ years, what is the annual interest rate as a percentage?
A recursive pattern starts with $a_1 = 3$ . Each subsequent term follows the rule $a_{n+1} = 2a_n - 1$ . Maria wants to find a direct formula for the $n^{\text{th}}$ term instead of using the recursive rule. What pattern should she recognize?
An expression contains the terms $4x^{n+1}$ , $-2x^{n+1}$ , and $3x^n$ , where $n$ is a positive integer. After combining like terms, how many terms remain in the simplified expression?
A candle burns at a constant rate. Initially it is 8 inches tall. After burning for 3 hours, it is 6.5 inches tall. After burning for 7 hours, it is 4.5 inches tall. Which equation models the candle's height $y$ (in inches) after burning for $x$ hours?
A train travels at a constant speed and covers 180 miles in 2.5 hours. At this same rate, how much additional time would be needed to travel a total distance of 396 miles from the starting point?
A delivery truck's distance from its starting point is recorded every hour. The data shows: Hour 1: 45 miles, Hour 2: 90 miles, Hour 3: 135 miles, Hour 4: 160 miles, Hour 5: 185 miles. Sarah claims the truck traveled at a constant rate for the entire trip. Which analysis correctly evaluates her claim?
Consider the system $\begin{cases} x + 2y = 8 \\ y = mx + b \end{cases}$ where $m$ and $b$ are constants. If substitution yields the equation $x + 2(mx + b) = 8$ , which simplifies to $(1 + 2m)x = 8 - 2b$ , under what condition will this system have no solution?
A student wants to compare the distributions of quiz scores between two different classes. She has already created box plots for both classes and notices that Class A has a larger IQR than Class B, but both have the same median. What additional display would provide the MOST useful information for understanding the difference between the classes?
The temperature at 6 AM was $-8.5°F$ . By noon, it had risen $12.7°F$ . In the afternoon, it dropped $15.3°F$ , and then in the evening it rose again by $6.8°F$ . What was the final temperature?
A swimming pool is being drained at a constant rate. The pool initially contains 8,000 gallons. After 2 hours, it contains 6,800 gallons. At this rate, how many hours after draining began will the pool contain exactly 4,000 gallons?
A baseball player's batting average dropped from $0.347$ to $0.298$ during a slump. By approximately what percent did their batting average decrease?
Two data sets each contain 15 values. Set A has a mean of 60 and MAD of 8. Set B has a mean of 60 and MAD of 12. If the data sets are combined into one set of 30 values, what can be determined about the combined set?
Marcus is simplifying the expression $3x^2 - 7xy + 4y^2 + 2x^2 + xy - 3y^2$ . After combining like terms, he claims his result has exactly 2 terms. Which statement best explains whether Marcus is correct?
The population of a town decreased by 15% in 2020, then increased by 20% in 2021. If the population at the end of 2021 was 40,800, what was the population at the beginning of 2020?
The area of a triangle is given by $A = \frac{1}{2}bh$ . If the base is $(6m + 4)$ and the height is $(m + 3)$ , which expression represents $\frac{1}{2}$ times the distributed product $bh$ ?
A population of bacteria doubles every 3 hours. If there are initially 250 bacteria, which expression represents the population after 15 hours?
Maria's checking account has a balance of $-\$47.25$ . She makes three deposits of $28.50, $15.75, and $22.00, then writes checks for $18.25 and $35.50. If her bank charges a $25.00 overdraft fee for each day her account is negative, and she started the day negative, what is her balance after all transactions and fees?
A researcher collected data on daily exercise minutes for two groups. Group X has a median of 45 minutes and an interquartile range (IQR) of 20 minutes. Group Y has a median of 40 minutes and an IQR of 35 minutes. Which conclusion is most appropriate?

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