TSIA2 Math
TSIA2 Quantitative Reasoning Practice: 12 Questions Solved
Twelve original TSIA2 Quantitative Reasoning questions that follow the official skills, from ratios and percents to money problems.
Quantitative Reasoning is the second-largest part of the TSIA2 math test: 6 of the 20 questions on the College Readiness Classification (CRC) test, according to the official test specifications. It is the "real-world numbers" area: comparing values, ratios and percents, money problems, and reading linear equations in context. Below are 12 original practice questions that follow the four skills the specifications list, each solved step by step.
If you are new to the TSIA2, start with our TSI math practice test, which explains how the test works and the 950 score you need.
The four Quantitative Reasoning skills
| Skill in the official specifications | Questions here |
|---|---|
| Compare the size of rational and irrational numbers | 1, 2 |
| Solve problems with ratios, proportions, and percents | 3 to 6 |
| Solve problems in context, such as linear relationships in money and everyday numbers | 7 to 10 |
| Identify, manipulate, and interpret linear equations, inequalities, and expressions | 11, 12 |
Comparing numbers
1.Which of these numbers is the greatest?
- A\(\tfrac{7}{9}\)
- B0.78
- C\(\sqrt{0.6}\)
- D77%
Show solution
Write each as a decimal to three or four places.
\[\begin{gathered}\tfrac{7}{9} \approx 0.778 \\ 0.78 = 0.780 \\ \sqrt{0.6} \approx 0.775 \\ 77\% = 0.770\end{gathered}\]The greatest is 0.780.
Common trap: Assuming a square root makes a number bigger. For numbers between 0 and 1, the square root is bigger than the number but can still be smaller than the others here, so convert everything before comparing.
Answer: B (0.78)
2.Between which two consecutive whole numbers is \(\sqrt{52}\)?
- A6 and 7
- B25 and 26
- C7 and 8
- D26 and 27
Show solution
Find the perfect squares on either side of 52.
\[\begin{gathered}7^2 = 49 \lt 52 \lt 64 = 8^2 \\ \Rightarrow\; 7 \lt \sqrt{52} \lt 8\end{gathered}\]Common trap: Dividing 52 by 2 and picking 26. A square root is the number that multiplies by itself to make 52, not half of 52.
Answer: C (7 and 8)
Ratios, proportions, and percents
3.A painter mixes blue and yellow paint in a ratio of 2 to 3 to make green. How many quarts of blue paint are in 15 quarts of green?
- A10
- B5
- C6
- D9
Show solution
The ratio 2 : 3 splits the mix into 5 equal parts, and 2 of them are blue.
\[\tfrac{2}{5} \times 15 = 6 \text{ quarts}\]Common trap: Using \(\tfrac{2}{3}\) of 15, which gives 10. The ratio compares blue to yellow, so the whole mix is \(2 + 3 = 5\) parts.
Answer: C (6)
4.A car travels 270 miles on 12 gallons of gas. At the same rate, how far can it travel on 20 gallons?
- A450 miles
- B162 miles
- C290 miles
- D540 miles
Show solution
Find the miles per gallon, then multiply.
\[\begin{gathered}\tfrac{270}{12} = 22.5 \text{ miles per gallon} \\ 22.5 \times 20 = 450\end{gathered}\]Common trap: Adding 20 to 270, or setting up the proportion upside down, which gives 162. More gallons must mean more miles.
Answer: A (450 miles)
5.In Texas, the state sales tax rate is 6.25%. How much state sales tax is charged on a $48 purchase?
- A$51.00
- B$30.00
- C$0.30
- D$3.00
Show solution
\[48 \times 0.0625 = 3.00\]Common trap: Writing 6.25% as 0.625, which gives $30.00. A percent becomes a decimal by moving the decimal point two places: \(6.25\% = 0.0625\).
Answer: D ($3.00)
6.A college's enrollment grew from 1,250 students to 1,400 students. By what percent did enrollment increase?
- A150%
- B12%
- C10.7%
- D112%
Show solution
\[\tfrac{1400 - 1250}{1250} = \tfrac{150}{1250} = 0.12 = 12\%\]Common trap: Dividing by the new total, 1,400, which gives about 10.7%. Percent change is always measured from the starting amount.
Answer: B (12%)
Money and everyday linear problems
7.A savings account starts with $300. You add $45 every week. Which equation gives the balance \(B\) after \(w\) weeks?
- A\(B = 45 + 300w\)
- B\(B = 345w\)
- C\(B = 300 - 45w\)
- D\(B = 300 + 45w\)
Show solution
The starting amount is added once; the weekly deposit is multiplied by the number of weeks.
\[B = 300 + 45w\]Check with \(w = 2\): \(300 + 90 = 390\), which matches two deposits.
Common trap: Swapping the roles of the numbers, as in \(B = 45 + 300w\). The number that repeats every week is the one multiplied by \(w\).
Answer: D (\(B = 300 + 45w\))
8.The cost \(C\), in dollars, of renting a moving truck for one day is \(C = 0.79m + 29.95\), where \(m\) is the number of miles driven. What does 0.79 represent?
- AThe daily fee
- BThe cost per mile
- CThe total cost for one day
- DThe number of miles driven
Show solution
In \(C = 0.79m + 29.95\), the number multiplied by \(m\) is the rate: every extra mile adds $0.79. The constant, 29.95, is the fee you pay even if you drive 0 miles.
Common trap: Picking the daily fee. The fee is the number that stands alone (the \(y\)-intercept); the number attached to the variable is the rate (the slope).
Answer: B (The cost per mile)
9.A phone plan costs $35 a month plus $5 for each gigabyte of data. Your budget is $60 a month. What is the greatest number of gigabytes you can use?
- A12
- B7
- C5
- D19
Show solution
\[\begin{gathered}35 + 5g \le 60 \\ \Rightarrow\; 5g \le 25 \\ \Rightarrow\; g \le 5\end{gathered}\]Common trap: Dividing the whole $60 by $5 and getting 12. The $35 monthly charge is paid first, so only $25 is left for data.
Answer: C (5)
10.You owe $1,800 on a credit card and pay $150 each month, with no new charges and no interest. After how many months will you owe $600?
- A4
- B12
- C16
- D8
Show solution
\[\begin{gathered}1800 - 150m = 600 \\ \Rightarrow\; 150m = 1200 \\ \Rightarrow\; m = 8\end{gathered}\]Common trap: Answering 12, which is how long it takes to pay off the whole balance, or 4, which is \(600 \div 150\). The question asks when $600 is still left.
Answer: D (8)
Equivalent expressions and comparisons
11.Which expression is equivalent to \(4(x - 3) - 2(x + 1)\)?
- A\(2x - 10\)
- B\(2x - 11\)
- C\(2x - 14\)
- D\(6x - 14\)
Show solution
Distribute both numbers, keeping the minus sign with the 2.
\[4x - 12 - 2x - 2 = 2x - 14\]Common trap: Distributing \(-2\) to the \(x\) but not to the \(+1\), which gives \(2x - 10\). The \(-2\) multiplies both terms in the parentheses.
Answer: C (\(2x - 14\))
12.Job A pays $16 per hour for 30 hours a week. Job B pays a flat $520 per week. Which job pays more per week, and by how much?
- AJob A, by $40
- BJob B, by $40
- CJob B, by $4
- DThey pay the same
Show solution
\[\begin{gathered}16 \times 30 = 480 \\ 520 - 480 = 40\end{gathered}\]Job B pays $40 more per week.
Common trap: Comparing the hourly rate with the weekly pay directly. Put both jobs in the same unit (dollars per week) before comparing.
Answer: B (Job B, by $40)
Answer key
Missed two or more percent questions? Our lesson on percent word problems covers every type on this page. If your score report already lists Quantitative Reasoning as "basic," our guide to TSI scores explains what that label means for your placement.
Teacher's note: Quantitative Reasoning rewards one habit above all: before you calculate, decide roughly what size the answer should be. A bigger tank means more miles, a tax is a small slice of the price, and a balance that is being paid down gets smaller. Ten seconds of estimating rules out at least one choice on almost every question here, and it catches decimal-point slips before they cost you.
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