Algebraic expressions and solving equations — ISEE Upper Quantitative Reasoning practice questions

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Practice 171 Algebraic expressions and solving equations questions in the app

What this topic is

Combining like terms, translating words into symbols and solving for an unknown make up Algebraic expressions and solving equations.

Quantitative comparison versions often place a sum of two polynomials in one column and a simplified form in the other; matching each power of x term by term shows whether the two are equal. Word problems about digits are a recognizable type: a two-digit number with tens digit t and ones digit u has value ten t plus u, not t plus u.

A frequent slip is dropping a negative sign when subtracting a whole expression in parentheses.

Sample questions

Pick an answer to see whether it is right — nothing is saved, and nothing needs an account.

Question 1Mid

x > 1

Column A	Column B
$x + \frac{1}{x}$	2

The quantity in Column A is greater✓ CorrectThe quantity in Column B is greater✗ Not this oneThe two quantities are equal✗ Not this oneThe relationship cannot be determined from the information given✗ Not this one

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Answer: A — The quantity in Column A is greater

For $x > 1$ , $(x - 1)^{2} > 0$ , so $x^{2} + 1 > 2 x$ . Dividing by positive $x$ gives $x + \frac{1}{x} > 2$ .

Question 2Mid

A two-digit number has a tens digit that is twice its ones digit. When the digits are reversed, the new number and the original number have a sum of 99. What is the original number?

36✗ Not this one42✗ Not this one63✓ Correct84✗ Not this one

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Answer: C — 63

The original number is $20 a + a = 21 a$ , and the reversed number is $10 a + 2 a = 12 a$ . Their sum is $33 a = 99$ , so $a = 3$ and the original number is 63.

Question 3Easier

Column A	Column B
$(3 x^{2} - 4 x + 6) + (2 x^{2} + 7 x - 9)$	$5 x^{2} + 3 x - 3$

The quantity in Column A is greater✗ Not this oneThe quantity in Column B is greater✗ Not this oneThe two quantities are equal✓ CorrectThe relationship cannot be determined from the information given✗ Not this one

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Answer: C — The two quantities are equal

Combine like terms: $3 x^{2} + 2 x^{2} = 5 x^{2}$ , $- 4 x + 7 x = 3 x$ , and $6 - 9 = - 3$ . The first expression is identical to $5 x^{2} + 3 x - 3$ , so the two quantities are equal.

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Practice 171 Algebraic expressions and solving equations questions in the app

Algebraic expressions and solving equations — ISEE Upper Quantitative Reasoning practice questions

What this topic is

Sample questions

More ISEE Upper topics

Quantitative Reasoning