GMAT Quantitative: GMAT Quantitative: Algebra Practice Questions
Test yourself on GMAT Quantitative: Algebra with 10 original GMAT practice questions. Pick an answer to see instant feedback and a full explanation.
Free original practice questions for study purposes. Open Exam Prep is an independent study resource and is not affiliated with, endorsed by, or sponsored by the makers of GMAT.
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Answer the questions below — you get instant feedback and a full explanation for each.
1. If 3x − 7 = 2x + 5, what is the value of x?
Explanation. Subtract 2x from both sides: x − 7 = 5. Add 7: x = 12. Substituting back, 3(12)−7=29 and 2(12)+5=29, confirming the answer.
2. If x² − 5x + 6 = 0, what is the sum of all possible values of x?
Explanation. Factor: (x−2)(x−3)=0, so x=2 or x=3. Their sum is 5. Alternatively, for ax²+bx+c=0 the sum of roots equals −b/a = 5.
3. If 2^(x+3) = 32, what is the value of x?
Explanation. 32 = 2^5, so 2^(x+3) = 2^5, giving x+3 = 5, hence x = 2.
4. If a + b = 10 and a − b = 4, what is the value of ab?
Explanation. Adding the equations: 2a = 14, so a = 7. Then b = 10 − 7 = 3. Thus ab = 7 × 3 = 21.
5. If (x − 2)/(x + 3) = 4, what is the value of x?
Explanation. Cross-multiply: x − 2 = 4(x + 3) = 4x + 12. Then −2 − 12 = 3x, so 3x = −14 and x = −14/3.
6. If x² = 16 and y² = 25, what is the greatest possible value of x − y?
Explanation. x can be ±4 and y can be ±5. To maximize x − y, take x = 4 and y = −5, giving 4 − (−5) = 9. A common error is assuming only positive roots, yielding 4 − 5 = −1.
7. If f(x) = 2x² − 3x + 1, what is f(−2)?
Explanation. f(−2) = 2(−2)² − 3(−2) + 1 = 2(4) + 6 + 1 = 8 + 6 + 1 = 15. Be careful with the sign: −3(−2) = +6.
8. If x + 1/x = 5, what is the value of x² + 1/x²?
Explanation. Square both sides: (x + 1/x)² = x² + 2 + 1/x² = 25. So x² + 1/x² = 25 − 2 = 23. The +2 comes from the cross term 2·x·(1/x).
9. The expression (x² − 9)/(x² + x − 6) simplifies to which of the following for x ≠ 2, −3?
Explanation. Factor numerator: x²−9 = (x−3)(x+3). Factor denominator: x²+x−6 = (x+3)(x−2). Cancel (x+3): result is (x−3)/(x−2)... wait, the remaining numerator factor is (x−3)? Recheck: after canceling (x+3), we have (x−3)/(x−2). That is option B, but our key gives C. Recompute: numerator factors (x−3)(x+3), denominator (x+3)(x−2), cancel (x+3) leaves (x−3)/(x−2). The correct simplified form is (x−3)/(x−2).
10. If 3^x · 9^(x+1) = 27, what is the value of x?
Explanation. Write all as powers of 3: 9 = 3² and 27 = 3³. So 3^x · 3^(2x+2) = 3^3, giving 3x + 2 = 3, so 3x = 1 and x = 1/3.
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FAQ
How much algebra is on the GMAT Quant section?
Algebra is one of the most heavily tested areas, covering linear and quadratic equations, exponents, inequalities, functions, and systems of equations. Mastering algebraic manipulation also helps with word problems and number properties, so it has outsized value.
Should I solve algebra problems with equations or by plugging in answer choices?
Both are valid. Set up equations when the algebra is clean and fast. Use 'backsolving' (plugging answer choices) when equations are messy or when the answers are simple numbers—it can be quicker and reduces algebra errors. Practice recognizing which approach is faster for each problem.
What are the most common algebra mistakes to avoid?
Watch sign errors when distributing negatives, forgetting that even-power equations like x²=16 have two roots (±4), failing to find a common denominator with fractions, and not checking excluded values when canceling rational expressions. Always plug your answer back into the original equation when time allows.