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GMAT Algebra — practice questions

Explore 31 free Algebra questions in GMAT Quantitative Reasoning. Open each question or exercise to read its content, reference answers and available explanation.

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Algebra questions and exercises with answers

Showing questions 1–30 of 31.

If 0 < a < b and a^2 + b^2 = 50, ab = 7, what is b − a?Read the answer and worked solution →If a = 2 and b = −3, value of a² − b²:Read the answer and worked solution →An equation of the form ax + by + c = 0, with a and b not both zero, is a linear equation in:Read the answer and worked solution →Substituting x = 1 and y = 1 in 2x + 3y = 5 gives 5, so this pair of values is:Read the answer and worked solution →Each solution of a linear equation in two variables corresponds to:Read the answer and worked solution →Two lines drawn in a plane can intersect, be coincident, or be:Read the answer and worked solution →If the two lines of a pair of linear equations intersect at one point, the pair has:Read the answer and worked solution →A pair of linear equations that has no solution is called:Read the answer and worked solution →A pair of linear equations whose lines coincide has:Read the answer and worked solution →A pair of equations which are equivalent, with infinitely many common solutions, is called:Read the answer and worked solution →Akhila's rides and games gave x - 2y = 0 and 3x + 4y = 20. The lines meet at:Read the answer and worked solution →Romila paid 9 for 2 pencils and 3 erasers; Sonali paid 18 for 4 pencils and 6 erasers. Their lines are:Read the answer and worked solution →Two rails are x + 2y - 4 = 0 and 2x + 4y - 12 = 0. Do they cross?Read the answer and worked solution →For x + 3y = 6 and 2x - 3y = 12, the common point is:Read the answer and worked solution →If a1/a2 is not equal to b1/b2, the two lines are:Read the answer and worked solution →If a1/a2 = b1/b2 = c1/c2, the two lines are:Read the answer and worked solution →If a1/a2 = b1/b2 but this differs from c1/c2, the two lines are:Read the answer and worked solution →A pair of linear equations that has a solution is called:Read the answer and worked solution →A coach buys 3 bats and 6 balls for 3,900 and later 1 bat and 3 balls for 1,300. This is a situation of:Read the answer and worked solution →2 kg apples with 1 kg grapes cost 160, and 4 kg apples with 2 kg grapes cost 300. The unknowns here are:Read the answer and worked solution →Putting x = 0 in the equation 3x + 4y = 20 gives y equal to:Read the answer and worked solution →Choosing y = 2 in 3x + 4y = 20 was preferred because it gives x as:Read the answer and worked solution →The graphical representation of a linear equation in two variables is:Read the answer and worked solution →Catch the consistent pairsRead the answer and worked solution →Pop the algebra wordsRead the answer and worked solution →Run the line casesRead the answer and worked solution →Slice the equation wordsRead the answer and worked solution →Consistent or inconsistentRead the answer and worked solution →Sort the three line casesRead the answer and worked solution →Type the numberRead the answer and worked solution →

Worked practice questions

If 0 < a < b and a^2 + b^2 = 50, ab = 7, what is b − a?

  1. 3
  2. 4
  3. 5
  4. 6
  5. 8
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Correct answer: B. 4

1. Identify what is being asked: this is a **Algebra** question. 2. Apply the standard approach for this question type to evaluate each option. 3. The correct answer is **B. 4** — it satisfies the conditions of the stem. _Source: GMAC Official 12 Sample Questions (mba.com)_

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If a = 2 and b = −3, value of a² − b²:

  1. 5
  2. −5
  3. 13
  4. −13
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Correct answer: B. −5

1. 4 − 9 = −5. _Source: 501-GMAT-Questions Section 4 / Manhattan Quant Bank_

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An equation of the form ax + by + c = 0, with a and b not both zero, is a linear equation in:

  1. Two variables
  2. One variable
  3. Three variables
  4. Four variables
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Correct answer: A. Two variables

1. Here a, b and c are real numbers. 2. Both x and y appear. 3. So it is a linear equation in two variables. _Source: syllabus Mathematics, Chapter 3, Pair of Linear Equations in Two Variables._

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More Quantitative Reasoning topics

Modern MathematicsQuantitative ReasoningPermutations and CombinationsLogical ReasoningQuantitative AptitudeAverages and MixturesSimple and Compound InterestBoats and Streams