# GMAT Quant Algebra

Linear & Quadratic Equations Sample Questions

Atypical question that appears in the GMAT quant section from Algbera - Linear Equations and quadratic equations is a word problem. You are expected to translate what is given in words in the question into mathematical expressions and equations and solve them to arrive at the answer. As part of the data sufficiency variant, you may be tested on your understanding of the different types of solutions (unique solution, no solution, infinite solution) possible for a system of linear equations and nature of roots in quadratic equation.

You could get one to three questions focusing on equations in the GMAT quant section - in both variants viz., problem solving and data sufficiency. The concepts covered in this questionbank include finding the roots of a quadratic equation, determining nature of roots of a quadratic equation, finding curve that a quadratic equation represents and word problems in quadratic equations.

Sample GMAT practice questions from equations, linear equations in algebra is given below. Attempt these questions and check whether you have got the correct answer. Explanatory answer with video explanations (wherever provided) is available to help you crack the questions.

1. A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totalled up to 200. However, when the number of legs was counted, the number totalled up to 540. How many more chickens were there in the farm? Note: Each pig had 4 legs and each chicken had 2 legs.

1. 70
2. 120
3. 60
4. 130
5. 80
2. Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?

1. 12 years
2. 6 years
3. 3 years
4. 9 years
5. 27 years
3. For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?

1. 9
2. 12
3. 3
4. 7.5
5. 2.5
4. The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs$327. What is the basic fare for the journey for an adult?

1. $111 2.$52.5
3. $210 4.$58.5
5. $6 5. Data Sufficiency : Is y = 3? 1. (y - 3)(x - 4) = 0 2. (x - 4) = 0 6. A children's gift store sells gift certificates in denominations of$3 and $5. The store sold 'm'$3 certificates and 'n' $5 certificates worth$93 on a Saturday afternoon. If 'm' and 'n' are natural numbers, how many different values can 'm' take?

1. 5
2. 7
3. 6
4. 31
5. 18
7. What is the largest integral value of 'k' for which the quadratic equation x2 - 6x + k = 0 will have two real and distinct roots?

1. 9
2. 7
3. 3
4. 8
5. 12
8. If one of the roots of the quadratic equation x2 + mx + 24 = 0 is 1.5, then what is the value of m?

1. -22.5
2. 16
3. -10.5
4. -17.5
5. Cannot be determined
9. For what value of 'm' will the quadratic equation x2 - mx + 4 = 0 have real and equal roots?

1. 16
2. 8
3. 2
4. -4
5. Choice (B) and (C)
10. y = x2 + bx + 256 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b?

1. -32
2. -256
3. -255
4. -257
5. 0
11. x2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for 'b'?

1. 3
2. 12
3. 6
4. 24
5. 8
12. If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?

1. 3
2. 6
3. 5
4. 4
5. Infinitely many
13. If p > 0, and x2 - 11x + p = 0 has integer roots, how many integer values can 'p' take?

1. 6
2. 11
3. 5
4. 10
5. Infinitely many
14. How many real solutions exist for the equation x2 – 11|x| - 60 = 0?

1. 3
2. 2
3. 1
4. 4
5. None
15. If the curve described by the equation y = x2 + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?

1. -1
2. 4
3. 1
4. -4
5. 0

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