A typical question that appears in the GMAT quant section from Algbera - Linear Equations and Quadratic Equations - is an algebra word problem. You are expected to translate what is given in words in the question into algebraic expressions and equations and solve them to arrive at the answer. The GMAT data sufficiency questions in algebra may test 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 maths section - in both variants viz., problem solving and data sufficiency. The concepts covered in this GMAT questionbank include framing and solving linear equations in two variables, linear equations in one variable, simultaneous equations solution, 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 for equations - linear equations and quadratic equations - in algebra is given below. Attempt these GMAT sample 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.
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 totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many more chickens were there in the farm? Note: In the farm, each pig had 4 legs and each chicken had 2 legs.
This GMAT question is an algebra word problem. Using the information about the number of heads and number of legs, frame a system of linear equations in two variables. Solve the two simultaneous equations to compute the number of pigs and number of chickens. Lastly, remember to find tha answer to the question asked. A 600 level GMAT question in linear equations of two variables.
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?
This GMAT sample question is an algebra word problem. With the information about the ages 3 years back frame a linear equation in two variables - one for the present age of the father and the other for the present age of the son. Frame a second linear equation in two variables using the information about their present ages. Solve the system of linear equations in two variables to compute their present ages. Lastly, remember to find tha answer to the question asked. A 600 level GMAT linear equations word problem.
For what values of 'k' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 NOT have a unique solution?
Rule: A system of linear equations in two variables will NOT have a unique solution if the ratio of the coefficients of the two variables of the two linear equations is the same. Apply this rule and find the value of 'k'. A sub 600 level GMAT practice question in linear equations of two variables.
The basic one-way air fare for a child aged between 3 and 10 years costs half the regular basic 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?
This GMAT math question is an algebra word problem. Frame a linear equation in two variables for the data given about the cost of one reserved adult ticket. Frame a second linear equation in two variables using the data about the cost of an adult and a child ticket. Use the basic fare for an adult ticket as one of the unknowns and the reservation cost as the second unknown. Solve the system of linear equations in two variables to compute the basic fare for an adult. A 600 to 650 level GMAT linear equations word problem.
Data Sufficiency: Is y = 3?
A GMAT data sufficiency question about solution to system of equations. Check whether you get a definite yes or no to the question asked using the information in the statements. If you get a definite answer, data is sufficient. If using the statements, you do not get a definite answer, the data is not sufficient. A 600 to 650 level GMAT data sufficiency sample question in system of equations.
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?
A hard GMAT linear equation word problem. Why? Because with the information in the question, we will get only one linear equation in two variables. The additional information we have is that 'm' and 'n' are natural numbers. You can start with an iterative approach to find the number of values that 'm' can take. Subsequently, check the explanatory answer to learn how to compute the value without the process of iteration. A 700 level GMAT sample question in linear equations.
What is the highest integral value of 'k' for which the quadratic equation x^{2} - 6x + k = 0 will have two real and distinct roots?
Rule: The quadratic equation's discriminant should be positive if the quadratic equation has real and distinct roots. So, frame an inequality for the discriminant being greater than 0. The expression for the discriminant will have 'k' as an unknown. Find the highest integer value that satisfies the inequality to find the answer to the question. A 650 level GMAT question in quadratic algebra and inequalities.
If one of the roots of the quadratic equation x^{2} + mx + 24 = 0 is 1.5, then what is the value of m?
A GMAT sample quadratic equations question. If 1.5 is one of the roots of the quadratic equation, substituting x = 1.5 in the equation will satisfy the quadratic equation. Solve the resultant equation to find the value of 'm'. A sub 600 level GMAT sample question in algebra.
For what value of 'm' will the quadratic equation x^{2} - mx + 4 = 0 have real and equal roots?
Rule: If the roots of a quadratic equation are real and equal, the quadratic equation's discriminant will be 0. Compute the discriminant for the quadratic equation, equate it to 0 to find the value of m. A 600 level GMAT practice question in quadratic equations.
y = x^{2} + 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?
The points where the curve defined by the quadratic equation cuts the x-axis are the roots of the quadratic equation. The product of the roots of this quadratic equation is 256. List down the different values that the roots (integer values) can take such that their product is 256. Identify the least values possible and compute the answer to the quadratic equations question. A 700 level GMAT maths question in quadratic algebra.
x^{2} + bx + 72 = 0 has two distinct integer roots; how many values are possible for 'b'?
The product of the roots of the quadratic equation is 72. List down the different distinct integer values the roots could take such that their product is 72. Approach to solve this GMAT sample question is the same as the last question. Check the explanatory answer for an alternative number properties method to compute the answer to this algebra question. A 650 to 700 level GMAT practice question in quadratic equations.
If x > 0, how many integer values of (x, y) will satisfy the equation 5x + 4|y| = 55?
'x' and 'y' are integers. Note 4|y| is non-negative. And remember that the question has stated that x > 0. Rewrite the equation with 4|y| on one side and the remaining terms on the other. Find number of values that 4|y| to find the answer. A 650 to 700 level GMAT sample question in linear algebra and absolute values of numbers.
If p > 0, and x^{2} - 11x + p = 0 has integer roots, how many integer values can 'p' take?
The product of the roots of this quadratic equation is p. Because p > 0, the product of the roots is positive. The sum of the roots of this quadratic equation is 11. List all different integer values for roots of this equation such that the sum if 11 and the product is a positive number to find the answer to this GMAT sample question. A 650 level GMAT sample question in algebra.
How many real solutions exist for the equation x^{2} – 11|x| - 60 = 0?
Assign |x| = y and rewrite the quadratic equation in y. Solve for 'y'. Compute feasible values for 'x' from the values computed for y keeping in mind that |x| cannot be negative. A 650 to 700 level GMAT question in algebra.
If the curve described by the equation y = x^{2} + bx + c cuts the x-axis at -4 and y axis at 4, at which other point does it cut the x-axis?
The x-coordinate where the curve cuts the y-axis is 0. Use it to find c. The product of the roots of this quadratic equation is 'c'. From the value of 'c' computed in the first step and the information that one of the roots is -4 (the point where the curve cuts the x-axis), compute the second root. A 650 to 700 level GMAT sample question in quadratic equations.
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