GMAT Maths | Quadratic Equations #10

GMAT Sample Questions | Algebra & Number Properties Practice

This GMAT sample question is a quant problem solving practice question in quadratic equations. It tests your understanding of sum and product of roots of quadratic equations. Interestingly, it also ties in an important number property concept of expressing a number as a product of two of its factors. A 700 level GMAT maths question in number properties and quadratic equations.

Question 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

Get to 705+ in the GMAT


Online GMAT Course
@ INR 6000


Video Explanation


GMAT Live Online Classes


Starts Sat, Apr 6, 2024


Explanatory Answer

Step 1 of solving this GMAT Quadratic Equations Question: Understand the equation and the points (h, 0) and (k, 0)

The given equation is a quadratic equation. A quadratic equation when plotted on a graph sheet (x - y plane) will result in a parabola.
The roots of the quadratic equation are computed by equating the quadratic expression to 0. i.e., the roots are the values that 'x' take when y = 0
So, the roots of the quadratic equation are the points where the parabola cuts the x-axis.
The question mentions that the curve described by the equation cuts the x-axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic equation.
For quadratic equations of the form ax2 + bx + c = 0, the sum of the roots = \-\frac{b}{a})
The sum of the roots of this equation is \-\frac {b} {1}) = -b.
Note : Higher the value of 'b', i.e., higher the sum of the roots of this quadratic equation, lower the value of b.

For quadratic equations of the form ax2 + bx + c = 0, the product of roots = \\frac{c}{a}).
Therefore, the product of the roots of this equation = \\frac{256}{1}) = 256.
i.e., h × k = 256 h and k are both integers.
So, h and k are both integral factors of 256.


Step 2 of solving this GMAT Quadratic Equations Question: List possible values of h and k and find the least value of ‘b’

This is the step in which number properties concepts kick in. 256 can be expressed as product of two numbers in the following ways:
1 × 256
2 × 128
4 × 64
8 × 32
16 × 16

The sum of the roots is maximum when the roots are 1 and 256 and the maximum sum is 1 + 256 = 257.
∴ The least value possible for b is -257.

Choice D is the correct answer.



GMAT Online Course
Try it free!

Register in 2 easy steps and
Start learning in 5 minutes!

★ Sign up

Already have an Account?

★ Login

GMAT Live Online Classes

Next Batch Apr 6, 2024

★ GMAT Live Info

GMAT Preparation Online | GMAT Algebra Videos On YouTube


Other useful sources for Algebra Question | Linear Equations and Quadratic Equations Sample Questions

2IIM CAT Question bank | CAT Questions in Linear Equations and Quadratic Equations

Ascent MBA entrace exam Question Bank in Algebra | Linear Equations and Quadratic Equations.

Maxtute CBSE Class 10 Practice Questions in Quadratic Equations


GMAT Sample Questions | Topicwise GMAT Questions


Work @ Wizako

How to reach Wizako?

Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com
Leave A Message