Here is an interesting quadratic equations question. Combines some concepts of number theory.Questiony = 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?A. –32B. –256C. –255D. –257E. 0Correct Answer : Choice D. -257ExplanationThe curve cuts the x axis at (h, 0) and (k, 0). So, h and k are the roots of the quadratic … [Read more...] about Quadratic Equation : Sum of Roots

# GMAT Number Properties

## GMAT Equations, Number Properties

Here is an interesting question that combines linear equations and properties of numbers to get an answer.QuestionA 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. 5B. 7C. 6D. … [Read more...] about GMAT Equations, Number Properties

## Inequalities Data Sufficiency

Inequalities and Data Sufficiency are a great combination. Many interesting questions have been framed in the DS format from this topic. Here is an interesting question Is a < b? 1. a^b < b^a 2. a/b > 1 This is a good question because it helps us consider several possibilities for examples. Let us start with Statement I alone: 1. a^b < b^a Now, if a … [Read more...] about Inequalities Data Sufficiency

## Number Properties Data Sufficiency

Here is an interesting data sufficiency question.How many of the numbers x, y, and z are positive if each of these numbers is less than 10?1. x + y + z = 202. x + y = 14Correct Answer : Choice A. Statement 1 alone is sufficient; Statement 2 is not sufficient.Explanatory Answer:Statement 1 : x + y + z = 20. From the question stem we know that each number is less than 10.So, x … [Read more...] about Number Properties Data Sufficiency

## GMAT Inequalities – Least integer

Here is an interesting inequalities question.What is the smallest integer that satisfies the inequality ?(x - 3)/ (x^2 - 8x - 20) > 0A. -2B. 10C. 3D. -1E. 0Correct Answer : -1. Choice D Explanatory AnswerLet us factorize the denominator and rewrite the expression as (x - 3) / {(x - 10)(x + 2)}The values of x that are of interest to us are x = 3, x = 10 and x = -2.Let us … [Read more...] about GMAT Inequalities – Least integer