This question is an interesting quadratic equation question that ties in concepts relating to factors in number properties.While solving questions of this kind exercise caution with what the question asks. You may do everything right and still end up with an incorrect answer.Questionx2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for 'b'?A. 3B. … [Read more...] about Quadratic Equation PS – Sum of roots
GMAT Number Theory
Number Properties – Factors
Here is a relatively easy number properties problem solving question.QuestionWhat is the largest 3 digit number to have an odd number of factors?A. 729B. 943C. 625D. 961E. 841Correct Answer : Choice D. 961Explanatory AnswerA perfect square has an odd number of factors.Of the numbers in the list, the largest 3 digit perfect square is 961 (312).Hence, Choice D is the correct … [Read more...] about Number Properties – Factors
Quadratic Equation : Sum of Roots
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 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