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
GMAT Number Properties
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
Number Properties DS – Remainders, divisors
Quite a lot of interesting DS questions appear from Number Properties and Number Theory. Here is one such question.When a positive integer 'x' is divided by a divisor 'd', the remainder is 24. What is d?1. When 2x is divided by d, the remainder is 23.2. When 3x is divided by d, the remainder is 22.Correct AnswerChoice A. Statement 1 alone is sufficient; statement 2 is not … [Read more...] about Number Properties DS – Remainders, divisors
Number Properties – Product of factors
What is the product of all positive factors of 18? A. 324 B. 5832 C. 39 D. 1521 E. 3042 The correct answer is 5832. Choice B. Let us first focus on how to find the answer methodically and then understand why the method works. The How? Step 1: Find the number of factors for 18. Step 1a. Express 18 as a product of its prime factors. 18 = 2 * 3^2 Step 1b. Increment the … [Read more...] about Number Properties – Product of factors