# Odd and Even

 Categories : Number Properties, Odd and Even, Sets When you think about Set Questions, the traditional form of representing numbers in Sets comes to our mind. In GMAT set questions however, several other concepts will be tested simultaneously. Let us look into an example where Set representation is used to  solve Probability and Number properties GMAT Question.Q) Rhonda’s Chocolate factory is creating packets of chocolates with 12, 13, 14, 25, 35, 44, 66, 77 and 88 chocolates in each packet. The manager at the Factory arranged the packets in such a way that all the bright colored packets were in one group, and dark colored packets in other. If the bright colored packet group had packets with 12, 25, 77, and 88 chocolates, and dark colored packet group had the remaining, what is the probability that picking a pair from dark and bright colored packet group gives even number of chocolates?Answersa)    1/3b)    1/2c)    1/5d)    2/3e)    1/8SolutionThe length of the question should not intimidate you. This simple set question tests the theory of Number... Categories : Odd and Even Q) If a is an even integer, which of the following is definitely not an odd integer?a) a*b, where b is oddb) a/b, where b is an even number greater than 0c) ab-1 where b is an even number greater than 3d) 3(ab-2) where b is an even numbere) 5(a+b)where b is an odd numberAnswerBefore we go into the question, remember the properties of odd and even number arithmetic operations:Odd x Even = EvenOdd x Odd = OddEven x Even = Even Odd + Even = OddEven – Odd = OddOdd + Odd = EvenNow let us look at the question: which of the following is definitely not an odd integer.The key phrase is definitely. You have to be 100% sure, than the number is not an Odd Integer. Let us look at the answer choices:a) (a*b)^3 - 1, where b is greater than or equal to 1This is a direct properties question. The product of even and odd integer will be even and the cube again will be even. But if you deduct 1, the result will be odd. Eliminate the answer choice.b) a/b, where b is an even number greater than 0This condition would have given a non-odd integer but for condition when a=b, the result will be odd.Eliminate the answer choice.... Categories : Odd and Even If a and b are positive integers, is ab even?1. a^b is odd2. a + b is evenA. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.D. EACH statement ALONE is sufficient.E. Statements (1) and (2) TOGETHER are NOT sufficient.AnswerRecall that the product of two integers is even if one or both of the integers are even. Therefore, ab is even if a or b is even. Statement 1 tells us that a^b is odd. Remember that the product of two or more integers is odd only if all of the integers are odd. Since a^b is equal to a × a × ...× a (b times), we know that a must be odd. However, a^b is odd whether the exponent, b, is even or odd. Therefore, we do not know whether b is even or odd, and so we do not know whether a^b is even.Statement 1 is NOT sufficient. Statement 2 tells us that the sum a + b is even. Remember that the sum of two integers is even if both integers are odd or if both integers are even. Therefore, if a is odd, then b is also odd. Alternatively, if a is even, b is also even. Yet if a and b are odd, then ab is odd; if a and b are even, then ab is even. Therefore... Categories : Odd and Even, Properties of Integers Which of the following must be even if A and B are integers and AB^2 + 3B is odd? A. B B. A C. AB + 3 D. AB - 3 E. A + 3Answer The first step is to completely factor our given expression. In this case, since B is in each term, we can factor it out as follows: AB^2 + 3B = B (AB + 3). Let's focus on this factored version of the expression. Since AB + 3 must be odd, and we know that the sum of two numbers is odd only when one of the numbers is odd and the other is even, AB must be even (because 3 is odd). The product of two integers is even only if at least one of the terms is even. Therefore, since AB is even, and B is odd, A must be even. So, the correct answer choice is B. Correct Answer - Choice B

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