# Number Properties

 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 : Number Properties Q) What is the unit digit of (2) ^29 * (5) ^29 * (7) ^29?A) 1B) 5c) 9D) 0E) 7To answer questions that involve multiplying large numbers and finding the unit digit, the solution is to find patterns within numbers. In this case, each number is raised to the 29th power and multiplied with each number. All numbers that are raised to a certain power follows a pattern. Let us look at each of them.(2)^29    (2)^1 = 2(2)^2 = 4(2)^3 = 8(2)^4 = 16(2)^5 = 32The power of 2 has unit digit in the following pattern (2,4,8,6)Unit Digit of (2)^29 = 2  -> First StatementWe know that Unit Digit (5)^29 = 5 -> Second StatementUnit Digits For (7)^29 has the following pattern(7)^1 = 7(7)^2 = 9(7)^3 = 3(7)^4 = 1(2)^5 = 7The power of 7 has unit digit in the following pattern (7,9,3,1)Unit Digit of (7)^29 = 7 -> Statement 3Unit Digit obtained by multiplying Statements 1, 2 and 3, we get 2 x 5 x 7 is 0Correct Answer: D Categories : Number Properties, Prime Numbers Let us start with the definition of a Prime Number. Do you remember?A natural number that can be divided by only 2 numbers – 1 and the number itself is called a prime number.The first prime number that comes to our mind is “1” but if you had paid attention to your Math teacher, then you will know that: 1 is neither primer nor composite. The reason behind this conclusion is a topic for another post. Let us look at identifying prime numbers.6 – Prime or Composite?Steps to identify prime numbers1) Divide the number into factors2) If the number of factors is more than two then it is composite.Ex: 6 has three factors 2, 3, 1. So 6 is not prime6 = 2 x 3 x 1Before going into shortcuts to find large prime number, here are a few properties of Prime Numbers1) The lowest even prime number is 22) The lowest odd prime number is 33) All prime numbers above 3 can be represented by the formula 6n + 1 and... Categories : Number Properties, Problem Solving GMAT Number properties may sound scary, but they just constitute elementary mathematical principles. You probably know most of these principles by memory; if not, you could easily execute a calculation to ascertain them. The best option, though, is to study these principles enough that they seem intuitive. The GMAT Quantitative section is all about saving time; making number theory second nature will definitely save you some valuable seconds. 1.Odds and EvensAdditionEven + even = even (12+14=36)Odd+ Odd = even (13+19=32)Even + Odd =  odd (8 + 11 = 19)To more easily remember these, just think that a sum is only odd if you add an even and an odd. MultiplicationEven x even = even (6 x 4 = 24)Odd x odd = odd  (5 x 3 = 15)Even x odd = even (6 x 5= 30)To more easily remember these, just think that a product is only odd if you multiply two odds. Example QuestionIf r is even and t is odd, which of the following is odd?A. rtB. 5rtC. 6... Categories : Number Properties The number 0 on the GMAT is tricky as its properties are the trap in to which a seemingly logical solution can lead you or are often either the key to unlocking a difficult solution. Learning the properties of zero (keep in mind that it is an even number) is a crucial skill, particularly on data sufficiency problems. Even more importantly, never forget to consider zero as a potential value for a variable, as it often produces surprising results. Consider the case of zero as an exponent:x^0 is, by definition, equal to 1. Noting the properties of exponents can help you to prove and more easily remember this useful device: take, for example, the expression x^2 * x^-2. You could rearrange this two ways: a) (x^2) / (x^2) --> The negative exponent moves that term to the denominatorb) x^(2-2), or x^0 --> When multiplying terms with the same base, taken to different exponents, you add the exponentsBecause we can prove that (x^2) / (x^2) must be equal to 1, and that the two expressions above are... Categories : Number Properties Jill's bank account has j dollars. Marcy's bank account has 5 times what Jill's bank account has and 1/3 of what Sarah's bank account has. How much more is in Sarah's bank account than is in Jill's bank account, in terms of j? A. 10j B. 14j C. 15j D. (2/5)j E. (1/5)j Answer Assign letters to the bank account of each woman: Jill = j. Marcy = m. Sarah = s. Now create equations based on the information given: m = 5j (Marcy has 5 times what Jill has). m = (1/3)s (Marcy has 1/3 of what Sarah has). Combine the two equations and simplify: 5j = m = (1/3)s. 5j = (1/3)s. 15j = s. Sarah has 15j dollars in her account so subtract j (Jill's bank account) from 15j and you get 14j. Correct Answer - Choice B Categories : Number Properties If X is an integer, is Y an integer? 1. The average of X and Y is not an integer. 2. The average of X, Y, and X + 6, is Y. A. 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. Answer Since we can pick both integer and non-integer values for X that satisfy Statement 1, we can conclude that Statement 1 alone is insufficient to answer the question. For statement 2, remember that the average of a group of terms is equal to the sum of the terms divided by the number of terms. If X is an integer, X + 3 is also an integer; therefore, we can conclude that Y is an integer. Statement 2 alone is sufficient to answer the question. Correct Answer - Choice B

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