# Prime Numbers

 Categories : Data Sufficiency, Prime Numbers Q) Is the sum of all the numbers between prime numbers x and y an even or an odd number?1)    x = 3  y = 312)    y is the largest two digit number, x 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.AnswerTo answer data sufficiency questions you don’t have to solve the problem. You just have to find the sufficient condition to prove the answer choice.Question:  sum(x+1, x+2….y-1) = Odd or EvenCondition 1: x = 3  y = 31Sum (4, 5,….30) = odd or EvenYou don’t have to solve this but since you are aware of the sequence of numbers between x and y, the answer can be found.Condition 1 is enough to answer the questionCondition 2: y is the largest two-digit number, x is evenThe question mentions that x and y are prime numbers. Condition 2 provides two more additional information about the prime numbers.Y is the largest two-digit numberLargest... 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 : Prime Numbers Is X, a prime number, equal to 41?1. X = A^2 + 5, where A is an integer2. X^2 > 1,000A. 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.AnswerWithout further information, we cannot definitively answer the question. Statement 1 alone is not sufficient to answer the question. Statement 2 tells us that X^2 > 1,000. This means that X > 32 or X < -32. For example, if X = -33, then X^2 = 1,089, which is greater than 1,000. This gives us a range for r but not a single value of X. Both statements together provide us with no additional information.Correct Answer - Choice E Categories : Factors, Prime Numbers What is the sum of the different positive prime factors of 1050? A. 6 B. 10 C. 12 D. 17 E. 22 AnswerThe first step is to find the prime factorization of 1050. Since 1050 is even, we can start by dividing by 2, giving us 1050 ÷ 2 = 525. Next, since 525 ends with a 5, it is divisible by 5: 525 ÷ 5 = 105. Divide by 5 again: 105 ÷ 5 = 21. Finally, 21 ÷ 3 = 7. So the prime factorization of 1050 = 2 × 3 × 5 × 5 × 7. Now sum the different factors: 2 + 3 + 5 + 7 = 17. Correct Answer - Choice D

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