Data sufficiency problems can be tricky, even for students who have studied a high level of mathematics. The problems often involve simple concepts such as fractions, percentages, multiples, and prime numbers. There are never questions involving trigonometry or calculus, and even advanced algebra concepts aren’t often present. Instead, data sufficiency questions are often complex and challenging questions based on simple concepts.ReTeks
This question is a great example. It is testing your knowledge of odd and even numbers and prime numbers. These are concepts that a fourth grade student should know, but the question is still challenging.
First, look at the question. We are given an equation, n = p + r. The variables n, p, r are all positive integers, which just means whole numbers. Also, the variable n is an odd number. Before looking at the two statements, there are some conclusions we can draw. There are rules involving the addition of even and odd numbers. Specifically, there are three possibilities when adding two integers together:
Even + Even = Even
Odd + Odd = Even
Even + Odd = Odd
Notice that the sum of p and r is an odd number. This means that one of the variables p and r is even and the other variable is odd. Now, let’s look at the statements.
1) The first statement says that both p and r are prime numbers. A prime number is defined as any integer which is evenly divisible by only two numbers: itself and one. Almost all prime numbers (3, 5, 7, 11, etc…) are odd numbers. However, 2 is also a prime number, and 2 is the only prime number which is also an even number.
Since we know that one of the numbers p and r is even and one of the numbers is odd, this statement then means that either p or r must be the number 2. However, we do not know which of the two it is. Therefore, this statement is not sufficient.
2) This statement says that r is not equal to 2. Remember, look at the statement alone! At this point, we are not allowed to use any information gleaned from the first statement.
With the second statement alone, we know that r is not 2. We also know from the question that one of the numbers p and r is even and one of the numbers is odd. This does not give enough information to find the value of p. The numbers could be 3 and 4, 3 and 6, 5 and 6, etc… There an infinite number of possibilities for the value of p, so this statement is not sufficient.
If we combine both statements, then we know all of the following:
The answer to the question is (C), because it is only by combining both statements that you can know the value of p.