Question

A series has 8 numbers. What is the last number of the series?
Statement 1: Sum of first 4 numbers in a series is 60
Statement 2: The numbers of series are prime numbers greater than10 in ascending order.

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

To determine the last number of the series, we need to analyze the given statements one by one and then together:

1. Statement 1: The sum of the first 4 numbers is 60.
   This statement alone is insufficient to find the last number of the series because we do not have any information about the properties or sequence of these numbers. We only know the sum of the first four numbers.
2. Statement 2: The numbers of the series are prime numbers greater than 10 in ascending order.
   This statement alone tells us that the numbers in the series are a sequence of prime numbers greater than 10, but it does not specify how many numbers there are or what the sum of any subset of these numbers is.
3. Combining both statements:
   From Statement 2, we list the prime numbers greater than 10: 11, 13, 17, 19, 23, 29, 31, and so on.
   We need to find which of these fit into the conditions stated in Statement 1:
   • Sum of the first 4 numbers is 60.
     Let's check the first four prime numbers greater than 10:
     • 11 + 13 + 17 + 19 = 60
     This matches the conditions specified in Statement 1.
   • This sequence continues in ascending order with 23, 29, 31, and the next is 37.
     Therefore, the eight numbers in the series are: 11, 13, 17, 19, 23, 29, 31, 37.
     The last number of the series is 37.

The correct answer is that both statements together are needed to answer the question, as Statement 1 alone does not provide enough information about the numbers being prime, and Statement 2 alone does not specify the number of terms or their sum. Together, they uniquely determine the series needed to find the last number.