Question

This question consists of a question and two statements numbered I and II. Decide whether the data given in the statements are sufficient to answer the question.
What is the 57th number in a series of numbers?
I. Each number in the series is three more than the preceding number.
II. The tenth number in the series is 29.

• A. The data in Statement I alone is sufficient to answer the question while the data in Statement II alone is not sufficient to answer the question.
• B. The data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question
• C. If the data either in Statement I or Statement II alone are sufficient to answer the question
• D. If the data in both Statements I and II together is necessary to answer the question

Answer 1

The Correct Option is D

To determine the 57th number in the series, we need to analyze the information provided by the two statements:

1. Statement I indicates that the difference between consecutive numbers in the series is constant at 3. However, without any initial value or any specific term in the series known, we cannot determine any term solely with this statement.
2. Statement II provides that the 10th number is 29, but without knowing the constant difference between numbers, we can't extrapolate to find the 57th number.

Since neither statement alone is sufficient, let's combine the information:

Combine Statements I and II:

1. From Statement II, the 10th term (a₁₀) is 29.
2. According to Statement I, each number increases by 3 from the previous number. The formula for the nth term of an arithmetic sequence is: a_n = a + (n - 1)d, where a is the first term, and d is the common difference.
3. With a₁₀ = 29 and n = 10, we substitute into the formula: 29 = a + (10 - 1)×3. Simplifying gives: 29 = a + 27, leading to a = 2.
4. Now, calculate the 57th term:
   a₅₇ = 2 + (57 - 1)×3 = 2 + 56×3 = 2 + 168 = 170.

Thus, both statements together provide the necessary data to calculate the 57th number in the series, which is 170.