Given below is a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
What will be the sum of a series of positive consecutive integers?
I. Last number of this series is 101 times the first number.
II. There are not more than 200 terms in the series.
Solution
Correct Answer: Option E
From statement I:
The series is of positive consecutive integers. Knowing ratio of last number and first number, we cannot determine the series uniquely. It can be numbers from 1 to 101, or from 2 to 202, or from 3 to 303, and so on. Hence, sum of series cannot be uniquely found.
∴ Statement I alone is not sufficient to answer the question.
From statement II:
There are not more than 200 terms in the series. Knowing this, we cannot determine the series uniquely. It can be numbers from 1 to 100, or from 1 to 101, or from 1 to 103, and many other options are possible. Hence, sum of series cannot be uniquely found.
∴ Statement II alone is not sufficient to answer the question.
From statements I and II together:
The series is of positive consecutive integers. Knowing that ratio of last number and first number, we can say that numbers in series would be from 1 to 101, or from 2 to 202, or from 3 to 303, and so on. Also, we know that there are not more than 200 terms in the series. So, only option possible is 1 to 101, as all other options will have more than 200 terms.
⇒ Series will be positive consecutive numbers from 1 to 101. Hence, sum of series can be uniquely found.
∴ Using both the statements together, we can answer the given question.
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