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 is the total number of apples that James and John have? I. If John gives 7 apples to James, James will have twice the number of apples that John has. II. If James gives an apple to John, they will have equal number of apples.

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 is the total number of apples that James and John have?

I. If John gives 7 apples to James, James will have twice the number of apples that John has.

II. If James gives an apple to John, they will have equal number of apples.

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 The data in statement I alone or in statement II alone is sufficient to answer the question.

D The data in both the statements I and II is not sufficient to answer the question.

E The data in both the statements I and II together is necessary to answer the question.

Solution

Correct Answer: Option E

From statement I:

Let number of apples with James be M and with John be N.

If John gives 7 apples to James, James will have twice the number of apples that John has.

⇒ M + 7 = 2(N – 7)

There are two variables and one equation, and hence unique values of M and N cannot be found.

∴ Statement I alone is not sufficient to answer the question.

From statement II:

Let number of apples with James be M and with John be N.

If James gives an apple to John, they will have equal number of apples.

⇒ M - 1 = N + 1

There are two variables and one equation, and hence unique values of M and N cannot be found.

∴ Statement II alone is not sufficient to answer the question.

From statements I and II together:

Let number of apples with James be M and with John be N.

If John gives 7 apples to James, James will have twice the number of apples that John has.

⇒ M + 7 = 2(N – 7)

If James gives an apple to John, they will have equal number of apples.

⇒ M - 1 = N + 1

There are two variables and two equations, which can be solved to find M and N, and subsequently M + N.

Solving, we get M = 25, N = 23.

∴ Using both the statements together, we can answer the given question.

Solution

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