Question: A sum of money doubles itself in 7 years. In how many years it becomes four fold?

(A) 14 years
(B) 21 years
(C) 28 years
(D) 35 years
(E) 49 years

“A sum of money doubles itself in 7 years. In how many years it becomes four fold”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

The candidates must know basic qualitative skills to decipher GMAT Problem Solving questions. GMAT quant examines the logical and mathematical proficiency of the candidates. The problem-solving part of the GMAT Quantitative section comes up with a question and a series of answers. The candidate has to choose the correct option by resolving the question mathematically. The GMAT Quant topic in the problem-solving part consists of mathematical problems that are highly calculative and must be cracked with suitable mathematical facts.

Solution and Explanation:

Approach Solution 1:

The problem statement informs that

Given:

• A sum of money doubles itself in 7 years.

Find Out:

• The number of years it would become four-fold

Let’s assume the initial sum of money is x dollars.
Then, after seven years, the sum of money will two times the original sum that is the amount will be 2x dollars

After another seven years, the amount of money will be again 2 times the sum of money that is 4x dollars.
Thus, we can say, that it takes nearly 14 years to make the entire sum of money four-fold.

Hence option A is the correct answer.

Approach Solution 2:

The problem statement discloses that

Given:

• A sum of money gets twice every 7 years.

Find Out:

• The number of years it would become four times the original money

Let the value of money be ‘n’ and the time period be ‘t’
Therefore, we can say, n at t = 0

From this equation, we can further derive, 2n at t = 7 (as per the argument of the question)
By multiplying 2 with 2n, we get 4n, which is four times the sum of money.

The final equation states that 2∗2n=4n at t = 14
Therefore, the period of time in which the original would become four-fold is 14 years.

Hence option A is the correct answer.

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