GMAT Quant | Linear Algebra Question 2

The gmat practice question given below is an Algebra word problem and tests your ability to frame a couple of linear equations in two variables and solve the system of equations to determine the answer to the age of the son 3 years from now. This GMAT sample question in quant is a 600 level problem solving question. A relatively easy question.

Question 2: Three years back, a father was 24 years older than his son. At present the father is 5 times as old as the son. How old will the son be three years from now?

1. 12 years
2. 6 years
3. 3 years
4. 9 years
5. 27 years

---

---

Video Explanation

---

---

Explanatory Answer

Step 1 of solving this GMAT Linear Equations Question: From words to mathematical equations

Let the age of the son 3 years back be 'x' years.
Information 1: Three years back, a father was 24 years older than his son.
Therefore, the age of the father 3 years back was (x + 24).

If the age of the son 3 years back was 'x' years, the present age of the son is x + 3.
Present age of father = x + 24 + 3

Information 2: The father is at present 5 times as old as the son.
i.e., (x + 24 + 3) = 5(x + 3)
Or x + 27 = 5x + 15
Or 4x = 12 or x = 3.

Step 2 of solving this GMAT Algebra Word Problem: From unknown to the answer

x was the age of the son 3 years back.
Therefore, the son was 3 years old 3 years back.

The question is "How old will the son be three years from now?"
If the son was 3 years old, 3 years back, the son is 6 years old now.
Hence, he will be 9 years old three years from now.

Choice D is the correct answer.

As a good practice when solving GMAT Math questions, after solving equations and finding values for the unknown, check whether further action has to be taken to get the answer. In this example, the value of x gave the age of the son 3 years back; the question was to find his age 3 years from now. (x + 6) was what was to be found.