GMAT Maths | GMAT Simultaneous Equations

This GMAT sample question in quant is an Algebra word problem in Linear Equations. The crux of solving this algebra practice question involves framing a pair of linear equations in two variables and solving those simultaneous equations. A typical example of a GMAT problem solving word problem question. A 600 to 650 level GMAT maths question. Medium difficulty question.

Question 4: The basic one-way air fare for a child aged between 3 and 10 years costs half the regular fare for an adult plus a reservation charge that is the same on the child's ticket as on the adult's ticket. One reserved ticket for an adult costs $216 and the cost of a reserved ticket for an adult and a child (aged between 3 and 10) costs $327. What is the basic fare for the journey for an adult?

1. $111
2. $52.5
3. $210
4. $58.5
5. $6

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Video Explanation

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Explanatory Answer

Step 1 of solving this GMAT Linear Equation Question: Assign variables and frame equations

Let the basic fare for the child be $X.

Information 1: Basic one-way air fare of a child costs half the regular fare for an adult.
Therefore, the basic fare for an adult = 2(basic one-way airfare for a child) = $2X.

Information 2: Reservation charge is the same on the child's ticket as on the adult's ticket.
Let the reservation charge per ticket be $Y
A child's ticket will cost (Basic fare + Reservation charges) = X + Y
Hence, an adult ticket will cost (Basic fare + Reservation charges) = 2X + Y.
Information 3: One reserved ticket for an adult costs $216. So, 2X + Y = $216 .... (1)
Information 4: The cost of a reserved ticket for an adult and a child (aged between 3 and 10) is $327.
So, the ticket for an adult and a child will cost (2X + Y) + (X + Y) = 3X + 2Y = $327 .... (2)

Step 2 of solving this GMAT Algebra Question: Solve the simultaneous equations and determine basic fare for an adult.

Multiply equation (1) by 2: 4X + 2Y = 432 .... (3)
Subtract equation (2) from equation (3):
4X + 2Y = 432
- (3X + 2Y = 327)
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X = $105
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The question is "What is the basic fare for an adult?"
The basic fare of an adult ticket = 2X = 2*105 = $210

Choice C is the correct answer.

As a good practice, after solving equations and finding values for the unknown, check whether further action has to be taken to get the answer. In this example, value of X is not the answer. We have to find the basic fare for an adult = 2X.