GMAT Quant | GMAT Algebra Questions

The GMAT maths question given below is a problem solving question in Algebra and requires framing a couple of linear equations in two variables and solving the equations. This GMAT sample question is a 600 level algebra word problem. A relatively easy one.

Question 1: A poultry farm has only chickens and pigs. When the manager of the poultry counted the heads of the stock in the farm, the number totaled up to 200. However, when the number of legs was counted, the number totaled up to 540. How many more chickens were there in the farm? Note: In the farm, each pig had 4 legs and each chicken had 2 legs.

1. 70
2. 120
3. 60
4. 130
5. 80

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Video Explanation

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Explanatory Answer

Step 1 of solving this GMAT Linear Equations Question: Assign Variables and Frame Equations

Let the number of chickens in the farm be 'x'.
Let the number of pigs in the farm be 'y'.

Each pig or each chicken has one head.
Therefore, number of heads will be the same as the sum of the chickens and pigs in the farm.
The count of the heads in the farm is 200. So, the sum of the number of chickens and pigs is 200.
So, x + y = 200 .... (1)

Each chicken has 2 legs and each pig has 4 legs
'x' chickens will therefore, have 2x legs and 'y' pigs will have 4y legs.
The count of the legs in the farm is 540. So, the sum of the number of legs of chickens and the number of legs of pigs is 540.
Therefore, 2x + 4y = 540 .... (2)

Step 2 of solving this GMAT Linear Equations Question: Solve the system of linear equations

Multiply equation (1) by 2. We get 2x + 2y = 400 .... (3)
Subtract equation (3) from equation (2).
2x + 4y = 540
-(2x + 2y = 400)
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2y = 140
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Or y = 70.

Substitute 'y' as 70 in equation (1).
70 + y = 200. So, x = 130

'x' is the number of chickens in the farm. 'y' is the number of pigs in the farm. So, the farm has 130 chickens and 70 pigs.

Note:The question is "How many more chickens were there in the farm?"
The farm has 130 chickens and 70 pigs. So, the farm has (130 - 70) = 60 more chickens

Choice C is the correct answer to this linear equations word problem.

As a good practice in any GMAT question, after solving the system of equations and computing values for the unknown, check whether further action has to be taken to get the answer. In this example, neither the value of x nor the value of y was the answer to the question. (x - y) was what was to be found.