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Que: How many more boys than girls are in the class?

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Que: How many more boys than girls are in the class?

by Max@Math Revolution » Tue Dec 08, 2020 9:05 am

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Que: How many more boys than girls are in the class?

(1) There are a total of 10 boys and girls in the class.
(2) The number of boys in the class equals the cube of the number of girls in the class.
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Source: — Data Sufficiency |
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Re: Que: How many more boys than girls are in the class?

by Max@Math Revolution » Fri Dec 11, 2020 1:21 am

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Solution: To save time and improve accuracy on DS questions in GMAT, learn, and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

Let us assign variables: Boys (b) and Girls (g)

We have to find the value of b – g.

Follow the second and the third step: From the original condition, we have 2 variables (b and g). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

Recall 3- Principles and Choose C as the most likely answer. Let’s look at both conditions together.

Condition (1) tells us that there are a total of 10 boys and girls in the class => b + g = 10

Condition (2) tells us that the number of boys in the class equals the cube of the number of girls in the class => b = \(g^3\)

=> b + g = 10

=> \(g^3\) + g = 10

=> g(\(g^2\) + 1) = 10

=> If g = 1: g(\(g^2\) + 1) = 1(\(1^2\) + 1) = 2 ≠10

=> If g = 2: g(\(g^2\) + 1) = 2(\(2^2\) + 1) = 10 = 10

Therefore g = 2 and b = \(g^3\) => b = \(2^3\) => b = 8

=> b – g = 8 – 2 = 6

The answer is unique and both conditions combined together are sufficient according to Common Mistake Type 2 which states that the answer should be a unique value.

Both conditions combined together are sufficient.

Therefore, C is the correct answer.

Answer: C
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