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Re: If 72 cupcakes must be divided equally among the students in a certain
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21 Jan 2020, 22:31
This is a question based on the concept of factors, but also tests your ability to develop an equation. The question says that we are to divide 72 cupcakes equally among students; this means that we are to look for factors of 72, because, only when you divide a number by its factor will you be able to divide it uniformly (or equally). The number of students in the class should represent the factors of 72.
Let the number of students in the class be 3x (since the first statement mentions reducing students by \(\frac{1}{3}\)rd ). If the number of students in the class be 3x, the number of cupcakes received by each student will be \(\frac{72 }{ 3x}\) = \(\frac{24 }{ x}\).
From statement I alone, if the number of students is reduced by one-third, each student will receive 3 more cupcakes.
If the number of students are reduced by one-third, the class would now have 2x students; therefore, the number of cupcakes received by each student will be \(\frac{72 }{ 2x}\) = \(\frac{36 }{ x}\).
Given that \(\frac{36}{x}\) = \(\frac{24}{x}\) + 3. The value of x can be determined from the equation above and hence the number of students in the class. Statement I alone is sufficient.
Answer options B, C and E can be eliminated. The possible answers at this stage are A or D.
From statement II alone, if the number of cupcakes is doubles, each student would receive 12 cupcakes.
This means that if the total number of cupcakes is made 144, each student would receive 12 cupcakes. But, when the number of cupcakes is 144, cupcakes received by each student = \(\frac{144}{3x}\).
Equating \(\frac{144}{3x}\) to 12, we can find out 3x which represents the number of students. Statement II alone is also sufficient.
Answer option A can be eliminated. The correct answer option is D.
Assuming the right kind of variables will decide how much time you can save in solving questions on equations. Clearly, I would have taken more time in this question had I taken the number of students to be x. Instead, I took it as 3x because I had read the entire question once before starting to solve. This is a good habit to develop because it can help you develop the right kind of variables.
Hope that helps!