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Ratios and Proportions on the GMAT

proportions-ratiosWe all have studied Ratios and Proportions in school and now the same is going to be tested on the GMAT as well. In schools, we were quite comfortable with them, but not on the GMAT; because they come in various forms, they have a tendency to give test-takers trouble by making them waste time unnecessarily.

Before moving to the forms of questions we see on the GMAT, let’s recall what we learned in school.

What is a Ratio?

A Ratio is a method of comparing two quantities. It can be represented by words, fraction, or colon. For example: “The ratio of apple pies to cherry pies is 3 to 7” or “The ratio of apple pies to cherry pies is 3:”

What is a Proportion?

poport..A proportion is different from a ratio. While a ratio is represented by a single fraction, a proportion is represented by an equation. Example, 3/4 is a fraction, whereas 3/4=5/6 is a proportion.

Let’s look at a few questions involving ratios and proportions and how we tackle them on the GMAT.

1. In class A, girls and boys are in the ratio 3 to 4, and in class B, girls and boys are in the ratio 4 to 5. If both classes are combined, the ratio of girls to boys is 18 to 23. How many girls are there in class A?

A.    6
B.    8
C.    10
D.    14
E.    18

Solution: We are not going to solve this question in a conventional way i.e. by making equations rather we are going to solve it in a very interesting way.

If you look at the question carefully, first statement tells you that in class A the ratio of boys to girls is 3 to 4 which means that the number of girls in class A should be a multiple of 4 and in the answer choices there is only one option which is a multiple of 4 i.e. option (B). Therefore, the answer to the question is (B).

2. A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department? (GMAC OG)

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.

(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.

images..1Solution:

Statement 1: Statement 1 gives us only the ratio of x, y, and z. We cannot find out the number of staff members from this information. Therefore, this statement is insufficient.

Statement 2: Statement 2 gives us the total number of pens, the total number of pencils, and the total number of pads. We cannot find out the number of staff members from this information. Therefore, this statement is also insufficient.

Even after combining the statements the information is insufficient to find the number of staff members. Therefore, the answer is (E).

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