GRE Quantitative: Arithmetic – Ratio

One of the topics in which GRE test designers love to frame questions on is ratios. Hence, ratios can pop up in any of the GRE Quantitative Reasoning section questions . Therefore having your concepts entirely clear can help you solve many complex problems with utmost ease during the exam.

Let us first understand what ratios are:

When a comparison between two or more similar objects is being made, then ratio is used. In other words, the ratio of one quantity concerning another is a method of expressing their relative scopes; usually, it is represented in the form of fractions, where the first quantity is the numerator while the second quantity is the denominator. For example, if p and q are two similar positive quantities, then their ratio can be represented as p/q. The notation used for representing the ratio is:

  • p : q
  • The ratio of p to q
  • p to q
  • p is to q

For example, If there are 7 men and 5 women in a meeting room, then their ratio can be expressed as 7:5.

Just like fractions, the ratio can also be reduced and expressed in their lowest terms. For example, if there are 8 peaches and 20 pears in a basket, then their ratio can be expressed as 8:20 which is equivalent to 2:5, alternatively for every 2 peaches there are 5 pears in the basket.

For three or more positive values, their ratios can be expressed as “p to r to s” or “p: r: s.” For example, if there are 4 peaches, 5 pears and 7 mangoes in a basket, then their ratio can be expressed as 4:5:7.

So, what is a proportion?

Proportion is the equation generated and is used for relating two ratios. Hence, to solve a problem that involves ratio, you can simply write it as proportion and then solve it using cross multiplication.

Let’s solve some problems and see what type of questions GRE devises with the motive of tricking you.

Question: The sum of p, q and r is 500, p is \(\frac{1}{4}q\) and q is \(\frac{1}{5}r\), then what is the value of p?

Solution: Since, p = \(\frac{1}{4}q\) and q = \(\frac{1}{5}r\), Therefore, \(\frac{1}{4}\left ( \frac{1}{5}r \right )\)

= \(p = \frac{1}{20}r\)

Now, put everything in terms of r. So according to question, the equation becomes

\(\frac{1}{20}r + \frac{1}{5}r + r = 500\)
\(\left ( \frac{1 + 4 + 20}{20} \right )r = 500\)
\(r = \frac{500 \times 20}{25}\)
\(r = 400\)
\(Therefore, \; p = \frac{1}{20}r = \frac{400}{20} = 20\)

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