GRE Quant – Learn Tips & Tricks to Crack ‘Mixed proportion or Chain Variation’ problems

‘Mixed Variation’ describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and varies inversely with others (when the rest of the variables are kept constant).

They appear in most competitive exams and also have a wide real time application. To successfully crack every ‘Mixed Variation’ problem that you face in any competitive exam and solve them in real-life situations, you might have to understand the basics, build a strong foundation and practice as much as possible.

The basic questions one might have to address before trying to solve a ‘Mixed Variation’ problem are,

  1. How do we identify if the variables are directly proportional to each other or inversely proportional to each other ?
  2. What if we have both proportionality in the same problem?
  3. How do we tackle such problems easily?

Understanding the following concepts will set the ground for you and help you solve ‘Mixed Variation’ problems quickly.

Direct Proportion:

Two quantities are said to be directly proportional if the increase in one leads to a corresponding increase in the other. Quantitatively, we write the relation as x = ky, for a non-zero real number ‘k’.


  1. If the cost of 1 apple is Rs 15 then the cost of 2 apples will be Rs 30.
  2. When speed is a constant, distance and time are directly proportional.
  3. Work done is directly proportional to the force applied.

Indirect Proportion:

If two quantities are inversely proportional or indirectly proportional, then the increase in one leads to a decrease in the other.


1) The number of men involved in a work and time taken to complete the work.

2) Speed of a vehicle and Time taken to cover a distance

3) The lesser the area, the higher the pressure applied. eg.: Knife, Needle

Recently, we conducted a webinar to help GRE test-takers to learn the tips and tricks to solve ‘Mixed Variation’ type problems. Our Quant Expert at Galvanize Test Prep, Sowmya Subramaniam, walked the attendees through the concepts involved in Mixed Variation problems, taught the steps in detail, and solved several problems. Watch the recording of the session below.

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