MAT Analogies: Logical/Mathematical

MAT logical/mathematical analogies are the last category to cover on the Miller Analogies Test. This category contains math, non-semantic wordplay (think palindromes), and a variety of analogies that have a “riddle” or a “brainteaser” feel to them.

Studying for logical/mathematical analogies

The majority of students who take the MAT tend to be verbally focused. Many of you are well-versed in both math and verbal. However, some of you may be the type of verbally gifted student who has avoided math like the plague.

While you don’t need to master high-level math to excel here, the following basic concepts are pivotal to success:

  • Fractions and Percents – You must know how to convert one to the other and vice versa.
  • Composites and Primes – Know the differences.
  • Primes – Much more important than the composite numbers, you should get familiar with prime numbers. If possible, memorize the order of primes from 1-100. Primes are a favorite test of pattern recognition on the MAT.
  • Squaring and Cubing – You should know how to do these operations. You won’t have to calculate big numbers, but you need to be able to see, for example, 10^3 and 1000 are equivalent.
  • Negative and Fractional Exponents – The MAT simply wants to see if you can spot the equivalence between two expressions: do you know that 10^-2 = 1/10^2 = 1/100? If you learn how to express a number with a negative or fractional exponent, that will be enough.
  • Positive and Negative radicals (Roots) – Again, no big calculations, just equivalencies. I put emphasis on the “radical” sign because the MAT loves to use radicals.
  • Geometric Shapes – The MAT likes to relate polygons through their number of sides. To answer such questions, you need to learn the common polygons: triangles, rectangles, pentagons, etc. You don’t necessarily need to learn the names of 12+ sided figures, but instant recall of the features of something like an octagon is necessary.
  • Geometric Formulas – You need to know how to calculate area and perimeter for triangles, rectangles, circles, and spheres.

If any of this is unfamiliar to you, it’s very easy to brush up on these concepts through Khan Academy. There may be other math concepts that appear, but the above will cover nearly any question thrown at you. On to examples–

MAT logical/mathematical subtypes

These items will contain any of the following: logical or mathematical equations, numerical fractions, multiples, negation, or letter and sound patterns.

1. One term is a fraction or multiple of another.

12 : 144          144 is the square of 12.

4/20 : 1/5      4/20 can be simplified to 1/5.

2. The terms are related through some non-semantic similarity or change: rhyming, homophones, letter reversal, or other wordplay.

Live : Evil             “Live” in reverse spells “evil.”

Listen : Silent      “Silent” is an anagram for “listen.”


  1. 125 : 64 :: 5 : (a. 1/2 b. 4 c. 1 d. 3)
  2. 3 : 5 :: (a. 13 b. 17 c. 11 d. 4) : 13
  3. (a. stuff b. though c. thought d. sow)  : Tough :: Brow : Bow

If you have not been to the MAT official Guide or looked through the other MAT analogy blogs, I suggest checking them out for more insight into the different types of analogies.


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