GMAT & MBA Admissions Blog

Improving Your GMAT Quant Score: Mental Math [Part 2]

Posted by Mark Skoskiewicz on Tue, Jun 25, 2013 @ 01:03 PM

gmat mental math

In a previous post on improving your GMAT Quant score, we discussed how certain GMAT Quant concepts are difficult because you may not have been exposed to them for many years – or you may never have learned them at all.  If the latter case, it’s critical to invest the time and potentially money to learn these concepts via online videos, book, classes, or GMAT tutoring.  Simply trying to do practice problems and then reading the answers as a learning strategy can be frustrating.

In this post, we’ll cover the second proven way to increase your GMAT quant score – build your mental math skills.  We’ll address the importance of mental math on the GMAT and provide some easy-to-implement ideas and tips for improving your mental math skills. 

The Importance of Mental Math on the GMAT

We don’t need to spend a lot of time explaining why mental math is important on the GMAT.  It’s a timed test, and most of us do end up pressed for time at the end.  You also don’t have a calculator. 

If you need to know 40% of 70, it won’t take that long to write out 70 x 0.40 on a piece of paper, multiply 7 x 4 to get 28, carry the two, get 280, move the decimal, and feel confident that the answer is 28.0.  However, it will take less time to say “10% of 70 is 7, and 7 times 4 = 28.  40% of 70 is 28.  I was not good at this type of thing, but it pays to practice to get good at it, because those dozens of seconds of extra time you lose when you don’t use mental math turn into tens of dozens of seconds, and ultimately you have 5 fewer minutes at the end of the test, causing you to quickly guess on the last few problems.

You want to avoid guessing on the GMAT.  However, I’d also argue that

Ideas for Improving Your Mental Math Skills

When it comes to improving your mental math skills, here are some ideas: -

  • Prime factor every number you see
  • Calculate your tip by hand
  • Check out mathfactcafe.com, and
  • Memorize all the facts below:

Prime factoring

In number theory, the prime factors of a positive integer are the prime numbers that divide that integer exactly. The process of finding these numbers is called integer factorization, or prime factorization

Squares

Memorize squares from 2 through 25 (i.e., 2^2 = 4, 25^2 = 625)

Cubes

Memorize cubes from 2 through 11

Prime Powers:

Definition: A prime number is a positive integer greater than 1 which is only divisible by itself and 1. For example, 2, 3, 5, 7, and 11 are prime numbers.

Fact: There are an infinite number of prime numbers

Definition: Two integers are relatively prime if they have no common factors greater than one. For example 2 and 7 are relatively prime while 8 and 12 are not (they have common factors 2 and 4).

Fact: A prime number is relatively prime to any integer except itself. 

Fact: The least common multiple of two relatively prime integers is their product. The greatest common divisor (greatest common factor) of two relatively prime integers is 1.

Three Irrationals: 

In general the GMAT sticks with rational numbers (Fractions, Decimals, Percents, and Integers – the kind of numbers we’ve been seeing since grade school). Occasionally, the problem writers go rogue and introduce an irrational number, so it’s good to know a few useful approximations:  

Divisibility Rules:

  • (2) A number is divisible by 2 if it ends in 0, 2, 4, 6, or 8. That is, it ends in a number divisible by 2
  • (4) A number is divisible by 4 if the last two digits form a number that is divisible by 4. A number is divisible by 4 if it is divisible by 2 twice
  • (8) A number is divisible by 8 if the last three digits form a number that is divisible by 8. A number is divisible by 8 if it is divisible by 2 three times.
  • (3) A number is divisible by 3 if the sum of its digits is divisible by 3. For example 729 is divisible by 3 because 7 + 2 + 9 = 18 which is divisible by 3. I you have any doubt you can repeat the process – 1 + 8 = 9 which is divisible by 3
  • …and more

Summary

Improving your mental math will improve your GMAT Quant score.  If you’ve having trouble on GMAT quant, contact us for more ideas on how to prep.

 

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