What To Memorize For the GMAT Quantitative Section

August 22, 2006

Yesterday I wrote that the GMAT doesn't really test rote memorization. That's true, but as I also mentioned yesterday, plenty of foundational knowledge (the sort of things you learn by rote memorization) is required to do well on the test. In other words, the GMAT takes for granted that you know certain basic things.

Some of those things (the equation for the circumference of a circle, perhaps) you already know, and others I'm sure you know you need to learn. Today I'd like to share with you a list I've put together of basic facts you simply need to know to succeed on the GMAT. This isn't exhaustive, but it focuses on items that will come up again and again.

Arithmetic / Properties of Numbers

Even/odd (e/o) identities:

1. e +/- e = e
2. e +/- o = o
3. o +/- e = o
4. o +/- o = e
5. e x e = e
6. e x o = e (also: o x e = e)
7. o x o = o

Decimal conversions:

1. ½ = .5
2. 1/3 = .33, 2/3 = .67
3. ¼ = .25, ¾ = .75
4. 1/5 = .2, 2/5 = .4, 3/5 = .6, 4/5 = .8
5. 1/9 = .11 (repeating), 2/9 = .22 (repeating), etc.
6. It's handy to know 6ths, 7ths, and 8^ths, but they require more memorization and don't come up as often.

Percent conversions:

1. 37% = 0.37 = 37/100
2. 0.2% = 0.002 = 0.2/100 = 2/1000

Exponents: (note: x^y = "x raised to the y power")

1. x^-y = 1/x^y
2. (x^y)(x^z) = x^(y+z)
3. (x^y)^z = x^(yz)
4. x^1/2 = radical (square root of) x.

Radicals (roots): (note: r2 = "radical 2" or "square root of 2")

1. r2 = approximately 1.4
2. r3 = approximately 1.7
3. Know the square of every integer up to 13.
4. r(xy) = r(x) times r(y)

Geometry

Area

1. Triangle: ½ times base times height
2. Rectangle: length times width
3. Circle: pi(r^2)

Circumference:

1. Circle: 2pi(r)
2. All other figures: the sum of the lengths of all sides

Right triangles:

1. a^2 + b^2 = c^2, where a and b are two sides of the triangle and c is the hypotenuse (Pythagorean theorem)2.Common integer solutions to the Pythagorean Theorem, including 3 : 4 : 5, 6 : 8 : 10 (and all other multiples of 3 : 4 : 5), and 5 : 12 : 13
2. The ratio of sides in a triangle with angles 30 : 60 : 90 is x : x(r3) : 2x
3. The ratio of sides in a triangle with angles 45 : 45 : 90 is x : x : x(r2)

Solids:

1. Volume: area of the base times height
2. Surface area: the sum of the areas of all faces of the solid

Coordinate Geometry:

1. Slope of a line = (change in y)/(change in x)
2. Equation of a line: y = mx + b, where m = slope and b = y-intercept (the point at which x = 0)

Miscellaneous

1. Rate = distance/time
2. Combined work: 1/a + 1/b = 1/t, where a and b are the amount of time it takes two entities working alone to complete a task and t is the amount of time it would take them to complete the task working together. (I'll go into this in more detail, including some shortcuts, in a future Tip.)
3. Average = sum of terms / number of terms
4. Probability = number of desired outcomes / number of possible outcomes

As you can see in the last few items of the list, the line between basic facts and foundational concepts is a blurry one: it's one thing to know the equation for probability, yet another to apply it on a difficult question. This is true to some extent for every single item in this list. If you haven't used it in a question, you don't really understand how the GMAT is going to expect you to apply it.

In other words, regardless of where you are in your GMAT study, learn all of these facts as soon as possible. If you don't, you'll be wasting your time on some practice problems, and cheating yourself of better-quality practice on others.

About the author: Jeff Sackmann is a GMAT tutor based in New York City. He has created many resources for GMAT preparation, including the popular Total GMAT Math and Total GMAT Verbal, as well as 1,800 practice GMAT math questions.

• Older: What Does the GMAT Test?
• Newer: Resource Review: Kaplan GMAT Books
• General GMAT Math: more articles
• All articles at GMAT HACKS