To begin, here are four reasonably challenging practice problems. 1) S is a set of n consecutive positive integers. Is the mean of the set a positive integer? Statement #1: the range of S is an even integer Statement #2: the median of S is a positive integer 2) If N = 255 is the […]

# Archive | Integer Properties

## GMAT Quant: Difficult Units Digits Questions

First, a couple 800+ practice questions (yes, you read that right – 800+) on which to whet your chops. 1) The units digit of is: (A) 1 (B) 3 (C) 5 (D) 7 (E) 9 2) The units digit of is: (A) 2 (B) 4 (C) 6 (D) 8 (E) 0 3) The units digit […]

## GMAT Number Properties

The single most-tested topic on the GMAT Quantitative Section is something called “Number Properties.” In a way, this statement, while absolutely true, is a bit deceptive. It’s like saying the biggest category at a particular zoo is mammals: even if that is completely true, that statement alone doesn’t give us a particular clear idea of […]

## GMAT Math: One is NOT a Prime Number

Fact: according to all mathematical definitions, the number 1 is not a prime number Primes One definition of a prime number is: any number that has only two positive integer factors —- itself and 1. The following are valid prime numbers. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 …. It is […]

## Number Sense for the GMAT

First, a practice problem. Remember, no calculator. I. II. III. 1) Rank those three in order from smallest to biggest. (A) I, II, III (B) I, III, II (C) II, I, III (D) II, III, I (E) III, I, II Number sense Many GMAT Quantitative Problems, like the foregoing one, test number sense. […]

## GMAT Math: The Many Meanings of Minus

First of all, for warm-up, a practice Data Sufficiency question. The symbol What does this symbol mean in math? Technically, this symbol, typographically a dash, has three different meanings in mathematics, viz.: a) a subtraction sign b) a negative sign c) an opposite sign The subtraction sign When the dash appears between two terms […]

## GMAT Math: Possibilities for Variables

How do we know what the possible values for a variable on the GMAT are? First of all, consider this DS problem 1) Is P > Q? Statement #1: P = 5*Q Statement #2: P = Q + R For folks who are not as comfortable with math, or are a bit rusty with math, […]

## GMAT Factorials

Learn how to simplify these seemingly devilishly complicated GMAT Quant problems! First, consider these problems 3) Consider these three quantities Rank these three quantities from least to greatest. (A) I, II, III (B) I, III, II (C) II, I, III (D) II, III, I (E) III, I, II These are challenging […]

## Function Notation on the GMAT

Consider these two practice GMAT Quantitative problems: 1) Given f(x) = 3x – 5, for what value of x does 2*[f(x)] – 1 = f(3x – 6) (A) 0 (B) 4 (C) 6 (D) 7 (E) 13 (A) –2 (B) 5/3 (C) 1 (D) 2 (E) 8 If you find these questions completely incomprehensible, then […]

## Simplifying Radical Expressions on the GMAT

Practice questions Let’s start out with a couple practice questions. 2) What is the length of the diagonal of a square with area 48? The geometry of those questions is not too difficult, but the trick is how to handle those radicals. If that befuddles you, this is just the post for you. Distributing […]