GMAT® Official Guide 2019 Quantitative Review
In the following example, the increase is greater than 100 percent: If the cost of a certain house in 1983
was 300 percent of its cost in 1970, by what percent did the cost increase?If n is the cost in 1970, then the percent increase is equal to^3 n - n =^2 n = 2, or 200%.
n n- Powers and Roots of Numbers
When a number k is to be used n times as a factor in a product, it can be expressed as kn, which means
the nth power ofk. For example, 22 = 2x 2 = 4 and 23 = 2x 2x 2 = 8 are powers of 2.
Squaring a number that is greater than 1, or raising it to a higher power, results in a larger number;
squaring a number between O and 1 results in a smaller number. For example:1
(½J 9
(0.1)2
= 0.01(9 > 3)(½<½)
(0. 01 < 0.1)A square root of a number n is a number that, when squared, is equal to n. The square root of a negative
number is not a real number. Every positive number n has two square roots, one positive and the other
negative, but ✓n denotes the positive number whose square is n. For example, J9 denotes 3. The two
square roots of 9 are .J9 = 3 and -.J9 = -3.Every real number r has exactly one real cube root, which is the number s such that s3 = r. The real cube
root of r is denoted by 'ef;. Since 23 = 8, ~ = 2. Similarly, :ef=~ = -2, because (-2)^3 = -8.- Descriptive Statistics
A list of numbers, or numerical data, can be described by various statistical measures. One of the most
common of these measures is the average, or (arithmetic) mean, which locates a type of "center" for the
data. The average of n numbers is defined as the sum of the n numbers divided by n. For example, the
average of 6, 4, 7, 10, and 4. 1s 6 + 4 +7+10+4^31
5= S = 6.2.
The median is another type of center for a list of numbers. To calculate the median of n numbers, first
order the numbers from least to greatest; if n is odd, the median is defined as the middle number,
whereas if n is even, the median is defined as the average of the two middle numbers. In the example
above, the numbers, in order, are 4, 4, 6, 7, 10, and the median is 6, the middle number.For the numbers 4, 6, 6, 8, 9, 12, the median is^6 +^8 = 7. Note that the mean of these numbers is 7.5.
2
The median of a set of data can be less than, equal to, or greater than the mean. Note that for a large set
of data (for example, the salaries of 800 company employees), it is often true that about half of the data
is less than the median and about half of the data is greater than the median; but this is not always the
case, as the following data show.3,5,7, 7, 7, 7, 7, 7,8,9,9,9,9,10,10
Here the median is 7, but only
1~ of the data is less than the median.