[2 (42– 9) + 3] – 1[2 (16 – 9) + 3] – 1 BEGIN WITH THE INNERMOST GR...

3. [2 (4

²

– 9) + 3] – 1[2 (16 – 9) + 3] – 1 Begin with the innermost grouping symbols and follow PEMDAS. (Here,exponents are first within the parentheses.)[2 (7) + 3] – 1 Continue with the order of operations, working from the inside out (sub-tract within the parentheses).[14 + 3] – 1 Multiply.[17] – 1 Add.16 Subtract to complete the problem.

S p e c i a l Ty p e s o f D e f i n e d O p e r a t i o n s

Some unfamiliar operations may appear on the GMAT exam. These questions may involve operations thatuse symbols like #, $, &, or @. Usually, these problems are solved by simple substitution and will only involveoperations that you already know.

Example

For a# bdefined as a

²

– 2b, what is the value of 3 # 2?a. –2b. 1c. 2d. 5e. 6

3 2 4

–

A R I T H M E T I C

–

For this question, use the definition of the operation as the formula and substitute the values 3 and 2for aand b, respectively.a

²

– 2b= 3

²

– 2(2) = 9 – 4 = 5. The correct answer is d.

F a c t o r s , M u l t i p l e s , a n d D i v i s i b i l i t y

In the following section, the principles of factors, multipliers, and divisibility are covered.FactorsA whole number is a factor of a number if it divides into the number without a remainder. For example, 5 is3056a factor of 30 because without a remainder left over.On the GMAT exam, a factor question could look like this:Ifxis a factor ofy, which of the following may not represent a whole number?a. xy

x

b.

y

c.

yx

d.

xy

e.This is a good example of where substituting may make a problem simpler. Suppose x= 2 and y= 10 (2 is afactor of 10). Then choice ais 20, and choice cis 5. Choice dreduces to just yand choice ereduces to just x,

2

so they will also be whole numbers. Choice bwould be

1