Each panel below shows a GMAT math sample problem with a breakdown of the slow/hard way and the fast/easy way to solve it:

### Sample Problem #1: Problem Solving

Albert will receive **$14,600** over the period of one year in equal monthly payments.

How much will he have received after three months?

### The Hard/Slow Way

**$14,600 / 12 = $1220**

Then multiply by three to find the three-month total:

**$1220 x 3 = $3660**

### The Easy/Fast Way

**$14,600 / 4 = $3660**

The arithmetic involved in this **fast/easy** solution is one short division (dividing by 3).

### SAMPLE PROBLEM #2: PROBLEM SOLVING

Which of the following values of *p* results in an integer value for the expression **(77 +p) / p**:

A) 4

B) 5

C) 6

D) 7

E) 8

### The Hard/Slow Way

A) **(77+4)/4 = 81/4**…..Not an integer

B) **(77+5)/5 = 82/5**…..Not an integer

C) **(77+6)/6 = 83/6**…..Not an integer

D) **(77+7)/7 = 84/7**…..Bingo

E) **(77+8)/8 = 85/8**…..Not an integer

### The Easy/Fast Way

**(77+p)/p = 77/p + p/p = 77/p + 1.**

The **+1** doesn’t affect the integer status of the result. So the question becomes: which of the following values of **p** makes **77 / p** an integer?

Expressed differently, which value of **p** goes into 77? The answer is immediately seen to be 7 because 77 is 7 times 11.

### SAMPLE PROBLEM #3: DATA SUFFICIENCY

Given the equation **30 + x = y – 42**, which statement below would be sufficient to determine the value of **y**?

A) **x = 3**

B) **y/x = 25**

C) A and B are each sufficient on their own

D) A and B are sufficient only when combined

D) None of the above

### The Hard/Slow Way

A) Plugging in **x=3** transforms the equation into **30+3 = y – 42** or **y=42+30+3 =75**. Conclusion: the information is sufficient.

B) Given **y/x=25**, we have **y=25x**. Substituting this, the original equation becomes **30+x = 25x – 42** or**24x=72**. This gives **x=3**, and so the equation can be solved for **y** in Statement B.

Conclusion: C.

### The Easy/Fast Way

**y**? My student’s approach is explained in detail below.

A) The equation given in the root is a linear equation in **x** and **y**. When a value of **x** is given, the equation becomes a linear equation one unknown, which has a solution; so the information is sufficient.

B) The equation given in the root is a linear equation in **x** and **y**, and the equation **y/x=25**, or **y=25x**, is another linear equation in two unknowns. Two independent linear equations in two unknowns determine a unique solution. So the information is sufficient.