## Plugging in I

Problem Solving Strategies - I

Most of GMAT Problem Solving would include variables. Questions involving variables are always tricky and most of the students face problems while tackling questions with variables. Here is an example:

Daniel starts reading a book from page ‘x’ and stops at page ‘y’. How many pages has he read?

(A)x + y

(B)x – y

(C)x + y + 1

(D)y - x + 1

(E)y – x

Notice in the question above the answer choices are expressed in terms of variables. This makes the question harder to imagine. What will help you to understand the question is converting the variables into numbers. We can use the Numbers approach here. This technique will be the primary focus of the chapter.

Since the answer options are variables we do not need to involve variables in our solution. We can simply say that Daniel starts at page number 2 (x = 2) and ends at page number 5 (y = 5) then he has read page 2, 3, 4, and 5 i.e. 4 pages. Now if we switch back to variables then Daniel starts from page number x and ends at page number y hence he would have read y – x + 1 i.e. 5 – 2 + 1.

The Number Approach: In action

Amelia travels from her home to office at the rate of ‘x’ miles per hour. She comes back to home via the same route in office cab. If distance between Amelia’s office and home is y miles and the entire trip took z hours, what is the speed of the office cab in terms of x, y and z?

(A) (zx – y) (B) (zy – x) (C) (yx)/(zx – y)

(D) (xyz)/(yz – x) (E) (zy – x)/(y)

Process:

The first step is the opportunity to use the technique. When the answer options are variables then you can go ahead and user numbers in the question. Now we have to pick numbers for all the variables.

Second step will be to plug in numbers in terms of variables. Let us say Amelia travels at the rate of x = 2 miles per hour and the distance between office and home is y = 10 miles. There might be variables which are not assigned a symbol for example the speed of the office cab. Those variables should also be assigned a number. It is important to keep the values assigned to the variables at one place as you will be referring back to it again and again.

 Variable Numbers Description x 2 Amelia’s rate of traveling to office y 6 Distance between office and home Unassigned 3 Speed of the office cab

Third step will be working the problem in terms of variables. It took 3 hours to reach office. Let us say that speed of the cab is 3 miles per hour hence z = 3 + 2 = 5 hours.

Now identify the target in the question. Target is defined as what is asked in the question as in this particular question is the speed of the office cab. Hence by plugging in x = 2, y = 6 and z = 5 the answer should be 3. Make sure you circle the target.

 By Plugging in x = 2, y = 6 and z = 5
 Target is 3

The last step will be to eliminate the answer options which do not match the target answer. The scratch paper set up should look like the following.

 (zx – y) 10 – 6 = 4 ELIMINATED (zy – x) 30 – 2 = 28 ELIMINATED (yx)/(zx – y) 12/4 = 3 YES (xyz)/(yz – x) (60)/(30 – 2) ELIMINATED (zy – x)/(y) (28)/(6) ELIMINATED

Picking up Good Numbers:

Here are some features of the numbers that you should be picking:

1. The numbers should be SMALL and calculation on those numbers should be easy.

2. Do not use 0 and 1 as they tend to mess up arithmetic calculations. For example if the answer options are a, 2a, 3a, 4a, 5a and you pick up a = 0 then all the answer options will give you the same answer.

3. Pick up different numbers for different variables. For example there are two variables in the question. If you pick up the same value for a and b then a/b and b/a would yield the same value.

4. Avoid picking numbers already in the question. Spice things up by picking up numbers which are not mentioned in the question. For example do not take value of minutes to be 60. Take it 120 or 30, if you go the obvious way then there is a chance that more than once answer option gives you the same answer.

Discussion