Source: Official Guide for the GMAT 13th Ed. Data Sufficiency; #132 Official Guide for the GMAT 2015 14th Ed. Data Sufficiency; #132

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# Joanna bought only \$0.15 stamps and \$0.29

Joanna bought only \$0.15 stamps and \$0.29 stamps. How many \$0.15 stamps did she buy?

### 2 Explanations

1

Varun S Nair

I have a query.

Mostly, when I see a single equation in 2 variables, on some questions, it is directly assumed that we cannot solve for an equation with 2 variables; and that statement is directly considered insufficient.

However here, I see that we are plugging in and somehow calculating the value of the variables (in this case, the number of 15 cent & 29 cent stamps); and that statement turns out to be sufficient.

I understood the approach; but could you please explain why this differentiation in approach for the same class of question exists (a single linear equation in 2 variables)?

When do I know that I need to substitute/plugin values & hunt for the answer, & when can I directly jump the statement since it is algebraically impossible to find the values of two different variables from a single equation?

Sep 16, 2019 • Comment

Sam Kinsman

Great question!

Here, we have the equation (0.15x + 0.29y = 4.40), which simplifies to: 15x + 29y = 440

Notice that x and y MUST be whole numbers; you cannot have half a stamp.

In these kinds of situations (when the variables must be whole numbers), you can sometimes solve an equation (even though it is 1 equation and 2 unknowns). So when the variables must be whole numbers, try plugging in numbers, and you may find that there's only one set of values for which the equation will work. If that happens, then you've solved it!

If you have 1 equation and 2 unkonwns, and the variables DON'T have to be whole numbers, you cannot solve the equation.

Here's an example. Let's say x represents men and y represents women, and we know that 2x + 5y = 14. In this case, since you cannot have half a man or half a woman, x and y must be whole numbers. The only values that will work x = 2 and y = 2. So this one can be solved, even though we have 1 equation and 2 unknowns.