GMAT Math : Variable sufficiency

We have often been told the rule that we need x number of unique equations to solve for x variables. As an example we need three unique equations to solve for three variables r, p and t. While this rule is true, it cannot be followed blindly. The GMAT has been known to create a lot of tricky data sufficiency questions based on this rule.

Let’s start with an example :

What is the value of z if z = y + x + 3?

  1. y = 14x + 21
  2. -2x + y/7 – 3 = 0

We may immediately think that we need three equations to solve this 3 variable system (consisting of z, x and y) and would be inclined to choose option (C) – both statements put together are sufficient (along with the given equation z = y + x + 3).

However, a closer look shows that statement (1) and (2) are actually identical equations just rearranged to appear different (reader’s are encouraged to bring the equations to the same form!). So the correct option is in fact (E) – information is not sufficient

Let’s do another example –

What is the value of z if 2z = y – x?

  1. z = y – x + 31
  2. 3z – 2y = -2x + 12

We may be inclined to choose option (C) – both statements together are sufficient. The equations do look unique. However, a closer look shows that we actually do not need 3 equations.

Given, 2z = y – x (lets call this equation (0))

Statement (1) gives us z = y – x + 31 (lets call this equation (1))

Subtracting equation (1) from equation (0)

gets us z = -31 so statement (1) is independently sufficient.

Statement (2) gives us 3z – 2y = -2x + 12.

Rearranging the above equation we have 3z = 2y – 2x + 12 (lets call this equation (2))

Now, equation (0) multiplied by 2 on both sides give us

2z = 2y – 2x

Subtracting equation (0) x 2 from equation (2) gives us

z =  12. Again statement (2) by itself is sufficient.

GMAT Quant questions that rely on determining the number of variables needed can be tricky. It is important to keep an open mind and be flexible in manipulating the equations given. We have covered two types of pitfalls above and comprehensively cover other types (including power equations) in our Hackbook. Being exposed to such pitfalls will help you avoid them in the real test and get you to a high percentile score.