Data Sufficiency

Que: If xy = 8, is x > y?

(1) y ≥ 4
(2) y ≤ 4

Solution: To save time and improve accuracy on DS questions in GMAT, learn and apply the Variable Approach.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Visit https://www.mathrevolution.com/gmat/lesson for details.

Now we will solve this DS question using the Variable Approach.

Let’s apply the 3 steps suggested previously.

Follow the first step of the Variable Approach by modifying and rechecking the original condition and the question.

Let’s apply the 3 steps suggested previously. [Watch lessons on our website to master these 3 steps]

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

We have to find ‘Is x > y’? - where 'xy = 8'

Second and the third step of Variable Approach: From the original condition, we have 2 variables (x, and y) and 1 Equation (xy = 8). To match the number of variables with the number of equations, we need 1 equation. Since conditions (1) and (2) will provide 1 equation each, D would most likely be the answer.

Recall 3- Principles and Choose D as the most likely answer. Let’s look at both conditions together.

Let’s take a look at each condition.

Condition (1) tells us that y ≥ 4.

If \(y=\frac{8}{x}\) into y ≥ 4, then we get \(\frac{8}{x}\ge4\).

Also y ≥ 4 > 0 and xy = 8 > 0, so we get x > 0 and if we multiply both sides of \(\frac{8}{x}\ge4\) by x, we get 8 ≥ 4x and divide by 4, we get 2 ≥ x.

And since y ≥ 4 > 2 ≥ x, we get y > x . Therefore, NO becomes an answer.

The answer is unique NO and condition (1) alone is sufficient according to Common Mistake Type 1 which states that the answer should be unique YES or a NO.

Condition (2) tells us that y ≤ 4.

=> If y = 2, then x * 2 = 8 => x = 4 => x > y - YES

=> If y = 3, then x * 3 = 8 => x = 2.xx => x > y - NO

The answer is not a unique YES or a NO therefore condition (2) alone is not sufficient according to Common Mistake Type 1 which states that the answer should be a unique YES or a NO.


Condition (1) alone is sufficient.

Therefore, A is the correct answer.

Answer: A