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GMAT Tip: You Don’t Need to Solve for S

Memorizing endless numbers of formulas is never the path to high-scoring success on the GMAT. Nevertheless, formulas can give you a leg up – provided you understand how to use them appropriately.

As with any quantitative question, the key is to be flexible, incorporating a variety of approaches to efficiently get to the correct answer choice. Problems that are primarily geometry-based are where utilizing formulas you have memorized can be the most helpful. Equilateral triangles are very commonly tested questions and knowing the formula for the area of an equilateral triangle:

s^2(sqrt 3) / 4

Can save you valuable seconds rather than taking the steps to derive the area of said equilateral triangle using common ratios and/or the pythagorean theorem.

But GMAT questions are never as easy and straight-forward as plugging in an equation. Consider this question for example:

If an equilateral triangle has an area of (sqrt 243), then what is the perimeter of that triangle?

1. 6
2. 12
3. 18 
4. 27 
5. 81

As with any quantitative problem, the first step is assessing and evaluating what your end game should be in selecting an answer choice. Here, we have been asked to solve for the perimeter of the triangle – which implies that the answer choice is each side multiplied by 3.

Many test takers, then, look at the formula and try to solve for s:

s^2(sqrt 3) / 4 = (sqrt 243)

But what steps next do we take? If we multiply both sides by 4, we are still left with square roots on both sides. Can we square both sides to get rid of the square root? Then, does s^2 become s^4?

Even test takers who are very comfortable working backwards and forwards from complex formulas have a high chance of making a mistake solving for s in the short period of time we have for this question.

Instead, recognizing we can work backwards from the answer choices is a much more efficient, and likely more accurate, way of getting to the correct answer.

Provided we’ve recognized the answer choices are perimeter and divided by 3, we should recognize the numbers we need to work backwards from are:

1. 2
2. 4
3. 6
4. 9
5. 27

From here, we can plug these values into the equation s^2(sqrt 3) / 4. To cut down on the amount of calculation we do, as effective test takers always try to do with quantitative questions,  we can also estimate some aspects of the equation.

Ask yourself: what is the sqrt 243 close to? If we know our squares (as we should!) then we know it is between 15^2 and 16^2 – 225 and 256.

We can also estimate the second square root – the (sqrt 3) is just a bit less than 2 (aka (sqrt 4)).

Quickly, we can work backwards and know with little effort that A) 2 is much too small and D) 9 and E) 27 are too large. B) 4 might be worth doing a few more calculations for, but C) 6 is clearly the contender answer.

(6)^2 ( 2) / 4 = 18, which is reasonably close to a number between 15 and 16.

There are a few risks we do take in this question, but if we try working it out two different ways – derived or by fudging numbers and getting “close” answers – we cut down on our calculation time significantly, and can apply that leftover time to a later more challenging problem.

When tackling your next geometry question, consider if using this mixed approach will help you get to the right answer more quickly!


The above GMAT Tip comes from Veritas Prep. Since its founding in 2002, Veritas Prep has helped more than 100,000 students prepare for the GMAT and offers the most highly rated GMAT Prep course in the industry.

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Posted in: Feature Small, GMAT, GMAT - Quantitative, GMAT Tips

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