Quarter Wit, Quarter Wisdom Beware of Sneaky Answer Choices on the GMAT!

Test-takers often ask for tips and short cuts to cut down the amount of work necessary to solve a GMAT problem.  As such, the Testmaker might want to award the test-taker who pays attention to detail and puts in the required effort. Today, we will look at an example of this concept if it seems to be too easy, it is a trap! In the figure given above, the area of the equilateral triangle is 48. If the other three figures are squares, what is the perimeter, approximately, of the nine-sided shape they form? (A) 8√(2) (B) 24√(3) (C) 72√(2) (D) 144√(2) (E) 384 The first thing I notice about  this question is that we have an  equilateral triangle. So I am thinking, the area = s^2 * √(3)/4 and/or the altitude = s*√(3)/2. The irrational number in play is √(3). There is only one  answer choice with √(3) in it, so will this be the answer? Now, it actually makes me uncomfortable that   there is only one option with √(3). At first glance, it seems that the answer has been served to us on a silver plate. But the question format doesn’t seem very easy it links two geometrical figures together. So I doubt very much that the correct answer would be that obvious. The next step will  be to think a bit harder: The area of the triangle has √(3) in it, so the side would be a further square root of √(3). This means the actual irrational number would be the fourth root of 3, but we don’t have any answer choice that has the fourth root of 3 in it. Let’s go deeper now and actually solve the question. The area of the equilateral triangle = Side^2 * (√(3)/4) = 48 Side^2 = 48*4/√(3) Side^2 = 4*4*4*3/√(3) Side = 8*FourthRoot(3) Now note that the side of the equilateral triangle is the same length as the sides of the squares, too. Hence, all sides of the three squares will be of length 8*FourthRoot(3). All nine sides of the figure are the sides of squares. Hence: The perimeter of the nine sided figure = 9*8*FourthRoot(3) The perimeter of the nine sided figure =72*FourthRoot(3) Now look at the answer choices. We have an option that is  72√(2). The other answer choices  are either much smaller or much greater than that. Think about it   the fourth root of 3 = √(√(3)) = √(1.732), which is actually very similar to √(2). Number properties will help you figure this out. Squares of smaller numbers (that are still greater than 1) are only a bit larger than the numbers themselves. For example: (1.1)^2 = 1.21 (1.2)^2 = 1.44 (1.3)^2 = 1.69 (1.414)^2 = 2 Since 1.732 is close to 1.69, the √(1.732) will be close to the √(1.69), i.e. 1.3. Also, √(2) = 1.414. The two values are quite close, therefore, the perimeter is approximately 72√(2). This is the reason the question specifically requests the  Ã¢â‚¬Å"approximate† perimeter. We hope you see how the Testmaker could sneak in a tempting answer choice   beware the easiest option! Getting ready to take the GMAT? We have  free online GMAT seminars  running all the time. And, be sure to follow us on  Facebook,  YouTube,  Google+, and  Twitter! Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the  GMAT  for Veritas Prep and regularly participates in content development projects such as  this blog!