Pattern Recognition, a key skill tested on the GMAT, is surely something that differentiates the higher percentile scorers from others. An efficient test taker makes sure that he understands the test maker as much as the test itself. Knowing the way a test is designed plays a huge role in understanding “how” a test maker plans on testing your abilities. A careful examination of the official tests from the GMAC and other official practice material reveal some, often tested, patterns in which skills and concepts are tested. These are worth knowing since they will give you an edge when approaching the Quantitative Reasoning section of the GMAT.

1. Wordy Groups/Sets Problems

These problem types test the test taker’s ability to read the full question carefully; it rewards individuals who can analyze information and mentally sort them out into necessary and trivial, and put the sorted information systematically on paper. A good test taker will approach this question type with a view to make the information simpler and manageable. Examples of ways to put the information in a systematic manner include the tree format, the double matrix. A lot of words in the question get compacted into a clear and concise pictorial representation which can be used seamlessly to answer the question.

Illustrative Question
This is a Data Sufficiency Question; this consists of a question and two statements, labelled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Last year in a group of 30 turtles, 21 survived a storm and 15 were living on the ground. How many of the turtles did not survive the storm nor lived on the ground.

• Last year 12 of the 30 turtles survived the storm and lived on the ground
• Last year 24 of the 30 turtles survived the storm or lived on the ground, or both

Solution Statement -1:  Survived-30

 Lived on the ground Did not live on the ground 12 9 3 6

Did not survive So, 6 of them did not survive the storm, nor lived on the ground. Hence, Sufficient Statement -2:  Survived-30

 Lived on the ground Did not live on the ground 30-24=6

Did not survive So, 6 of them did not survive the storm, nor lived on the ground. Hence, Sufficient Observe the pictorial format (Double Matrix) into which the information is fed. The answer for this question is D. EACH statement ALONE is sufficient… Take Away:  The GMAT is a test that rewards students who can break down and simplify complex information. Using the Noteboard effectively is an important aspect in achieve this.

These are simple and commonly known concepts to test takers. The simplest amongst them (a+b)2 , a2-b2 are often a basis to solve certain kind of questions. The key to get the solutions right in less time is to identify quickly that a question is based on classic quadratics!

Illustrative Question:
38-28 is divisible by all of the following except:

1. A) 5 B)   13            C)   35            D)   65        E)   97

Solution: Since the GMAT doesn’t allow the use of a calculator on the quantitative reasoning section, calculation of 38 and then 28 and then the difference between them would take some time.

However, observing the pattern in the question and being able to relate it to a2-b2 would make the calculations simpler!

Rewriting 38-28 as (34-24)*(34+24) and further as (32-22)*(32+22)*(34+24) and lastly as 5*13*97 will clearly rule out A, B, E as possible right answers. Also, choice D, 65 is 13*5. So the only answer choice left would be C – 35 which is not a factor of the given value. Hence,

C. Take Away: Looking for such patterns – when you feel that a question might require a lot of mathematical calculations to solve – will save you a lot of time: the GMAT rewards test takers who look for patterns to get to a solution efficiently.

The Right Angles of Geometry

Hidden or obvious, Right Angles in geometry often act as a pivotal piece of the puzzle and can help you break down a seemingly abstruse geometry problem. GMAT’s favourites amongst the right angled triangle problems are the ones that constitute 45-45-90 degrees and 30-60-90 degrees. Identifying these triangles in a relevant geometry problem and hence applying their inferences (ratio of sides) can make solving such problems quite straightforward.

Illustrative Question:

In the triangle shown, if angles A, B, C are 105, 30 and 45 degrees respectively, what is the value of AB? Also, given AC= 4√2. Solution:

The triangle given doesn’t have any right angles in it. However, the value of AC given to be 4√2 can be used as a hint to check whether the special right angled triangles and their properties can be related to this problem.

For an instance, if we drop a perpendicular from A to BC, then the triangle will be split into two special right angled triangles – one 45, 45, 90 and another 30, 60, 90 triangle Now, applying the special right angled triangles property to the above figure, we can infer that the perpendicular (height) of the triangle would be 4 and hence AB would be equal to 8.

Because,  a : a √3 : 2a for a 30,60,90 triangle and a : a : a √2 for a 45,45,90 triangle.

Take Away: GMAT seldom expects you to apply complex formulae to solve a question; many times the quickest way to answering a seemingly complex problem is hiding right in plain sight. The key is to consciously look for such patterns when faced with difficult problems in mathematics.