How can I tell if I’m looking at a “Parallel Reasoning” question? The question-stem will contain an argument, and the question itself will contain phrases like “method of reasoning,” “parallel reasoning,” “most similar,” “similar reasoning,” or “most closely parallel.” You’ll also see that each answer choice is its own argument, as opposed to an assumption, inference, or flaw.

Let’s look at a simply example!

Argument #1: If someone has blonde hair, then they have blue eyes. My father has blonde hair, therefore my father has blue eyes.

The reasoning here is presented as a conditional A -> B, “blonde hair” means “blue eyes.” This reasoning is then used to make a conclusion, using the exact same pattern: A -> B. Here’s an example of a simple argument that uses parallel reasoning to Argument #1:

Argument #2: The best internet cafes have free wifi. All cafes with free wifi serve unlimited coffee. Therefore, the best internet cafes serve unlimited coffee.

It’s the same reasoning because the logic moves in the same direction from A -> B , going from “wifi” to “coffee,” then “best cafes” to “wifi.” Don’t worry that this argument  is not arranged in exactly the same order as Argument #1, it’s the method of reasoning that must be similar. A correct answer choice can be a little bit different from the question-stem. It’s the LOGIC that counts!

Watch out for…

•  Answer choices that merely mimic the topic of the argument. The correct answer’s argument usually focuses on an entirely different topic. It’s not what is being discussed that matters, but how the reasoning is laid out.
• Answer choices that have the same structure as the question-stem argument, but do not have the same logic! Just because an answer choice contains similar keywords, or has a similar number of sentences, doesn’t mean its logic matches! The premises and conclusion can be rearranged, but the logic of an argument doesn’t change.
• Pacing! These question-types typically take longer than strengthen or weaken CR, because you have 6 arguments to break down, as opposed to 1 (whew!). Practice untimed at first, but as you gain more confident with this question-type, set a timer and try to do them in under 3 minutes, then under 2 minutes.

Look out for Part 2 of this series, where we’ll look at what strategies we can use to break down Parallel Reasoning questions quickly and effectively, and get them correct every time.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

Question: If 10, 12 and ‘x’ are sides of an acute angled triangle, how many integer values of ‘x’ are possible?

(A) 7
(B) 12
(C) 9
(D) 13
(E) 11

Solution: The question is very interesting. It asks you for an acute triangle i.e. a triangle with all angles less than 90 degrees. It’s a little hard to wrap your head around it, isn’t it? We know that the third side of a triangle can take many values. Right from a little more than the difference of the other two sides to a little less than the sum of the other two sides (Since we know that the sum of any two sides of a triangle is always greater than the third side). So x can be anything from a little more than 2 to a little less than 22. But how do we find out the values for which all the angles will be less than 90?

We want no obtuse or right angles. An obtuse angled triangle has one angle more than 90. So the thought here is that before one of the angles reaches 90, find out all the values that x can take.

Look at the figure given above. The value of x in the first figure is very small – slightly more than 2 – minimum required to make a triangle. There is an obtuse angle in that triangle. We keep making x bigger and bigger and the angle keeps becoming smaller till it reaches 90 (Fig III). We use Pythagorean theorem to get the value of x in that case:

x = √(12^2 – 10^2)
x = √44 which is 6.something
x should be greater than 6.something because the angle cannot be 90.

We further keep increasing x and all the angles are acute now. We reach Fig V where we hit another right triangle. We use Pythagorean theorem again to get the value of x (the hypotenuse) in this case:

x = √(12^2 + 10^2)
x = √244 which is 15.something
x should be less than 15.something so that the angle is not 90.

Further on, in Fig VI, we obtain an obtuse angle again.

We only need integral values of x so values that x can take range from 7 to 15 which is 9 values.

Answer (C).

Note: We made two angles 90 and found the values of x in between those two angles. The third angle cannot be 90 because that will make 10 the hypotenuse but hypotenuse is always the greatest side.

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!

Step one: Student begins to work on problem, places scratch paper directly underneath problem covering answer choices.
Step two: Instructor slaps the note paper away and yells “no touching (the answer choices)”

Why?

Particularly on Problem Solving questions, the answer choices are often the most important assets you have in solving the problem. Some problems require you to plug in answer choices (“backsolve”) in order to solve; other problems embed clues in the answer choice (if there’s a square root of 3, you should be looking for a 30-60-90 triangle somewhere; if all the denominators in the answer choices are either 3 or 5, you should be thinking about divisibility rules). A higher-than-you’d-think percentage of Problem Solving questions reward users for glancing at the answer choices before they start their work, but a higher-than-you’d-think percentage of students never look past the question mark in the problem before they diligently start calculating. Let’s see a few examples to show you how looking at answer choices can drastically increase your efficiency and accuracy:

Which of the following is equal to 124/93?

(A) 6/5
(B) 5/4
(C) 4/3
(D) 3/2
(E) 8/9

If you were to try to factor out the common term between 124 and 93, you’d have a tough time identifying it on its own. 124 = 4(31) and 93 = 3(31), but very few people will quickly see “oh, they’re both divisible by 31″. Instead, you’re much more likely to make that determination by looking at the answer choices. Choices A, B, and D are clearly wrong because the denominator – 93 – is not divisible by 5 and not even, so it cannot factor down to have a denominator of 5, 4, or 2. And choice E should be clearly wrong because in the original, 124/93, the numerator is greater than the denominator, but choice E reverses that. So C is the only plausible choice, and if you test it it gives you a clue as to what to factor out. You’d need to divide the numerator, 124, by 4 (leaving 31) and then test the denominator to make sure it’s also divisible by 31 (and it is, producing that 3).

When you need to reduce a fraction as the last step of a problem, try looking at the answer choices for clues as to which factors to break out – after all, one of the answer choices MUST BE correct, and several should be impossible to begin to factor, thereby lightening your load.

Take a look at another example:

3^8 + 3^7 – 3^6 – 3^5 =

(A) (3^5)(2^4)
(B) (3^6)(2^5)
(C) (3^5)(2^6)
(D) 6^5
(E) none of the above

If you aren’t sure how to even start the problem, look at the answer choices – none of them has addition or subtraction, and most of them involve multiplication. So what’s your next move? Make your math look like the answer choices – you have to factor away that add/subtract to form multiplication (try it and see if you can D-termine the answer).

The takeaway – answer choices are an absolutely integral part of problem solving questions, so make sure to glance at them before you begin your work, and to lean on them if you’re struggling at any point of your calculation. Answer choices are assets!

Plan on taking the GMAT soon? We run a free online GMAT prep seminar every couple of weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Though it is easy to get oneself into a tizzy and wallow in frustration at a question of this sort, it is important to remember that nothing is a matter of opinion on the SAT. Every answer is objectively true and supported by the text.  The trick is examining what the passage is accomplishing.         

The first task when you are approaching a question like this is to look at the story or article and describe, in one or two sentences, what it is about.  We all do this with content much more complicated than short passages.  When someone asks you what a movie, let say, The Lion King, is about, you would probably say something like, “It’s a coming of age story about lion cub who finds his place in the world.” This is similar to what we do with passages, but in making our description of a passage, we want to state what a passage does as well as what content it engages.

A passage could deal with dinosaurs, for example, but it is too reductive to state the passage is about dinosaurs.  What is the author doing? The author could be:

• Convincing you of a viewpoint (are there arguments and examples to support an argument?)
• Comparing two different viewpoints (different arguments are presented, but the author doesn’t pick a side)
• Describing or explaining a phenomenon (is it mostly descriptive or explanatory?)
• Telling a story (is there a clear narrative?)

These are the kinds of questions that we must ask in determining purpose.  Usually if we only look at the first few words of the answer choices for these key indicator words (describing, arguing, comparing, etc.), we can eliminate the majority of the possibilities because the answers describe something that is not accomplished by the text.  If our imaginary article is comparing existing theories about the extinction of the dinosaurs without making a judgment on which argument is stronger, then any answer choice that states that the author is arguing, or convincing, and not comparing or explaining is WRONG.  What if an answer choice states that the author is making an argument on a possible cause of the extinction of the dinosaurs? That’s sort of what the author is doing, right? Nope! It’s wrong, wrong, wrong. “Sort of” true answers are not correct. All parts of an answer choice MUST be correct and supported by the passage in order for the answer to be true.  It is often easier to figure out what the author is NOT doing and eliminate all choices that describe an untruth.

As long as we follow these simple steps, we should be able to approach this kind of question with ease:

• Describe what passage accomplishes (is the author explaining, arguing, comparing, etc.)
• Examine the answer choices to see which actions the author is and isn’t accomplishing
• Eliminate choices that don’t describe what the author is doing
• Examine all parts of remaining answer choices and make sure they are supported in the text (ALL ANSWERS ARE STATED IN OR SUPPORTED BY THE TEXT)

Don’t fear these types of questions.  There are many difficult searches for purpose that you may engage with in your life, the purpose of an SAT article is easy to find: it’s all in the text.

Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy.

Veritas Prep GMAT on Demand is our  all-online GMAT course delivered in high-definition streaming video, using the same course materials and curriculum that students cover in every live Veritas Prep GMAT course. Taught by the co-author of the Veritas Prep GMAT course curriculum, Brian Galvin and co-hosted by Lissette Padilla, Dean’s Fellow at the MIT Sloan MBA program, Veritas Prep GMAT on Demand  is the most comprehensive self-study program available.

The course comes with over 20 hours of streaming video, broken down into easily digestible lessons that correspond with the Veritas Prep lesson books.  Brian and Lissette are engaging and thorough in their coverage of the course.  You’ll come to think of them as your own personal tutors who are just as invested in your success as you are.

We’re especially proud of the fact that Veritas Prep GMAT on Demand can be accessed across a host of devices, including your computer, iPad, or any other iOS device.  Our goal with Veritas Prep on Demand was to create a program as user friendly and accessible as possible.  No other self-study program is delivered across so many platforms or offers the amount of  expertise and depth as Veritas Prep GMAT on Demand.

We are so confident that you’ll love Veritas Prep GMAT on Demand that we’re making it available to everyone for free through a 7-day, no risk free trial.  You’ll get access the first full lesson and then you will be able to view selections of the remaining eleven lessons – that’s more than four hours of instruction, all in HD video!  All you need to do is provide your name and email address (no credit card  is required) and you’ll get immediate access to the program.  Try it out now!

1. Strengthening the conclusion
2. Weakening the conclusion
3. Inferring based on the conclusion
4. Method of reasoning used

As you can easily tell from the categories above, the conclusion usually plays a pivotal role in correctly answering the question at hand. Thus, identifying the author’s point is a necessary step that cannot be circumvented. In particular, let’s focus in on strengthening the argument or weakening the argument, two sides of the same coin that can often be solved the exact same way (you may need to insert the word “not” somewhere)

Within the context of a strengthening or weakening question, the three steps to correctly solving the question are always the same (and very similar to casing a joint for a heist)

1. Identify the conclusion
2. Evaluate the premise(s)
3. Find the gap between the conclusion and the premise.

Again, the conclusion is the key to everything. If you correctly identify the conclusion, you’re on the right path to success. If you misidentify the conclusion, you will likely fall into a clever trap laid out for you. Let’s look at an example:

Nate: Recently a craze has developed for home juicers, $300 machines that separate the pulp of the fruits and vegetables from the juice they contain. Outrageous claims are being made about the benefits of these devices: Drinking the juice they produce is said to help one lose weight or acquire a clear complexion, to aid in digestion, and even to prevent cancer. But there is no indication that juice separated from the pulp of the fruit or vegetable has any properties that it does not have when unseparated. Save your money, if you want carrot juice, eat a carrot.

Which of the following, if true, most calls into question Nate’s argument?

(A)  Most people find it much easier to consume a given quantity of nutrients in liquid form than to eat solid foods containing the same quantity of the same nutrients.

(B)  Drinking juice from home juicers is less healthy than is eating fruits and vegetables because such juice does not contain the fiber that is eaten if one consumes the entire fruit or vegetable.

(C)  To most people who would be tempted to buy a home juicer, $300 would not be a major expense.

(D)  Nate was a member of a panel that extensively evaluated early prototypes of home juicers

(E)  Vitamin pills that supposedly contain nutrients available elsewhere only in fruits and vegetables often contain a form of those compounds that cannot be as easily metabolized as the varieties found in fruit and vegetables.

After quickly identifying the type of question (calls into question = weaken), the next step on the road to success is to identify the conclusion. Looking over Nate’s soliloquy, the majority of it is context as to how the juicing craze came about, the positive aspects of juicers (the unexpected plot twist when the juicer was betrayed by Cobra) and the negative aspects of juicers. The conclusion, summed up in a succinct manner at the end is simply “Save your money, if you want carrot juice, eat a carrot.”

The trap that many people fall for here is that Nate’s argument is based primarily on monetary issues. Yes the juicer separates the juice from the pulp, but it’s not worth the money! (C’mon you could take that money and buy ¾ of an Apple share). If you focus in on the money aspect, you probably want to pick answer choice C, because it indicates that the money won’t be a big concern for prospective clients. However, this is a trap based on the phrasing of the conclusion.

The conclusion could have just as easily read “Don’t be a fool, if you want carrot juice, eat a carrot”. This conveys the exact same message, but answer choice C would now have to be something akin to “Most people who would buy this juicer have IQs above 114½”. The call for saving your money is simply used for emphasis; it has little bearing on the actual issue, which is that you get the same nutrients from solid foods as you would from consuming only the juice.

For strengthening/weakening questions, the third step of minding the gap between the premise and the conclusion is necessary to determine which answer choice to select. In this question, the premise is talking about the nutrients of one form versus the other, and the conclusion states that there’s no reason to ever want the juice instead of the solid. What’s the gap? Maybe there’s another reason we would want the juice! Perhaps it tastes better, or your teeth aren’t as solid as they used to be and juice is preferable to trying to bite into an apple (or perhaps you’re trying to cross a border and fruits are illegal but the juice is fine).

Upon rereading the answer choices, A is exactly what you want. The others all fall down in various ways.

(A)  Most people find it much easier to consume a given quantity of nutrients in liquid form than to eat solid foods containing the same quantity of the same nutrients.

Perfect. This gives us a valid reason to want to drink the juice.

(B)  Drinking juice from home juicers is less healthy than is eating fruits and vegetables because such juice does not contain the fiber that is eaten if one consumes the entire fruit or vegetable.

Tempting, but this strengthens the argument instead of weakening it. 180 °.

(C)  To most people who would be tempted to buy a home juicer, $300 would not be a major expense.

Trap answer based on financial considerations.

(D)  Nate was a member of a panel that extensively evaluated early prototypes of home juicers

Again, wouldn’t this make Nate an expert on the subject? Strengthener and 180 °.

(E)  Vitamin pills that supposedly contain nutrients available elsewhere only in fruits and vegetables often contain a form of those compounds that cannot be as easily metabolized as the varieties found in fruit and vegetables.

New topic. Why are we introducing vitamin pills here? Out of scope.

The correct answer is (A). 

On these types of critical reasoning questions, correctly identifying the conclusion is paramount to correctly answering the question. Hijacking the conclusion will result in an answer choice that seems correct, but doesn’t address the underlying point the author is making. And since strengthening and weakening questions make up the majority of Critical Reasoning questions on the GMAT, the only conclusion you should come to is to practice these questions regularly.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Ron Awad is a GMAT instructor for Veritas Prep based in Montreal, bringing you occasional tips and tricks for success on your exam.  After graduating from McGill and receiving his MBA from Concordia, Ron started teaching GMAT prep and his Veritas Prep students have given him rave reviews ever since.

We have sailed through the easy math problems, eliminating impossible answers and plugging in numbers or answer choices to save time until we come upon the dreaded HARD MATH PROBLEM. Our bodies tense and we begin to sweat.  We have never seen a problem like this, we aren’t even sure if there is a way to answer this question.  All of our work, and our dreams of attending PrinceHarvCamb-ford University are dashed.

Before we allow our nervous energy to waste too much time, we pause, we breathe, and we remember the words of Lao-Tsu, “A journey of a thousand miles, begins with a single step”. We do not know the destination but we begin to work anyway. Use the example in these four steps.

1. Start Working: Even when you are unsure of the exact method of solving the problem, you can illuminate information that may not be readily apparent simply by beginning to work.

2. Write What You Know: Perhaps the problem tells you that there is a rectangular pasture that has twelve equally spaced poles on its northern border, and sixteen equally spaced poles on its eastern border.  We label the distance between poles as X and we notice that we now have two sides of a triangle, one 12x and one 16x.

3. Remember the Rules: We remember the rules of Pythagorean triples and deduce that the diagonal of this triangle would have to be 20x.  We then look for what the problem is asking us to find.  We have to find the perimeter of the pasture, but all that is given is the length of a pathway from the eastern corner of the pasture to the center of the pasture.  AHA! We now have the length of HALF of the distance of the diagonal of the rectangular pasture!  We also know that the FULL diagonal is 20x.

4. Set up the Equation: We set up a simple equation to solve for X, remembering to double the length given from the center to the corner of the field.  We then use our answer for X to find the length and width of the pasture and add everything together, remembering to multiply the length and width by two, to find the perimeter.

Now some of you might say, “This problem was much easier than hard SAT problems!” ITS NOT!  Even problems that seem hard have a simple, though often multi-step, solution. If you start to work and look for what the clues in the problem tell you, the path to finding the answer is often illuminated.  By taking it one step at a time, we can complete our journey and arrive at an end we did not think ourselves capable of finding.

Plan on taking the SAT soon? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

David Greenslade is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy.

1. Don’t study where you sleep.
   We’re all guilty of studying in bed, cross-legged, furiously typing away at a last-minute Quant practice section, but studies have shown that our bodies becomes conditioned with routines. If you consistently use your bed as your office-space, it will be harder for you to mentally “switch off” once you climb under the covers. If possible, do most of your computer-work at a desk or kitchen table, away from your bedroom (or at least a few feet away from your bed).
2. Exercise, even in small bursts.
   We all KNOW we should exercise, but it can be tough to find even 30-60 minutes a day to go for a jog or take a yoga class when you’re in a 3-month GMAT study zone. Even if you have no time to get a true workout in, make yourself take at least three five minute stretch and meditation breaks – one in the morning, one in the afternoon, and one before bedtime. For each break, set your phone alarm for five minutes and quickly stretch out on the floor. Stretch out your spine and listen to yourself breathe. This allows your muscles (especially those around your head and shoulders) to relax into the floor, and remove any tension you may be subconsciously “holding” in your body.
3. Fight insomnia with a total black-out.
   Noise, light, and cold are three of the most common things that can prevent us from drifting off. If you have street lights or a neighbor’s lamp shining in through your bedroom window, consider covering them up with a large blanket before you hit the hay. Try to make your bedroom as pitch-black as possible.  Buy some ear plugs, even if you don’t have noisy roommates. With them in, you’ll be able to listen to your heartbeat, which will lull you to sleep more quickly after a stressful day. Take the plugs to the library to get a more focused study-session in as well!
4. Find some inspirational quotes.
   It may sound silly, but putting up some inspirational quotes or mantras on your wall above your desk such as, “what you seek is seeking you,” or “thoroughness characterizes all great men” or even something as simple as, “I am going to ROCK my GMAT!” can create a less stressful study atmosphere.

Remember: You’ve come this far, and you know you’re going to get your MBA somewhere – all you’ve got to do is stay positive for just a few more months! Good luck!

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT. 

Click here to read the intro to this blog series! Send your admissions questions to timeout[at]veritasprep[dot]com.
–
Dear Trav,
I want to change careers so my employer can’t know I’m applying to b-school. How should I navigate letters of recommendation if I can’t ask my direct supervisor for help?
–

As you probably already know based on your question, pretty much every MBA program asks for a recommendation from your current supervisor.  In fact, if your current supervisor does not provide a recommendation, the school will usually ask you to explain the circumstances in your optional essay. Because of this very strong language on their website, most candidates believe that if they can’t provide a recommendation from their current supervisor, they are put at a huge disadvantage.  They think of it like a homework assignment that doesn’t fulfill all the requirements, so you’re automatically deducted a full letter grade.  Please don’t think like that!  The admissions process is much more holistic and flexible than you might think!

There are many circumstances when an applicant cannot get a recommendation from their current supervisor.  In many cases, they are not comfortable telling their current employer that they may be leaving the company to go to business school.  In others, they may have worked with their current supervisor for a very short time, and the person does not know them well.  In other cases, the applicant may be concerned that if they tell their current supervisor that they will be leaving the company, their projects or bonuses may be affected. Or let’s be honest, sometimes you can’t get a recommendation from your current supervisor because you absolutely HATE them, and the feeling is likely mutual, so you don’t think they will offer you a strong recommendation.

It’s okay!  Admissions officers know that there are many circumstances where obtaining a recommendation from your current supervisor is not possible. In most cases, you may simply explain the situation in a straightforward and candid way in your optional essay.  For example, I worked with an applicant in investment banking who simply said, “I have not informed my direct supervisor of my intentions to apply to business school because I am concerned that it may impact the projects to which I am assigned and my quarterly bonuses.”  He was admitted to his first-choice school.

The key is to select another recommender who can offer a similar perspective on your strengths and weaknesses.  Think about what your current supervisor knows about you: they know your day-to-day job responsibilities and working habits, they have firsthand knowledge of projects where you’ve shown initiative, they understand your interpersonal skills, they can compare your performance to peers, and so on. You need to find someone who can replicate this intimate level of understanding as closely as possible. A peer is usually NOT the best answer, as it’s pretty easy to just find our best friend at work and have them write a glowing review. Do you have a former supervisor from the fairly recent past (past 2-3 years)?  Do you work in a matrix-style organization where you’ve reported to other supervisors on different projects? Do you have a mentor within your organization with whom you feel comfortable discussing your future career goals—including business school? You need someone who has served in a supervisory role to you and who can speak very personally about your performance, strengths and weaknesses.

Once you have selected the proper replacement, be sure to mention why you selected them in your optional essay.  So after explaining why you have not asked your current supervisor for a recommendation, you need to add a sentence stating something like, “Therefore, I have asked Travis Morgan to write a recommendation on my behalf, as he is my most recent former supervisor and can speak directly to my professional experience, performance relative to my peers, and personal strengths and weaknesses.”

The MBA admissions committee places the greatest value on recommendations from your current supervisor, as they can speak to your current circumstances and achievements. Besides, if you show the courage to speak with them about your future plans, this shows the level of trust that you have with them. So obtaining a recommendation from your current supervisor is always the best option.  However, admissions officers will understand your circumstances and recognize that this is not always possible. You will not be automatically “demoted” in consideration for this one omission. Instead, just find your best alternative recommender and prepare them properly so that their recommendation is strong, personal and specific.

I hope that comes as a relief to you as you prepare to apply!

Trav

If you’re thinking about applying to business school, call us at 1-800-925-7737 and speak with an MBA admissions expert today. And, as always, be sure to find us on Facebook and Google+, and follow us on Twitter! If you have any admissions questions for the blog, please send them to timeout[at]veritasprep[dot]com.

Travis Morgan is the Director of Admissions Consulting for Veritas Prep and earned his MBA with distinction from the Kellogg School of Management at Northwestern University. He served in the Kellogg Student Admissions Office, Alumni Admissions Organization and Diversity & Inclusion Council, among several other posts. Travis joined Veritas Prep as an admissions consultant and GMAT instructor, and he was named Worldwide Instructor of the Year in 2011.

Basic Properties

A quadrilateral, by definition, is a polygon with four sides created by four straight lines. Some common quadrilaterals are: a square, a rectangle, a parallelogram, and a trapezoid.

Need-to-know fact: The sum of the interior angles of any quadrilateral is 360.

Remember that every time you add a side to a figure, you add 180 degrees to the sum of its interior angles. That is why a triangle’s sum is 180, and any quadrilateral’s sum is 360.  Keep in mind that definition-wise, quadrilaterals are inclusive. This means that a square is ALSO a rectangle, so be aware that just because a question states that a shape is a “rectangle” doesn’t necessarily mean it can’t have four equivalent sides!

Perimeter

The perimeter of a quadrilateral is the sum of its four sides. For a rectangle, the formula is P = l + l + w + w, or P = 2l + 2w. For a square, this becomes P = 4s. For other quadrilaterals, you need to know the length of each side in order to find the perimeter, unless you are given more information about the comparative lengths of the sides. For example, for a parallelogram we know that the opposite sides are equal in value, so knowing two adjacent sides would be sufficient to find the perimeter.

Area

The area of a quadrilateral is the measurement contained within its four sides. There is no one area formula for all quadrilaterals. Instead, each one has a unique equation that must be memorized.

• To find the area of a square, we use the formula A = s², where s = side of the square.
• To find the area of a rectangle, we use the formula A = lw, where l = length and w = width.  T
• To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. We do NOT simply multiply the two side lengths. Remember the base and the height must be perpendicular.
• To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. We essentially take the average of the two bases, and multiply it by the height. Again, the height is perpendicular to each base.

Remember to analyze your incorrect questions from Veritas Prep’s question bank. Use this data to understand your strengths and weaknesses and focus your GMAT prep on the area that need it most!

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT.