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# Veritas Prep Blog

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Veritas Prep Representative
Joined: 21 Jan 2010
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Veritas Prep Representative
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Veritas Prep Representative
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Veritas Prep Representative
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Understanding the Changes to the U.S. Visa Process [#permalink]
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Quarter Wit, Quarter Wisdom: Ignore the Diagram in That GMAT Geometry [#permalink]
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How to Quickly Interpret Ranges of Variables in GMAT Questions [#permalink]
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Using “Few” vs. “A Few” vs. “Quite a Few” in a GMAT Verbal Question [#permalink]
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This Blog post was imported into the forum automatically. We hope you found it helpful. Please use the Kudos button if you did, or please PM/DM me if you found it disruptive and I will take care of it. -BB
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The Pythagorean Triples Properties You’ll See on the GMAT [#permalink]
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 FROM Veritas Prep Blog: The Pythagorean Triples Properties You’ll See on the GMAT Today, let’s discuss a few useful properties of primitive Pythagorean triples. A primitive Pythagorean triple is one in which a, b and c (the length of the two legs and the hypotenuse, respectively) are co-prime. So, for example, (3, 4, 5) is a primitive Pythagorean triple while its multiple, (6, 8, 10), is not.Now, without further ado, here are the properties of primitive Pythagorean triples that you’ll probably encounter on the GMAT:I. One of a and b is odd and the other is even.II. From property I, we can then say that c is odd.III. Exactly one of a, b is divisible by 3.IV. Exactly one of a, b is divisible by 4.V. Exactly one of a, b, c is divisible by 5.If you keep in mind the first primitive Pythagorean triple that we used as an example (3, 4, 5), it is very easy to remember all these properties.If we look at some other examples:(3, 4, 5), (5, 12, 13), (8, 15, 17) (7, 24, 25) (20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53) (11, 60, 61) (16, 63, 65) (33, 56, 65) (48, 55, 73), etc.we will see that these properties hold for all primitive Pythagorean triples.Now, let’s take a look at an example GMAT question which can be easily solved if we know these properties:The three sides of a triangle have lengths p, q and r, each an integer. Is this triangle a right triangle?Statement 1: The perimeter of the triangle is an odd integer.Statement 2: If the triangle’s area is doubled, the result is not an integer.We know that the three sides of the triangle are all integers. So if the triangle is a right triangle, the three sides will represent a Pythagorean triple. Given that p, q and r are all integers, let’s use the properties of primitive Pythagorean triples to break down each of the statements.Statement 1: The perimeter of the triangle is an odd integer.Looking at the properties above, we know that a primitive Pythagorean triple can be represented as:(Odd, Even, Odd) (The first two are interchangeable.)Non-primitive triples are made by multiplying each member of the primitive triple by an integer n greater than 1. Depending on whether n is odd or even, the three sides can be represented as:(Odd*Odd, Even*Odd, Odd*Odd) = (Odd, Even, Odd)or(Odd*Even, Even*Even, Odd*Even) = (Even, Even, Even)However, the perimeter of a right triangle can never be odd because:Odd + Even + Odd = EvenEven + Even + Even = EvenHence, the perimeter will be even in all cases. (If the perimeter of the given triangle is odd, we can say for sure that it is not a right triangle.) This statement alone is sufficient.Statement 2: If the triangle’s area is doubled, the result is not an integer.If p, q and r are the sides of a right triangle such that r is the hypotenuse (the hypotenuse could actually be either p, q, or r but for the sake of this example, let’s say it’s r), we can say that:The area of this triangle = (1/2)*p*qandDouble of area of this triangle = p*qDouble the area of the triangle has to be an integer because we are given that both p and q are integers, but this statement tells us that this is not an integer. In that case, this triangle cannot be a right triangle. If the triangle is not a right triangle, double the area would be the base * the altitude, and the altitude would not be an integer in this case.This statement alone is sufficient, too. Therefore, our answer is D.As you can see, understanding the special properties of primitive Pythagorean triples can come in handy on the GMAT – especially in tackling complicated geometry questions.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!The post The Pythagorean Triples Properties You’ll See on the GMAT appeared first on Veritas Prep Blog.
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Time Management Tips for the SAT with the Optional Essay [#permalink]
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Learn How to Begin a GMAT Problem by Focusing on Keywords in the Quest [#permalink]
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This Blog post was imported into the forum automatically. We hope you found it helpful. Please use the Kudos button if you did, or please PM/DM me if you found it disruptive and I will take care of it. -BB
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Should You Reapply to the MBA Program that Rejected You? [#permalink]
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Quarter Wit, Quarter Wisdom: Using Ingenuity on GMAT Remainder Questio [#permalink]
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SAT Subject Tests: Which to Take and Why [#permalink]
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10 Things You Should Be Doing to Prep for College the Summer Before Se [#permalink]
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3 Ways to Solve a 750+ Level GMAT Question About Irregular Polygons [#permalink]
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5 Basic ACT English Rules to Live By [#permalink]
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