Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Join my MyGuru for Free GMAT Math Refresher is the best workshop to learn about the basics and the advanced strategies required to get a 700+ GMAT score.

Working in collaboration with examPAL we will provide you with a unique online learning experience which will help you reach that higher score. Start your free 7 day trial today.

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

Re: If x is a positive integer, which of the following COULD [#permalink]
26 May 2018, 21:09

There are some triangle rules that apply for all triangles. One of that is the length of a side of a triangle is always less than the sum of other two sides of the triangle.

Let us test option i

x, 2x +2, x+2

If we add the first and the third side x + x +2 = 2x+2 which is equal to the second side so this is false

Let us test option ii 2x, 3x, 2x - 7

Since the third side of this triangle includes a constant we can get some scenarios where the triangle can satisfy triangle properties and in some instance it does not satisfy the triangle property. However, this is a could be question so a single possibility is good enough to be true.

For eg. If the said integer is 1 we would have the three sides as, 2,3, -5 since length cannot be -ve this is not a possibility However let us take x = 10 then, 20, 30, 13 This satisfys the triangle property

Let us test option iii \(\frac{x}{2}, \frac{x}{6}, \frac{x}{4}\) The two smallest sides are x/6 and x/2. Option iii can only be a triangle if x/2 < x/6 + x/4 \(\frac{x}{6} + \frac{x}{4} = \frac{2x + 3x}{12} = \frac{5x}{12}\) Since \(\frac{x}{2}\) > \(\frac{5x}{12}\) option iii also is not correct.

A) i only B) ii only C) iii only D) i and ii only E) ii and iii only

There's a triangle property that says: (length of LONGEST side) < (SUM of the other two lengths) So, for example, 2, 3, 6 CANNOT be the lengths of sides in a triangle, because 6 > 2 + 3

i) x, 2x + 2, x + 2 Since x is a positive integer, we can see that 2x+2 will be the LONGEST side. Now compare this length to the SUM of the two other side lengths. Is it true that 2x + 2 < x + (x + 2)? Simplify: 2x + 2 < 2x + 2 This is NOT true. So, x, 2x + 2, x + 2 CANNOT represent the lengths of the 3 sides of a triangle Check the answer choices.... eliminate A and D

ii) 2x, 3x, 2x - 7 Since x is a positive integer, we can see that 3x will be the LONGEST side. Now compare this length to the SUM of the two other side lengths. Is it true that 3x < 2x + (2x - 7)? Simplify: 3x < 4x - 7 This COULD be true. For example, if x = 10, then we get: 3(10) < 4(10) - 7, which IS true. So, 2x, 3x, 2x - 7 COULD represent the lengths of the 3 sides of a triangle Check the answer choices.... eliminate C

iii) x/2, x/6, x/4 In this case, x/2 will be the LONGEST side. Now compare this length to the SUM of the two other side lengths. Is it true that x/2 < x/6 + x/4? Let's eliminate the fractions to make is easier for us to determine whether the inequality holds true. Multiply both sides of the inequality by 12 to get: 6x < 2x + 3x Simplify: 6x < 5x Since x is POSITIVE, we can see that this inequality is NOT true. So, x/2, x/6, x/4 CANNOT represent the lengths of the 3 sides of a triangle Check the answer choices.... eliminate E

Answer: B

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com If you enjoy my solutions, you'll like my GRE prep course. Sign up for GRE Question of the Dayemails

greprepclubot

Re: If x is a positive integer, which of the following COULD
[#permalink]
28 May 2018, 06:42