GRE Prep Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x is a positive integer, which of the following COULD
[#permalink]
26 May 2018, 09:51
26 May 2018, 09:51
2
4
Bookmarks
00:00
Question Stats:
54% (02:12) correct
45% (01:33) wrong based on 64 sessions
Hide Show timer Statistics
If x is a positive integer, which of the following COULD represent the lengths of the 3 sides of a triangle?
i) x, 2x + 2, x + 2
ii) 2x, 3x, 2x - 7
i) x/2, x/6, x/4
A) i only
B) ii only
C) iii only
D) i and ii only
E) ii and iii only
i) x, 2x + 2, x + 2
ii) 2x, 3x, 2x - 7
i) x/2, x/6, x/4
A) i only
B) ii only
C) iii only
D) i and ii only
E) ii and iii only
Re: If x is a positive integer, which of the following COULD
[#permalink]
26 May 2018, 21:09
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.
option B
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.
option B
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If x is a positive integer, which of the following COULD
[#permalink]
28 May 2018, 06:42
28 May 2018, 06:42
GreenlightTestPrep wrote:
If x is a positive integer, which of the following COULD represent the lengths of the 3 sides of a triangle?
i) x, 2x + 2, x + 2
ii) 2x, 3x, 2x - 7
i) x/2, x/6, x/4
A) i only
B) ii only
C) iii only
D) i and ii only
E) ii and iii only
i) x, 2x + 2, x + 2
ii) 2x, 3x, 2x - 7
i) x/2, x/6, x/4
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
