Last visit was: 08 Nov 2024, 13:13 It is currently 08 Nov 2024, 13:13

Close

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

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 GRE 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.

Close

Request Expert Reply

Confirm Cancel
avatar
Intern
Intern
Joined: 03 Jun 2016
Posts: 37
Own Kudos [?]: 135 [12]
Given Kudos: 0
Send PM
Most Helpful Community Reply
avatar
Intern
Intern
Joined: 03 Jun 2016
Posts: 37
Own Kudos [?]: 135 [6]
Given Kudos: 0
Send PM
General Discussion
User avatar
Retired Moderator
Joined: 07 Jun 2014
Posts: 4813
Own Kudos [?]: 11143 [2]
Given Kudos: 0
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Send PM
avatar
Intern
Intern
Joined: 20 Sep 2018
Posts: 14
Own Kudos [?]: 4 [0]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
Hey I got the answer as A, C ,E..I took x as 1,3 and 8... But my workbook still shows the answer as incorrect. Can somebody help me with this question.
avatar
Supreme Moderator
Joined: 01 Nov 2017
Posts: 371
Own Kudos [?]: 469 [1]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
1
Expert Reply
Reetika1990 wrote:
Hey I got the answer as A, C ,E..I took x as 1,3 and 8... But my workbook still shows the answer as incorrect. Can somebody help me with this question.



The answer is correct as A, C and E.
the equations can be formed in following way..
(I) the third side is less than the sum of the other two sides...
so third side < (2x+1) + (3x+4) or third side < 5x+5
(II) the third side is greater than the difference of the other two sides...
so third side > |(2x+1) - (3x+4)| or > |x+3|
Therefore, equation becomes \(x+3 < third side < 5x+5\)
avatar
Intern
Intern
Joined: 12 Sep 2019
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
Hi All ,
While 4x+5 , 6x+1 , and 2x +17 are mentioned as correct answers for x>0 there might e challenge


X tending to 0 e.g. 0.01
2x+1 = 1.02
3x+4 = 4.03

here 6x+1 as third side will become 1.06 thus three sides as 1.02,1.06, 4.03 which is not possible
here 2x+17 = 17.02 which again is not possible

Again if x is big as x=1000
2x+1 =2001
3x+4 =3004
6x+1 becomes 6001

Not so sure about the answers now ?
avatar
Intern
Intern
Joined: 09 Aug 2018
Posts: 5
Own Kudos [?]: 8 [3]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
3
x+3<3rd side length<5x+5
let's say x=1000
1003<3rd side<5005
option E: 2(1000)+17= 2017 which falls right into the region. N.B if you consider small values for x, ie 2/3 then option E is invalid. but the ques asks for which of the following could be** the length. not which of the following must be**. you have to go for every possible way out there.
avatar
Intern
Intern
Joined: 19 May 2020
Posts: 6
Own Kudos [?]: 11 [4]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
4
phoenixio wrote:
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

A) 4x+5
B) x+2
C) 6x+1
D) 5x+6
E) 2x+17


solution:
of course 3x+4 > 2x+1 so, third side of the triangle is 3X+4-(2x+1)<third_side<3x+4+2x+1.
which gives x+3<third_side<5x+5.
note: question asked which "could be" the length of third side.
x>0:
A) x+3<4x+5<5x+5 which is true.

B) x+3<x+2<5x+5 never true.

C) x+3<6X+1<5x+5 which is not true for all value of x, but is true for x<4. so, could be true.

D) x+3<5x+6<5x+5 never true.

E) x+3<2x+17<5x+5 which is not true for all value of x, but is true for x>=5.
A,C,E :clap: :clap:
:twisted: :twisted:
Manager
Manager
Joined: 16 Aug 2021
Posts: 139
Own Kudos [?]: 46 [1]
Given Kudos: 86
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
1
C and E should be out of the answers because we don't know the real value of X
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12184 [2]
Given Kudos: 136
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
2
phoenixio wrote:
If x>0, and two sides of a certain triangle have lengths 2x+1 and 3x+4 respectively, which of the following could be the length of the third side of the triangle?

Indicate all possible lengths.

A) 4x+5
B) x+2
C) 6x+1
D) 5x+6
E) 2x+17


IMPORTANT PROPERTY: If two sides of a triangle have lengths A and B, then . . .
DIFFERENCE between A and B < length of third side < SUM of A and B

ASIDE: If x > 0, then we can be certain that 3x+4 is greater than 2x+1

Let's plug the two given lengths into the above property to get: (3x+4) - (2x+1) < length of 3rd side < (3x+4) + (2x+1)
Simplify to get: x + 3 < length of 3rd side < 5x + 5

So any length that could satisfy the above inequality will be a possible length.
So let's start testing!!!

A) 4x+5
Plug this value into our inequality: x+3 < 4x+5 < 5x+5
If x = 1, the inequality holds.
So answer choice A COULD be the length of the third side.

B) x+2
Plug this value into our inequality: x+3 < x+2 < 5x+5
Let's focus on this part of the inequality: x+3 < x+2
Subtract x from both sides to get: 3 < 2
At this point, we can conclude that there are no possible values of x that will satisfy the inequality.
So answer choice B CANNOT be the length of the third side.

C) 6x+1
Plug this value into our inequality: x+3 < 6x+1 < 5x+5
If x = 1, the inequality holds.
So answer choice C COULD be the length of the third side.

D) 5x+6
Plug this value into our inequality: x+3 < 5x+6 < 5x+5
Let's focus on this part of the inequality: 5x+6 < 5x+5
Subtract 5x from both sides to get: 6 < 5
At this point, we can conclude that there are no possible values of x that will satisfy the inequality.
So answer choice D CANNOT be the length of the third side.

E) 2x+17
Plug this value into our inequality: x+3 < 2x+17 < 5x+5
Don't forget that all we need is one value of x that satisfies the above any quality in order to show that the answer choice COULD be the length of the third side.
After a bit of testing I found that when x = 10, the inequality holds.
So answer choice E COULD be the length of the third side.

Answer: A, C, E
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5009
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: If x>0, and two sides of a certain triangle [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: If x>0, and two sides of a certain triangle [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
234 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne