NEW HERE? LEARN MORE
closeclose
Last visit was: 26 Apr 2024, 14:58 It is currently 26 Apr 2024, 14:58
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT 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 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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If 7 and 10 are the lengths of two sides of a triangle, which of the

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92948
Own Kudos [?]: 619234 [1]
Given Kudos: 81609
Send PM
CAT Tests Forum Quiz Mode
If 7 and 10 are the lengths of two sides of a triangle, which of the [#permalink] New post   21 Aug 2018, 20:48
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

76% (00:33) correct 24% (00:30) wrong based on 101 sessions
Hide Show timer Statistics
If 7 and 10 are the lengths of two sides of a triangle, which of the following can be the length of the third side?

I. 2
II. 8
III. 17

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III
ShowHide Answer
Official Answer
A
User avatar
L
Chethan92
Director
Director
Joined: 18 Jul 2018
Posts: 926
Own Kudos [?]: 1288 [0]
Given Kudos: 95
Location: India
Concentration: Operations, General Management
Schools: IIMB EPGP'22 (M)
GMAT 1: 590 Q46 V25
GMAT 2: 690 Q49 V34
WE:Engineering (Energy and Utilities)
Send PM
Reviews Badge
Re: If 7 and 10 are the lengths of two sides of a triangle, which of the [#permalink] New post   21 Aug 2018, 20:54
The third side of triangle should be greater than the difference between the other two sides and less than the sum of the other two sides.

10-7 < x < 10+7

3 < x < 17

Only 8 satisfies the answer.

A is the answer.

Posted from my mobile device
User avatar
D
PKN
Director
Director
Joined: 01 Oct 2017
Status:Learning stage
Posts: 827
Own Kudos [?]: 1300 [0]
Given Kudos: 41
WE:Supply Chain Management (Energy and Utilities)
Send PM
If 7 and 10 are the lengths of two sides of a triangle, which of the [#permalink] New post   21 Aug 2018, 21:33
Bunuel wrote:
If 7 and 10 are the lengths of two sides of a triangle, which of the following can be the length of the third side?

I. 2
II. 8
III. 17

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III


The length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.

So, \((10-7)<x<(10+7)\)
Or, \(3<x<17\).
Hence 2 and 17 cannot be the length of the third side but 8 can be.

Ans.(A)
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16844 [0]
Given Kudos: 165
Send PM
Re: If 7 and 10 are the lengths of two sides of a triangle, which of the [#permalink] New post   21 Aug 2018, 21:58
Expert Reply

Solution



Given:
    • 7 and 10 are the lengths of two sides of a triangle.

To find:
    • The possible length of the third side.

Approach and Working:
We know that for any triangle, the sum of any two sides is always greater than the third side.
Similarly, the difference of any two sides is always less than the third side.

So, if the length of the third side is T, then we can say
    • 7 + 10 > T
    Or, T < 17

    • Similarly, 10 – 7 < T
    Or, T > 3

Combining them, we can write 3 < T < 17

From the given choices, we can say T can only be 8.
Hence, the correct answer is option A.

Answer: A

GMAT Club Bot
gmatclubot
Re: If 7 and 10 are the lengths of two sides of a triangle, which of the [#permalink]
21 Aug 2018, 21:58
Moderators:
Bunuel
Math Expert
92948 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions