|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
24 Jan 2023, 08:15
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
23% (01:48) correct
77%
(01:50)
wrong
based on 26
sessions
History
Date
Time
Result
Not Attempted Yet
All possible obtuse angled triangle with sides of integers lengths are constructed , such that two of the sides have lengths 7 and 14.How many such triangles exist ?
A. 13
B. 11
C. 10
D. 8
E. 7
A. 13
B. 11
C. 10
D. 8
E. 7
24 Jan 2023, 09:00
Kudos
Bookmarks
Bunuel
Two properties of triangles that can help us solve this question -
1) The third side of a triangle is always greater than the positive difference between the other two sides and is less than the sum of the other two sides.
In this case
14 - 7 < Third Side < 14+7
7 < Third Side < 21
2) In an obtuse-angled triangle, the square of the sum of the longest side is greater than the sum of the other two sides
(Longest Side) ^ 2 > (Side 1)^2 + (Side 2)^2
Let's apply these two properties -
Case 1: Assume the side with length 14 is the longest side
\(14^2 > 7^2 + x^2\)
x is the length of the third side
\(x^2 < 14^2 - 7^2\)
\(x^2 < (14+7)(14-7)\)
\(x^2 < 147\)
x < 12.XX (x is greater than 12 but less than 13)
Possible values of x = 8, 9, 10 , 11, 12
Case 2: Assume the unknown side is the longest side
\(x^2 > 14^2 + 7^2\)
\(x^2 > 196 + 49\)
\(x^2 > 245\)
\(x > 15.XX\)
Possible values of x = 16, 17, 18, 19, 20
Note that we cannot exceed 20, as the side should be less than 21
Number of possible values of the third side = 10
Option C
27 Mar 2024, 19:05
Kudos
Bookmarks
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
