Events & Promotions
|
|
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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
08 Dec 2018, 10:16
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
31% (02:01) correct
69%
(02:56)
wrong
based on 71
sessions
History
Date
Time
Result
Not Attempted Yet
In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of the following could be the positive difference between the maximum and minimum value of AT, if all the sides shown in the figure are positive integers?
A) 16
B) 18
C) 20
D) 21
E) 23
Attachment:
Ques fig.jpg
This Question is Locked Due to Poor Quality
Hi there,
The question you've reached has been archived due to not meeting our community quality standards. No more replies are possible here.
Looking for better-quality questions? Check out the 'Similar Questions' block below
for a list of similar but high-quality questions.
Want to join other relevant Problem Solving discussions? Visit our Problem Solving (PS) Forum
for the most recent and top-quality discussions.
Thank you for understanding, and happy exploring!
10 Dec 2018, 07:40
Kudos
Bookmarks
Official Solution:
Given:
AS = 10 cm
SN = 5 cm
TN = 8 cm
Find:
What could be the value of AT?
Since we have been given the lengths of the triangle and we do not have any information on the angles of the triangles, we will have to use the side property of the triangle to solve this question.
In triangle ASN –AS = 10 cm, SN = 5 cm
We know that sum of two sides > third side and we also know that difference of two sides < third side, thus, we can write –
10-5 < AN < 10+5
5 < AN < 15
Thus the value of AN can be {6,7,8,9,10,11,12,13,14}
Find the maximum value of AT. In triangle ATN, we can write –
AT < AN + TN
AT < 14 + 8
AT < 22
Thus, we can say that the maximum value of AT is 21 units.
Now, let us find the minimum value of AT
In triangle ATN, we can write –
TN ~ AN < AT
From the possible value of AN - {6,7,8,9,10,11,12,13,14}, if we take AN = 8, we will get AT > 8 – 8
AT > 0
Thus, the minimum value of AT will be 1 unit.
Therefore, the positive difference between the maximum and minimum value of AT could be = ( 21 – 1) = 20 units
The correct answer is Option C.
General Discussion
08 Dec 2018, 11:20
Kudos
Bookmarks
No figure appears.
Now figure has finally appeared!
The rule is that the sum of the lengths of any two sides of a triangle is greater the length of the third. Thus considering triangle ANS first, we have:
5 + AN > 10 => AN > 5. Also AN < 15, hence 5 < AN < 15. Since only integral values are allowed, AN = {6, 7, 8,...,14}.
Using only the extremal values of AN in triangle ATN, we get:
Use AN = 6 to get minimum value of AT: AT + 6 > 8 => AT > 2; therefore minimum value = 3.
Use AN = 14 to get maximum value of AT: AT < 22; therefore maximum value = 21.
Positive difference = 21-3 = 18.
Now figure has finally appeared!
The rule is that the sum of the lengths of any two sides of a triangle is greater the length of the third. Thus considering triangle ANS first, we have:
5 + AN > 10 => AN > 5. Also AN < 15, hence 5 < AN < 15. Since only integral values are allowed, AN = {6, 7, 8,...,14}.
Using only the extremal values of AN in triangle ATN, we get:
Use AN = 6 to get minimum value of AT: AT + 6 > 8 => AT > 2; therefore minimum value = 3.
Use AN = 14 to get maximum value of AT: AT < 22; therefore maximum value = 21.
Positive difference = 21-3 = 18.
