GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 26 May 2020, 19:53 ### 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

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.  # In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of

Author Message
TAGS:

### Hide Tags

Retired Moderator V
Joined: 27 Oct 2017
Posts: 1786
WE: General Management (Education)
In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of  [#permalink]

### Show Tags

1
11 00:00

Difficulty:   85% (hard)

Question Stats: 33% (01:48) correct 67% (02:57) wrong based on 43 sessions

### HideShow timer Statistics

GMATbuster's Weekly Quant Quiz#12 Ques #7 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 [ 8.3 KiB | Viewed 1325 times ]

_________________
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1786
WE: General Management (Education)
Re: In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of  [#permalink]

### Show Tags

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
Intern  B
Joined: 16 Jul 2018
Posts: 13
Re: In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of  [#permalink]

### Show Tags

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.
Non-Human User Joined: 09 Sep 2013
Posts: 14985
Re: In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
_________________ Re: In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of   [#permalink] 02 Apr 2020, 09:14

# In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm, which of  