In the given figure, if AS = 10 cm, SN = 5 cm and TN = 8 cm,
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Third-side rule:
The third side a triangle must be LESS THAN THE SUM OF and GREATER THAN THE DIFFERENCE OF the other two sides.
Here, all the sides must be INTEGER values.
In triangle ANS, AS=10 and NS=5.
Thus, third side AN must be an integer value less than 10+5 = 15 and greater than 10-5 = 5, yielding the following options for AN:
6, 7, 8, 9, 10, 11, 12, 13, 14
In triangle ANT, TN=8.
If AN=8, then third side AT must be an integer value less than 8+8=16 and greater than 8-8=0, making it possible that AT=1.
Since AT must be a positive value, the minimum possible value for AT=1.
If AN=14, then third side AT must be an integer value less than 14+8=22 and greater than 14-8=6, making it possible that AT=21.
Since any other value for AN will yield a lower upper limit than the blue equation above, it is not possible that AN>21.
Implication:
The greatest possible value for AN=21.
Thus:
Maximum - minimum = 21-1 = 20.
The correct answer is C.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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