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

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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

OA C

Source: e-GMAT
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by deloitte247 » Fri Jan 18, 2019 8:59 am
Given that ;
AS = 10cm
SN = 5cm
TN = 8cm

In the triangle ABC with the sides abc : the sum of the length of any two sides of the triangle is greater than the length of the third considering ANS $$5+AN=10$$
$$AN<15$$
$$AN>5$$
$$5<AN<15$$
$$Hence,\ \ AN=6,7,\ ...............,\ 14$$
Minimum value of AN=6 Maximum value =14
Using the minimum and maximum value of AN in triangle ATN
$$AT>TN-AN\left(\min imum\ value\ of\ AT\right)$$
$$AT>8-6\left(where\ 6\ =\min\ no\ of\ AN\right)$$
$$AT>2$$
$$AT>2\left(\min\ value\ of\ AT\right)$$
$$AT<AN+TN\left(Maximum\ value\ of\ AT\right)$$
$$AT<14+8\left(where\ 8\ is\ the\ \max imum\ value\ of\ AN\right)$$
$$AT<22$$
$$Maximum\ value\ of\ AT\ is\ 21$$
$$Positive\ difference\ =21-3=18$$

$$answer\ is\ Option\ B$$
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by deloitte247 » Fri Jan 18, 2019 8:59 am
Given that ;
AS = 10cm
SN = 5cm
TN = 8cm

In the triangle ABC with the sides abc : the sum of the length of any two sides of the triangle is greater than the length of the third considering ANS $$5+AN=10$$
$$AN<15$$
$$AN>5$$
$$5<AN<15$$
$$Hence,\ \ AN=6,7,\ ...............,\ 14$$
Minimum value of AN=6 Maximum value =14
Using the minimum and maximum value of AN in triangle ATN
$$AT>TN-AN\left(\min imum\ value\ of\ AT\right)$$
$$AT>8-6\left(where\ 6\ =\min\ no\ of\ AN\right)$$
$$AT>2$$
$$AT>2\left(\min\ value\ of\ AT\right)$$
$$AT<AN+TN\left(Maximum\ value\ of\ AT\right)$$
$$AT<14+8\left(where\ 8\ is\ the\ \max imum\ value\ of\ AN\right)$$
$$AT<22$$
$$Maximum\ value\ of\ AT\ is\ 21$$
$$Positive\ difference\ =21-3=18$$

$$answer\ is\ Option\ B$$
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by deloitte247 » Sun Jan 20, 2019 7:38 am
Given that ;
AS = 10cm
SN = 5cm
TN = 8cm

In the triangle ABC with the sides abc : the sum of the length of any two sides of the triangle is greater than the length of the third considering ANS $$5+AN=10$$
$$AN<15$$
$$AN>5$$
5<AN<15

$$Hence,\ \ AN=6,7,\ ...............,\ 14$$

Minimum value of AN=6 Maximum value =14
Using the minimum and maximum value of AN in triangle ATN
$$AT>TN-AN\left(\minimum\ value\ of\ AT\right)$$
$$AT>8-6\left(where\ 6\ =\min\ no\ of\ AN\right)$$
$$AT>2$$
$$AT>2\left(\min\ value\ of\ AT\right)$$
$$AT<AN+TN\left(Maximum\ value\ of\ AT\right)$$
$$AT<14+8\left(where\ 8\ is\ the\ \maximum\ value\ of\ AN\right)$$
$$AT<22$$
$$Maximum\ value\ of\ AT\ is\ 21$$
$$Positive\ difference\ =21-3=18$$

$$answer\ is\ Option\ B$$
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