The shortest distance between city X and city Y is 100 miles. The shortest distance between city Y and city Z is 450 miles. What can be the distance, in miles, between city X and city Z?
The shortest distance between city X and city Y is 100 miles. The shortest distance between city Y and city Z is 450 miles. What can be the distance, in miles, between city X and city Z?
The correct options are
A 550 miles
C 350 miles
D 400 miles
We know that the length of each side of any triangle is greater than the difference between the lengths of the other two sides. Then XZ is greater than (450 miles - 100 miles) or 350 miles.
Since the lengths of each side of a triangle are also less than the sum of the lengths of the other two sides, we can say that XZ is less than (450 miles + 100 miles) or 550 miles.
We can conclude that XZ must be between 350 miles and 550 miles. The only answer that makes sense in the choices provided is choice D or 400 miles.
But if X, Y and Z are in straight lines as shown in the figure, option C, 350 miles and 550 miles can also be the answer (as shown in the figure).
A
550 miles
C
350 miles
D
400 miles
We know that the length of each side of any triangle is greater than the difference between the lengths of the other two sides. Then XZ is greater than (450 miles - 100 miles) or 350 miles.
Since the lengths of each side of a triangle are also less than the sum of the lengths of the other two sides, we can say that XZ is less than (450 miles + 100 miles) or 550 miles.
We can conclude that XZ must be between 350 miles and 550 miles. The only answer that makes sense in the choices provided is choice D or 400 miles.
But if X, Y and Z are in straight lines as shown in the figure, option C, 350 miles and 550 miles can also be the answer (as shown in the figure).
