Problem Solving

sumasajja wrote:if x,y and z are the three angles of a triangle and are integers such that x<y<z,then the least and the greatest possible values of x+z are
a]59 and 91
b]59 and 135
c]91 and 178
d]120 and 135
e]120 and 179
the answer is c

x + z will be least when y is maximum. The greatest value among the 3 angles, so that their sum is 180º, is 90º. Now since y < z, so z = 90º. Next, we move on to the possible values of x and z. Minimum value of x = 1, and maximum possible value of y (considering x < y < z) = 89º (we have taken it as 89º, as z = 90º).

So, least value of x + z = 1 + 90 = 91

Now, x + z will b greatest when y is minimum. In this case x = 1, y = 2, z = 177 (so that x + y + z = 180º). So, the greatest value of x + z = 1 + 177 = 178.

The correct answer is C.

ArpanaAmishi wrote:Hi Anurag,
I am not clear on 'x + z will be least when y is maximum. The greatest value among the 3 angles, so that their sum is 180º, is 90º. Now since y < z, so z = 90º'

Request to elaborate on this.

You are right. Since z > y, that's why in this case I have taken z = 90, and y = 89, which is the 2nd largest value so that the condition y < z is true.