In the figure above, if x, y and z are integers such that x < y < zIn

Hi chetan2u,

How did you deduce this "For this make y=z-1 and z the least that is 1"?
Can you kindly explain?

Thanks,
Abhishek

The answer is C.

x+y+z = 180
For the greatest value of x+z, y must be minimal, but greater than 1: 1+2+177 = 180. 1+177 = 178
For least value of x+z, y must be maximal, but less than 90: 1+89+90 = 180. 1+90 = 91

Why C?
180-91=89 which could be y
and z>y
Why not D


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Since x, y, and z are the interior angles of a triangle, the relation x + y + z = 180 holds. Passing y to the right-hand side of the equality, we get x + z = 180 - y. Therefore, if we can determine the least and the greatest possible value for y, we will be able to determine the greatest and the least possible value of x + z.

Since x and y are integers and x cannot be zero, the least possible value of x is 1. Therefore, the least possible value of y is 2. Then, the greatest possible value of x + z is 180 - 2 = 178.

Let’s determine the greatest possible value of y. To do that, we need to minimize the values of x and z. We already know the smallest possible value of x is 1. Thus, we are looking for the greatest integer value of y where y < z and y + z = 179. We note that y attains its greatest value when y and z are as close to each other as possible. Since 179/2 = 89.5, we see that the greatest integer value of y is 89 (and the smallest possible integer value of z is 90). Then, the least possible value of x + z is 180 - 89 = 91.

Answer: C

Similar question to practice: https://gmatclub.com/forum/in-the-figur ... 28448.html

Sum of angles in a triangle is 180 degree.
So x+y+z=180
If you go with the first option 59 and 91 then x=59 and z=91
X+z =150 then you will get y=30
Since x<y. So the 1st option is not correct.
Options B, C, D, E are also incorrect.because in these options x+z value is more than 180 degrees.
They not given the correct option for this question.

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