EgmatQuantExpert wrote:
a, b and c are three interior angles of a triangle ABC. If a, b and c are three integers, then what is the number of possible values of a – b + c, which are less than zero ?
A. 88
B. 90
C. 178
D. 179
E. 180
For a triangle the sum of three sides a+b+c=180
since here in we need to find
"the number of possible values of a – b + c, which are less than zero"or say a+c<b and (a+c)-b <0 ;
since c=180-a-b
a – b + c, substitute value of c that a-b+180-a-b
=> -2b=-180
=> b=90
so if b=90 , then a+c has to be 90 , and value of a,c can be any thing (89,1), (81,9) ... but since we need to find the number of possible values of a – b + c, which are less than zero ,value of b has to be 91 and the values of a & c can be anything from (88,1) , (1,88) total values such values which we would fetch us sum < 0 would be IMO 88 ; so IMO A is correct..