The minimum possible value of the largest of ab, 1-a-b+ab, and a+b-2ab if 0 <= a <= b <=1 is a 4/9 b 1/9 c 5/9 d 1/3 e 7/9

shashank.ism wrote:The minimum possible value of the largest of ab, 1-a-b+ab, and a+b-2ab if 0 <= a <= b <=1 is a 4/9 b 1/9 c 5/9 d 1/3 e 7/9 1-a-b+ab + a+b-2ab +ab = 1 So the minimum will be when each of these equals 1/3 (1-a)(1-b) =1/3 1-a-b +1/3 =1/3 1-a-b = 0 a+b=1 ab =1/3 x^2 -x +1/3 =0 doesnt have any roots when a=b =1/3 a minimum of 4/9 (2/3*2/3) is created

shashank.ism wrote:The minimum possible value of the largest of ab, 1-a-b+ab, and a+b-2ab if 0 =0 . If one of the three quantities is less than or equal to 1/9, then at least one of the others is at least 4/9 by the pigeonhole principle since they add up to 1. Assume that s-2p =4/9 , and either way we're done. This minimum is achieved if a and b are both 1/3, so the answer is 4/9

komal wrote:shashank.ism wrote:The minimum possible value of the largest of ab, 1-a-b+ab, and a+b-2ab if 0 =0 . If one of the three quantities is less than or equal to 1/9, then at least one of the others is at least 4/9 by the pigeonhole principle since they add up to 1. Assume that s-2p =4/9 , and either way we're done. This minimum is achieved if a and b are both 1/3, so the answer is 4/9 Now we have source, OA and OE and do not tell me this is GMAT question

ajith wrote: Now we have source, OA and OE and do not tell me this is GMAT question Yes this does not seem like a gmat question but it was nice to learn something new.

komal wrote:ajith wrote: Now we have source, OA and OE and do not tell me this is GMAT question Yes this does not seem like a gmat question but it was nice to learn something new. Since you have brought it up, Could you explain me the solution, that you have learned? I do not want to discourage anybody but, copy pasting something from somewhere may not help anybody.