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what is the concept behind to find the minimum value

i have been regularly score 150-160 in nmat, score 45 in english weak in vocab barely score 2-3 answers correct out of 10 and grammar i leave rcs in nmat because it take too much time and unable to solve implicit questions in logical reasoning part, i have no idea about these questions..in quant sometimes i score 90+ , 70-75 and sometimes 50 based on difficulty level.

In an isosceles triangle ABC with AB=AC, AD and AE trisects BC such that BD = DE = EC. IF angle DAE is equal to angle ABC and the area of triangle ABC is equal to , then find AC.

If x, y , z are three distinct positive real numbers such that x+ y+ z= 1 then the values of (1/x - 1)(1/y -1 ) (1/z - 1) is? (Answer is 8)

There is a lot of interest in the first five ranks Class XI students. One student guessed the rank order as Ankita, Bhagyashree, Chanchal, Devroopa and Esha. Later upon announcement of the results, it was found that not only did he get each student out off her true position, none of the students in his ranking correctly followed her immediate predecessor. Another student guessed Devroopa, Ankita, Esha, Chanchal and Bhagyashree. Even his guess was wrong. It was found that he had got two positions correct, and two students in his ranking correctly followed their immediate predecessors. Which of the following is true about the correct rank order? A. Ankita got the third position B. Bhagyashree got the fourth position C. Chanchal got the second position D. Dev roop a stood first E. Esha got the fourth position

Two cars P and Q are moving at uniform speeds, 50 km/hr and 25 km/hr respectively, on two straight roads intersecting at right angle to each other. P passes the intersecting point of the roads when Q has still to travel 50 km to reach it. What is the shortest distance between the cars during the journey?

I am not good in geometry should I invest time in geometry now or shall I leave that section and use that time for those sections in which I have good hold?

How can I improve in Quant? Given enough time I can solve at least 25-30 questions of a mock while analyzing it, but while taking mocks I am able to attempt only 12-15 questions?

how to get udated about current affairs??

If the equation 9x+13y=k has exactly 5 solutions, where x and y are positive integers, what is the minimum possible value of k ?