GMAT math concept - difficulty level - hard

Difficulty level - hard
Concept - Maxima - minima of functions

In GMAT, you will encounter problems based on functions.

These questions require higher order reasoning skills.

Ideally, you need to know calculus  to solve. But, it is not necessary. 

Some of you don't have a math background, don't worry. 

This tip can help you crack questions from this chapter.


Remember to : 

Develop math reasoning skills. The math section test you on reasoning 
  
This video will give you insights into the reasoning skills required..




Now lets take a problem

A and B can complete a work in x and y days respectively. Working together they can complete the same work in 15 days. If X and Y are integers, what can be the maximum difference between x and y? 

This problem is from the concept of time and work.

As you know. You will have to represent the equation wrt the amount of work done in a day.

Hence A will complete the job in 1/x days

B will complete the job in 1/y days.

As they together take 15 days to complete the work.

We need to calculate the maximum value of (x - y)
that means x should be the largest possible number and y should be lowest number

TIP: to calculate the maximum value of x- y  or maximum value of x+y, always factorize the equation 

15y+15x= xy

15y-xy +15x = 0

y(15-x) + 15x = 0

To factorize the equation i need to reduce the above equation in this format

(x+a)(y+b) = constant

I need (15-x) so lets add 225 which is 15²

i need to add +225 and -225

y(15-x)  +15x +225 -225 =0

y(15-x)  +15x -225 +225 =0

y(15-x) -15(15- x) +225 =0

(15-x) (y-15) = -225

(x-15)(y-15) = 225 or

(x-15)(y-15) = (225)(1)

Which is

x-15 =225 and y-15 =1

X = 240 and y = 16

Hence maximum difference is 224

Hope you understood this sum.. 

You can reach me if you are targeting Q51 in the math section. There are few skills you need to master. 

my linkedin profile - https://www.linkedin.com/in/georgeanand

My facebook learning community - https://www.facebook.com/groups/semanticsGMAT

What next

You can try this problem and check your reasoning skills.

solution here:

http://letsgmat.blogspot.com/2020/07/gmat-math-thinking-skills-4.html