Problem Solving

Q)If 3/(p+q)=l/(q+r)=m/(r-p),then which of the follwoing pairs of values for(l,m) is not possible?

A(0,3)
B(0,-3)
C(6,3)
D(4,1)
E(5,2)

OA-A

satyavegi wrote:Q)If 3/(p+q)=l/(q+r)=m/(r-p),then which of the follwoing pairs of values for(l,m) is not possible?

A(0,3)
B(0,-3)
C(6,3)
D(4,1)
E(5,2)

OA-A

l = 3(q + r)/(p + q) -- (1)
m = 3(r - p)/(p + q) -- (2)
Subtracting (2) from (1),
l - m
= 3[(q + r) - (r - p)]/(p + q)
= 3[(p + q)/(p + q)]
= 3

l - m has to be equal to 3.
All options, except (A) for which l - m = -3, yield l - m = 3.

[spoiler](A)[/spoiler] is correct.

Aneesh

Can you explain me the concept of arriving the methodology of working out the problem

regards
Vegi

satyavegi wrote:Aneesh

Can you explain me the concept of arriving the methodology of working out the problem

regards
Vegi

Hi Vegi,

I will try to articulate my thought-process.

Given: 3/(p+q)=l/(q+r)=m/(r-p)
I can see a lot of unnecessary variables - p, q, r - in the equations above. The question is about 'l' and 'm', which can be written in the form of the unnecessary variables as follows:
l = 3*(q + r)/(p + q)
m = 3*(r - p)/(p + q)

Pause for a few seconds here. Remember this is a problem that is expected to be solved inside two minutes. We've to manipulate the equations above such that p,q and r vanish.

Adding and Subtracting the two equations are two very common approaches.

If you try adding them:
l + m
= 3*(q + 2r - p)/(p + q)
p, q and r don't vanish.

Try subtracting them:
l - m
= 3*(p + q)/(p + q)
= 3
First r vanishes, and them (p + q) vanishes.

Now, look for the option for which l - m is not equal to 3.

Having said all of that, there is no substitute to practice. When you have solved a lot of similar problems, it becomes easier for you anticipate what will work out and what will not.

Does that help?