Problem Solving

If x + y = 5 and xy = 6, then 1/x + 1/y =?

A. 1/6
B. 1/5
C. 5/6
D. 6/5
E. 5

Answer is C

I'll show you a shortcut to this problem.

Notice that the problem is symmetrical. That is, you can swap the values of x and y, and their solutions don't change. x+y=5. But also y+x=5. xy=6, but also yx=6. Symmetrical.

When this happens on the GMAT, often you can solve the equations by inspection. That is, don't do too much math. Instead, ask yourself this. What two numbers when added equal 5, but when multiplied equal 6. You will quickly come up with 3 and 2.

Those are your solutions for x and y. (3 and 2)

1 / x + 1 / y = 1 / (2) + 1 / (3) = 5/6

Though calculation method of Anurag is the best...but u can solve in this way also..

Given

x + y = 5 and xy = 6

divide, x + y = 5 by xy, u get

x/xy + y/xy = 5/xy ===> 1/y + 1/x = 5/6 hence Op C

yes 5/6.

Anurag, can you elaborate on your method?

How can you assume 1/x + 1/y = (y + x)/xy?

Thanks in advance.

ccassel wrote:Anurag, can you elaborate on your method?

How can you assume 1/x + 1/y = (y + x)/xy?

Thanks in advance.

divide (x+y) with xy, you will get 1/x+1/y

I see now. Would combining 2 equations like this be a regular practice on the GMAT? Is there a rule to follow? I am not a math major so performing this type of function is foreign to me. I usually plug in numbers but would like to understand short-cuts when good numbers are not available.

Thanks again.

ccassel wrote:I see now. Would combining 2 equations like this be a regular practice on the GMAT? Is there a rule to follow? I am not a math major so performing this type of function is foreign to me. I usually plug in numbers but would like to understand short-cuts when good numbers are not available.

Thanks again.

it varies from question to question, for some question you can go for a plug in method and for others like this one you can look for an alternate way of solving it, don't worry if you don't get it in first time, that's why you're here to learn new things and share the knowledge that you possess with yourself, keep on practicing and learning new stuff, than all these things will come naturally to you..!!!

Ok manpsingh87, thanks.

Cheers

Anurag, it has been discussed. Thank you for the reply.

Cheers,