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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Tue Apr 19, 2011 3:06 pm

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

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Source: Beat The GMAT — Problem Solving | Tue Apr 19, 2011 3:06 pm

therealtomrose: MBA Student; Posts: 91; Joined: Wed Apr 06, 2011 5:54 pmFollowed by: 26 members; Location: Cambridge, Massachusetts; Thanked: 46 times; GMAT Score:760

by therealtomrose » Tue Apr 19, 2011 5:48 pm

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

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Tue Apr 19, 2011 7:49 pm

ccassel wrote: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

1/x + 1/y = (y + x)/xy
Now we are given the values of x + y and xy.
So, 1/x + 1/y = 5/6

The correct answer is C.

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atulmangal: Legendary Member; Posts: 1112; Joined: Sat Feb 26, 2011 11:16 amFollowed by: 49 members; Thanked: 77 times

by atulmangal » Tue Apr 19, 2011 8:48 pm

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

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force5: Legendary Member; Posts: 582; Joined: Tue Mar 08, 2011 12:48 amFollowed by: 6 members; Thanked: 61 times; GMAT Score:740

by force5 » Wed Apr 20, 2011 1:27 am

yes 5/6.

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Wed Apr 20, 2011 7:38 am

Anurag, can you elaborate on your method?

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

Thanks in advance.

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Wed Apr 20, 2011 7:50 am

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

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Wed Apr 20, 2011 7:56 am

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.

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Wed Apr 20, 2011 8:02 am

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..!!!

Last edited by manpsingh87 on Wed Apr 20, 2011 10:37 am, edited 1 time in total.

O Excellence... my search for you is on... you can be far.. but not beyond my reach!

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Wed Apr 20, 2011 10:34 am

Ok manpsingh87, thanks.

Cheers

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Wed Apr 20, 2011 5:31 pm

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

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

Thanks in advance.

I hope you have got an answer to your query. If not, please let me know.

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ccassel: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 1:44 pmFollowed by: 2 members; Location: Canada; GMAT Score:530

by ccassel » Fri Apr 22, 2011 7:00 am

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

Cheers,

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

by Anurag@Gurome » Fri Apr 22, 2011 7:02 am

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

Cheers,

Great. Thanks.

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