OG QR 2nd Ed. DS #124

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tofubeans: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Thu Apr 19, 2012 2:23 pm

OG QR 2nd Ed. DS #124

by tofubeans » Mon Apr 30, 2012 11:58 am

124) If rs does not = 0, is 1/r + 1/s = 4?

1) r + s = 4rs

2) r = s

Sorry this may be a silly question or maybe my brain is tired but...

I'm not sure I understand why A is correct. I understand that the equation in (1) will come out to the be the same equation in the question but isn't that just restating the equation? I'm confused.

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 30, 2012 11:58 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Mon Apr 30, 2012 12:11 pm

You're probably just mentally exhausted and might figure out your mistake if you solve it again after a break. Let me try to help you to save your time.

The question is whether
1/r + 1/s = 4 or not.

Statement (1), as you said, upon manipulation says that
1/r + 1/s = 4.
So, is 1/r + 1/s equal to 4 as asked in the question?
YES!

So, statement (1) is sufficient.

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pm; Location: Vancouver, BC; Thanked: 5254 times; Followed by:1268 members; GMAT Score:770

by Brent@GMATPrepNow » Mon Apr 30, 2012 2:48 pm

tofubeans wrote:124) If rs does not = 0, is 1/r + 1/s = 4?

1) r + s = 4rs
2) r = s

Target question: Is 1/r + 1/s = 4?

This one is a great candidate for rephrasing the target question
Let's add 1/r + 1/s to create one rational expression.
Find common denominator: s/rs + r/rs
Add numerators: (s+r)/rs
So, 1/r + 1/s = (s+r)/rs

So, rather than ask "Does 1/r + 1/s = 4?" we can ask "Does (s+r)/rs = 4?"

Even better, we can cross multiply the equation to get: "Does s+r = 4sr?"

Statement 1: r + s = 4rs
This is exactly what one of our rephrased target questions asks.
So, statement 1 is SUFFICIENT

Statement 2: r = s
Knowing that r=s does not help us determine whether s+r = 4sr
So, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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mido362: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Fri Mar 30, 2012 10:56 pm

by mido362 » Tue May 01, 2012 9:55 pm

Hi Guys,
Please correct me if I am wrong.
I agree regarding statement 1

Regarding Statement 2:
r=s
1/r +1/s=4
1/r + 1/r=4
2/r=4
r=1/2
By substituting in the original equation 1/r+1/s=4 so (1/ 1/2) + (1/ 1/2)=4
Sufficient

Is that right?

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

by Anurag@Gurome » Tue May 01, 2012 10:47 pm

tofubeans wrote:124) If rs does not = 0, is 1/r + 1/s = 4?

1) r + s = 4rs

2) r = s

Sorry this may be a silly question or maybe my brain is tired but...

I'm not sure I understand why A is correct. I understand that the equation in (1) will come out to the be the same equation in the question but isn't that just restating the equation? I'm confused.

The question is asking whether (1/r + 1/s) = 4 or not.
If you replace r = s from the statement 2 into the equation, obviously you'll get a value of r which satisfies the equation. The solutions are in fact r = s = 1/2. But the question is not really asking you to do this! For this particular set of values of r and s the relation satisfies. But not for all r and s that satisfies the relation r = s. For instance, r = s = 1 does not satisfies the equation. Thus statement 2 is not sufficient to answer the question.

But for statement 1, (r + s) = 4rs => (r + s)/rs = 4 => (1/r + 1/s) = 4.
Therefore for any set of values of r and s that satisfies the condition given in statement 1, satisfies the equation given in question stem. Hence statement 1 is sufficient.

The correct answer is A.

Hope that clears your confusion.

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GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)

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p111: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jun 12, 2012 12:23 pm; GMAT Score:640

by p111 » Fri Jul 05, 2013 1:53 am

Hi Anurag/Instructors,
I have a confusion here in this Q.
as to How you & the OG deduce:

1/r +1/s as (r+s)/rs.

I know it is by taking LCM but one IMO shouldnt generalize it. As teh same holds true for 1/4+1/3 BUT CANNOT for 1/4 +1/12.

SO IMO: the solution should be: (from A)

r-s=4rs
=> s=4rs-r
=> r=s/(4s-1)

putting value in 1/r +1/s becomes (4s-1)/s + 1/s => 4s/s => 4

Please correct me OR let me know if my concepts are not correct as I want this to clear so that I can avoid any mistakes.

Thanks !!

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aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 am; Location: Pune, India; Thanked: 186 times; Followed by:29 members

by aneesh.kg » Fri Jul 05, 2013 2:34 am

p111 wrote:Hi Anurag/Instructors,
I have a confusion here in this Q.
as to How you & the OG deduce:

1/r +1/s as (r+s)/rs.

I know it is by taking LCM but one IMO shouldnt generalize it. As teh same holds true for 1/4+1/3 BUT CANNOT for 1/4 +1/12.

SO IMO: the solution should be: (from A)

r-s=4rs
=> s=4rs-r
=> r=s/(4s-1)

putting value in 1/r +1/s becomes (4s-1)/s + 1/s => 4s/s => 4

Please correct me OR let me know if my concepts are not correct as I want this to clear so that I can avoid any mistakes.

Thanks !! :

Hi p111,

You're right. It's wrong to generalise it.
Your solution is also correct.

However, here's how I would do it and I think it's more elegant.

Statement(1):
r + s = 4rs
Dividing both the sides of the equation by rs. (We can do this ONLY BECAUSE rs is not 0)
(r + s) / rs = 4rs / rs
1/s + 1/r = 4

So, is 1/r + 1/s = 4?

Hell yeah!

Aneesh Bangia
GMAT Math Coach
[email protected]

GMATPad:
Facebook Page: https://www.facebook.com/GMATPad