Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

How did you find that only these values would satisfy? Did you test several numbers?

The question also doesn't give us the clue whether the numbers are the same or different.So, we have to test many numbers.right? Can you please show the steps or any other way to get to the correct answer?

You actually dont need to test numbers. It could be purely algebric approach coupled with some logical deductions.

we have\(c= ab/(a+b)\) or \(c = \frac{1}{(1/a+1/b)}\)

If you notice this expression and remember that c has to be integer, that would mean Denominator has to be 1 (Since numerator is already 1). There is only one such possiblity of a and b that could give you 1/a+1/b =1 So you dont need to test any number.

given is c= ab/(a+b) thus, since c is integer, ab/a+b must be an integer.

statement 1: b ≤ 4 No information can be drawn. Not sufficient statement 2: ab ≤ 15 Only possible value of ab, such that ab/a+b is integer could be when a=2,b=2. Thus, c=1. Sufficient.

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

27 Oct 2013, 12:01

3

This post received KUDOS

4

This post was BOOKMARKED

jlgdr wrote:

monsoon1 wrote:

If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4 (2) ab ≤ 15

Hey all,

This one was a bit tricky indeed. Is there some other way we can notice quickly which number satisfies the ab/a+b constraint giving 'c' as an integer value

Cheers! J

From F.S 1, we know that for a to be positive, c<b. The given equation is valid for b=2,c=1 and also for b=3,c=2. Insufficient.

Now, back to your question.

We know that\(\frac{a+b}{2}\geq{\sqrt{ab}}\)

Also, from the question stem, we know that \(\frac{a+b}{ab} =\frac{1}{c}\)

Thus, \((a+b) = \frac{ab}{c}\). Replacing this in the first equation, we get \(\frac{ab}{2c}\geq{\sqrt{ab}}\)

Or,\(c\leq{\frac{\sqrt{ab}}{2}} \to c\leq{\frac{\sqrt{15}}{2}} \to c<{2}\). Thus, the only positive integer less than 2 is One and thus c=1.Sufficient.
_________________

Doesn't mau5's solution, if correct, bring us back to Nilohit's point of 'why do we need know statement 1 and 2 if we already know C equals 1'? Regardless, this is definitely a challenging question. I would like to know if there is a shortcut to this problem, especially for statement #2. Just plugging in some numbers would be impossible given the time limit...

Actually, this is not correct. c needn't be 1 in every case.

Take a = 2, b = 2. In this case c = 1

Take a = 4, b = 4. In this case, 1/4 + 1/4 = 1/2 c = 2

Take a = 3, b = 6. In this case, 1/3 + 1/6 = 1/2 c = 2

Take a = 15, b = 30. In this case 1/15 + 1/30 = 1/10 etc

Basically, you have to look for values such that when the numerators add up, the sum is divisible by the denominator. a and b cannot be 1 since we need the sum to be less than 1.

Statement 1: b <= 4 This gives you different values of c. c could be 1 or 2. Not sufficient.

Statement 2: ab <= 15 a and b could be 2 each. There is no other set of values. Try the small pairs (2, 4), (3, 3). Hence (B) alone is sufficient. (Note the algebraic solution provided by mau5 for statement 2.)
_________________

given is c= ab/(a+b) thus, since c is integer, ab/a+b must be an integer.

statement 1: b ≤ 4 No information can be drawn. Not sufficient statement 2: ab ≤ 15 Only possible value of ab, such that ab/a+b is integer could be when a=2,b=2. Thus, c=1. Sufficient.

Ans B it is.

How did you find that only these values would satisfy? Did you test several numbers?

The question also doesn't give us the clue whether the numbers are the same or different.So, we have to test many numbers.right?

Can you please show the steps or any other way to get to the correct answer?

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

07 Oct 2013, 11:38

I have a question here. If the solution given by Vips0000 is correct and to me it seems perfect, then neither of the statements is actually needed to solve the question there can be only one combination possible from the question stem itself; a=b=2 and consequently c=1. In such a scenario shouldn't the answer be D, since both statements independently will lead us to the answer.

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

07 Oct 2013, 12:19

1

This post was BOOKMARKED

Nilohit wrote:

I have a question here. If the solution given by Vips0000 is correct and to me it seems perfect, then neither of the statements is actually needed to solve the question there can be only one combination possible from the question stem itself; a=b=2 and consequently c=1. In such a scenario shouldn't the answer be D, since both statements independently will lead us to the answer.

Well, lets say the ab<or= 15 restriction was not there. Then if a=10 and b=10 then ab/(a+b) would equal 100/20...which is an integer.

The only possible values when ab<or=15 are 2 and 2.

but for the b<or=4 statement, you could still have a case where say b=4 and a=12, and ab/a+b=48/16=3. Then you would have 2 (or more) possible values for a and b if you also include the possible value set of "a=2 and b=2".

Vips0000 reasoning isn't actually perfect. In the case of \(\frac{1}{1/a+1/b}\) the denominator does not have to be "1". \(\frac{1}{1/a+1/b}\) could equal \(\frac{1}{1/4+1/12}\) which reduces to \(\frac{1}{4/12}\) then \(1*\frac{12}{4}\) which equals 3

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

27 Oct 2013, 10:42

monsoon1 wrote:

If a, b, and c are positive integers such that 1/a + 1/b = 1/c, what is the value of c?

(1) b ≤ 4 (2) ab ≤ 15

Updating with new solution by jlgdr

OK so we have that ab / a+b = C is an integer. Therefore let's hit the first statement.

Statement 1 says that b<=4. We have two choices here (actually 3). Let's begin with (2,2) C would equal 2. Now if we pick (4,4), C is again two so same answer. But if we pick (6,6) then C= 3. So not sufficient.

From statement 2 we know that ab<=15. Hence ab has to be 2,2 since both a,b are positive integers and of course C = 2.

Therefore B stands

Gimme kudos Cheers J

Last edited by jlgdr on 29 Mar 2014, 06:09, edited 1 time in total.

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

13 Nov 2013, 22:07

Doesn't mau5's solution, if correct, bring us back to Nilohit's point of 'why do we need know statement 1 and 2 if we already know C equals 1'? Regardless, this is definitely a challenging question. I would like to know if there is a shortcut to this problem, especially for statement #2. Just plugging in some numbers would be impossible given the time limit...

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

13 Nov 2013, 22:22

JepicPhail wrote:

Doesn't mau5's solution, if correct, bring us back to Nilohit's point of 'why do we need know statement 1 and 2 if we already know C equals 1'? Regardless, this is definitely a challenging question. I would like to know if there is a shortcut to this problem, especially for statement #2. Just plugging in some numbers would be impossible given the time limit...

I don't understand how you can get the answer from the First fact statement.

Also, how can you get that c=1, without fact statement 2?
_________________

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

13 Nov 2013, 22:44

mau5 wrote:

JepicPhail wrote:

Also, how can you get that c=1, without fact statement 2?

Oh, I see now why you need 15. \(sqrt(15)\) is less than 4, so C is less than or equal to something like 1/2, 2/2, 3/2, etc... and since only integer here is 1, C equals 1.

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

20 Feb 2014, 19:20

Quote:

Statement 2: ab <= 15 a and b could be 2 each. There is no other set of values. Try the small pairs (2, 4), (3, 3). Hence (B) alone is sufficient.

What if a = 1 and b =1, it would still satisfy all the conditions i.e. ab<15 and c would be an integer only. Doesnt this gives 2 solutions for statement 2 as well??

Statement 2: ab <= 15 a and b could be 2 each. There is no other set of values. Try the small pairs (2, 4), (3, 3). Hence (B) alone is sufficient.

What if a = 1 and b =1, it would still satisfy all the conditions i.e. ab<15 and c would be an integer only. Doesnt this gives 2 solutions for statement 2 as well??

If a = 1, b = 1,

1 + 1 = 1/c c = 1/2 c is not an integer in this case.
_________________

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

17 Apr 2015, 23:21

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: If a, b, and c are positive integers such that 1/a + 1/b = 1 [#permalink]

Show Tags

30 Jun 2016, 08:10

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...