What will be the value of a/b ? Given that a and b are : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 19 Jan 2017, 20:38

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What will be the value of a/b ? Given that a and b are

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Apr 2012
Posts: 42
Followers: 0

Kudos [?]: 57 [0], given: 93

What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

17 Oct 2012, 03:01
7
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

53% (02:33) correct 47% (01:29) wrong based on 192 sessions

### HideShow timer Statistics

What will be the value of a/b ? Given that a and b are positive integers

(1) a^2 – b^2 = 169
(2) a – b = 1
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93220 [4] , given: 10553

Re: What will be the value of a/b ? [#permalink]

### Show Tags

17 Oct 2012, 03:06
4
KUDOS
Expert's post
1
This post was
BOOKMARKED
GMATBaumgartner wrote:
What will be the value of a/b ? Given that a and b are positive integers
(1) a^2 – b^2 = 169
(2) a – b = 1

I am unable to prove statement 1 is sufficient here. The only thing i could think of first is the 5-12-13 triplet but that would hold good only for a^2 + b^2 = 169. please help.

What will be the value of a/b ? Given that a and b are positive integers

(1) a^2 – b^2 = 169 --> as given that $$a$$ and $$b$$ are positive integers then $$a>b$$. Next, $$a^2-b^2=(a-b)(a+b)=169=1*169=13*13$$ --> again as $$a$$ and $$b$$ are positive integers and $$a>b$$ then: $$a-b=1$$ and $$a+b=169$$. Solving gives: $$a=85$$ and $$b=84$$ --> $$\frac{a}{b}=\frac{85}{84}$$. Sufficient.

(2) a – b = 1. Clearly insufficient.

_________________
Director
Joined: 22 Mar 2011
Posts: 612
WE: Science (Education)
Followers: 100

Kudos [?]: 889 [1] , given: 43

Re: What will be the value of a/b ? [#permalink]

### Show Tags

17 Oct 2012, 03:07
1
KUDOS
GMATBaumgartner wrote:
What will be the value of a/b ? Given that a and b are positive integers
(1) a^2 – b^2 = 169
(2) a – b = 1

I am unable to prove statement 1 is sufficient here. The only thing i could think of first is the 5-12-13 triplet but that would hold good only for a^2 + b^2 = 169. please help.

$$169 = 13^2$$. $$a^2-b^2=(a+b)(a-b)$$. Since $$a$$ and $$b$$ are positive integers, $$a+b>a-b$$ and $$a+b>0$$, so the only possible factorization is $$a+b=169$$ and $$a-b=1$$, from which $$a$$ and $$b$$ can be deduced, as well as the ratio $$a/b$$. Therefore, (1) is sufficient. (2) obviously not sufficient.

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93220 [0], given: 10553

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

19 Aug 2013, 08:12
Bumping for review and further discussion.
_________________
Intern
Joined: 23 Jul 2013
Posts: 4
Schools: ISB '15
GMAT 1: 730 Q51 V38
Followers: 0

Kudos [?]: 0 [0], given: 9

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

21 Aug 2013, 03:16
Can we also say that: a^2 - b^2 = 13^2, This is in the form of a pythagorean triplet.
Since a and b are given as integers, there can be only one integral value for a and b which will satisfy such a condition.
Thus this is a sufficient condition.
Manager
Joined: 15 Aug 2013
Posts: 59
Followers: 1

Kudos [?]: 4 [0], given: 7

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

22 Aug 2013, 03:58
ashivapu wrote:
Can we also say that: a^2 - b^2 = 13^2, This is in the form of a pythagorean triplet.
Since a and b are given as integers, there can be only one integral value for a and b which will satisfy such a condition.
Thus this is a sufficient condition.

Hi, Since it is already given both a and b are positive integers and a^2 - b^2 = 169 (POSITIVE), w can say a > b. If we as assume 169 as 13^2 we are contracdicting our assumption becasue a and b cant be equal. I hope it helps.
Intern
Joined: 18 Aug 2013
Posts: 18
Followers: 0

Kudos [?]: 4 [0], given: 6

Re: What will be the value of a/b ? [#permalink]

### Show Tags

27 Aug 2013, 17:44
1
This post was
BOOKMARKED
EvaJager wrote:
GMATBaumgartner wrote:
What will be the value of a/b ? Given that a and b are positive integers
(1) a^2 – b^2 = 169
(2) a – b = 1

I am unable to prove statement 1 is sufficient here. The only thing i could think of first is the 5-12-13 triplet but that would hold good only for a^2 + b^2 = 169. please help.

$$169 = 13^2$$. $$a^2-b^2=(a+b)(a-b)$$. Since $$a$$ and $$b$$ are positive integers, $$a+b>a-b$$ and $$a+b>0$$, so the only possible factorization is $$a+b=169$$ and $$a-b=1$$, from which $$a$$ and $$b$$ can be deduced, as well as the ratio $$a/b$$. Therefore, (1) is sufficient. (2) obviously not sufficient.

Can you please expand on why we know that the only possible factorization of a+b = 169? Is this because 169 is a square of a prime number and only has factors of 1 - 169, and 13-13? Hence, since a+b>a-b, the factors cannot be 13 * 13 and must be 169 * 1?

Therefore, if 169 was another number with varying positive factors, (1) would not be sufficient?

Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 36567
Followers: 7081

Kudos [?]: 93220 [1] , given: 10553

Re: What will be the value of a/b ? [#permalink]

### Show Tags

28 Aug 2013, 08:58
1
KUDOS
Expert's post
grant1377 wrote:
EvaJager wrote:
GMATBaumgartner wrote:
What will be the value of a/b ? Given that a and b are positive integers
(1) a^2 – b^2 = 169
(2) a – b = 1

I am unable to prove statement 1 is sufficient here. The only thing i could think of first is the 5-12-13 triplet but that would hold good only for a^2 + b^2 = 169. please help.

$$169 = 13^2$$. $$a^2-b^2=(a+b)(a-b)$$. Since $$a$$ and $$b$$ are positive integers, $$a+b>a-b$$ and $$a+b>0$$, so the only possible factorization is $$a+b=169$$ and $$a-b=1$$, from which $$a$$ and $$b$$ can be deduced, as well as the ratio $$a/b$$. Therefore, (1) is sufficient. (2) obviously not sufficient.

Can you please expand on why we know that the only possible factorization of a+b = 169? Is this because 169 is a square of a prime number and only has factors of 1 - 169, and 13-13? Hence, since a+b>a-b, the factors cannot be 13 * 13 and must be 169 * 1?

Therefore, if 169 was another number with varying positive factors, (1) would not be sufficient?

Thanks

Yes, 169 can be broken into the product of two multiples in two ways: 13*13 and 1*169. Since we know that one multiple is greater than the other, then only 1*169 is OK.
_________________
Intern
Joined: 15 Oct 2012
Posts: 25
Followers: 0

Kudos [?]: 13 [0], given: 1

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

28 Aug 2013, 11:26
Hi Bunnel,

As per the question stem - we just know that a and b are >0 and we have to find the value of a/b.

how can we say that a>b - though that we came to know from the 2nd statement only i.e. a = b+1

Now a^2 - b^2 = 169 -
(a+b) (a-b) = 13*13 or 169 *1
Now over here how can we say that a>b??

Can you explain!!

Thanks
Nikhil
Verbal Forum Moderator
Joined: 15 Jun 2012
Posts: 1153
Location: United States
Followers: 259

Kudos [?]: 2867 [1] , given: 123

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

28 Aug 2013, 11:42
1
KUDOS
nikhilsehgal wrote:
Hi Bunnel,

As per the question stem - we just know that a and b are >0 and we have to find the value of a/b.

how can we say that a>b - though that we came to know from the 2nd statement only i.e. a = b+1

Now a^2 - b^2 = 169 -
(a+b) (a-b) = 13*13 or 169 *1
Now over here how can we say that a>b??

Can you explain!!

Thanks
Nikhil

Hi nikhil

a & b are positive integers ==> (a + b) MUST be positive
(a - b)(a +b) = 169 ==> (a - b) MUST be positive too ==> a > b

We know that (a-b)(a+b) = 1x169 (It cannot be 13x13 cause there are no two positive integers that have equal sum and deduction)
==> (a - b) = 1
==> (a + b) = 169
==> a = 85, b = 84

Hope it helps.

PS:Sorry Bunuel for jumping in. I just want to share what I'm thinking.
_________________

Please +1 KUDO if my post helps. Thank you.

"Designing cars consumes you; it has a hold on your spirit which is incredibly powerful. It's not something you can do part time, you have do it with all your heart and soul or you're going to get it wrong."

Chris Bangle - Former BMW Chief of Design.

Intern
Joined: 15 Oct 2012
Posts: 25
Followers: 0

Kudos [?]: 13 [0], given: 1

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

28 Aug 2013, 11:45
Great Thanks

Missed on that one.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13459
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

30 Sep 2014, 06:56
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.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13459
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: What will be the value of a/b ? Given that a and b are [#permalink]

### Show Tags

21 May 2016, 09:04
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: What will be the value of a/b ? Given that a and b are   [#permalink] 21 May 2016, 09:04
Similar topics Replies Last post
Similar
Topics:
3 What is the value of (a+b)? 5 08 Jul 2016, 06:55
What is the value of a+b ? 2 02 Jun 2013, 04:05
1 What will be the value of a/b ? Given that a and b are 3 19 May 2012, 07:56
7 What will be the value of a/b ? Given that a and b are 6 23 Jan 2011, 10:24
What is the Value of (a-b)? 1 04 May 2010, 05:24
Display posts from previous: Sort by