NEW HERE? LEARN MORE
closeclose
Last visit was: 07 May 2024, 11:17 It is currently 07 May 2024, 11:17
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
avatar
GMATBaumgartner
Intern
Intern
Joined: 11 Apr 2012
Posts: 32
Own Kudos [?]: 600 [78]
Given Kudos: 93
Send PM
What will be the value of a/b ? Given that a and b are [#permalink] New post   17 Oct 2012, 04:01
6
Kudos
72
Bookmarks
00:00
A
B
C
D
E

Difficulty:

75% (hard)

Question Stats:

55% (02:09) correct 45% (02:09) wrong based on 1266 sessions
Hide Show 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
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93079
Own Kudos [?]: 621949 [15]
Given Kudos: 81785
Send PM
CAT Tests Forum Quiz Mode
Re: What will be the value of a/b ? [#permalink] New post   17 Oct 2012, 04:06
10
Kudos
5
Bookmarks
Expert Reply
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.

Answer: A.
User avatar
EvaJager
Director
Director
Joined: 22 Mar 2011
Posts: 520
Own Kudos [?]: 2139 [8]
Given Kudos: 43
WE:Science (Education)
Send PM
Re: What will be the value of a/b ? [#permalink] New post   17 Oct 2012, 04:07
6
Kudos
2
Bookmarks
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.

Answer A.
General Discussion
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93079
Own Kudos [?]: 621949 [3]
Given Kudos: 81785
Send PM
CAT Tests Forum Quiz Mode
Re: What will be the value of a/b ? [#permalink] New post   28 Aug 2013, 09:58
2
Kudos
1
Bookmarks
Expert Reply
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.

Answer A.



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.
avatar
ashivapu
Intern
Intern
Joined: 23 Jul 2013
Posts: 1
Own Kudos [?]: 2 [2]
Given Kudos: 9
Schools: ISB '15
GMAT 1: 730 Q51 V38
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   21 Aug 2013, 04:16
1
Kudos
1
Bookmarks
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.
avatar
grant1377
Intern
Intern
Joined: 18 Aug 2013
Posts: 9
Own Kudos [?]: 10 [1]
Given Kudos: 6
Send PM
Re: What will be the value of a/b ? [#permalink] New post   27 Aug 2013, 18:44
1
Bookmarks
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.

Answer A.



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
avatar
nikhilsehgal
Intern
Intern
Joined: 15 Oct 2012
Posts: 19
Own Kudos [?]: 36 [1]
Given Kudos: 1
Send PM
GMAT ToolKit User
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   28 Aug 2013, 12:26
1
Kudos
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
User avatar
pqhai
Retired Moderator
Joined: 16 Jun 2012
Posts: 871
Own Kudos [?]: 8567 [1]
Given Kudos: 123
Location: United States
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   28 Aug 2013, 12:42
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.
User avatar
D
GMATGuruNY
Tutor
Joined: 04 Aug 2010
Posts: 1321
Own Kudos [?]: 3152 [1]
Given Kudos: 9
Schools:Dartmouth College
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   14 Sep 2020, 13:25
1
Kudos
Expert Reply
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


Statement 1: \(a^2-b^2=169\)
Case 1: (a+b)(a-b) = 169*1, implying that a+b=169 and a-b=1
Adding together a+b=169 and a-b=1, we get:
2a = 170
a=85
Since a=85 and a-b=1, b=84.
Thus:
\(\frac{a}{b} = \frac{85}{84}\\
\)

Case 2: (a+b)(a-b) = 13*13, implying that a+b=13 and a-b=13
Adding together a+b=13 and a-b=13, we get:
2a = 26
a=13
Since a=13 and a-b=13, b=0.
Not viable, since a and b must both be positive.

Since only Case 1 is viable, SUFFICIENT.

Statement 2: a-b=1
Clearly INSUFFICIENT.

Show Spoiler
A
avatar
zerosleep
Intern
Intern
Joined: 15 Aug 2013
Posts: 44
Own Kudos [?]: 117 [0]
Given Kudos: 7
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   22 Aug 2013, 04:58
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.
avatar
nikhilsehgal
Intern
Intern
Joined: 15 Oct 2012
Posts: 19
Own Kudos [?]: 36 [0]
Given Kudos: 1
Send PM
GMAT ToolKit User
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   28 Aug 2013, 12:45
Great Thanks :)

Missed on that one.
User avatar
S
Bambi2021
Senior Manager
Senior Manager
Joined: 13 Mar 2021
Posts: 336
Own Kudos [?]: 101 [0]
Given Kudos: 227
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   08 Jul 2021, 08:55
It is helpful here to know that only one difference of squares will be 169 (if both numbers must be positive).

For any difference of squares, the greater number in (a+b) will be half of "the difference of the squares plus one". For example:

169 = difference between 85^2 and 84^2; 170/2 = 85

7351 = difference between 3676^2 and 3675^2; 7352/2 = 3676

a = (diff + 1)/2

Posted from my mobile device
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32825
Own Kudos [?]: 827 [0]
Given Kudos: 0
Send PM
Re: What will be the value of a/b ? Given that a and b are [#permalink] New post   11 Jul 2023, 16:47
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 Bot
gmatclubot
Re: What will be the value of a/b ? Given that a and b are [#permalink]
11 Jul 2023, 16:47
Moderator:
Bunuel
Math Expert
93079 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions